河海大学
力学院
HHU Site
XFEM文献
 
专著:
 
1.Soheil Mohammadi. EXTENDED FINITE ELEMENT METHOD, Wiley-Blackwell, 2008.
 
2.Lambert M Surhone,Mariam T Tennoe,Susan F Henssonow. Extended Finite Element Method, Betascript Publishing, 2010.
 
3.Sylvie Pommier,Anthony Gravouil,Nicolas Moes,Alain Combescure. Extended Finite Element Method for Crack Propagation, Wiley-ISTE, 2011.
 
4.Soheil Mohammadi. XFEM FRACTURE ANALYSIS OF COMPOSITES, John Wiley & Sons, 2012.
 
5.庄茁,柳占立,成斌斌,廖剑晖. 扩展有限单元法, 清华大学出版社, 2012.
 
6.余天堂. 扩展有限单元法—理论、应用及程序, 科学出版社, 2014.
 
7.Zhuo Zhuang,Zhanli Liu,Binbin Cheng,Jianhui Liao. Extended finite element method, Elsevier/Tsinghua University Press, 2014.
 
8.Stéphane Bordas, Alexander Menk. XFEM - The Extended Finite Element Method, Wiley, 2014.
 
9.Amir Khoei. Extended Finite Element Method: Theory and Applications, Wiley, 2015.
 
 
论 文:
 
1.Review
 
1). B.L. Karihaloo, Q.Z. Xiao. Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Computers and Structures 2003;81: 119–129
 
2).李录贤,王铁军.扩展有限元法(XFEM)及其应用. 力学进展 2005;35(1):5-20
 
3).Ted Belytschko, Robert Gracie, Giulio Ventura. A review of extended/generalized finite element methods for material modeling. Modelling Simul. Mater. Sci. Eng. 2009;17: 043001 (24pp)
 
4). Abdelaziz Yazid, Nabbou Abdelkader, Hamouine Abdelmadjid. A state-of-the-art review of the X-FEM for computational fracture mechanics. Applied Mathematical Modelling 2009;33:4269–4282
 
5). Yazid Abdelaziz, Abdelmadjid Hamouine. A survey of the extended finite element. Computers and Structures 2009;86: 1141–1151
 
6). Thomas-Peter Fries, Ted Belytschko. The extended/generalized finite element method: An overview of the method and its applications. Int. J. Numer. Meth. Engng 2010; 84:253–304
 
 
2.Crack
 
1).Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International journal for numerical methods in engineering, 1999, 45(5): 601-620.
 
2).Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. Int. J. Numer. Meth. Eng, 1999, 46(1): 131-150.
 
3).Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method[J]. Int. J. Numer. Meth. Eng, 2000, 48: 1741-1760.
 
4).Belytschko T, Moës N, Usui S, et al. Arbitrary discontinuities in finite elements[J]. International Journal for Numerical Methods in Engineering, 2001, 50(4): 993-1013.
 
5).Stolarska M, Chopp D L, Moës N, et al. Modelling crack growth by level sets in the extended finite element method[J]. International journal for numerical methods in Engineering, 2001, 51(8): 943-960.
 
6).Jirásek M, Belytschko T. Computational resolution of strong discontinuities[C]//Proceedings of Fifth World Congress on Computational Mechanics, WCCM V, Vienna University of Technology, Austria. 2002.
 
7).Dolbow J E, Nadeau J C. On the use of effective properties for the fracture analysis of microstructured materials[J]. Engineering Fracture Mechanics, 2002, 69(14): 1607-1634.
 
8).Nagashima T, Omoto Y, Tani S. Stress intensity factor analysis of interface cracks using X‐FEM[J]. International Journal for Numerical Methods in Engineering, 2003, 56(8): 1151-1173.
 
9).Belytschko T, Zi G, Xu J, et al. The extended finite element method for arbitrary discontinuities[J]. Computational Mechanics-Theory And Practice. Barcelona, Spain: CIMNE, 2003.
 
10).Belytschko T, Parimi C, Moës N, et al. Structured extended finite element methods for solids defined by implicit surfaces[J]. International journal for numerical methods in engineering, 2003, 56(4): 609-635.
 
11).Bellec J, Dolbow J E. A note on enrichment functions for modelling crack nucleation[J]. Communications in Numerical Methods in Engineering, 2003, 19(12): 921-932.
 
12).Sukumar N, Srolovitz D J, Baker T J, et al. Brittle fracture in polycrystalline microstructures with the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2003, 56(14): 2015-2037.
 
13).Lee S H, Song J H, Kim M W. Crack Propagation Analysis without Mesh-Dependency by Using Extended Finite Element Method[J]. Journal of The Korean Society of Civil Engineers, 2003, 23(6A): 1077-1086.
 
14).Xiao Q Z, Karihaloo B L. Direct evaluation of accurate coefficients of the linear elastic crack tip asymptotic field[J]. Fatigue & Fracture of Engineering Materials & Structures, 2003, 26(8): 719-729.
 
15).Huang R, Sukumar N, Prévost J H. Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications[J]. International Journal of Solids and Structures, 2003, 40(26): 7539-7552.
 
16).Sukumar N, Prévost J H. Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation[J]. International journal of solids and structures, 2003, 40(26): 7513-7537.
 
17).Vigneron L M, Verly J G, Warfield S K. On extended finite element method (XFEM) for modelling of organ deformations associated with surgical cuts[C]//Medical Simulation. Springer Berlin Heidelberg, 2004: 134-143.
 
18).Vigneron L M, Verly J G, Warfield S K. Modelling surgical cuts, retractions, and resections via extended finite element method[C]//Medical Image Computing and Computer-Assisted Intervention–MICCAI 2004. Springer Berlin Heidelberg, 2004: 311-318.
 
19).Sukumar N, Srolovitz D J. Finite element-based model for crack propagation in polycrystalline materials[J]. Computational & Applied Mathematics, 2004, 23(2-3): 363-380.
 
20).Budyn E, Zi G, Moës N, et al. A method for multiple crack growth in brittle materials without remeshing[J]. International journal for numerical methods in engineering, 2004, 61(10): 1741-1770.
 
21).Lee S H, Song J H, Yoon Y C, et al. Combined extended and superimposed finite element method for cracks[J]. International Journal for Numerical Methods in Engineering, 2004, 59(8): 1119-1136.
 
22).Dolbow J E, Devan A. Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test[J]. International journal for numerical methods in engineering, 2004, 59(1): 47-67.
 
23).Karihaloo B L, Xiao Q Z. Recent Developments In Computational Fracture Mechanics At Cardiff[C]//Structural Integrity and Fracture International Conference (SIF'04). 2004: 179-180.
 
24).Peters M, Hoppe U, Hackl K. Simulation of crack-propagation using embedded discontinuities[J]. PAMM, 2004, 4(1): 366-367.
 
25).Legay A, Wang H W, Belytschko T. Strong and weak arbitrary discontinuities in spectral finite elements[J]. International Journal for Numerical Methods in Engineering, 2005, 64(8): 991-1008.
 
26).Larsson R, Fagerström M. A framework for fracture modelling based on the material forces concept with xfem kinematics[J]. International Journal for Numerical Methods in Engineering, 2005, 62(13): 1763-1788.
 
27).Béchet É, Minnebo H, Moës N, et al. Improved implementation and robustness study of the X‐FEM for stress analysis around cracks[J]. International Journal for Numerical Methods in Engineering, 2005, 64(8): 1033-1056.
 
28).Shamloo A, Azami A R, Khoei A R. Modeling of pressure-sensitive materials using a cap plasticity theory in extended finite element method[J]. Journal of materials processing technology, 2005, 164: 1248-1257.
 
29).Mombartz M, Chudoba R, Hegger J. NUMERICAL AND EXPERIMENTAL TRACING OF THE CRACK PROPAGATION USING ADAPTIVE EXTENDED FINITE ELEMENTS AND PHOTOGRAMMETRY[C]//International Conference on Fracture, Turin. 2005.
 
30).Peters M, Hackl K. Numerical aspects of the eXtended finite element method[J]. PAMM, 2005, 5(1): 355-356.
 
31).Peters M, Hackl K. Numerical aspects of the XFEM—The XFEM p–Version[J]. PAMM, 2006, 6(1): 189-190.
 
32).Xiao Q Z, Karihaloo B L. Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery[J]. International Journal for Numerical Methods in Engineering, 2006, 66(9): 1378-1410.
 
33).Areias P M A, Belytschko T. A comment on the article “A finite element method for simulation of strong and weak discontinuities in solid mechanics” by A. Hansbo and P. Hansbo [Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523–3540][J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(9): 1275-1276.
 
34).Oliver J, Huespe A E, Sanchez P J. A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM[J]. Computer methods in applied mechanics and engineering, 2006, 195(37): 4732-4752.
 
35).Bordas S, Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures[J]. Engineering Fracture Mechanics, 2006, 73(9): 1176-1201.
 
36).Asferg J L, Belytschko T, Poulsen P N, et al. Partly Cracked XFEM Interface for Intersecting Cracks[M]//Fracture of Nano and Engineering Materials and Structures. Springer Netherlands, 2006: 397-398.
 
37).Fries T P, Belytschko T. The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns[J]. International journal for numerical methods in engineering, 2006, 68(13): 1358-1385.
 
38).Khoei A R, Shamloo A, Anahid M, et al. The extended finite element method (X-FEM) for powder forming problems[J]. Journal of materials processing technology, 2006, 177(1): 53-57.
 
39).Laborde P, Pommier J, Renard Y, et al. Some Improvements for Extended Finite Element Methods in Fracture Mechanics[M]//Fracture of Nano and Engineering Materials and Structures. Springer Netherlands, 2006: 953-954.
 
40).Unger J F, Könke C. Simulation of concrete using the extended finite element method[C]//Proceedings of international conference on computational modelling of concrete structures (EURO-C 2006), Balkema. 2006: 239-247.
 
41).方修君, 金峰, 王进廷. 用扩展有限元方法模拟混凝土的复合型开裂过程[J]. 工程力学, 2007, 24(1): 46-52.
 
42).方修君, 金峰. 基于 ABAQUS 平台的扩展有限元法[J]. 工程力学, 2007, 24(7): 6-10.
 
43).Fries T P, Belytschko T. New shape functions for arbitrary discontinuities without additional unknowns[M]//Meshfree Methods for Partial Differential Equations III. Springer Berlin Heidelberg, 2007: 87-103.
 
44).Jovicic G, Zivkovic M, Jovicic N. Extended Finite Element Method for Two-dimensional Crack Modeling[J]. Journal of the Serbian Society for Computational Mechanics, 2007, 1(1): 184-196.
 
45).Comi C, Mariani S, Perego U. An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(2): 213-238.
 
46).Dunant C, Vinh P N, Belgasmia M, et al. Architecture tradeoffs of integrating a mesh generator to partition of unity enriched object-oriented finite element software[J]. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 2007, 16(2): 237-258.
 
47).Vaughan B, Smith B, Chopp D. A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources[J]. Communications in Applied Mathematics and Computational Science, 2007, 1(1): 207-228.
 
48).Dumstorff P, Meschke G. Crack propagation criteria in the framework of X-FEM-based structural analyses[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(2): 239-259.
 
49).Xiao Q Z, Karihaloo B L, Liu X Y. Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM[J]. International journal for numerical methods in engineering, 2007, 69(12): 2606-2635.
 
50).Xiao Q Z, Karihaloo B L. Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM[J]. Computer methods in applied mechanics and engineering, 2007, 196(13): 1864-1873.
 
51).Nguyen D H, Bilteryst F, Lazard M, et al. Coupling of the eXtended Finite Element Method and the matching asymptotic development in the modelling of brazed assembly[J]. International Journal of Material Forming, 2008, 1(1): 1119-1122.
 
52).Benvenuti E, Tralli A, Ventura G. A regularized XFEM model for the transition from continuous to discontinuous displacements[J]. International Journal for Numerical Methods in Engineering, 2008, 74(6): 911-944.
 
53).Yan Y, Park S H. An extended finite element method for modeling near-interfacial crack propagation in a layered structure[J]. International Journal of Solids and Structures, 2008, 45(17): 4756-4765.
 
54).Chahine E, Laborde P, Renard Y. Spider XFEM, an extended finite element variant for partially unknown crack-tip displacement[J]. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 2008, 17(5-7): 625-636.
 
55).Yvonnet J, Quang H L, He Q C. An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites[J]. Computational Mechanics, 2008, 42(1): 119-131.
 
56).Tabarraei A, Sukumar N. Extended finite element method on polygonal and quadtree meshes[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(5): 425-438.
 
57).Shi J, Lua J, Waisman H, et al. X-FEM toolkit for automated crack onset and growth prediction[C]//AIAA Proceedings. 2008.
 
58).Holdych D J, Noble D R, Secor R B. Quadrature rules for triangular and tetrahedral elements with generalized functions[J]. International Journal for Numerical Methods in Engineering, 2008, 73(9): 1310-1327.
 
59).Legrain G, Moës N, Verron E. Robust and direct evaluation of J2 in linear elastic fracture mechanics with the X‐FEM[J]. International journal for numerical methods in engineering, 2008, 76(10): 1471-1488.
 
60).Chahine E, Laborde P, Renard Y. Spider XFEM, an extended finite element variant for partially unknown crack-tip displacement[J]. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 2008, 17(5-7): 625-636.
 
61).Jovičić G, Živković M, Maksimović K, et al. The crack growth analysis on the real structure using the XFEM and EFG methods[J]. Scientific Technical Review, 2008, 58(2): 21-26.
 
62).Panetier J, Ladevèze P, Louf F. Strict bounds for computed stress intensity factors[J]. Computers & Structures, 2009, 87(15): 1015-1021.
 
63).Van der Bos F, Gravemeier V. Numerical simulation of premixed combustion using an enriched finite element method[J]. Journal of Computational Physics, 2009, 228(10): 3605-3624.
 
64).Budyn E, Jonvaux J, Hoc T. Physical imaging of fracturing human cortical bone[C]//Proceeding of the Conference on Computational Mechanics: Giens. 2009: 25-29.
 
65).Jovičić G, Živković M, Jovičić N. Numerical simulation of crack modeling using extended finite element method[J]. Strojniški vestnik–Journal of mechanical engineering, 2009, 55(9): 549-554.
 
66).Hille T S, Suiker A S J, Turteltaub S. Microcrack nucleation in thermal barrier coating systems[J]. Engineering fracture mechanics, 2009, 76(6): 813-825.
 
67).Yu H, Wu L, Guo L, et al. Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method[J]. International Journal of Solids and Structures, 2009, 46(20): 3710-3724.
 
68).Xu B, Chen X, Waisman H. Crack propagation toward a desired path by controlling the force direction[J]. Engineering Fracture Mechanics, 2009, 76(16): 2554-2559.
 
69).Wyart E, Coulon D, Pardoen T, et al. Application of the substructured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures[J]. Engineering Fracture Mechanics, 2009, 76(1): 44-58.
 
70).Gracie R, Belytschko T. Concurrently coupled atomistic and XFEM models for dislocations and cracks[J]. International Journal for Numerical Methods in Engineering, 2009, 78(3): 354-378.
 
71).Miura N, Nagashima T. Simulation of Ductile Crack Propagation for Pipe Structures Using X-FEM[J]. Journal of Solid Mechanics and Materials Engineering, 2010, 4(3): 356-364.
 
72).Dhia H B, Jamond O. On the use of XFEM within the Arlequin framework for the simulation of crack propagation[J]. Computer methods in applied mechanics and engineering, 2010, 199(21): 1403-1414.
 
73).Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods[J]. Computers & structures, 2010, 88(23): 1391-1411.
 
74).Pais M, Kim N H, Davis T. Reanalysis of the extended finite element method for crack initiation and propagation[C]//Proceedings of AIAA Structures, Structural Dynamics, and Materials Conference. 2010.
 
75).Agwai A, Guven I, Madenci E. Predicting crack initiation and propagation using XFEM, CZM and peridynamics: A comparative study[C]//2010 Proceedings 60th Electronic Components and Technology Conference (ECTC). 2010.
 
76).Menk A, Bordas S. Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals[J]. International Journal for Numerical Methods in Engineering, 2010, 83(7): 805-828.
 
77).Colombo C, Vergani L. A numerical and experimental study of crack tip shielding in presence of overloads[J]. Engineering Fracture Mechanics, 2010, 77(11): 1644-1655.
 
78).Bordas S, Rabczuk T, Ródenas J J, et al. Alleviating the Mesh Burden in Computational Solid Mechanics[J]. Proceedings of ECT2010, 2010.
 
79).Waisman H. An analytical stiffness derivative extended finite element technique for extraction of crack tip strain energy release rates[J]. Engineering Fracture Mechanics, 2010, 77(16): 3204-3215.
 
80).Farsad M, Vernerey F J, Park H S. An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials[J]. International Journal for Numerical Methods in Engineering, 2010, 84(12): 1466-1489.
 
81).Xun J, Li Y, Chen X, et al. Characteristics of windshield cracking upon low-speed impact: numerical simulation based on the extended finite element method[J]. Computational Materials Science, 2010, 48(3): 582-588.
 
82).Réthoré J, Roux S, Hild F. Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids[J]. International Journal for Numerical Methods in Engineering, 2010, 81(3): 269-285.
 
83).Jovicic G, Zivkovic M, Jovicic N, et al. Improvement of algorithm for numerical crack modelling[J]. Archives of civil and mechanical engineering, 2010, 10(3): 19-35.
 
84).Dunant C F, Scrivener K L. Micro-mechanical modelling of alkali–silica-reaction-induced degradation using the AMIE framework[J]. Cement and Concrete research, 2010, 40(4): 517-525.
 
85).Ibrahimbegovic A, Boulkertous A, Davenne L, et al. Modelling of reinforced‐concrete structures providing crack‐spacing based on X‐FEM, ED‐FEM and novel operator split solution procedure[J]. International Journal for Numerical Methods in Engineering, 2010, 83(4): 452-481.
 
86).Legrain G, Allais R, Cartraud P. On the use of the extended finite element method with quadtree/octree meshes[J]. International Journal for Numerical Methods in Engineering, 2011, 86(6): 717-743.
 
87).Ng K, Dai Q. Tailored extended finite-element model for predicting crack propagation and fracture properties within idealized and digital cementitious material samples[J]. Journal of Engineering Mechanics, 2011, 138(1): 89-100.
 
88).Zhang W X, Fan X L, Wang T J. The surface cracking behavior in air plasma sprayed thermal barrier coating system incorporating interface roughness effect[J]. Applied Surface Science, 2011, 258(2): 811-817.
 
89).De Luycker E, Benson D J, Belytschko T, et al. X‐FEM in isogeometric analysis for linear fracture mechanics[J]. International Journal for Numerical Methods in Engineering, 2011, 87(6): 541-565.
 
90).Ng K, Dai Q. Investigation of fracture behavior of heterogeneous infrastructure materials with extended-finite-element method and image analysis[J]. Journal of Materials in Civil Engineering, 2011, 23(12): 1662-1671.
 
91).Fan X, Zhang W, Wang T, et al. Investigation on periodic cracking of elastic film/substrate system by the extended finite element method[J]. Applied Surface Science, 2011, 257(15): 6718-6724.
 
92).Moumnassi M, Belouettar S, Béchet É, et al. Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(5): 774-796.
 
93).Sanborn S E, Prévost J H. Frictional slip plane growth by localization detection and the extended finite element method (XFEM)[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35(11): 1278-1298.
 
94).Fries T P, Byfut A, Alizada A, et al. Hanging nodes and XFEM[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 404-430.
 
95).Mousavi S E, Grinspun E, Sukumar N. Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2011, 85(10): 1306-1322.
 
96).Menk A, Bordas S P A. Crack growth calculations in solder joints based on microstructural phenomena with X-FEM[J]. Computational Materials Science, 2011, 50(3): 1145-1156.
 
97).Haasemann G, Kästner M, Prüger S, et al. Development of a quadratic finite element formulation based on the XFEM and NURBS[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 598-617.
 
98).Passieux J C, Gravouil A, Réthoré J, et al. Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM[J]. International Journal for Numerical Methods in Engineering, 2011, 85(13): 1648-1666.
 
99).Häusler S M, Lindhorst K, Horst P. Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations[J]. International Journal for Numerical Methods in Engineering, 2011, 85(12): 1522-1542.
 
100).Legrain G, Cartraud P, Perreard I, et al. An X‐FEM and level set computational approach for image‐based modelling: Application to homogenization[J]. International Journal for Numerical Methods in Engineering, 2011, 86(7): 915-934.
 
101).Richardson C L, Hegemann J, Sifakis E, et al. An XFEM method for modeling geometrically elaborate crack propagation in brittle materials[J]. International Journal for Numerical Methods in Engineering, 2011, 88(10): 1042-1065.
 
102).Cernescu A, Faur N, Bortun C, et al. A methodology for fracture strength evaluation of complete denture[J]. Engineering Failure Analysis, 2011, 18(5): 1253-1261.
 
103).Menk A, Bordas S. A robust preconditioning technique for the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2011, 85(13): 1609-1632.
 
104).Chahine E, Laborde P, Renard Y. A non-conformal eXtended Finite Element approach: Integral matching Xfem[J]. Applied Numerical Mathematics, 2011, 61(3): 322-343.
 
105).Rochus V, Van Miegroet L, Rixen D J, et al. Electrostatic simulation using XFEM for conductor and dielectric interfaces[J]. International Journal for Numerical Methods in Engineering, 2011, 85(10): 1207-1226.
 
106).Zamani A, Eslami M R. Embedded interfaces by polytope FEM[J]. International Journal for Numerical Methods in Engineering, 2011, 88(8): 715-748.
 
107).Thomas-Peter Fries, Andreas Zilian, Nicolas Moës . Extended Finite Element Method[J]. International Journal for Numerical Methods in Engineering, 2011, 86: 403.
 
108).Nielsen C V, Legarth B N, Niordson C F. Extended FEM modeling of crack paths near inclusions[J]. International Journal for Numerical Methods in Engineering, 2012, 89(6): 786-804.
 
109).Yu T, Shi L. Determination of sharp V-notch stress intensity factors using the extended finite element method[J]. The Journal of Strain Analysis for Engineering Design, 2012, 47(2): 95-103.
 
110).Vajragupta N, Uthaisangsuk V, Schmaling B, et al. A micromechanical damage simulation of dual phase steels using XFEM[J]. Computational Materials Science, 2012, 54: 271-279.
 
111).Gupta V, Kim D J, Duarte C A. Analysis and improvements of global–local enrichments for the generalized finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 47-62.
 
112).Xu J, Lee C K, Tan K H. A two-dimensional co-rotational Timoshenko beam element with XFEM formulation[J]. Computational Mechanics, 2012, 49(5): 667-683.
 
113).Pais M J, Yeralan S N, Davis T A, et al. An exact reanalysis algorithm using incremental Cholesky factorization and its application to crack growth modeling[J]. International Journal for Numerical Methods in Engineering, 2012, 91(12): 1358-1364.
 
114).Fries T P, Baydoun M. Crack propagation with the extended finite element method and a hybrid explicit–implicit crack description[J]. International Journal for numerical methods in engineering, 2012, 89(12): 1527-1558.
 
115).Fries T P, Baydoun M. Crack propagation with the extended finite element method and a hybrid explicit–implicit crack description[J]. International Journal for numerical methods in engineering, 2012, 89(12): 1527-1558.
 
116).Berger‐Vergiat L, Waisman H, Hiriyur B, et al. Inexact Schwarz‐algebraic multigrid preconditioners for crack problems modeled by extended finite element methods[J]. International Journal for Numerical Methods in Engineering, 2012, 90(3): 311-328.
 
117).Bonfils N, Chevaugeon N, Moës N. Treating volumetric inequality constraint in a continuum media with a coupled X-FEM/level-set strategy[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 205: 16-28.
 
118).Seabra M R R, de Sa J M A C, Šuštarič P, et al. Some numerical issues on the use of XFEM for ductile fracture[J]. Computational Mechanics, 2012, 50(5): 611-629.
 
119).Natarajan S, Song C. Representation of singular fields without asymptotic enrichment in the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2013, 96(13): 813-841.
 
120).Mougaard J F, Poulsen P N, Nielsen L O. Complete Tangent Stiffness for eXtended Finite Element Method by including crack growth parameters[J]. International Journal for Numerical Methods in Engineering, 2013, 95(1): 33-45.
 
121).Rashvand A. Modelling rigid line and Dirichlet boundary conditions with arbitrary geometry by intrinsic XFEM[J]. International Journal for Numerical Methods in Engineering, 2013, 96(13): 867-874.
 
122).Legrain G, Geuzaine C, Remacle J F, et al. Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets[J]. Finite Elements in Analysis and Design, 2013, 77: 40-58.
 
123).Gerstenberger A, Tuminaro R S. An algebraic multigrid approach to solve extended finite element method based fracture problems[J]. International Journal for Numerical Methods in Engineering, 2013, 94(3): 248-272.
 
124).Legay A. An extended finite element method approach for structural‐acoustic problems involving immersed structures at arbitrary positions[J]. International Journal for Numerical Methods in Engineering, 2013, 93(4): 376-399.
 
125).Muthu N, Maiti S K, Falzon B G, et al. A comparison of stress intensity factors obtained through crack closure integral and other approaches using eXtended element-free Galerkin method[J]. Computational Mechanics, 2013, 52(3): 587-605.
 
126).Lan M, Waisman H, Harari I. A direct analytical method to extract mixed‐mode components of strain energy release rates from Irwin's integral using extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2013, 95(12): 1033-1052.
 
127).González‐Albuixech V F, Giner E, Tarancon J E, et al. Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2013, 94(8): 740-757.
 
128).Seabra M R R, Šuštarič P, de Sa J M A C, et al. Damage driven crack initiation and propagation in ductile metals using XFEM[J]. Computational Mechanics, 2013, 52(1): 161-179.
 
129).Chen C, Ji H, Wang H. Damage properties simulations of self-healing composites[J]. Journal of nanoscience and nanotechnology, 2013, 13(10): 6679-6686.
 
130).Tanaka S, Okada H, Okazawa S, et al. Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2013, 93(10): 1082-1108.
 
131).Lian W D, Legrain G, Cartraud P. Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches[J]. Computational Mechanics, 2013, 51(3): 279-293.
 
132).Nasri K, Abbadi M, Zenasni M, et al. Double crack growth analysis in the presence of a bi-material interface using XFEM and FEM modelling[J]. Engineering Fracture Mechanics, 2014, 132: 189-199.
 
133).Gill P, Davey K. Analysis of thermo-mechanical behaviour of a crack using XFEM for Leak-before-Break assessments[J]. International Journal of Solids and Structures, 2014, 51(11): 2062-2072.
 
134).Shibanuma K, Utsunomiya T, Aihara S. An explicit application of partition of unity approach to XFEM approximation for precise reproduction of a priori knowledge of solution[J]. International Journal for Numerical Methods in Engineering, 2014, 97(8): 551-581.
 
135).Wen L, Tian R. An extra dof-free and well conditioned XFEM[C]//The 5th International Conference on Computational Methods. 2014.
 
136).Loehnert S. A stabilization technique for the regularization of nearly singular extended finite elements[J]. Computational Mechanics, 2014, 54(2): 523-533.
 
137).Lang C, Makhija D, Doostan A, et al. A simple and efficient preconditioning scheme for heaviside enriched XFEM[J]. Computational Mechanics, 2014, 54(5): 1357-1374.
 
138).Shen Y, Lew A J. A locking-free and optimally convergent discontinuous-Galerkin-based extended finite element method for cracked nearly incompressible solids[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 273: 119-142.
 
139).Natarajan S, Song C, Belouettar S. Numerical evaluation of stress intensity factors and T-stress for interfacial cracks and cracks terminating at the interface without asymptotic enrichment[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 279: 86-112.
 
140).Duddu R. Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method[J]. Computational Mechanics, 2014, 54(3): 613-627.
 
141).Crété J P, Longère P, Cadou J M. Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 275: 204-233.
 
142).Karoui A, Mansouri K, Renard Y, et al. The eXtended finite element method for cracked hyperelastic materials: A convergence study[J]. International Journal for Numerical Methods in Engineering, 2014, 100(3): 222-242.
 
143).Amiri F, Anitescu C, Arroyo M, et al. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods[J]. Computational Mechanics, 2014, 53(1): 45-57.
 
144).Dompierre B, Mesbah M, Wyart E. Crack propagation methodology under complex loadings[J]. Engineering Fracture Mechanics, 2015, 142: 287-302.
 
145).Torres D A F, de Barcellos C S, Paulo de Tarso R M. Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 243-279.
 
146).Torres D A F, de Barcellos C S, Paulo de Tarso R M. Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 243-279.
 
147).Tian R, Wen L. Improved XFEM—An extra-dof free, well-conditioning, and interpolating XFEM[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 285: 639-658.
 
148).Gómez D G, Gilabert F A, Tsangouri E, et al. In-depth numerical analysis of the TDCB specimen for characterization of self-healing polymers[J]. International Journal of Solids and Structures, 2015, 64: 145-154.
 
149).Duarte A P C, Silva B A, Silvestre N, et al. Mechanical characterization of rubberized concrete using an image-processing/XFEM coupled procedure[J]. Composites Part B: Engineering, 2015, 78: 214-226.
 
150).Eftekhari M, Baghbanan A, Hashemolhosseini H, et al. Mechanism of fracture in macro-and micro-scales in hollow centre cracked disc specimen[J]. Journal of Central South University, 2015, 22(11): 4426-4433.
 
151).Kumar S, Singh I V, Mishra B K, et al. Modeling and simulation of kinked cracks by virtual node XFEM[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 1425-1466.
 
152).Cao-Rial M T, Moreno C, Quintela P. A new methodology for element partition and integration procedures for XFEM[J]. Finite Elements in Analysis and Design, 2016, 113: 1-13.
 
153). Alessandro Schiavone, Gayan Abeygunawardana-Arachchige,Vadim V. Silberschmidt. Crack initiation and propagation in ductile specimens with notches: experimental and numerical study. Acta Mech, 2016, 227:203–215.
 
154).Yongxiang Wang, Haim Waisman, Isaac Harari. Direct evaluation of stress intensity factors for curved cracks using Irwin’s integral and XFEM with high-order enrichment functions. Int. J. Numer. Meth. Engng 2017; 00:1–30, DOI: 10.1002/nme.5517.
 
155). Mohammad Malekan,Felicio Bruzzi Barros. Well-conditioning global–local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics. Comput Mech (2016) 58:819–831.
 
156). Bianca Giovanardi, Anna Scotti, Luca Formaggia. A hybrid XFEM –Phase field (Xfield) method for crack propagation in brittle elastic materials. Comput. Methods Appl. Mech. Engrg. 320 (2017) 396–420.
 
157). Siddharth Suman, Mohd. Kaleem Khan, Manabendra Pathak,R.N. Singh. 3D simulation of hydride-assisted crack propagation in zircaloy-4 using XFEM. International journal of hydrogen energy 42 (2017) 18668-18673..
 
158). Yongxiang Wang, Chiara Cerigato, Haim Waisman, Elena Benvenuti. XFEM with high-order material-dependent enrichment functions for stress intensity factors calculation of interface cracks using Irwin’s crack closure integral. Engineering Fracture Mechanics 178 (2017) 148–168.
 
159). Zuoyi Kang, Tinh Quoc Bui, Takahiro Saitoh, Sohichi Hirose. Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments. Theoretical and Applied Fracture Mechanics 87 (2017) 61–77.
 
160). F. Duboeuf, E. Béchet. Embedded solids of any dimension in the X-FEM. Part II – Imposing Dirichlet boundary conditions. Finite Elements in Analysis and Design 128 (2017) 32–50.
 
161). S. Mostofizadeh, M. Fagerström and R. Larsson. XFEM-based element subscale refinement for detailed representation of crack propagation in large-scale analyses. Int. J. Numer. Meth. Engng 2017; 110:549–572.
 
162). Cheng Hou, Zhiyong Wang, Weiguo Liang, Hongjun Yu, Zhihua Wang. Investigation of the effects of confining pressure on SIFs and T-stress for CCBD specimens using the XFEM and the interaction integral method. Engineering Fracture Mechanics 178 (2017) 279–300.
 
163). P. Gupta, C.A. Duarte, A. Dhankhar. Accuracy and robustness of stress intensity factor extraction methods for the generalized/eXtended Finite Element Method. Engineering Fracture Mechanics 179 (2017) 120–153.
 
164). E. B. Chin, J. B. Lasserre and N. Sukumar. Modeling crack discontinuities without element-partitioning in the extended finite element method. Int. J. Numer. Meth. Engng 2017; 110:1021–1048.
 
165). Karuppasamy Pandian Marimuthu, Felix Rickhey, Jin Haeng Lee, Hyungyil Lee. Spherical indentation for brittle fracture toughness evaluation byconsidering kinked-cone-crack. Journal of the European Ceramic Society 37 (2017) 381–391.
 
166). Diego Said Schicchi, Franz Hoffmann, Friedhelm Frerichs. A mesoscopic approach of the quench cracking phenomenon influenced by chemical inhomogeneities. Engineering Failure Analysis 78 (2017) 67–86.
 
167). Yue Gao, Zhanli Liu, Qinglei Zeng, Tao Wang, Zhuo Zhuang, Keh-Chih Hwang. Theoretical and numerical prediction of crack path in the material with anisotropic fracture toughness. Engineering Fracture Mechanics 180 (2017) 330–347.
 
168). Xin Sun, Guozhong Chai, Yumei Bao. Ultimate bearing capacity analysis of a reactor pressure vessel subjected to pressurized thermal shock with XFEM. Engineering Failure Analysis 80 (2017) 102–111.
 
169). T.F. Santos, R.D.S.G. Campilho. Numerical modelling of adhesively-bonded double-lap joints by the eXtended Finite Element Method. Finite Elements in Analysis and Design 133 (2017) 1–9.
 
170). Varun Gupta, C. Armando Duarte. On the enrichment zone size for optimal convergence rate of the Generalized/Extended Finite Element Method. Computers and Mathematics with Applications 72 (2016) 481–493.
 
171). N. Stein, S. Dölling, K. Chalkiadaki, W. Becker, P. Weißgraeber. Enhanced XFEM for crack deflection in multi-material joints. Int J Fract (2017) 207:193–210.
 
172). Jan Březina, Pavel Exner. Fast algorithms for intersection of non-matching grids using Plücker coordinates. Computers and Mathematics with Applications 74 (2017) 174–187.
 
173). T.P. Fries, S. Omerovi´c, D. Sch¨ollhammer, J. Steidl. Higher-order meshing of implicit geometries—Part I: Integration and interpolation in cut elements. Comput. Methods Appl. Mech. Engrg. 313 (2017) 759–784.
 
174). Yuan Shuowei, Yang Zichun. Microstructure model and crack initiation for a SiC-reinforced Si3N4 ceramic with differently sized SiC particles. Computational Materials Science 131 (2017) 202–208.
 
175). Siddharth Suman, Mohd. Kaleem Khan, Manabendra Pathak, R.N.Singh. Effects of hydride on crack propagation in zircaloy-4. Procedia Engineering 173 ( 2017 ) 1185 – 1190.
 
176). Lukas Schwerdt, Thomas Hauptmann, Artsem Kunin, J¨org R. Seume, J¨org Wallaschek, Peter Wriggers, Lars Panning-von Scheidt, Stefan L¨ohnert. Aerodynamical and structural analysis of operationally used turbine blades. Procedia CIRP 59 ( 2017 ) 77 – 82.
 
 
 
3.3D crack
 
1). N. Sukumar, N. Moës, B. Moran, T. Belytschko. Extended finite element method for three-dimensional crack modeling. Int. J. Numer. Meth. Engng 2000; 48:1549-1570
 
2). N. Moës, A. Gravouil, T. Belytschko. Non-planar 3D crack growth by the extended 5nite element and level sets—Part I: Mechanical model. Int. J. Numer. Meth. Engng 2002; 53:2549–2568
 
3). A. Gravouil, N. Moës, T. Belytschko.Non-planar 3D crack growth by the extended 5nite element and level sets—Part II: Level set update. Int. J. Numer. Meth. Engng 2002; 53:2569–2586
 
4). N. Sukumar, D.L. Chopp, B. Moran. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics 2003;70:29–48
 
5). Pedro M. A. Areias, Ted Belytschko. Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int. J. Numer. Meth. Engng 2005; 63:760–788
 
6). N. Sukumar, D. L. Chopp, E. Béchet, N. Moës. Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method. Int. J. Numer. Meth. Engng 2008; 76:727–748
 
7). J. Rannou, A. Gravouil, M. C. Baïetto-Dubourg. A local multigrid X-FEM strategy for 3-D crack propagation. Int. J. Numer. Meth. Engng 2009; 77:581–600
 
8). Timon Rabczuk, Stéphane Bordas, Goangseup Zi. On three-dimensional modelling of crack growth using partition of unity methods.Computers & Structures 2010; 83(23-24):1391-1411
 
9). Daniele Colombo, Patrick Massin. Fast and robust level set update for 3D non-planar X-FEM crack propagation modeling. Comput. Methods Appl. Mech. Engrg. 2011;200:2160–2180
 
10). H. Ozer, C. A. Duarte, I. L. Al-Qadi. Formulation and implementation of a high-order 3-D domain integral method for the extraction of energy release rates. Comput Mech 2012;49:459–476
 
11). M. Baydoun, T. P. Fries. Crack propagation criteria in three dimensions using the XFEM and an explicit–implicit crack description. Int J Fract 2012;178:51–70
 
12). Daniele Colombo. An implicit geometrical approach to level sets update for 3D non planar X-FEM crack propagation. Comput. Methods Appl. Mech. Engrg. 2012;237–240:39–50
 
13). Himanshu Pathak, Akhilendra Singh, Indra Vir Singh, Saurabh Kumar Yadav. A simple and efficient XFEM approach for 3-D cracks simulations. Int J Fract 2013; 181:189–208
 
14). Leiting Dong, Satya N. Atluri. Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids. CMES 2013;90(5):379-413
 
15). Vicente F. González-Albuixech, Eugenio Giner, José E. Tarancón, F. Javier Fuenmayor, Anthony Gravouil. Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method. Comput. Methods Appl. Mech. Engrg. 2013;264:129–144
 
16). Matthias Holl, Timo Rogge, Stefan Loehnert, Peter Wriggers, Raimund Rolfes. 3D multiscale crack propagation using the XFEM applied to a gas turbine blade. Comput Mech 2014;53:173–188
 
17). C. Roux Langlois, A. Gravouil, M.-C. Baietto, J. Réthoré. Three-dimensional simulation of crack with curved front with direct estimation of stress intensity factors. Int. J. Numer. Meth. Engng 2015; 101:635–652
 
18). Y. Jiang, T. E. Tay, L. Chen, Y. W. Zhang. Extended finite element method coupled with face-based strain smoothing technique for three-dimensional fracture problems. Int. J. Numer. Meth. Engng (2015)
 
19). Hossein Talebi, Mohammad Silani, Timon Rabczuk. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software 2015;80: 82–92
 
20). Elena Benvenuti, Giulio Ventura, Nicola Ponara, Antonio Tralli. Accuracy of three-dimensional analysis of regularized singularities.Int. J. Numer. Meth. Engng 2014; 101:29–53
 
21). Jean H.Prévost, N.Sukumar. Faults simulations for three-dimensional reservoir-geomechanical models with the extended finite element method [J]. Journal of the Mechanics and Physics of Solids 2016;86:1–18
 
22). Konstantinos Agathos, Eleni Chatzi, Stéphane P. A. Bordas, Demosthenes Talaslidis. A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture. Int. J. Numer. Meth. Engng 2016; 105:643–677.
 
23). Konstantinos Agathos, Eleni Chatzi, Stéphane P.A. Bordas. Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture. Comput. Methods Appl. Mech. Engrg. 306 (2016) 19–46.
 
24)Hans Minnebo. Three-dimensional integration strategies of singular functions introduced by the XFEM in the LEFM. Int. J. Numer. Meth. Engng 2012; 92:1117–1138.
 
25).S. Loehnert, D. S. Mueller-Hoeppe, P. Wriggers. 3D corrected XFEM approach and extension to finite deformation theory. Int. J. Numer. Meth. Engng 2011; 86:431–452.
 
26). John H.L. Pang, Kin Shun Tsang, Hsin Jen Hoh. 3D stress intensity factors for weld toe semi-elliptical surface cracks using XFEM. Marine Structures 2016;48:1-14.
 
27). Zhen Wang, Tiantang Yu, Tinh Quoc Bui, Satoyuki Tanaka, Chuanzeng Zhang,Sohichi Hirose, Jose L. Curiel-Sosa. 3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks. Comput. Methods Appl. Mech. Engrg. 313 (2017) 375–405.
 
28). Xiang Ren, Xuefei Guan. Three dimensional crack propagation through mesh-based explicit representation for arbitrarily shaped cracks using the extended finite element method. Engineering Fracture Mechanics 177 (2017) 218–238.
 
29). V.F. González-Albuixech, E. Giner y J.E. Tarancón. Modelado de la singularidad de borde libre en grietas 3D medianteXFEM y armónicos esféricos. Rev. int. métodos numér. cálc. diseño ing. 2015;31(1):50–54.
 
30). B. Paul, M. Ndeffo, P. Massin, N. Moës. An integration technique for 3D curved cracks and branched discontinuities within the extended Finite Element Method. Finite Elements in Analysis and Design 123 (2017) 19–50.
 
 
4.Blending elements
 
1). Jack Chessa, Hongwu Wang, Ted Belytschko. On the construction of blending elements for local partition of unity enriched finite elements. Int. J. Numer. Meth. Engng 2003; 57:1015–1038
 
2). Thomas-Peter Fries. A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engng 2008; 75:503–532
 
3). Robert Gracie, Hongwu Wang,Ted Belytschko. Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. Int. J. Numer. Meth. Engng 2008; 74:1645–1669
 
4). J. E. Tarancón, A. Vercher, E. Giner, F. J. Fuenmayor.Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. Int. J. Numer. Meth. Engng 2009; 77:126–148
 
5). Giulio Ventura, Robert Gracie, Ted Belytschko. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Meth. Engng 2009; 77:1–29
 
6). Kazuki Shibanuma, TomoakiUtsunomiya. Reformulation of XFEM based on PUFEM for solving problem caused by blending elements. Finite Elements in Analysis and Design 2009;45: 806 - 816
 
7). S. Loehnert, D. S. Mueller-Hoeppe, P. Wriggers. 3D corrected XFEM approach and extension to finite deformation theory. Int. J. Numer. Meth. Engng 2011; 86:431–452
 
 
5.Detection of flaws
 
1). Daniel Rabinovich, Dan Givoli, Shmuel Vigdergauz. XFEM-based crack detection scheme using a genetic algorithm. Int. J. Numer. Meth. Engng 2007; 71:1051–1080
 
2).Daniel Rabinovich, Dan Givoli, Shmuel Vigdergauz. Crack identification by ‘arrival time’ using XFEM and a genetic algorithm. Int. J. Numer. Meth. Engng 2009; 77:337–359
 
3). Haim Waisman, Eleni Chatzi, Andrew W. Smyth. Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms. Int. J. Numer. Meth. Engng 2010; 82:303–328
 
4). T. Krishnamurthy, Adam M. Gallegos. Damage Characterization Using the Extended Finite Element Method for Structural Health Management.52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 4-7 April 2011, Denver, Colorado
 
5). Eleni N. Chatzi, Badri Hiriyur, Haim Waisman, Andrew W. Smyth. Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures. Computers and Structures 2011;89: 556–570
 
6). J. Jung, C. Jeong, E. Taciroglu. Identification of a scatterer embedded in elastic heterogeneous media using dynamic XFEM. Comput. Methods Appl. Mech. Engrg. 2013; 259: 50–63
 
7). S. S. Nanthakumar, T. Lahmer, T. Rabczuk. Detection of flaws in piezoelectric structures using extended FEM.Int. J. Numer. Meth. Engng 2013; 96:373–389
 
8). Hao Sun, Haim Waisman, Raimondo Betti. Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm. Int. J. Numer. Meth. Engng 2013; 95:871–900
 
9). S.S. Nanthakumar, T. Lahmer, T. Rabczuk. Detection of multiple flaws in piezoelectric structures using XFEM and level sets. Comput. Methods Appl. Mech. Engrg. 2014;275: 98–112
 
10). J. Jung,E. Taciroglu. Modeling and identification of an arbitrarily shaped scatterer using dynamic XFEM with cubic splines. Comput. Methods Appl. Mech. Engrg. 2014;278: 101–118
 
11). Hao Sun, Haim Waisman, Raimondo Betti. A multiscale flaw detection algorithm based on XFEM. Int. J. Numer. Meth. Engng 2014; 100:477–503
 
12). Gang Yan, Hao Sun, Haim Waisman. A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method. Computers and Structures 2015;152:27–44
 
13). Gang Yan, Hao Sun, Haim Waisman. A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method. Computers and Structures 2015;152:27–44
 
14). Chao Zhang, Cuixia Wang, Tom Lahmer, Pengfei He, Timon Rabczuk. A dynamic XFEM formulation for crack identification. Int J Mech Mater Des DOI 10.1007/s10999-015-9312-3
 
15). Lyazid Bouhala, Ahmed Makradi, Salim Belouettar, Anis Younes, Sundararajan Natarajan. An XFEM/CZM based inverse method for identification of composite failure parameters. Computers and Structures 2015;153:91–97
 
16). KONSTANTINOS AGATHOS, ELENI CHATZI AND STE´ PHANE P. A. BORDAS. 3D CRACK DETECTION USING AN XFEM VARIANT AND GLOBAL OPTIMIZATION ALGORTITHMS. 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures..
 
17). C. Zhang,S. S. Nanthakumar,T. Lahmer, T. Rabczuk. Multiple cracks identification for piezoelectric structures. Int J Fract (2017) 206:151–169.
 
18). Hao Sun, Haim Waisman and Raimondo Betti. A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers. Int. J. Numer. Meth. Engng 2016; 105:1014–1040.
 
 
6.Geomechamics
 
1). Debasis Deb, Kamal Ch Das. Extended Finite Element Method (XFEM) for analysis of cohesive rock joint. Journal of Scientific & Industrial Research 2009; 68:575–583
 
2). Debasis Deb, Kamal C. Das. Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses. Geotech Geol Eng 2010; 28:643–659
 
3). Scott E. Sanborn, Jean H. Prévost. Frictional slip plane growth by localization detection and the extended finite element method (XFEM). Int. J. Numer. Anal. Meth. Geomech. 2011; 35:1278–1298
 
4). T.T. Yu. The extended finite element method (XFEM) for discontinuous rock masses. Engineering Computations 2011;28(3):40-369.
 
5). A.R. Khoei, S. Moallemi, E. Haghighat. Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique. Engineering Fracture Mechanics 2012;96:701–723
 
6). T. Mohammadnejad, A. R. Khoei. An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies. Comput Mech 2013; 51:327–345
 
7). F. Pasenow, A. Zilian, D. Dinkler. Extended space–time finite elements for landslide dynamics. Int. J. Numer. Meth. Engng 2013; 93:329–354
 
8). T. Mohammadnejad, A. R. Khoei.Hydro-mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method. Int. J. Numer. Anal. Meth. Geomech. 2013; 37:1247–1279
 
9). Qian Shao, Lyazid Bouhala, Anis Younes, Pedro Núñez, Ahmed Makradi, Salim Belouettar. An XFEM model for cracked porous media: effects of fluid flow and heat transfer. Int J Fract 2014;185:155–169
 
10). Senjun Wu, Dashnor Hoxha, Naima Belayachi, Duc Phi Do. Modeling mechanical behavior of geomaterials by the extended finite-element method. The Fifth International Conference on Multiscale Materials Modeling, Freiburg: Germany, 2010
 
11). A. R. Khoei, M. Vahab, E. Haghighat, S. Moallemi. A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique. Int J Fract 2014; 188:79–108
 
12). Majid Goodarzi, Soheil Mohammadi, Ahmad Jafari. Numerical analysis of rock fracturing by gas pressure using the extended finite element method. Pet. Sci. 2015; 12:304–315
 
13). Debasis Deb, Ranjan Pramanik, Kamal Ch Das. A generalized XFEM procedure for analyzing intersecting joints in rock masses with excavation. Engineering Computations 2015,32(3):806 -833
 
14). Mao Sheng, Gensheng Li, Subhash Shah, Anthony R. Lamb, Stéphane P.A. Bordas. Enriched finite elements for branching cracks in deformable porous media. Engineering Analysis with Boundary Elements 2015;50:435–446
 
15). S. Berrone, C. Fidelibus, S. Pieraccini, S. Scialo`. Simulation of the Steady-State Flow in Discrete Fracture Networks with Non-Conforming Meshes and Extended Finite Elements. Rock Mech Rock Eng 2014;47:2171–2182
 
16). Jose Roberto Silvestre, Euripedes do Amaral Vargas Jr., Luiz Eloy Vaz, Antonio Claudio Soares. Modelling of coupled fluid-mechanical problems in fractured geological media using enriched finite elements. Int. J. Numer. Anal. Meth. Geomech. 2015; 39:1104–1140
 
17). ZHENG An-xing, LUO Xian-qi. Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method. J. Cent. South Univ. 2015; 22: 4337−4346
 
18). Mr. Zhan Tang, Dr. Ali Tolooiyan, Prof. Rae Mackay.Unconfined Expansion Test (UET) for measuring the tensile strength of organic soft rock. Computers and Geotechnics 82 (2017) 54–66.
 
19). Hongjian Wang, Daan Liu, Zhendong Cui, Cheng Cheng, Zhou Jian. Investigation of the fracture modes of red sandstone using XFEM and acoustic emissions. Theoretical and Applied Fracture Mechanics 85 (2016) 283–293.
 
20). Toan Duc Cao, Enrico Milanese, Ernst W. Remij, Paolo Rizzato, Joris J.C. Remmers,Luciano Simoni, Jacques M. Huyghe, Fazle Hussain, Bernhard A. Schrefler. Interaction between crack tip advancement and fluid flow infracturing saturated porous media. Mechanics Research Communications 80 (2017) 24–37.
 
21). Ehsan Mohtarami, Alireza Baghbanan, Mosleh Eftekhari, Hamid Hashemolhosseini. Investigating of chemical effects on rock fracturing using extended finite element method. Theoretical and Applied Fracture Mechanics 89 (2017) 110–126.
 
22). Yousheng Xie, Ping Cao, Jin Jin, Min Wang. Mixed mode fracture analysis of semi-circular bend (SCB) specimen: A numerical study based on extended finite element method. Computers and Geotechnics 82 (2017) 157–172.
 
 
7.Uncertainty
 
1). J. GRASA, J. A. BEA, J. F. RODRíGUEZ, M. DOBLARÉ. The perturbation method and the extended finite element method. An application to fracture mechanics problems. Fatigue Fract Engng Mater Struct 2006;29: 581–587
 
2). Jorge Grasa, José Antonio Bea, Manuel Doblaré. A Probabilistic Extended Finite Element Approach: Application to the Prediction of Bone Crack Propagation. Key Engineering Materials 2007;348-349:77-80
 
3). A. Nouy, A. Clément, F. Schoefs, N. Moës. An extended stochastic finite element method for solving stochastic partial differential equations on random domains. Comput. Methods Appl. Mech. Engrg. 2008;197:4663–4682
 
4).Badri Hiriyur, Haim Waisman, George Deodatis. Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM. Int. J. Numer. Meth. Engng 2011; 88:257–278
 
5). Christapher Lang, Alireza Doostan, Kurt Maute. Extended stochastic FEM for diffusion problems with uncertain material interfaces. Comput Mech 2013; 51:1031–1049
 
6). Achchhe Lal, Shailesh P. Palekar. Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM. Int J Mech Mater Des DOI 10.1007/s10999-015-9325-y
 
7). Christapher Lang, Ashesh Sharma, Alireza Doostan, Kurt Maute. Heaviside enriched extended stochastic FEM for problems with uncertain material interfaces. Comput Mech 2015; 56:753–767
 
8). F.-J. Barthold, D. Materna.A modified extended finite element method approach for design sensitivity analysis. Int. J. Numer. Meth. Engng 2015; 104:209–234
 
9). George Stefanou, Dimitrios Savvas, Manolis Papadrakakis. Stochastic finite element analysis of composite structures based on material microstructure. Composite Structures 2015;132:384–392
 
10). Dimitris Savvas,George Stefanou, Manolis Papadrakakis,George Deodatis. Homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by XFEM. Comput Mech 2014;54:1221–1235
 
11). Benjin Wang, Hans De Backer, Airong Chen. An XFEM based uncertainty study on crack growth in welded joints with defects. Theoretical and Applied Fracture Mechanics 86 (2016) 125–142.
 
12). Manik Bansal, I.V. Singh, B.K. Mishra, Kamal Sharma, I.A. Khan. A stochastic XFEM model for the tensile strength prediction of heterogeneous graphite based on microstructural observations. Journal of Nuclear Materials 487 (2017) 143-157.
 
13). Achchhe Lal, Shailesh P.Palekar, Sameer B.Mulani, Rakesh K.Kapania.Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack. Aerospace Science and Technology 60 (2017) 131–151.
 
14). Jingjing He, Jinsong Yang, Yongxiang Wang, Haim Waisman and Weifang Zhang. Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method. Sensors 2016, 16, 1956; doi:10.3390/s16111956.
 
15). D. Motamedi, A. S. Milani, M. Komeili, M. N. Bureau, F. Thibault, D. Trudel-Boucher. A Stochastic XFEM Model to Study Delamination in PPS/Glass UD Composites: Effect of Uncertain Fracture Properties. Appl Compos Mater (2014) 21:341–358.
 
16). Manolis Georgioudakis, Nikos D. Lagaros, Manolis Papadrakakis. Probabilistic shape design optimization of structural components under fatigue. Computers and Structures 182 (2017) 252–266.
 
17). Jung-Hoon Kim, Thanh Chau-Dinh, Goangseup Zi, Won Woo Lee, Jung Sik Kong. Probabilistic fatigue integrity assessment in multiple crack growth analysis associated with equivalent initial flaw and material variability. Engineering Fracture Mechanics 156 (2016) 182–196.
 
18). Stefano Berrone, Sandra Pieraccini, Stefano Scialo. Non-stationary transport phenomena in networks of fractures:Effective simulations and stochastic analysis. Comput. Methods Appl. Mech. Engrg. 315 (2017) 1098–1112.
 
 
8.Viscoelastic
 
1). H.H. Zhang, G. Rong L.X.Li. Numerical study on deformations in a cracked viscoelastic body with the extended finite element method. Engineering Analysis with Boundary Elements 2010;34: 619–624
 
2). YU TianTang, Ren QingWen. Modeling crack in viscoelastic media using the extended finite element. Science China Technological Sciences 2011;54(6):1599-1606
 
 
9.Computer Implementation
 
1). N. Sukumar, J.-H. Prévost. Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation. International Journal of Solids and Structures 2003;40:7513–7537
 
2). Stéphane Bordas, Phu Vinh Nguyen, Cyrille Dunant, Hung Nguyen-Dang, Amor Guidoum. An extended finite element library. Int. J. Numer. Meth. Engng 2006; 2:1–33
 
3). Ebrahim Mousavi .Computer Implementation of Extended Finite Element Method for Crack Modeling. Progress Report on Final Project, Department of Civil and Environmental Engineering University of California, Davis,2008
 
4). E. Giner, N. Sukumar, J.E. Tarancón, F.J. Fuenmayor. An Abaqus implementation of the extended finite element method. Engineering Fracture Mechanics 2009;76:347–368
 
5). Jianxu Shi, David Chopp, Jim Lua, N. Sukumar, Ted Belytschko. Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions. Engineering Fracture Mechanics 2010;77: 2840–2863
 
6). Lei Jiang .Implementation of 2D XFEM in VAST. Defence R&D Canada – Atlantic ,2010
 
7). Yazid Abdelaziz, K. Bendahane, A. Baraka. Extended Finite Element Modeling: Basic Review and Programming. Engineering 2011; 3: 713-718
 
 
10.Strain localization
 
1). Richard A. Regueiro, Ronaldo I. Borja. A finite element model of localized deformation in frictional materials taking a strong discontinuity approach. Finite Elements in Analysis and Design 1999;33: 283-315
 
2). Ronaldo I. Borja. A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation. Comput. Methods Appl. Mech. Engrg. 2000;190: 1529-1549
 
3). G. N. Wells, L. J. Sluys, R. deBorst. Simulating the propagation of displacement discontinuities in a regularized strain-softening medium. Int. J. Numer. Meth. Engng 2002; 53:1235–1256
 
4). Paolo Maria Mariano, Furio Lorenzo Stazi. Strain localization due to crack–microcrack interactions: X-FEM for a multifield approach. Comput. Methods Appl. Mech. Engrg. 2004;193: 5035–5062
 
5). Esteban Samaniego, Ted Belytschko. Continuum–discontinuum modelling of shear bands. Int. J. Numer. Meth. Engng 2005; 62:1857–1872
 
6). Pedro M. A. Areias, Ted Belytschko. Two-scale shear band evolution by local partition of unity. Int. J. Numer. Meth. Engng 2006; 66:878–910
 
7). Julien Re′thore′, François Hild, Stéphane Roux. Shear-band capturing using a multiscale extended digital image correlation technique. Comput. Methods Appl. Mech. Engrg. 2007;196: 5016–5030
 
8). A.R. Khoei, K. Karimi. An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory. Computational Materials Science 2008;44:733–749
 
9). Scott E. Sanborn, Jean H. Prévost. Frictional slip plane growth by localization detection and the extended finite element method (XFEM). Int. J. Numer. Anal. Meth. Geomech. 2011; 35:1278–1298
 
10). Elena Benvenuti. Mesh-size-objective XFEM for regularized continuous–discontinuous transition. Finite Elements in Analysis and Design 2011;47: 1326–1336
 
11). J. Oliver, A.E. Huespe, I.F. Dias. Strain localization, strong discontinuities and material fracture: Matches and mismatches. Comput. Methods Appl. Mech. Engrg. 2012;241–244: 323–336
 
12). Alireza Daneshyar, Soheil Mohammadi. Strong tangential discontinuity modeling of shear bands using the extended finite element method. Comput Mech 2013; 52:1023–1038
 
13). Pengfei Liu. Extended finite element method for strong discontinuity analysis of strain localization of non-associative plasticity materials. International Journal of Solids and Structures 2015;72:174–189
 
 
11.Thermal problem
 
1). R. Merle, J. Dolbow. Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics 2002;28: 339–350
 
2). P. Michlik, C. Berndt.Image-based extended finite element modeling of thermal barrier coatings. Surface & Coatings Technology 2006;201: 2369–2380
 
3). Huidi Ji, Hashem Mourad, Eliot Fried, John Dolbow. Kinetics of thermally induced swelling of hydrogels. International Journal of Solids and Structures 2006;43: 1878–1907
 
4). Marc Duflot. The extended finite element method in thermoelastic fracture mechanics. Int. J. Numer. Meth. Engng 2008; 74:827–847
 
5). Arash Zamani, M. Reza Eslami. Implementation of the extended finite element method for dynamic thermoelastic fracture initiation. International Journal of Solids and Structures 2010;47: 1392–1404
 
6). J. Yvonnet, Q.-C. He, Q.-Z. Zhu, J.-F. Shao. A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM. Computational Materials Science 2011; 50:1220–1224
 
7). Thomas Menouillard, Ted Belytschko. Analysis and computations of oscillating crack propagation in a heated strip. Int J Fract 2011; 167:57–70
 
8). S.T. Gu, Eric Monteiro, Q.C. He. Coordinate-free derivation and weak formulation of a general imperfect interface model for thermal conduction in composites. Composites Science and Technology 2011;71:1209–1216
 
9). P. O’Hara, C.A. Duarte, T. Eason. Transient analysis of sharp thermal gradients using coarse finite element meshes. Comput. Methods Appl. Mech. Engrg. 2011;200 : 812–829
 
10). Guowei Liu, Yu Hu, Qingbin Li, Zheng Zuo. XFEM for Thermal Crack of Massive Concrete. Mathematical Problems in Engineering 2013; Article ID 343842, 9 pages
 
11). Pawel Stapór. The XFEM for nonlinear thermal and phase change problems. International Journal of Numerical Methods for Heat & Fluid Flow 2015;25(2):400 - 421
 
12). Zheng Zuo,Yu Hu, Qingbin Li,Guowei Liu. An extended finite element method for pipe-embedded plane thermal analysis. Finite Elements in Analysis and Design 2015;102-103:52–64
 
13). Muyuan Li, Ewald Werner, Jeong-Ha You. Influence of heat flux loading patterns on the surface cracking features of tungsten armor under ELM-like thermal shocks. Journal of Nuclear Materials 2015;457:256–265
 
14). J. Jas´kowiec. A model for heat transfer in cohesive cracks. Computers and Structures 180 (2017) 89–103.
 
15). Kuanfang He, Qing Yang, Dongming Xiao and Xuejun Li. Analysis of Thermo-Elastic Fracture Problem during Aluminium Alloy MIG Welding Using the Extended Finite Element Method. Appl. Sci. 2017, 7, 69; doi:10.3390/app7010069.
 
 
12.Hydraulic fracture
 
1). REN QingWen, DONG YuWen, YU TianTang.Numerical modeling of concrete hydraulic fracturing with extended finite element method. Science in China Series E: Technological Sciences 2009; 52(3): 559-565
 
2). Brice Lecampion. An extended finite element method for hydraulic fracture problems. Commun. Numer. Meth. Engng 2009; 25:121–133
 
3). N. Watanabe, W. Wang, J. Taron, U. J. Görke, O. Kolditz. Lower-dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media. Int. J. Numer. Meth. Engng 2012; 90:1010–1034
 
4). T. Mohammadnejad, A.R. Khoei. An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elements in Analysis and Design 2013;73:77–95
 
5). Elizaveta Gordeliy, Anthony Peirce. Implicit level set schemes for modeling hydraulic fractures using the XFEM. Comput. Methods Appl. Mech. Engrg. 2013;266:125–143
 
6). Elizaveta Gordeliy, Anthony Peirce. Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Comput. Methods Appl. Mech. Engrg. 2013;253:305–322
 
7). NikolaiWeber,Thomas-Peter Fries.The XFEM with an Implicit-Explicit Crack Description for a Plane-Strain Hydraulic Fracture Problem. Proc. Appl. Math. Mech. 2013;13:83 – 84
 
8). P. Gupta, C. A. Duarte. Simulation of non-planar three-dimensional hydraulic fracture propagation. Int. J. Numer. Anal. Meth. Geomech. 2014; 38:1397–1430
 
9). Zuorong Chen. Implementation of the XFEM for Hydraulic Fracture Problems. 13th International Conference on Fracture, June 16–21, 2013, Beijing, China
 
10). Ashkan. Mahdavi, Soheil. Mohammadi. A Numerical Hydraulic Fracture Model Using the Extended Finite Element Method. International Conference on Mechanical and Industrial Engineering (ICMIE'2013) August 28-29, 2013 Penang (Malaysia)
 
11). Reza Keshavarzi, Reza Jahanbakhshi. Investigation of Hydraulic and Natural Fracture Interaction: Numerical Modeling or Artificial Intelligence? http://dx.doi.org/10.5772/56382
 
12). N. Weber, P. Siebert, K. Willbrand, M. Feinendegen, C. Clauser, T. P. Fries. The XFEM With An Explicit-Implicit Crack Description For Hydraulic Fracture Problems. http://dx.doi.org/10.5772/56383
 
13). Zuorong Chen. An ABAQUS Implementation of the XFEM for Hydraulic Fracture Problems. http://dx.doi.org/10.5772/56287
 
14). Elizaveta Gordeliy, Anthony Peirce.Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems. Comput. Methods Appl. Mech. Engrg. (2014), http://dx.doi.org/10.1016/j.cma.2014.09.004
 
15). 盛 茂, 李根生. 水力压裂过程的扩展有限元数值模拟方法. 工程力学2014;31(10):123-128.
 
16). Saeed Salimzadeh, Nasser Khalili. A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation. Computers and Geotechnics 2015;69:82–92.
 
17). A.R. Khoei, M. Hirmand, M. Vahab, M. Bazargan. An enriched FEM technique for modeling hydraulically driven cohesive fracture propagation in impermeable media with frictional natural faults: Numerical and experimental investigations. Int. J. Numer. Meth. Engng 2015; 104:439–468
 
18). E.W. Remij, J.J.C. Remmers, J.M. Huyghe, D.M.J. Smeulders. The enhanced local pressure model for the accurate ana lysis of fluid pressure driven fracture in porous materials. Comput. Methods Appl. Mech. Engrg. 2015;286:293–312
 
19). Lei Zhou, Yang Gou, Zhengmeng Hou, Patrick Were. Numerical modeling and investigation of fracture propagation with arbitrary orientation through fluid injection in tight gas reservoirs with combined XFEM and FVM. Environ Earth Sci 2015;73:5801–5813
 
20). Mahdi Haddad, Kamy Sepehrnoori. XFEM-Based CZM for the Simulation of 3D Multiple-Cluster Hydraulic Fracturing in Quasi-Brittle Shale Formations. Rock Mech Rock Eng (2016) 49:4731–4748.
 
21). Ali Naghi Dehghan, Kamran Goshtasbi, Kaveh Ahangari, Yan Jin, Aram Bahmani. 3D Numerical Modeling of the Propagation of Hydraulic Fracture at Its Intersection with Natural (Pre-existing) Fracture. Rock Mech Rock Eng (2017) 50:367–386.
 
22). Tao Wang, ZhanLi Liu, QingLei Zeng, Yue Gao, and Zhuo Zhuang. XFEM modeling of hydraulic fracture in porous rocks with natural fractures. SCIENCE CHINA:Physics, Mechanics & AstronomyAugust 2017; 60(8): 084612.
 
23). M. Vahab, N. Khalili. Numerical investigation of the flow regimes through hydraulic fractures using the X-FEM technique. Engineering Fracture Mechanics 169 (2017) 146–162.
 
24). Seyed Erfan Saberhosseini & Reza Keshavarzi & Kaveh Ahangari. A fully coupled three-dimensional hydraulic fracture model to investigate the impact of formation rock mechanical properties and operational parameters on hydraulic fracture opening using cohesive elements method. Arab J Geosci (2017) 10: 157.
 
25). Fang Shi, Xiaolong Wang, Chuang Liu, He Liu, Hengan Wu. An XFEM-based method with reduction technique for modeling hydraulic fracture propagation in formations containing frictional natural fractures. Engineering Fracture Mechanics 173 (2017) 64–90.
 
26). Fei Liu, Zhifeng Luo, Yu Sang, Liqiang Zhao, and Changlin Zhou. Deformation Behavior between Hydraulic and Natural Fractures Using Fully Coupled Hydromechanical Model with XFEM. Mathematical Problems in Engineering, Volume 2017, Article ID 6373957, 12 pages.
 
27). P. Gupta and C. A. Duarte. Coupled formulation and algorithms for the simulation of non-planar three-dimensional hydraulic fractures using the generalized finite element method. Int. J. Numer. Anal. Meth. Geomech. 2016; 40:1402–1437.
 
28). Fushen Liu, Peter Gordon, Holger Meier and Dakshina Valiveti. A stabilized extended finite element framework for hydraulic fracturing simulations. Int. J. Numer. Anal. Meth. Geomech. 2017; 41:654–681.
 
29). T. Mohammadnejad and J.E. Andrade. Numerical modeling of hydraulic fracture propagation, closure and reopening using XFEM with application to in-situ stress estimation. Int. J. Numer. Anal. Meth. Geomech. 2016; 40:2033–2060.
 
30). Chuang Liu, Fang Shi, YongPing Zhang, YuGuang Zhang, DaWei Deng, XiaoLong Wang, He Liu, HengAn Wu. High injection rate stimulation for improving the fracture complexity in tight-oil sandstone reservoirs. Journal of Natural Gas Science and Engineering 42 (2017) 133-141.
 
 
13.Anisotropic media
 
1). A. Asadpoure, S. Mohammadi, A. Vafai. Modeling crack in orthotropic media using a coupled finite element and partition of unity methods. Finite Elements in Analysis and Design 2006;42: 1165 – 1175
 
2). Alireza Asadpoure, Soheil Mohammadi, Abolhasan Vafai. Crack analysis in orthotropic media using the extended finite element method. Thin-Walled Structures 2006;44:1031–1038
 
3). A. Asadpoure, S. Mohammadi. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int. J. Numer. Meth. Engng 2007; 69:2150–2172
 
4). Alexander Menk, Stéphane P. A. Bordas. Numerically determined enrichment functions for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int. J. Numer. Meth. Engng 2010; 83:805–828
 
5). D. Motamedi, S. Mohammadi. Dynamic crack propagation analysis of orthotropic media by the extended finite element method. Int J Fract 2010; 161:21–39
 
6). S. Esna Ashari, S. Mohammadi. Delamination analysis of composites by new orthotropic biomaterial extended finite element method. Int. J. Numer. Meth. Engng 2011; 86:1507–1543
 
7). D. Motamedi,S.Mohammadi. Fracture analysis of composites by time independent moving-crack orthotropic XFEM. International Journal of Mechanical Sciences 2012;54: 20–37
 
8). G. Hattori, R. Rojas-Díaz, A. Sáez, N. Sukumar, F. García-Sánchez. New anisotropic crack-tip enrichment functions for the extended finite element method. Comput Mech 2012; 50:591–601
 
9). M. Toolabi, A.S. Fallah, P.M. Baiz, L.A. Louca. Dynamic analysis of a viscoelastic orthotropic cracked body using the extended finite element method. Engineering Fracture Mechanics 2013;109:17–32
 
10).Y. Jiang, T. E. Tay, L. Chen, X. S. Sun. An edge-based smoothed XFEM for fracture in composite materials. Int J Fract 2013; 179:179–199
 
11). Himanshu Pathak, Akhilendra Singh, Indra Vir Singh. Fracture analysis of 3D orthotropic cracked domain by extended finite element method (XFEM).
 
 
14.Biomechanics
 
1). A. Cernescu, N. Faur, C. Bortun, M. Hluscu. A methodology for fracture strength evaluation of complete denture. Engineering Failure Analysis 2011;18: 1253–1261
 
2). Mehdi Farsad, Franck J. Vernerey. An XFEM-based numerical strategy to model mechanical interactions between biological cells and a deformable substrate. Int. J. Numer. Meth. Engng 2012; 92:238–267
 
3). Simin Li, Adel Abdel-Wahab, Vadim V. Silberschmidt. Analysis of fracture processes in cortical bone tissue. Engineering Fracture Mechanics 2013;110: 448–458
 
4). Simin Li, Adel Abdel-Wahab, Emrah Demirci, Vadim V. Silberschmidt. Fracture process in cortical bone: X-FEM analysis of microstructured models. Int J Fract 2013;184:43–55
 
5). Y.Y. Zhang, M.D. Peng, Y.N. Wang, Q. Li. The effects of ferrule configuration on the anti-fracture ability of fiber post-restored teeth. Journal of dentistry 2015; 43:117-125
 
6). Zhongpu Zhang, Shiwei Zhou, etc. Design for minimizing fracture risk of all-ceramic cantilever dental bridge. Bio-medical materials and engineering 2015;26:s19-s25.
 
7). Ashraf Idkaidek and Iwona Jasiuk. Cortical bone fracture analysis using XFEM – case study. Int. J. Numer. Meth. Biomed. Engng. (2017); e02809.
 
 
15.Plate and shell
 
1). Pedro M. A. Areias, Ted Belytschko. Non-linear analysis of shells with arbitrary evolving cracks using XFEM. Int. J. Numer. Meth. Engng 2005; 62:384–415
 
2). Pedro M.A. Areias, J.H. Song, Ted Belytschko. Analysis of fracture in thin shells by overlapping paired elements. Comput. Methods Appl. Mech. Engrg. 2006;195:5343–5360
 
3). M. Bachene,R. Tiberkak,S. Rechak. Vibration analysis of cracked plates using the extended finite element method. Arch Appl Mech 2009;79: 249–262
 
4). Toshio Nagashima, Hiroshi Suemasu. X-FEM analyses of a thin-walled composite shell structure with a delamination. Computers and Structures 2010;88:549–557
 
5). Jérémie Lasry, Julien Pommier, Yves Renard, Michel Salaün.eXtended finite element methods for thin cracked plates with Kirchhoff–Love theory. Int. J. Numer. Meth. Engng 2010; 84:1115–1138
 
6). John Dolbow, Nicolas Moës, Ted Belytschko. Modeling fracture in Mindlin-Reissner plates with the extended finite element method. International Journal of Solids and Structures 2000;37:7161-7183
 
7). S. Natarajan, P.M. Baiz, S. Bordas , T. Rabczuk, P. Kerfriden. Natural frequencies of cracked functionally graded material plates by the extended finite element method. Composite Structures 2011;93:3082–3092
 
8). Pedro M. BAIZ, Sundararajan Natarajan, Stéphane P. A. Bordas, Pierre Kerfriden, Timon Rabczuk. Linear buckling analysis of cracked plates by SFEM and XFEM. Journal of mechanics of materials and structures 2011;6(9-10):1213-1238
 
9). H. Bayesteh, S. Mohammadi. XFEM fracture analysis of shells: The effect of crack tip enrichments. Computational Materials Science 2011;50:2793–2813
 
10). 庄 茁,成斌斌. 发展基于 CB 壳单元的扩展有限元模拟三维任意扩展裂纹. 工程力学 2012;29(6):12-21
 
11). Jérémie Lasry, Yves Renard, Michel Salaün. Stress intensity factors computation for bending plates with extended finite element method. Int. J. Numer. Meth. Engng 2012; 91:909–928
 
12). Jin Xu, C.K. Lee, K.H. Tan. An enriched 6-node MITC plate element for yield line analysis. Computers and Structures 2013;128: 64–76
 
13). Jin Xu, C. K. Lee, K. H. Tan. An XFEM frame for plate elements in yield line analyses. Int. J. Numer. Meth. Engng 2013; 96:150–175
 
14). Jin Xu, C. K. Lee, K. H. Tan. An XFEM plate element for high gradient zones resulted from yield lines. Int. J. Numer. Meth. Engng 2013; 93:1314–1344
 
15). S. Natarajan, S. Chakraborty, M. Ganapathi, M. Subramanian. A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method. European Journal of Mechanics A/Solids 2014;44: 136-147
 
16). T. Nguyen-Thoi , T. Rabczuk, T. Lam-Phat, V. Ho-Huu, P. Phung-Van.Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3). Theoretical and Applied Fracture Mechanics 2014;72:150–163
 
17). Tiantang Yu, Tinh Quoc Bui, Peng Liu. A stabilized discrete shear gap extended finite element for the analysis of cracked Reissner-Mindlin plate vibration problems involving distorted meshes. International Journal of Mechanics and Materials in Design. Int J Mech Mater Des, DOI 10.1007/s10999-014-9282-x
 
18). Jim Brouzoulis, Martin Fagerström. An enriched shell element formulation for efficient modeling of multiple delamination propagation in laminates. Composite Structures 2015;126: 196–206
 
19). Amir Nasirmanesh, Soheil Mohammadi. XFEM buckling analysis of cracked composite plates. Composite Structures 2015;131:333–343
 
20). J. Jas´kowiec, P. Plucin´ ski, J. Pamin. Thermo-mechanical XFEM-type modeling of laminated structure with thin inner layer. Engineering Structures 2015;100:511–521.
 
21). Anand Venkatachari, Sundararajan Natarajan, Manickam Ganapathi, Mohamed Haboussi. Mechanical buckling of curvilinear fibre composite laminate with material discontinuities and environmental effects. Composite Structures 2015;131:790–798
 
22). Saleh Yazdani, Wilhelm J.H. Rust, Peter Wriggers. An XFEM approach for modelling delamination in composite laminates. Composite Structures 2016;135:353–364
 
23). Amir Nasirmanesh, Soheil Mohammadi. Eigenvalue buckling analysis of cracked functionally graded cylindrical shells in the framework of the extended finite element method. Composite Structures 159 (2017) 548–566.
 
24). Elena Benvenuti. An effective XFEM with equivalent eigenstrain for stress intensity factors of homogeneous plates. Comput. Methods Appl. Mech. Engrg. 321 (2017) 427–454.
 
25). Chukwuemeke William Isaac, Oluleke Oluwole. Numerical modelling of the effect of non-propagating crack in circular thinwalled tubes under dynamic axial crushing. Thin-Walled Structures 115 (2017) 119–128.
 
 
16.Optimization
 
1). Laurent Van Miegroet, Pierre Duysinx. Stress concentration minimization of 2D filets using X-FEM and level set description. Struct Multidisc Optim 2007;33:425–438
 
2). Mangesh Edke, Kuang-Hua Chang. Shape design sensitivity analysis (DSA) for 2-D structural fracture using extended FEM (XFEM). International Journal of Pure and Applied Mathematics 2008;49(3):365-372
 
3). Julien Réthoré, Franc¸ois Hild, Stéphane Roux. Extended digital image correlation with crack shape optimization. Int. J. Numer. Meth. Engng 2008; 73:248–272
 
4).Peng Wei, Michael Yu Wang, Xianghua Xing. A study on X-FEM in continuum structural optimization using a level set model. Computer-Aided Design 2010;42:708-719
 
5). Mangesh S. Edke,Kuang-Hua Chang. Shape optimization for 2-D mixed-mode fracture using Extended FEM (XFEM) and Level Set Method (LSM). Struct Multidisc Optim 2011;44:165–181
 
6). Xu Guo, Wei Sheng Zhang, Michael Yu Wang, Peng Wei. Stress-related topology optimization via level set approach. Comput. Methods Appl. Mech. Engrg. 2011;200: 3439–3452
 
7). J. Zhang, W.H. Zhang, J.H. Zhu, L. Xia. Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput. Methods Appl. Mech. Engrg. 2012;245–246:75–89
 
8). Li LI, Michael Yu WANG, Peng WEI. XFEM schemes for level set based structural optimization. Front. Mech. Eng. 2012, 7(4): 335–356.
 
9). Carlos H. Villanueva,Kurt Maute. Density and level set-XFEM schemes for topology optimization of 3-D structures. Comput Mech 2014;54:133–150
 
10). Dongkyu Lee, Soomi Shin. Extended-finite element method as analysis model for Gauss point density topology optimization method. Journal of Mechanical Science and Technology 2015;29 (4):1341-1348
 
11). Ahmad R. Najafi, Masoud Safdari, Daniel A. Tortorelli, Philippe H. Geubelle. A gradient-based shape optimization scheme using an interface-enriched generalized FEM. Comput. Methods Appl. Mech. Engrg. 2015;296: 1–17
 
12). F.-J. Barthold, D. Materna. A modified extended finite element method approach for design sensitivity analysis. Int. J. Numer. Meth. Engng 2015; 104:209–234
 
13). David Makhija, Kurt Maute. Level set topology optimization of scalar transport problems. Struct Multidisc Optim 2015;51:267–285
 
14). Lise Noël, Laurent Van Miegroet and Pierre Duysinx. Analytical sensitivity analysis using the extended finite element method in shape optimization of bimaterial structures. Int. J. Numer. Meth. Engng 2016; 107:669–695.
 
15). Lise No¨el1,Pierre Duysinx. Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework. Struct Multidisc Optim (2017) 55:2323–2338.
 
16). Ashesh Sharma, Hernan Villanueva, Kurt Maute. On shape sensitivities with heaviside-enriched XFEM. Struct Multidisc Optim (2017) 55:385–408.
 
 
17.Smoothed XFEM
 
1). Stéphane P.A. Bordas a, Timon Rabczuk, Nguyen-Xuan Hung, Vinh Phu Nguyen, Sundararajan Natarajan, Tino Bog, Do Minh Quan, Nguyen Vinh Hiep. Strain smoothing in FEM and XFEM. Computers and Structures 2010;88:1419–1443
 
2). Stéphane P. A. Bordas, Sundararajan Natarajan, Pierre Kerfriden, Charles Edward Augarde, D. Roy Mahapatra, Timon Rabczuk, Stefano Dal Pont. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). Int. J. Numer. Meth. Engng 2011; 86:637–666
 
3). N. Vu-Bac, H. Nguyen-Xuan, L. Chen, S. Bordas, P. Kerfriden,R.N. Simpson, G.R. Liu, T. Rabczuk. A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis. CMES 2011;1898(1);1-25
 
4). L. Chen, T. Rabczuk , S.P.A. Bordas, G.R. Liu, K.Y. Zeng, P. Kerfriden. Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth. Comput. Methods Appl. Mech. Engrg. 2012;209–212:250–265
 
5). Xujun Zhao,Stéphane P. A. Bordas,Jianmin Qu. A hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities. Comput Mech 2013; 52:1417–1428
 
6). Y. Jiang, T. E. Tay, L. Chen, X. S. Sun. An edge-based smoothed XFEM for fracture in composite materials. Int J Fract 2013;179:179–199
 
7). Y. Jiang, T. E. Tay, L. Chen, Y. W. Zhang. Extended finite element method coupled with face-based strain smoothing technique for three-dimensional fracture problems. Int. J. Numer. Meth. Engng (2015)
 
8). Li Ming Zhou, Guang WeiMeng, Feng Li, Shuai Gu. A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials. Advances in Materials Science and Engineering, 2016, Volume 2016, Article ID 4125307, 14 pages.
 
9). Detao Wan, Dean Hu, Sundararajan Natarajan, Stéphane P.A. Bordas and Gang Yang. A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities. Int. J. Numer. Meth. Engng 2017; 110:203–226.
 
 
18.Dislocation
 
1). G. Ventura, B. Moran, T. Belytschko. Dislocations by partition of unity. Int. J. Numer. Meth. Engng 2005; 62:1463–1487
 
2).Robert Gracie, Giulio Ventura, Ted Belytschko. A new fast finite element method for dislocations based on interior discontinuities. Int. J. Numer. Meth. Engng 2007; 69:423–441
 
3). Ted Belytschko, Robert Gracie. On XFEM applications to dislocations and interfaces. International Journal of Plasticity 2007;23:1721–1738
 
4). Robert Gracie, Jay Oswald, Ted Belytschko. On a new extended finite element method for dislocations: Core enrichment and nonlinear formulation. Journal of the Mechanics and Physics of Solids 2008;56:200–214
 
5). Jay Oswald, Robert Gracie, Roopam Khare, Ted Belytschko. An extended finite element method for dislocations in complex geometries: Thin films and nanotubes. Comput. Methods Appl. Mech. Engrg. 2009;198:1872–1886
 
6). Robert Gracie, Ted Belytschko. Concurrently coupled atomistic and XFEM models for dislocations and cracks. Int. J. Numer. Meth. Engng 2009; 78:354–378
 
7). Amirreza Keyhani, Mohsen Goudarzi, Soheil Mohammadi, Reza Roumina. XFEM–dislocation dynamics multi-scale modeling of plasticity and fracture. Computational Materials Science 2015;104:98–107
 
8). Yang Jiao, Jacob Fish. Adaptive delamination analysis. Int. J. Numer. Meth. Engng 2015; 104:1008–1037
 
9). J. Zhao, M. A. Bessa, J. Oswald, Z. Liu, T. Belytschko.A method for modeling the transition of weak discontinuities to strong discontinuities: from interfaces to cracks. Int. J. Numer. Meth. Engng 2016; 105:834–854
 
10). Elena Benvenuti, Nicola Orlando, Daniele Ferretti, Antonio Tralli. A new 3D experimentally consistent XFEM to simulate delamination in FRP-reinforced concrete. Composites Part B 91 (2016) 346-360.
 
11). Libin Zhao, Yana Wang, Jianyu Zhang, Yu Gong, Ning Hu, Ning Li.XFEM-based model for simulating zigzag delamination growth in laminated composites under mode I loading. Composite Structures 160 (2017) 1155–1162.
 
 
19.Piezoelectric, magnetoelectroelastic, FGMs
 
1). J.E. Dolbow, M. Gosz. On the computation of mixed-mode stress intensity factors in functionally graded materials. International Journal of Solids and Structures 2002;39:2557–2574
 
2). Claudia Comi, Stefano Mariani. Extended finite element simulation of quasi-brittle fracture in functionally graded materials. Comput. Methods Appl. Mech. Engrg. 2007;196:4013–4026
 
3). E. Béchet, M. Scherzer, M. Kuna. Application of the X-FEM to the fracture of piezoelectric materials. Int. J. Numer. Meth. Engng 2009; 77:1535–1565
 
4). Ramón rojas-díaz, Natarajan sukumar, Andrés sáez, Felipe garcía-sánchez. Crack analysis in magnetoelectroelastic media using the extended finite element method. International Conference on Extended Finite Element Methods – Recent Developments and Applications XFEM 2009; T.P. Fries and A. Zilian (Eds), RWTH Aachen, Germany, 2009
 
5). R.R. Bhargava, Kuldeep Sharma. A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method. Computational Materials Science 2011;50:1834–1845
 
6). R. Rojas-Díaz, N. Sukumar, A. Sáez, F. García-Sánchez. Fracture in magnetoelectroelastic materials using the extended finite element method. Int. J. Numer. Meth. Engng 2011; 88:1238–1259
 
7). H. Nguyen-Vinh, I. Bakar, M.A. Msekh, J.-H. Song, J. Muthu, G. Zi, P. Lea, S.P.A. Bordas, R. Simpson, S. Natarajan, T. Lahmer, T. Rabczuk. Extended finite element method for dynamic fracture of piezo-electric materials. Engineering Fracture Mechanics 2012;92:19–31
 
8). R. R. Bhargava, Kuldeep Sharma. X-FEM simulation for two-unequal-collinear cracks in 2-D finite piezoelectric specimen. Int J Mech Mater Des 2012;8:129–148
 
9). Tinh Quoc Bui, Chuanzeng Zhang. Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading. Computational Materials Science 2012;62:243–257
 
10). K. Sharma, T.Q. Bui, Ch. Zhang, R.R. Bhargava. Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method. Engineering Fracture Mechanics 2013;104:114–139
 
11). Tinh Quoc Bui, Chuanzeng Zhang. Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM. Finite Elements in Analysis and Design 2013;69:19–36
 
12). S. Bhattacharya, I. V. Singh, B. K. Mishra, T. Q. Bui. Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM. Comput Mech 2013;52:799–814
 
13). S. Bhattacharya, I. V. Singh, B. K. Mishra. Fatigue-life estimation of functionally graded materials using XFEM. Engineering with Computers 2013;29:427–448
 
14). M. Kästner, S. Müller, J. Goldmann, C. Spieler, J. Brummund, V. Ulbricht. Higher-order extended FEM for weak discontinuities – level set representation, quadrature and application to magneto-mechanical problems. Int. J. Numer. Meth. Engng 2013; 93:1403–1424
 
15). S. Bhattacharya, I. V. Singh, B. K. Mishra. Mixed-mode fatigue crack growth analysis of functionally graded materials by XFEM. Int J Fract 2013; 83:81–97
 
16).Peng Liu, Tiantang Yu,Tinh Quoc Bui, Chuanzeng Zhang.Transient dynamic crack analysis in non-homogeneous functionally graded piezoelectric materials by the X-FEM. Computational Materials Science 2013;69:542-558
 
17). Peng Liu, Tiantang Yu, Tinh Quoc Bui, Chuanzeng Zhang,Yepeng Xu. Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method. International Journal of Solids and Structures 2014;51(11-12):2167-2182
 
18). P. Ma, R. K. L. Su, W. J. Feng, Y. S. Li. The extended finite element method with new crack-tip enrichment functions for an interface crack between two dissimilar piezoelectric materials. Int. J. Numer. Meth. Engng (2015)
 
19). Nana Duan, Weijie Xu, Shuhong Wang, Jianguo Zhu, Youguang Guo. An Improved XFEM With Multiple High-Order Enrichment Functions and Low-Order Meshing Elements for Field Analysis of Electromagnetic Devices With Multiple Nearby Geometrical Interfaces. IEEE TRANSACTIONS ON MAGNETICS 2015; 51(3):paper ID 7206004
 
20). I. V. Singh, B. K. Mishra, S. Bhattacharya. XFEM simulation of cracks, holes and inclusions in functionally graded materials. Int J Mech Mater Des 2011;7:199–218
 
21). BingRui Wang, JianTao Liu, ShuiTao Gu. An XFEM/level set strategy for simulating the piezoelectric spring-type interfaces with apparent physical background. Finite Elements in Analysis and Design 133 (2017) 62–75.
 
22). Tong Shen,Franck Vernerey. Phoretic motion of soft vesicles and droplets: an XFEM/particle-based numerical solution. Comput Mech (2017) 60:143–161.
 
23). E. Martı´nez-Pan˜eda, R. Gallego. Numerical analysis of quasi-static fracture in functionally graded materials. Int J Mech Mater Des (2015) 11:405–424.
 
 
20.Beam
 
1). Jian-Ying Wu. New enriched finite elements with softening plastic hinges for the modeling of localized failure in beams. Computers and Structures 2013;128:203–218
 
2). N.N. Bui, M. Ngo, M. Nikolic, D. Brancherie, A. Ibrahimbegovic. Enriched Timoshenko beam finite element for modeling bending and shear failure of reinforced concrete frames. Computers and Structures 2014;143:9–18
 
3). M.R. Shirazizadeh, H.Shahverdi. An extended finite element model for structural analysis of cracked beam-columns with arbitrary cross-section. International Journal of Mechanical Sciences 2015;99:1–9
 
4) Efrat Ben Dror,Oded Rabinovitch. Bridging the gap between small scale phenomena and large scale beams strengthened with FRP – A 1D XFEM high order approach. International Journal of Mechanical Sciences 2015;94-95:49–62
 
5). D. H. Li, Y. Liu, X. Zhang. An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks. Int. J. Numer. Meth. Engng 2015; 101:407–434
 
6). Elena Benvenuti, Nicola Orlando. Failure of FRP-strengthened SFRC beams through an effective mechanism-based regularized XFEM framework. Composite Structures 172 (2017) 345–358.
 
 
21.Thin film, biofilm
 
1). R. Huang, J.H. Prévost, Z.Y. Huang, Z. Suo. Channel-cracking of thin films with the extended finite element method. Engineering Fracture Mechanics 2003;70:2513–2526
 
2). J. Liang, R. Huang, J.H. Pr_evost, Z. Suo.Evolving crack patterns in thin films with the extended finite element method. International Journal of Solids and Structures 2003;40:2343–2354
 
3). Ravindra Duddu, Stéphane Bordas, David Chopp, Brian Moran. A combined extended finite element and level set method for biofilm growth. Int. J. Numer. Meth. Engng 2006; 2:1-33
 
 
22.Fatigue crack
 
1). M. Stolarska, D.L. Chopp. Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method. International Journal of Engineering Science 2003;41:2381–2410
 
2). D.L. Chopp, N. Sukumar. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. International Journal of Engineering Science 2003;41:845–869
 
3). N. Sukumar, D.L. Chopp, B. Moran. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics 2003;70:29–48
 
4). Goangseup Zi, Jeong-Hoon Song, Elisa Budyn, Sang-Ho Lee, Ted Belytschko. A method for growing multiple cracks without remeshing and its application to fatigue crack growth. Modelling Simul. Mater. Sci. Eng. 2004;12:901–915
 
5). Emilie Ferrie´, Jean-Yves Buffière, Wolfgang Ludwig, Anthony Gravouil, Lyndon Edwards. Fatigue crack propagation: In situ visualization using X-ray microtomography and 3D simulation using the extended finite element method. Acta Materialia 2006;54:1111–1122
 
6). E. Giner, N. Sukumar, F.D. Denia, F.J. Fuenmayor. Extended finite element method for fretting fatigue crack propagation. International Journal of Solids and Structures 2008;45:5675–5687
 
7). Yangjian Xu, Huang Yuan. Computational analysis of mixed-mode fatigue crack growth in quasi-brittle materials using extended finite element methods. Engineering Fracture Mechanics 2009;76:165–181
 
8). Yangjian Xu,Huang Yuan. Computational modeling of mixed-mode fatigue crack growth using extended finite element methods. Int J Fract 2009;159:151–165
 
9). Yangjian Xu, Huang Yuan. On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth. Computational Materials Science 2009; 46(3):579-585.
 
10). Johann Rannou, Nathalie Limodin, Julien Réthoré, Anthony Gravouil, Wolfgang Ludwig, Marie-Christine Baïtto-Dubourg, Jean-Yves Buffière, Alain Combescure, Francis Hild, Stéphane Roux. Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput. Methods Appl. Mech. Engrg. 2010;199:1307–1325
 
11). M.C. Baietto, E. Pierres, A. Gravouil. A multi-model X-FEM strategy dedicated to frictional crack growth under cyclic fretting fatigue loadings. International Journal of Solids and Structures 2010;47:1405–1423
 
12). M. Sabsabi, E. Giner, F.J. Fuenmayor. Experimental fatigue testing of a fretting complete contact and numerical life correlation using X-FEM. International Journal of Fatigue 2011;33:811–822
 
13). E. Giner, C.Navarro, M.Sabsabi, M.Tur, J.Domínguez, F.J.Fuenmayor. Fretting fatigue life prediction using the extended finite element method. International Journal of Mechanical Sciences 2011;53:217–225
 
14). I.V. Singh, B.K. Mishra, S. Bhattacharya, R.U. Patil. The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue 2012;36:109–119
 
15). S. Bhattacharya, I. V. Singh, B. K. Mishra, T. Q. Bui. Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM. Comput Mech 2013;52:799–814
 
16). S. Bhattacharya, I. V. Singh, B. K. Mishra. Mixed-mode fatigue crack growth analysis of functionally graded materials by XFEM. Int J Fract 2013;183:81–97
 
17). C. Roux-Langlois, A. Gravouil, M.-C. Baietto, J. Rethore, F. Mathieu, F. Hild , S. Roux. DIC identification and X-FEM simulation of fatigue crack growth based on the Williams’ series. International Journal of Solids and Structures 2015;53:38–47
 
18). Sachin Kumar, I.V. Singh, B.K. Mishra. A homogenized XFEM approach to simulate fatigue crack growth problems. Computers and Structures 2015;150:1–22
 
19). M. Naderi, N. Iyyer. Fatigue life prediction of cracked attachment lugs using XFEM. International Journal of Fatigue 2015;77:186–193
 
20). Andrijana Đurđević, Danijela Živojinović , Aleksandar Grbović, Aleksandar Sedmak, Marko Rakin, Horia Dascau, Snežana Kirin. Numerical simulation of fatigue crack propagation in friction stir welded joint made of Al 2024-T351 alloy. Engineering Failure Analysis 2015;58: 477–484
 
21). Zeeshan Anjum, Faisal Qayyum, Shahab Khushnood, Sagheer Ahmed, Masood Shah. Prediction of non-propagating fretting fatigue cracks in Ti6Al4V sheet tested under pin-in-dovetail configuration: Experimentation and numerical simulation. Materials and Design 2015;87:750–758
 
22). Juan Carlos Martínez, Libardo Vicente Vanegas Useche, Magd Abdel Wahab. Numerical prediction of fretting fatigue crack trajectory in a railway axle using XFEM. International Journal of Fatigue 100 (2017) 32–49.
 
23). Manish Kumar, A.S. Bhuwal, I.V. Singh, B.K. Mishra, S. Ahmad, A. Venugopal Rao, Vikas Kumar. Nonlinear Fatigue Crack Growth Simulations using J-integral Decomposition and XFEM. Procedia Engineering 173 ( 2017 ) 1209 – 1214.
 
24). Mohit Pant,Kamal Sharma,Somnath Bhattacharya. Application of EFGM and XFEM for Fatigue Crack growth Analysis of Functionally Graded Materials. Procedia Engineering 173 ( 2017 ) 1231 – 1238.
 
25). H. Zarrinzadeh, M.Z. Kabir, A. Deylami. Crack growth and debonding analysis of an aluminum pipe repaired by composite patch under fatigue loading. Thin-Walled Structures 112 (2017) 140–148.
 
26). Khalid Nasri, Mohammed Zenasni. Fatigue crack growth simulation in coated materials using X-FEM. C. R. Mecanique 345 (2017) 271–280.
 
27). A. Bergara, J.I. Dorado, A. Martin-Meizoso, J.M. Martínez-Esnaola. Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). International Journal of Fatigue 103 (2017) 112–121.
 
28). H. Zarrinzadeh, M.Z. Kabir, A. Deylami. Experimental and numerical fatigue crack growth of an aluminium pipe repaired by composite patch. Engineering Structures 133 (2017) 24–32.
 
29). Zhixin Zhan, Weiping Hu, Binkai Li, Yanjun Zhang, Qingchun Meng, Zhidong Guan. Continuum damage mechanics combined with the extended finite element method for the total life prediction of a metallic component. International Journal of Mechanical Sciences 124–125 (2017) 48–58.
 
30). Said Taheri, Emricka Julan, Xuan-Van Tran, Nicolas Robert. Impacts of weld residual stresses and fatigue crack growth threshold on crack arrest under high-cycle thermal fluctuations. Nuclear Engineering and Design 311 (2017) 16–27.
 
 
23.Quadrature
 
1).G. Ventura. On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method. Int. J. Numer. Meth. Engng 2006; 66:761–795
 
2). Kyoungsoo Park, Jeronymo P. Pereira, C. Armando Duarte, Glaucio H. Paulino. Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems. Int. J. Numer. Meth. Engng 2009; 78:1220–1257
 
3). Sundararajan Natarajan, St´ephane Bordas, D. Roy Mahapatra. Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping. Int. J. Numer. Meth. Engng 2009; 80:103–134
 
4).Giulio Ventura, Robert Gracie, Ted Belytschko. Fast integration and weight function blending in the extended finite element method. Int. J. Numer. Meth. Engng 2009; 77:1–29
 
5). S. E. Mousavi, N. Sukumar. Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method. Comput. Methods Appl. Mech. Engrg. 2010;199(49-52):3237-3249
 
6). Sundararajan Natarajan, D. RoyMahapatra, St´ephane P. A. Bordas. Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework. Int. J. Numer. Meth. Engng 2010; 83:269–294
 
7). Hans Minnebo. Three-dimensional integration strategies of singular functions introduced by the XFEM in the LEFM. Int. J. Numer. Meth. Engng 2012; 92:1117–1138
 
8). Y. Sudhakar,Wolfgang A.Wall.Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods. Comput. Methods Appl. Mech. Engrg. 2013;258:39–54
 
9).A. Martin, J.-B. Esnault, P. Massin. About the use of standard integration schemes for X-FEM in solid mechanics plasticity. Comput. Methods Appl. Mech. Engrg. 2015;283: 551–572
 
10). B. Paul, M. Ndeffo, P. Massin, N. Moës. An integration technique for 3D curved cracks and branched discontinuities within the extended Finite Element Method. Finite Elements in Analysis and Design 123 (2017) 19–50
 
11). Thomas-Peter Fries and Samir Omerovi´c. Higher-order accurate integration of implicit geometries. Int. J. Numer. Meth. Engng 2016; 106:323–371
 
 
24.Plasticity
 
1). T. Nagashima, N. Miura. ELASTIC-PLASTIC FRACTURE ANALYSIS FOR SURFACE CRACKS USING X-FEM. VIII International Conference on Computational Plasticity COMPLAS VIII E. Oñate and D. R. J. Owen (Eds) © CIMNE, Barcelona, 2005
 
2).T. Elguedj, A. Gravouil, A. Combescure. Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Comput. Methods Appl. Mech. Engrg. 2006;195:501–515
 
3). C. Colombo, L. Vergani. A numerical and experimental study of crack tip shielding in presence of overloads. Engineering Fracture Mechanics 2010;77:1644–1655
 
4). Eric Feulvarch, MickaelFontaine, Jean-Michel Bergheau. XFEM investigation of a crack path in residual stresses resulting from quenching. Finite Elements in Analysis and Design 2013;75:62–70
 
5). Sachin Kumar, I. V. Singh, B. K. Mishra. XFEM simulation of stable crack growth using J–R curve under finite strain plasticity. Int J Mech Mater Des 2014;10:165–177
 
6). J.P. Cre′te, P. Longe`re, J.M. Cadou. Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM. Comput. Methods Appl. Mech. Engrg. 2014;275:204–233
 
7).T. D. Tran, C. V. Le. Extended finite element method for plastic limit load computation of cracked structures. International Journal for Numerical Methods in Engineering 2015. DOI: 10.1002/nme.4922
 
8). Pengfei Liu. Extended finite element method for strong discontinuity analysis of strain localization of non-associative plasticity materials. International Journal of Solids and Structures 2015;72:174–189
 
9). F. Farukh, L.G. Zhao, R. Jiang, P. Reed, D. Proprentner, B.A. Shollock. Realistic microstructure-based modelling of cyclic deformation and crack growth using crystal plasticity. Computational Materials Science 2016;111:395–405
 
10). E. Martínez-Pañeda, S. Natarajan, S. Bordas. Gradient plasticity crack tip characterization by means of the extended finite element method. Comput Mech (2017) 59:831–842
 
 
25.High-gradient
 
1). Safdar Abbas, Alaskar Alizada,Thomas-Peter Fries. The XFEM for high-gradient solutions in convection-dominated problems. Int. J. Numer. Meth. Engng 2010; 82:1044–1072
 
2).Arash Zamani, M.Reza Eslami. Gradient-enhanced damage modeling of cracked bodies by reproducing kernel element method. Comput. Methods Appl. Mech. Engrg. 2012;213:266-288.
 
 
26.Harmonic enrichment
 
1). S. E. Mousavi,E. Grinspun, N. Sukumar. Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method. Int. J. Numer. Meth. Engng 2011; 85:1306–1322
 
2). S. E. Mousavi, E. Grinspun, N. Sukumar. Higher-order extended finite elements with harmonic enrichmentfunctions for complex crack problems. Int. J. Numer. Meth. Engng 2011; 86:560–574
 
 
27.High-order XFEM
 
1).Jay Oswald, Eugen Wintersberger, Günther Bauer, Ted Belytschko. A higher-order extended finite element method for dislocation energetics in strained layers and epitaxial islands. Int. J. Numer. Meth. Engng 2011; 85:920–938
 
2).Mengyu Lan, Haim Waisman, Isaac Harari. A High-order extended finite element method for extraction of mixed-mode strain energy release rates in arbitrary crack settings based on Irwin’s integral. Int. J. Numer. Meth. Engng 2013; 96:787–812
 
3). KWOKWAH CHENG, THOMAS-PETER FRIES. A SYSTEMATIC STUDY OF DIFFERENT XFEM-FORMULATIONS WITH RESPECT TO HIGHER-ORDER ACCURACY FOR ARBITRARILY CURVEDWEAK DISCONTINUITIES. International Conference on Extended Finite Element Methods – Recent Developments and Applications XFEM 2009 T.P. Fries and A. Zilian (Eds) c RWTH Aachen, Germany, 2009
 
4). F. L. Stazi, E. Budyn, J. Chessa, T. Belytschko. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics 2003;31:38–48
 
5). G. Legrain, N. Chevaugeon, K. Dreau. High order X-FEM and levelsets for complex microstructures: Uncoupling geometry and approximation. Comput. Methods Appl. Mech. Engrg. 2012;241–244:172–189
 
6). Arash Zamani, Robert Gracie,M. Reza Eslami. Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity. Comput Mech 2010; 46:851–866
 
7). M. Kästner, S. Müller, J. Goldmann, C. Spieler, J. Brummund, V. Ulbricht.Higher-order extended FEM for weak discontinuities – level set representation, quadrature and application to magneto-mechanical problems. Int. J. Numer. Meth. Engng 2013; 93:1403–1424
 
8). Kwok Wah Cheng, Thomas-Peter Fries.Higher-order XFEM for curved strong and weak discontinuities. Int. J. Numer. Meth. Engng 2010; 82:564–590
 
9). Patrick Laborde, Julien Pommier, Yves Renard, Michel Salaün.High-order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng 2005; 64:354–381
 
10). Ursula M. Mayer, Axel Gerstenberger,Wolfgang A. Wall.Interface handling for three-dimensional higher-order XFEM-computations in fluid–structure interaction. Int. J. Numer. Meth. Engng 2009; 79:846–869
 
11). E. V. Iarve.Mesh independent modelling of cracks by using higher order shape functions. Int. J. Numer. Meth. Engng 2003; 56:869–882
 
12). Kristell Dréau, Nicolas Chevaugeon, Nicolas Moës.Studied X-FEM enrichment to handle material interfaces with higher order finite element. Computer Methods in Applied Mechanics and Engineering 2010;199:1922–1936
 
13). Gan Song, Haim Waisman, Mengyu Lan, Isaac Harari. Extraction of stress intensity factors from Irwin’s integral using high-order XFEM on triangular meshes. Int. J. Numer. Meth. Engng 2015; 102:528–550
 
14). Gerd Brandstetter, Sanjay Govindjee. A high-order immersed boundary discontinuous-Galerkin method for Poisson’s equation with discontinuous coefficients and singular sources. Int. J. Numer. Meth. Engng 2015; 101:847–869
 
 
28.Finite deformation
 
1). J. Oliver, A. E. Huespe, M. D. G. Pulido, E. Samaniego.On the strong discontinuity approach in finite deformation settings. Int. J. Numer. Meth. Engng 2003; 56:1051–1082
 
2).G. Legrain, N. Moës, E. Verron. Stress analysis around crack tips in finite strain problems using the eXtended finite element method. Int. J. Numer. Meth. Engng 2005; 63:290–314
 
3). Martin Fagerstr, Ragnar Larsson.Theory and numerics for finite deformation fracture modelling using strong discontinuities. Int. J. Numer. Meth. Engng 2006; 66:911–948
 
4). Julia Mergheim, Paul Steinmann. A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities. Comput. Methods Appl. Mech. Engrg. 2006;195:5037–5052
 
5). Pedro M. A. Areias, Ted Belytschko.Analysis of Finite Strain Anisotropic Elastoplastic Fracture in Thin Plates and Shells. Journal of Aerospace Engineering 2006; 19(4):259-270
 
6). M. Anahid, A. R. Khoei.New development in extended finite element modeling of large elasto-plastic deformations. Int. J. Numer. Meth. Engng 2008; 75:1133–1171
 
7). A.R. Khoei, M. Anahid, K. Shahim. An extended arbitrary Lagrangian–Eulerian finite element method for large deformation of solid mechanics. Finite Elements in Analysis and Design 2008;44:401–416
 
8). A.R. Khoei, S.O.R. Biabanaki, M. Anahid.Extended finite element method for three-dimensional large plasticity deformations on arbitrary interfaces. Comput. Methods Appl. Mech. Engrg. 2008;197:1100–1114
 
9). J. Mergheim. A variational multiscale method to model crack propagation at finite strains. Int. J. Numer. Meth. Engng 2009; 80:269–289
 
10).Fushen Liu, Ronaldo I. Borja. Finite deformation formulation for embedded frictional crack with the extended finite element method. Int. J. Numer. Meth. Engng 2010; 82:773–804
 
11). S. Loehnert, D. S. Mueller-Hoeppe, P. Wriggers. 3D corrected XFEMapproach and extension to finite deformation theory. Int. J. Numer. Meth. Engng 2011; 86:431–452
 
12). 苏静波,范晓晨,邵国建.几何非线性扩展有限元法及其断裂力学应用. 工程力学 2013; 30(4):42-46
 
13).P. Broumand, A.R. Khoei. The extended finite element method for large deformation ductile fracture problems with a non-local damage-plasticity model. Engineering Fracture Mechanics 2013;112–113:97–125
 
14). Brett A. Benowitz, Haim Waisman. A spline-based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations. Int. J. Numer. Meth. Engng 2013; 95:361–386
 
15). Louis Foucard, Anup Aryal, Ravindra Duddu, Franck Vernerey. A coupled Eulerian–Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries. Comput. Methods Appl. Mech. Engrg. 2015;283:280–302
 
16). R. Rashetnia, S. Mohammadi. Finite strain fracture analysis using the extended finite element method with new set of enrichment functions. Int. J. Numer. Meth. Engng (2015)
 
17). Xiaoping Zhou and Hao Cheng. Multidimensional Space Method for Geometrically Nonlinear Problems under Total Lagrangian Formulation Based on the Extended Finite-Element Method. J. Eng. Mech., 2017, 143(7): 04017036
 
 
29.Nitsche XFEM
 
1).Roland Becker, Erik Burman, Peter Hansbo.A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity. Comput. Methods Appl. Mech. Engrg. 2009;198:3352–3360
 
2). Roland Becker, Erik Burman, Peter Hansbo.A hierarchical NXFEM for fictitious domain simulations. Int. J. Numer. Meth. Engng 2011; 86:549–559
 
3).E.T. Coon, B.E. Shaw, M. Spiegelman.A Nitsche-extended finite element method for earthquake rupture on complex fault systems. Comput. Methods Appl. Mech. Engrg. 2011;200:2859–2870
 
4). Chandrasekhar Annavarapu, Martin Hautefeuille, John E. Dolbow. A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: Intersecting interfaces. Comput. Methods Appl. Mech. Engrg. 2013;267:318–341
 
5). Chandrasekhar Annavarapu, Martin Hautefeuille, John E. Dolbow. A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: Single interface. Comput. Methods Appl. Mech. Engrg. 2014;268:417–436
 
6). Frédéric Alauzet, Benoit Fabrèges, Miguel A. Fernández, Mikel Landajuela. Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures. Comput. Methods Appl. Mech. Engrg. 2016;301:300–335
 
7). Christoph Lehrenfeld, Arnold Reusken. Optimal preconditioners for Nitsche-XFEM discretizations of interface problems. Numer. Math. (2017) 135:313–332
 
 
30.Composite
 
1).N. Sukumar, Z. Y. Huang, J.-H. Prévost, Z. Suo. Partition of unity enrichment for bimaterial interface cracks. Int. J. Numer. Meth. Engng 2004; 59:1075–1102
 
2). X. Y. Liu, Q. Z. Xiao, B. L. Karihaloo.XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials. Int. J. Numer. Meth. Engng 2004; 59:1103–1118
 
3). Thomas Hettich, Andrea Hund, Ekkehard Ramm. Modeling of failure in composites by X-FEM and level sets within a multiscale framework. Comput. Methods Appl. Mech. Engrg. 2008;197:414–424
 
4). J. Yvonnet, Q.-C. He, C. Toulemonde. Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface. Composites Science and Technology 2008;68:2818–2825
 
5). Yuhai Yan, Si-Hwan Park.An extended finite element method for modeling near-interfacial crack propagation in a layered structure. International Journal of Solids and Structures 2008;45:4756–4765
 
6). S.H. Ebrahimi, S. Mohammadi, A. Asadpoure. An Extended Finite Element (XFEM) Approach for Crack Analysis in Composite Media. International Journal of Civil Engineerng 2008; 6(3):198-207
 
7). X. S. Sun, V. B. C. Tan, G. Liu, T. E. Tay.An enriched element-failure method (REFM) for delamination analysis of composite structures. Int. J. Numer. Meth. Engng 2009; 79:639–666
 
8). D. B. P. Huynh, T. Belytschko.The extended finite element method for fracture in composite materials. Int. J. Numer. Meth. Engng 2009; 77:214–239
 
9). Alexander Menk, St´ephane P. A. Bordas. Numerically determined enrichment functions for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int. J. Numer. Meth. Engng 2010; 83:805–828
 
10). D. Motamedi, S. Mohammadi.Dynamic analysis of fixed cracks in composites by the extended finite element method. Engineering Fracture Mechanics 2010;77:3373–3393
 
11). Hongjun Yu, Linzhi Wu, Licheng Guo, Qilin He, Shanyi Du. Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials. MECHANICS OF MATERIALS 2010; 42(4):435-450
 
12). S Esna Ashari, S Mohammadi.Modeling delamination in composite laminates using XFEM by new orthotropic enrichment functions. IOP Conf. Series: Materials Science and Engineering 10 (2010) 012240 doi:10.1088/1757-899X/10/1/012240
 
13). S. Esna Ashari, S. Mohammadi.Delamination analysis of composites by new orthotropic bimaterial extended finite element method. Int. J. Numer. Meth. Engng 2011; 86:1507–1543
 
14). Z. Zhuang, B. B. Cheng. Equilibrium state of mode-I sub-interfacial crack growth in bi-materials. Int J Fract 2011;170:27–36
 
15). Huaiwen Wang, Qing-Hua Qin, Hongwei Ji, Ying Sun. Comparison Among Different Modeling Techniques of 3D Micromechanical Modeling of Damage in Unidirectional Composites. Advanced Science Letters 2011; 4:400–407
 
16). Endel V. Iarve, Mark R. Gurvich, David H. Mollenhauer, Cheryl A. Rose, Carlos G. Dávila. Mesh-independent matrix cracking and delamination modeling in laminated composites. Int. J. Numer. Meth. Engng 2011; 88:749–773
 
17). Q.-Z. Zhu, S.-T. Gu, J. Yvonnet, J.-F. Shao, Q.-C. He. Three-dimensional numerical modelling by XFEM of spring-layer imperfect curved interfaces with applications to linearly elastic composite materials. Int. J. Numer. Meth. Engng 2011; 88:307–328
 
18). Yao Koutsawa, Salim Belouettar, Ahmed Makradi, Sonnou Tiem. X-FEM implementation of VAMUCH: Application to active structural fiber multi-functional composite materials. Composite Structures 2012;94:1297–1304
 
19). D. Motamedi,S.Mohammadi. Fracture analysis of composites by time independent moving-crack orthotropic XFEM. International Journal of Mechanical Sciences 2012;54: 20–37
 
20). L. Bouhala, Q. Shao, Y. Koutsawa, A. Younes, P. Núñez , A. Makradi, S. Belouettar.An XFEM crack-tip enrichment for a crack terminating at a bi-material interface. Engineering Fracture Mechanics 2013;102:51–64
 
21). L.M.A. Cahill, S. Natarajan, S.P.A. Bordas, R.M. O’Higgins, C.T. McCarthy. An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae. Composite Structures 2014;107:119–130
 
22). M.C. Serna Moreno, J.L. Curiel-Sosa, J. Navarro-Zafra, J.L. Martínez Vicente, J.J. López Cela. Crack propagation in a chopped glass-reinforced composite under biaxial testing by means of XFEM. Composite Structures 2015;119:264–271
 
23). A. Afshar, A. Daneshyar, S. Mohammadi. XFEM analysis of fiber bridging in mixed-mode crack propagation in composites. Composite Structures 2015;125: 314–327
 
24). D.M. Grogan, C.M. ó Brádaigh, S.B. Leen. A combined XFEM and cohesive zone model for composite laminate microcracking and permeability. Composite Structures 2015;120:246–261
 
25). Yongxiang Wang,Haim Waisman. XFEM and a discrete damage zone model. Comput Mech 2015; 55:1–26
 
26). B.R. Wang, J.T. Liu, S.T. Gu, Q.C. He. Numerical evaluation of the effective conductivities of composites with interfacial weak and strong discontinuities. International Journal of Thermal Sciences 2015;93:1-20
 
27). Yang Jiao,Jacob Fish. On the equivalence between the s-method, the XFEM and the ply-by-ply discretization for delamination analyses of laminated composites. Int J Fract 2015;191:107–129
 
28). Matthew G.Pike,CaglarOskay. XFEM modeling of short microfiber reinforced composites with cohesive interfaces. Finite Elements in Analysis and Design 2015;106:16–31
 
29). Guillermo Vigueras, Federico Sket, Cristóbal Samaniego, etc. An XFEM/CZM implementation for massively parallel simulations of composites fracture. Composite Structures 2015;125: 542–557
 
30). Saleh Yazdani, Wilhelm J.H. Rust, Peter Wriggers. An XFEM approach for modelling delamination in composite laminates. Composite Structures, http://dx.doi.org/10.1016/j.compstruct.2015.09.035
 
31). K. Nasri, M. Abbadi, M. Zenasni, M. Ghammouri, Z. Azari. Double crack growth analysis in the presence of a bi-material interface using XFEM and FEM modelling. Engineering Fracture Mechanics 2014;132:189–199
 
32). D.M. Grogan, C.M. Ó Brádaigh, J.P. McGarry, S.B. Leen. Damage and permeability in tape-laid thermoplastic composite cryogenic tanks. Composites: Part A 2015;78:390–402
 
33). Zhiyong Wang, Hongjun Yu, Zhihua Wang. A local mesh replacement method for modeling near-interfacial crack growth in 2D composite structures. Theoretical and Applied Fracture Mechanics 2015;75:70–77
 
34). Lehua Qi, Wenlong Tian, Jiming Zhou. Homogenization of transverse elastic properties of Cf/Mg composites at an elevated temperature and containing a small fraction of liquid phase. Composites Science and Technology 2015;117:234-243
 
35). Matthew G. Pike, Caglar Oskay. Three-Dimensional Modeling of Short Fiber-Reinforced Composites with Extended Finite-Element Method. J. Eng. Mech., 2016, 142(11): 04016087.
 
36). Yongxiang Wang, Haim Waisman. Material-dependent crack-tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials. Int J Numer Meth Engng. 2017;1–24..
 
37). R. Higuchi, T. Okabe, T. Nagashima. Numerical simulation of progressive damage and failure in composite laminates using XFEM/CZM coupled approach. Composites: Part A 95 (2017) 197–207.
 
38). Nur Azam Abdullah, Jose Luis Curiel-Sosa, Zeike A. Taylo, Behrooz Tafazzolimoghaddam, J.L. Martinez Vicente, Chao Zhang. Transversal crack and delamination of laminates using XFEM. Composite Structures 173 (2017) 78–85.
 
39). A.P.C. Duarte, A. Díaz Sáez, N. Silvestre. Comparative study between XFEM and Hashin damage criterion applied to failure of composites. Thin-Walled Structures 115 (2017) 277–288.
 
40). Sh. Akhondzadeh, A.R. Khoei, P. Broumand. An efficient enrichment strategy for modeling stress singularities in isotropic composite materials with X-FEM technique. Engineering Fracture Mechanics 169 (2017) 201–225.
 
41). Rossana Dimitri, Nicholas Fantuzzi , Yong Li, Francesco Tornabene. Numerical computation of the crack development and SIF in composite materials with XFEM and SFEM. Composite Structures 160 (2017) 468–490.
 
42) X Li, J Chen. A highly efficient prediction of delamination migration in laminatedcomposites using the extended cohesive damage model. Composite Structures 160 (2017) 712–721.
 
43). Duc Hong Doan, Tinh Quoc Bui, etal. Hybrid phase field simulation of dynamic crack propagation in functionally graded glass-filled epoxy. Composte part B 99(2016):266-276.
 
44). Debski Hubert, Sadowski Tomasz. Modelling of the damage process of interfaces inside the WC/Co composite microstructure: 2-D versus 3-D modelling technique. Composite Structures 159 (2017) 121–127.
 
45). A.P.C. Duarte, N. Silvestre, J. de Brito, E. Júlio. Numerical study of the compressive mechanical behaviour of rubberized concrete using the eXtended Finite Element Method (XFEM). Composite Structures 179 (2017) 132–145.
 
46). Markus Lukacevic, Wolfgang Lederer, Josef Füssl. A microstructure-based multisurface failure criterion for the description of brittle and ductile failure mechanisms of clearwood. Engineering Fracture Mechanics 176 (2017) 83–99.
 
 
31.Space-time XFEM
 
1). Jack Chessa, Ted Belytschko. Arbitrary discontinuities in space–time finite elements by level sets and X-FEM. Int. J. Numer. Meth. Engng 2004; 61:2595–2614
 
2). J. Réthoré, A. Gravouil, A. Combescure.A combined space–time extended finite element method. Int. J. Numer. Meth. Engng 2005; 64:260–284
 
3). Jack Chessaa, Ted Belytschko. A local space–time discontinuous finite element method. Comput. Methods Appl. Mech. Engrg. 2006;195:1325–1343
 
4). Thomas-Peter Fries, Andreas Zilian.On time integration in the XFEM. Int. J. Numer. Meth. Engng 2009; 79:69–93
 
 
32.Multiscale
 
1). Julien R´ethor´e, Ren´e de Borst, Marie-Ang`ele Abellan. A two-scale approach for fluid flow in fractured porous media. Int. J. Numer. Meth. Engng 2007; 71:780–800
 
2). P.A. Guidault, O. Allix, L. Champaney, J.P. Navarro. A two-scale approach with homogenization for the computation of cracked structures. Computers and Structures 2007;85: 1360–1371
 
3). Thomas ELGUEDJ, Anthony GRAVOUIL, Alain COMBESCURE. Simulation of plastic fatigue crack growth by a two scale eXtended Finite ElementMethod. 18 ème Congrès Français de Mécanique Grenoble, 27-31 août 2007
 
4). Thomas Hettich, Andrea Hund, Ekkehard Ramm. Modeling of failure in composites by X-FEM and level sets within a multiscale framework. Comput. Methods Appl. Mech. Engrg. 2008;197:414–424
 
5). Ted Belytschko, Stefan Loehnert, Jeong-Hoon Song. Multiscale aggregating discontinuities: A method for circumventing loss of material stability. Int. J. Numer. Meth. Engng 2008; 73:869–894
 
6). J. Rannou, A. Gravouil, M. C. Ba¨ıetto-Dubourg. A local multigrid X-FEM strategy for 3-D crack propagation. Int. J. Numer. Meth. Engng 2009; 77:581–600
 
7).Hachmi Ben Dhia, Olivier Jamond. On the use of XFEM within the Arlequin framework for the simulation of crack propagation. Comput. Methods Appl. Mech. Engrg. 2010;199:1403–1414
 
8). 乔 华,陈伟球.基于ARLEQUIN 方法和XFEM 的结构多尺度模拟. 工程力学 2010;27(s1):29-33
 
9). E. Pierres, M.C.Baietto, A.Gravouil, G.Morales-Espejel. 3D two scale X-FEM crack model with interfacial frictional contact: Application to fretting fatigue. Tribology International 2010;43:1831–1841
 
10).E. Pierrès, M.C. Baietto, A. Gravouil. A two-scale extended finite element method for modelling 3D crack growth with interfacial contact. Comput. Methods Appl. Mech. Engrg. 2010;199:1165–1177
 
11). Johann Rannou, Nathalie Limodin, Julien Réthoré, Anthony Gravouil, Wolfgang Ludwig, etc. Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput. Methods Appl. Mech. Engrg. 2010;199:1307–1325
 
12). D.-J. Kim, J. P. Pereira, C. A. Duarte. Analysis of three-dimensional fracture mechanics problems: A two-scale approach using coarse-generalized FEM meshes. Int. J. Numer. Meth. Engng 2010; 81:335–365
 
13). Thomas-Peter Fries, Andreas Byfut, Alaskar Alizada, Kwok Wah Cheng, Andreas Schr¨oder. Hanging nodes and XFEM. Int. J. Numer. Meth. Engng 2011; 86(4-5):404-430
 
14).U. Rasthofer, F. Henke, W.A. Wall, V. Gravemeier. An extended residual-based variational multiscale method for two-phase flow including surface tension. Comput. Methods Appl. Mech. Engrg. 2011;200:1866–1876
 
15). Flavio V. Souza, David H. Allen. Modeling the transition of microcracks into macrocracks in heterogeneous viscoelastic media using a two-way coupled multiscale model. International Journal of Solids and Structures 2011;48:3160–3175
 
16). Robert Gracie, Ted Belytschko. An adaptive concurrent multiscale method for the dynamic simulation of dislocations. Int. J. Numer. Meth. Engng 2011; 86:575–597
 
17).Jian-Ying Wu. Unified analysis of enriched finite elements for modeling cohesive cracks. Comput. Methods Appl. Mech. Engrg. 2011;200:3031–3050
 
18). Vinh Phu Nguyen, Martijn Stroeven, Lambertus Johannes Sluys. Multiscale failure modeling of concrete: Micromechanical modeling, discontinuous homogenization and parallel computations. Comput. Methods Appl. Mech. Engrg. 2012;201–204:139–156
 
19). A. Sarhangi Fard, M. A. Hulsen, H. E. H. Meijer, N. M. H. Famili, P. D. Anderson. Adaptive non-conformal mesh refinement and extended finite element method for viscous flow inside complex moving geometries. Int. J. Numer. Meth. Fluids 2012; 68:1031–1052
 
20).J. P. A. Pereira, D.-J. Kim, C. A. Duarte. A two-scale approach for the analysis of propagating three-dimensional fractures. Comput Mech 2012;49:99–121
 
21). Markus Kästner, Sebastian Müller, Volker Ulbricht. XFEM modelling of inelastic material behaviour and interface failure in textile-reinforced composites. Procedia Materials Science 2013;2:43–51
 
22).Jean-Charles Passieux, Julien Réthoré, Anthony Gravouil, Marie-Christine Baietto. Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver. Comput Mech 2013;52:1381–1393
 
23).B. Vandoren, K. De Proft, A. Simone , L.J. Sluys. Mesoscopic modelling of masonry using weak and strong discontinuities. Comput. Methods Appl. Mech. Engrg. 2013;255:167–182
 
24). Axel Gerstenberger, Raymond S. Tuminaro. An algebraic multigrid approach to solve extended finite element method based fracture problems. Int. J. Numer. Meth. Engng 2013; 94:248–272
 
25). M. Holl, S. Loehnert, P. Wriggers. An adaptive multiscale method for crack propagation and crack coalescence. Int. J. Numer. Meth. Engng 2013; 93:23–51
 
26). Mirmohammadreza Kabiri, Franck J. Vernerey. AN XFEM BASED MULTISCALE APPROACH TO FRACTURE OF HETEROGENEOUS MEDIA. Journal for Multiscale Computational Engineering 2013;11 (6): 565–580
 
27). Pattabhi R. Budarapu, Robert Gracie, Stéphane P.A. Bordas, Timon Rabczuk. An adaptive multiscale method for quasi-static crack growth. Comput Mech 2014; 53:1129–1148
 
28). 王 振,余天堂.模拟三维裂纹问题的多尺度扩展有限元法.岩土力学2014;35(9):2702-2708.
 
29). Hossein Talebi, Mohammad Silani, Stéphane P. A. Bordas, Pierre Kerfriden, Timon Rabczuk. A computational library for multiscale modeling of material failure. Comput Mech 2014; 53:1047–1071
 
30). Matthias Holl,Timo Rogge,Stefan Loehnert, Peter Wriggers, Raimund Rolfes.3D multiscale crack propagation using the XFEM applied to a gas turbine blade. Comput Mech 2014; 53:173–188
 
31). S. Toro, P. J. Sánchez, A. E. Huespe, S. M. Giusti, P. J. Blanco4, R. A. Feijóo. A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method. Int. J. Numer. Meth. Engng 2014; 97:313–351
 
32). Hossein Talebi , Mohammad Silani, Timon Rabczuk. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software 2015;80:82–92
 
33). Mohammad Silani, Hossein Talebi, Saeed Ziaei-Rad, Abdel Magid Hamoud, Goangseup Zi, Timon Rabczuk.A three dimensional extended Arlequin method for dynamic fracture. Computational Materials Science 2015;96:425–431
 
34).Yongming Li, Youshi Jiang, Jinzhou Zhao, Changyu Liu, Liehui Zhang. Extended finite element method for analysis of multi-scale flow in fractured shale gas reservoirs. Environ Earth Sci 2015;73:6035–6045
 
35). Amirreza Keyhani, Mohsen Goudarzi, Soheil Mohammadi, Reza Roumina. XFEM–dislocation dynamics multi-scale modeling of plasticity and fracture. Computational Materials Science 2015;104:98–107
 
36). Bekim Berisha, Christian Raemy, Christoph Becker, Maysam Gorji, Pavel Hora. Multiscale modeling of failure initiation in a ferritic–pearlitic steel. Acta Materialia 2015;100: 191–201
 
37). P.-A. Guidault, O. Allix, L. Champaney, C. Cornuault. A multiscale extended finite element method for crack propagation. Comput. Methods Appl. Mech. Engrg. 197 (2008) 381–399
 
38). Stefan Loehnert, Ted Belytschko. A multiscale projection method for macro/microcrack simulations. Int. J. Numer. Meth. Engng 2007; 71:1466–1482
 
39). X.P. Zhou, H.Q.Yang. Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses. International Journal of Rock Mechanics & Mining Sciences 55 (2012) 15–27
 
40). Mehdi Eftekhari, Saeed Hatefi Ardakani, Soheil Mohammadi. An XFEM multiscale approach for fracture analysis of carbon nanotube reinforced concrete. Theoretical and Applied Fracture Mechanics 72 (2014) 64–75
 
41). Guangzhong Liu, Dai Zhou, Yan Bao, Jin Ma, Zhaolong Han. Multiscale analysis of interaction between macro crack and microdefects by using multiscale projection method. Theoretical and Applied Fracture Mechanics 90 (2017) 65–74.
 
42). Guangzhong Liu, Dai Zhou, Yan Bao, Jin Ma, Zhaolong Han. Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM. Arc hives of civil and mechanical engineering 17 ( 2017 ) 410 – 418.
 
43). R.U. Patil, B.K. Mishra, I.V. Singh. A new multiscale XFEM for the elastic properties evaluation of heterogeneous materials. International Journal of Mechanical Sciences 122 (2017) 277–287.
 
44). K. Perzyński, A. Wrożyna, R. Kuziak, A. Legwand, L. Madej. Development and validation of multi scale failure model for dual phase steels. Finite Elements in Analysis and Design 124 (2017) 7–21.
 
45). Hamid Bayesteh, Soheil Mohammadi. Micro-base d enriche d multiscale homogenization method for analysis of heterogeneous materials. International Journal of Solids and Structures 125 (2017) 22–42 .
 
46).Mohammad Malekan, Felício Barros, Roque Luiz da Silva Pitangueira, Phillipe Daniel Alves, Samuel Silva Penna, (2017) "A computational framework for a two-scale generalized/extended finite element method: Generic imposition of boundary conditions", Engineering Computations, Vol. 34 Issue: 3, pp.988-1019.
 
47). J. A. Plews and C. A. Duarte. Bridging multiple structural scales with a generalized finite element method. Int. J. Numer. Meth. Engng 2015; 102:180–201.
 
48). P. O’Hara, C.A. Duarte, T. Eason. A two-scale generalized finite element method for interaction and coalescence of multiple crack surfaces. Engineering Fracture Mechanics 163 (2016) 274–302.
 
 
33.cohesive cracks
 
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5). Remmers J J C, de Borst R, Needleman A. A cohesive segments method for the simulation of crack growth[J]. Computational mechanics, 2003, 31(1-2): 69-77.
 
6). Patzák B, Jirásek M. Process zone resolution by extended finite elements[J]. Engineering Fracture Mechanics, 2003, 70(7): 957-977.
 
7).Zi G, Belytschko T. New crack‐tip elements for XFEM and applications to cohesive cracks[J]. International Journal for Numerical Methods in Engineering, 2003, 57(15): 2221-2240.
 
8).Borst R, Gutiérrez M A, Wells G N, et al. Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis[J]. International Journal for Numerical Methods in Engineering, 2004, 60(1): 289-315.
 
9).Mergheim J, Kuhl E, Steinmann P. A finite element method for the computational modelling of cohesive cracks[J]. International Journal for Numerical Methods in Engineering, 2005, 63(2): 276-289.
 
10).Svahn P O, Runesson K. Cohesive crack model with anisotropic damage and its implementation in an improved xfem format[C]//Colloquium 460, Numerical Modeling of Concrete. 2005.
 
11).Dumstorff P, Meschke G. Modelling of cohesive and non-cohesive cracks via X-FEM based on global energy criteria[C]//VIII International Conference on Computational Plasticity. 2005.
 
12).杜效鹄, 段云岭, 王光纶. 混凝土断裂的连续-非连续方法[J]. 固体力学学报, 2005, 26(4): 405-413.
 
13).杜效鹄, 段云岭, 王光纶. 重力坝断裂数值分析研究[J]. 水利学报, 2005, 36(9): 1035-1042.
 
14).Karihaloo B L, Xiao Q Z, Liu X Y. Accurate Determination of Cohesive Crack Tip Fields Using XFEM and Admissible Stress Recovery[J]. Fracture of Nano and Engineering Materials and Structures, 2006: 935-936.
 
15).de Borst R, Remmers J J C, Needleman A. Mesh-independent discrete numerical representations of cohesive-zone models[J]. Engineering fracture mechanics, 2006, 73(2): 160-177.
 
16).Asferg J L, Poulsen P N, Nielsen L O. A consistent partly cracked XFEM element for cohesive crack growth[J]. International Journal for Numerical Methods in Engineering, 2007, 72(4): 464-485.
 
17).Meschke G, Dumstorff P. Energy-based modeling of cohesive and cohesionless cracks via X-FEM[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(21): 2338-2357.
 
18).Zi G, Rabczuk T, Wall W. Extended meshfree methods without branch enrichment for cohesive cracks[J]. Computational Mechanics, 2007, 40(2): 367-382.
 
19).Unger J F, Eckardt S, Könke C. Modelling of cohesive crack growth in concrete structures with the extended finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(41): 4087-4100.
 
20). Sancho J M, Planas J, Fathy A M, et al. Three‐dimensional simulation of concrete fracture using embedded crack elements without enforcing crack path continuity[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(2): 173-187.
 
21).方修君, 金峰, 王进廷. 基于扩展有限元法的粘聚裂纹模型[J]. 清华大学学报: 自然科学版, 2007, 47(3): 344-347.
 
22). Fagerström M, Larsson R. A thermo-mechanical cohesive zone formulation for ductile fracture[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(10): 3037-3058.
 
23).Benvenuti E. A regularized XFEM framework for embedded cohesive interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(49): 4367-4378.
 
24).Cox J V. An extended finite element method with analytical enrichment for cohesive crack modeling[J]. International Journal for Numerical Methods in Engineering, 2009, 78(1): 48-83.
 
25).Xu Y, Yuan H. Computational modeling of mixed-mode fatigue crack growth using extended finite element methods[J]. International journal of fracture, 2009, 159(2): 151-165.
 
26).Theiner Y, Hofstetter G. Numerical prediction of crack propagation and crack widths in concrete structures[J]. Engineering Structures, 2009, 31(8): 1832-1840.
 
27).Bruss I, Ramm E. Modeling of continuous curved crack surfaces in three dimensional composite structures[C]//Proc. of the Int. Conf. on Extended Finite Element Methods–Recent Developments and Applications. 2009: 23-26.
 
28).Xu Y, Yuan H. On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth[J]. Computational Materials Science, 2009, 46(3): 579-585.
 
29).Moonen P, Sluys L J, Carmeliet J. A continuous–discontinuous approach to simulate physical degradation processes in porous media[J]. International Journal for Numerical Methods in Engineering, 2010, 84(9): 1009-1037.
 
30).Karihaloo B L, Xiao Q Z. Asymptotic fields ahead of mixed mode frictional cohesive cracks[J]. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 2010, 90(9): 710-720.
 
31).Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods[J]. Computers & structures, 2010, 88(23): 1391-1411.
 
32).Yong Guo, Cheng-Tang Wu. EFG and XFEM Cohesive Fracture Analysis Methods in LS- - DYNA. LS-DYNA Seminar. 2010. 11. 24.
 
33).Mougaard J F, Poulsen P N, Nielsen L O. A partly and fully cracked triangular XFEM element for modeling cohesive fracture[J]. International Journal for Numerical Methods in Engineering, 2011, 85(13): 1667-1686.
 
34).Campilho R, Banea M D, Chaves F J P, et al. eXtended Finite Element Method for fracture characterization of adhesive joints in pure mode I[J]. Computational Materials Science, 2011, 50(4): 1543-1549.
 
35).Xu Y, Yuan H. Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods[J]. Engineering Fracture Mechanics, 2011, 78(3): 544-558.
 
36).Giang N T, Nhu N H. Cast3M implementation of the extended finite element method for cohesive crack[J]. Vietnam Journal of Mechanics, 2011, 33(1): 55-64.
 
37).Campilho R, Banea M D, Pinto A M G, et al. Strength prediction of single-and double-lap joints by standard and extended finite element modelling[J]. International Journal of Adhesion and Adhesives, 2011, 31(5): 363-372.
 
38).Wu J Y. Unified analysis of enriched finite elements for modeling cohesive cracks[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(45): 3031-3050.
 
39).潘坚文, 张楚汉, 金峰. 基于扩展有限元法的含纵向裂缝重力坝破坏分析[J]. 水力发电学报, 2011, 30(3): 138-144.
 
40).Zamani A, Gracie R, Reza Eslami M. Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM[J]. International Journal for Numerical Methods in Engineering, 2012, 90(4): 452-483.
 
41).Benvenuti E, Tralli A. Simulation of finite-width process zone in concrete-like materials by means of a regularized extended finite element model[J]. Computational Mechanics, 2012, 50(4): 479-497.
 
42).Gálvez J C, Planas J, Sancho J M, et al. An embedded cohesive crack model for finite element analysis of quasi-brittle materials[J]. Engineering Fracture Mechanics, 2013, 109: 369-386.
 
43).Bouhala L, Makradi A, Belouettar S, et al. Modelling of failure in long fibres reinforced composites by X-FEM and cohesive zone model[J]. Composites Part B: Engineering, 2013, 55: 352-361.
 
44).Olesen J F, Poulsen P N. An embedded crack in a constant strain triangle utilizing extended finite element concepts[J]. Computers & Structures, 2013, 117: 1-9.
 
45).Ahmed A, Sluys L J. Anomalous behavior of bilinear quadrilateral finite elements for modeling cohesive cracks with XFEM/GFEM[J]. International Journal for Numerical Methods in Engineering, 2013, 94(5): 454-472.
 
46).Remmers J J C, de Borst R, Verhoosel C V, et al. The cohesive band model: a cohesive surface formulation with stress triaxiality[J]. International Journal of Fracture, 2013, 181(2): 177-188.
 
47).Mougaard J F, Poulsen P N, Nielsen L O. Complete Tangent Stiffness for eXtended Finite Element Method by including crack growth parameters[J]. International Journal for Numerical Methods in Engineering, 2013, 95(1): 33-45.
 
48).Rashid F M, Banerjee A. Implementation and validation of a triaxiality dependent cohesive model: experiments and simulations[J]. International Journal of Fracture, 2013, 181(2): 227-239.
 
49).Jaśkowiec J, van der Meer F P. A consistent iterative scheme for 2D and 3D cohesive crack analysis in XFEM[J]. Computers & Structures, 2014, 136: 98-107.
 
50).Lu P, Xiao X, Chou Y K. Interface delamination study of diamond-coated carbide tools considering coating fractures[J]. Surface and Coatings Technology, 2014, 260: 239-245.
 
51).Grogan D M, Brádaigh C M Ó, Leen S B. A combined XFEM and cohesive zone model for composite laminate microcracking and permeability[J]. Composite Structures, 2015, 120: 246-261.
 
52). Vigueras G, Sket F, Samaniego C, et al. An XFEM/CZM implementation for massively parallel simulations of composites fracture[J]. Composite Structures, 2015, 125: 542-557.
 
53).Liao F, Huang Z. An extended finite element model for modelling localised fracture of reinforced concrete beams in fire[J]. Computers & Structures, 2015, 152: 11-26.
 
54).Roth S N, Léger P, Soulaïmani A. A combined XFEM–damage mechanics approach for concrete crack propagation[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 923-955.
 
55).Wu J Y, Li F B. An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 295: 77-107.
 
56).Zhang X, Bui T Q. A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures[J]. Engineering Computations, 2015, 32(2): 473-497.
 
57).Sadaba S, Romero I, Gonzalez C, et al. A stable X‐FEM in cohesive transition from closed to open crack[J]. International Journal for Numerical Methods in Engineering, 2015, 101(7): 540-570.
 
58).Ferretti D, Michelini E, Rosati G. Cracking in autoclaved aerated concrete: Experimental investigation and XFEM modeling[J]. Cement and Concrete Research, 2015, 67: 156-167.
 
59).Na S, Spatari S, Hsuan Y G. Fracture characterization of pristine/post-consumer HDPE blends using the essential work of fracture (EWF) concept and extended finite element method (XFEM)[J]. Engineering Fracture Mechanics, 2015, 139: 1-17.
 
60).Haghighat E, Pietruszczak S. On modeling of discrete propagation of localized damage in cohesive‐frictional materials[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39(16): 1774-1790.
 
61).Zhang Y, Lackner R, Zeiml M, et al. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 335-366.
 
62).Jaśkowiec J. Three-dimensional analysis of a cohesive crack coupled with heat flux through the crack[J]. Advances in Engineering Software, 2015, 89: 98-107.
 
63).Pike M G, Oskay C. XFEM modeling of short microfiber reinforced composites with cohesive interfaces[J]. Finite Elements in Analysis and Design, 2015, 106: 16-31.
 
64).Hosseini-Toudeshky H, Jamalian M. Simulation of micromechanical damage to obtain mechanical properties of bimodal Al using XFEM[J]. Mechanics of Materials, 2015, 89: 229-240.
 
65).Ferté G, Massin P, Moës N. 3D crack propagation with cohesive elements in the extended finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 300: 347-374.
 
66).Wang Y, Waisman H. From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 299: 57-89.
 
67).X. Li, J. Chen.The implementation of the extended cohesive damage model for multicrack evolution in laminated composites[J]. Composite Structures 139 (2016) 68–76
 
68).Libin Zhao, Jie Zhi, Jianyu Zhang, Zhanli Liu, Ning Hu. XFEM simulation of delamination in composite laminates [J]. Composites: Part A 80 (2016) 61–71
 
69). M. Ghamgosar, N. Erarslan. Experimental and Numerical Studies on Development of Fracture Process Zone (FPZ) in Rocks under Cyclic and Static Loadings. Rock Mech Rock Eng,2016,49:893–908.
 
70). Yongxiang Wang, Haim Waisman.From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials. Comput. Methods Appl. Mech. Engrg. 2016,299:57–89.
 
71). S. Beizaee, G. Xotta, K.J. Willam. Perforation studies on flat bars for XFEM-based failure analysis. Engineering Fracture Mechanics, 2016,155:67–87.
 
71). Wenting Li, Zhengwu Jiang and Zhenghong Yang. Crack Extension and Possibility of Debonding in Encapsulation-Based Self-Healing Materials. Materials 2017, 10, 589; doi:10.3390/ma10060589.
 
72). F.A. Gilabert, D. Garoz, W. Van Paepegem.Macro- and micro-modeling of crack propagation in encapsulation-based self-healing materials: Application of XFEM and cohesive surface techniques. Materials & Design 130 (2017) 459–478.
 
73). X. Li, J. Chen. An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials. Comput. Methods Appl. Mech. Engrg. 315 (2017) 744–759.
 
 
34.M-integration
 
1).Yu H, Wu L, Guo L, et al. Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method[J]. International Journal of Solids and Structures, 2009, 46(20): 3710-3724.
 
2).Yu H, Wu L, Guo L, et al. Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials[J]. Mechanics of Materials, 2010, 42(4): 435-450.
 
3).Guo L, Guo F, Yu H, et al. An interaction energy integral method for nonhomogeneous materials with interfaces under thermal loading[J]. International Journal of Solids and Structures, 2012, 49(2): 355-365.
 
4).González‐Albuixech V F, Giner E, Tarancon J E, et al. Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2013, 94(8): 740-757.
 
5).Yu H, Sumigawa T, Kitamura T. A domain-independent interaction integral for linear elastic fracture analysis of micropolar materials[J]. Mechanics of Materials, 2014, 74: 1-13.
 
6).Yu H, Kitamura T. A new domain-independent interaction integral for solving the stress intensity factors of the materials with complex thermo-mechanical interfaces[J]. European Journal of Mechanics-A/Solids, 2015, 49: 500-509.
 
 
35.Solidification
 
1).Ji H, Chopp D, Dolbow J E. A hybrid extended finite element/level set method for modeling phase transformations[J]. International Journal for Numerical Methods in Engineering, 2002, 54(8): 1209-1233.
 
2).Chessa J, Smolinski P, Belytschko T. The extended finite element method (XFEM) for solidification problems[J]. International Journal for Numerical Methods in Engineering, 2002, 53(8): 1959-1977.
 
3).Merle R, Dolbow J. Solving thermal and phase change problems with the extended finite element method[J]. Computational mechanics, 2002, 28(5): 339-350.
 
4).Dolbow J, Fried E, Ji H. Chemically induced swelling of hydrogels[J]. Journal of the Mechanics and Physics of Solids, 2004, 52(1): 51-84.
 
5).Zabaras N, Ganapathysubramanian B, Tan L. Modelling dendritic solidification with melt convection using the extended finite element method[J]. Journal of Computational Physics, 2006, 218(1): 200-227.
 
6).Tan L, Zabaras N. Modeling the growth and interaction of multiple dendrites in solidification using a level set method[J]. Journal of Computational Physics, 2007, 226(1): 131-155.
 
7).Ji H, Mourad H, Fried E, et al. Kinetics of thermally induced swelling of hydrogels[J]. International Journal of Solids and Structures, 2006, 43(7): 1878-1907.
 
8).Zhou J M, Qi L H. Treatment of discontinuous interface in liquid-solid forming with extended finite element method[J]. Transactions of Nonferrous Metals Society of China, 2010, 20: s911-s915.
 
9).Menouillard T, Belytschko T. Analysis and computations of oscillating crack propagation in a heated strip[J]. International Journal of Fracture, 2011, 167(1): 57-70.
 
10).Duddu R, Chopp D L, Voorhees P, et al. Diffusional evolution of precipitates in elastic media using the extended finite element and the level set methods[J]. Journal of Computational Physics, 2011, 230(4): 1249-1264.
 
11).Shadi Mohamed M, Seaid M, Trevelyan J, et al. A partition of unity FEM for time‐dependent diffusion problems using multiple enrichment functions[J]. International Journal for Numerical Methods in Engineering, 2013, 93(3): 245-265.
 
12).Cosimo A, Fachinotti V, Cardona A. An enrichment scheme for solidification problems[J]. Computational Mechanics, 2013, 52(1): 17-35.
 
13).Stapór P. The XFEM for nonlinear thermal and phase change problems[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2015, 25(2): 400-421.
 
 
36.XIGA
 
1).Benson D J, Bazilevs Y, De Luycker E, et al. A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM[J]. International Journal for Numerical Methods in Engineering, 2010, 83(6): 765-785.
 
2).Ghorashi S S, Valizadeh N, Mohammadi S. Analysis of cracked orthotropic media using the extended isogeometric analysis (XIGA)[C]//Proceedings of the 2nd European Conference on Extended Finite Element (XFEM’11). 2011.
 
3).De Luycker E, Benson D J, Belytschko T, et al. X‐FEM in isogeometric analysis for linear fracture mechanics[J]. International Journal for Numerical Methods in Engineering, 2011, 87(6): 541-565.
 
4).Haasemann G, Kästner M, Prüger S, et al. Development of a quadratic finite element formulation based on the XFEM and NURBS[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 598-617.
 
5).Ghorashi S S, Valizadeh N, Mohammadi S. Extended isogeometric analysis for simulation of stationary and propagating cracks[J]. International Journal for Numerical Methods in Engineering, 2012, 89(9): 1069-1101.
 
6).Legrain G. A NURBS enhanced extended finite element approach for unfitted CAD analysis[J]. Computational Mechanics, 2013, 52(4): 913-929.
 
7).TRAN L, NGUYEN V P, HAI L V, et al. An assessment of limit loads of cracked structures using extended isogeometric analysis[C]//Proceedings of the Thirteenth East Asia-Pacific Conference on Structural Engineering and Construction (EASEC-13). The Thirteenth East Asia-Pacific Conference on Structural Engineering and Construction (EASEC-13), 2013: H-4-4.
 
8).Bhardwaj G, Singh I V, Mishra B K. Numerical simulation of plane crack problems using extended isogeometric analysis[J]. Procedia Engineering, 2013, 64: 661-670.
 
9).Guo Y, Ruess M, Gürdal Z. A contact extended isogeometric layerwise approach for the buckling analysis of delaminated composites[J]. Composite Structures, 2014, 116: 55-66.
 
10).Tran L V, Nguyen V P, Wahab M A, et al. An extended isogeometric analysis for vibration of cracked FGM plates using higher-order shear deformation theory[J]. arXiv preprint arXiv:1403.0306, 2014.
 
11).Nguyen-Xuan H, Tran L V, Thai C H, et al. Plastic collapse analysis of cracked structures using extended isogeometric elements and second-order cone programming[J]. Theoretical and Applied Fracture Mechanics, 2014, 72: 13-27.
 
12).Oh H S, Kim H, Jeong J W. Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners[J]. International Journal for Numerical Methods in Engineering, 2014, 97(3): 149-180.
 
13).Jung J, Taciroglu E. Modeling and identification of an arbitrarily shaped scatterer using dynamic XFEM with cubic splines[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 278: 101-118.
 
14).Tan M H Y, Safdari M, Najafi A R, et al. A NURBS-based interface-enriched generalized finite element scheme for the thermal analysis and design of microvascular composites[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 1382-1400.
 
15).Singh I V, Bhardwaj G, Mishra B K. A new criterion for modeling multiple discontinuities passing through an element using XIGA[J]. Journal of Mechanical Science and Technology, 2015, 29(3): 1131-1143.
 
16).Nguyen-Thanh N, Valizadeh N, Nguyen M N, et al. An extended isogeometric thin shell analysis based on Kirchhoff–Love theory[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265-291.
 
17).Jia Y, Anitescu C, Ghorashi S S, et al. Extended isogeometric analysis for material interface problems[J]. IMA Journal of Applied Mathematics, 2015, 80(3): 608-633.
 
18).Nguyen V P, Bordas S. Extended isogeometric analysis for strong and weak discontinuities[M]//Isogeometric methods for numerical simulation. Springer Vienna, 2015: 21-120.
 
19).Bhardwaj G, Singh I V. Fatigue crack growth analysis of a homogeneous plate in the presence of multiple defects using extended isogeometric analysis[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(4): 1065-1082.
 
20).Bhardwaj G, Singh I V, Mishra B K. Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 186-229.
 
21).Bayesteh H, Afshar A, Mohammdi S. Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method[J]. European Journal of Mechanics-A/Solids, 2015, 51: 123-139.
 
22).Ghorashi S S, Valizadeh N, Mohammadi S, et al. T-spline based XIGA for fracture analysis of orthotropic media[J]. Computers & Structures, 2015, 147: 138-146.
 
23).Tran L V, Ly H A, Lee J, et al. Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach[J]. International Journal of Mechanical Sciences, 2015, 96: 65-78.
 
24). Pengfei Tan, Nhon Nguyen-Thanh, Kun Zhou. Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory. Theoretical and Applied Fracture Mechanics 89 (2017) 127–138.
 
25). S.K. Singh, I.V. Singh, B.K. Mishra, G. Bhardwaj, T.Q. Bui. A simple, efficient and accurate Bézier extraction based T-spline XIGA for crack simulations. Theoretical and Applied Fracture Mechanics 88 (2017) 74–96.
 
 
37.Bolt
 
1). Debasis Deb, Kamal C. Das. Enriched finite element procedures for analyzing decoupled bolts installed in rock mass. Int. J. Numer. Anal. Meth. Geomech. 2011; 35:1636–1655
 
2). Debasis Deb, Kamal C. Das. Modelling of fully grouted rock bolt based on enriched finite element method. International Journal of Rock Mechanics & Mining Sciences 2011;48:283–293
 
3). Debasis Deb, Kamal C. Das. A new doubly enriched finite element for modeling grouted bolt crossed by rock joint. International Journal of Rock Mechanics & Mining Sciences 2014;70:47–58
 
 
38.Contact
 
1).Dolbow J, Moës N, Belytschko T. An extended finite element method for modeling crack growth with frictional contact[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(51): 6825-6846.
 
2).Ji H, Dolbow J E. On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2004, 61(14): 2508-2535.
 
3).Khoei A R, Nikbakht M. Contact friction modeling with the extended finite element method (X-FEM)[J]. Journal of materials processing technology, 2006, 177(1): 58-62.
 
4).Khoei A R, Shamloo A, Azami A R. Extended finite element method in plasticity forming of powder compaction with contact friction[J]. International Journal of Solids and Structures, 2006, 43(18): 5421-5448.
 
5).Geniaut S, Massin P, Moës N. X-FEM for 3D Cracks in Shaft with Contact[M]//Fracture of Nano and Engineering Materials and Structures. Springer Netherlands, 2006: 951-952.
 
6).Moës N, Béchet E, Tourbier M. Imposing Dirichlet boundary conditions in the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2006, 67(12): 1641-1669.
 
7).Elguedj T, Gravouil A, Combescure A. A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact[J]. International Journal for Numerical Methods in Engineering, 2007, 71(13): 1569-1597.
 
8).Khoei A R, Nikbakht M. An enriched finite element algorithm for numerical computation of contact friction problems[J]. International Journal of Mechanical Sciences, 2007, 49(2): 183-199.
 
9).Kim T Y, Dolbow J, Laursen T. A mortared finite element method for frictional contact on arbitrary interfaces[J]. Computational Mechanics, 2007, 39(3): 223-235.
 
10).Liu F, Borja R I. A contact algorithm for frictional crack propagation with the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2008, 76(10): 1489-1512.
 
11).Vitali E, Benson D J. Contact with friction in multi‐material arbitrary Lagrangian‐Eulerian formulations using X‐FEM[J]. International journal for numerical methods in engineering, 2008, 76(6): 893-921.
 
12).Giner E, Sukumar N, Fuenmayor F J, et al. Singularity enrichment for complete sliding contact using the partition of unity finite element method[J]. International journal for numerical methods in engineering, 2008, 76(9): 1402-1418.
 
13).Khoei A R, Biabanaki S O R, Anahid M. A Lagrangian-extended finite-element method in modeling large-plasticity deformations and contact problems[J]. International Journal of Mechanical Sciences, 2009, 51(5): 384-401.
 
14).Zilian A, Fries T P. A localized mixed‐hybrid method for imposing interfacial constraints in the extended finite element method (XFEM)[J]. International journal for numerical methods in engineering, 2009, 79(6): 733-752.
 
15).Nistor I, Guiton M L E, Massin P, et al. An X‐FEM approach for large sliding contact along discontinuities[J]. International Journal for Numerical Methods in Engineering, 2009, 78(12): 1407-1435.
 
16).董玉文, 任青文, 苏琴. 接触摩擦问题的扩展有限元数值模拟方法[J]. 长江科学院院报, 2009, 26(5): 45-49.
 
17).Liu F, Borja R I. An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction[J]. International journal for numerical and analytical methods in geomechanics, 2009, 33(13): 1535-1560.
 
18).Dolbow J, Harari I. An efficient finite element method for embedded interface problems[J]. International journal for numerical methods in engineering, 2009, 78(2): 229-252.
 
19).Giner E, Tur M, Vercher A, et al. Numerical modelling of crack–contact interaction in 2D incomplete fretting contacts using X-FEM[J]. Tribology International, 2009, 42(9): 1269-1275.
 
20).Bechet E, Moës N, Wohlmuth B. A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2009, 78(8): 931-954.
 
21).Sanders J D, Dolbow J E, Laursen T A. On methods for stabilizing constraints over enriched interfaces in elasticity[J]. International Journal for Numerical Methods in Engineering, 2009, 78(9): 1009-1036.
 
22).Pierres E, Baietto M C, Gravouil A, et al. 3D two scale X-FEM crack model with interfacial frictional contact: application to fretting fatigue[J]. Tribology International, 2010, 43(10): 1831-1841.
 
23).Giner E, Tur M, Tarancón J E, et al. Crack face contact in X‐FEM using a segment‐to‐segment approach[J]. International journal for numerical methods in engineering, 2010, 82(11): 1424-1449.
 
24).Embar A, Dolbow J, Harari I. Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements[J]. International Journal for Numerical Methods in Engineering, 2010, 83(7): 877-898.
 
25).Khoei A R, Mousavi S M T. Modeling of large deformation–Large sliding contact via the penalty X-FEM technique[J]. Computational Materials Science, 2010, 48(3): 471-480.
 
26).Liu F, Borja R I. Stabilized low-order finite elements for frictional contact with the extended finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37): 2456-2471.
 
27).Giner E, Sabsabi M, Fuenmayor F J. Calculation of K II in crack face contacts using X-FEM. Application to fretting fatigue[J]. Engineering Fracture Mechanics, 2011, 78(2): 428-445.
 
28).石露, 李小春, 王伟, 等. 基于互补理论的扩展有限元接触问题实现[J]. 岩土力学, 2011, 32(12): 3805-3811.
 
29).周小平, 杨海清. 压应力状态下多裂纹扩展过程数值模拟[J]. 岩土工程学报, 2011, 32(2): 192-197.
 
30).Gravouil A, Pierres E, Baietto M C. Stabilized global–local X‐FEM for 3D non‐planar frictional crack using relevant meshes[J]. International Journal for Numerical Methods in Engineering, 2011, 88(13): 1449-1475.
 
31).Pierres E, Baietto M C, Gravouil A. Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model[J]. Comptes Rendus Mécanique, 2011, 339(7): 532-551.
 
32).TaheriMousavi S M J, Mousavi S M T. Modeling large sliding frictional contact along non-smooth discontinuities in X-FEM[J]. International Journal of Modeling and Optimization, 2011, 1(2): 169-173.
 
33).Yu T T. Considering contact conditions between discontinuity surfaces in extended finite element method (XFEM)[J]. International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(6): 899-908.
 
34).Amdouni S, Hild P, Lleras V, et al. A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies[J]. ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46(04): 813-839.
 
35).Bonfils N, Chevaugeon N, Moës N. Treating volumetric inequality constraint in a continuum media with a coupled X-FEM/level-set strategy[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 205: 16-28.
 
36).Siavelis M, Guiton M L E, Massin P, et al. Large sliding contact along branched discontinuities with X-FEM[J]. Computational Mechanics, 2013, 52(1): 201-219.
 
37).Khoei A R, Vahab M. A numerical contact algorithm in saturated porous media with the extended finite element method[J]. Computational Mechanics, 2014, 54(5): 1089-1110.
 
38).Amdouni S, Moakher M, Renard Y. A stabilized Lagrange multiplier method for the enriched finite-element approximation of Tresca contact problems of cracked elastic bodies[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 270: 178-200.
 
39).Ramos A C, Aragón A M, Soghrati S, et al. A new formulation for imposing Dirichlet boundary conditions on non‐matching meshes[J]. International Journal for Numerical Methods in Engineering, 2015, 103(6): 430-444.
 
40).Hirmand M, Vahab M, Khoei A R. An augmented Lagrangian contact formulation for frictional discontinuities with the extended finite element method[J]. Finite Elements in Analysis and Design, 2015, 107: 28-43.
 
 
39.Dynamic
 
1).Belytschko T, Chen H, Xu J, et al. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment[J]. International Journal for Numerical Methods in Engineering, 2003, 58(12): 1873-1905.
 
2).Chessa J, Belytschko T. Arbitrary discontinuities in space–time finite elements by level sets and X‐FEM[J]. International Journal for Numerical Methods in Engineering, 2004, 61(15): 2595-2614.
 
3).Zhou F, Molinari J F, Li Y. Three-dimensional numerical simulations of dynamic fracture in silicon carbide reinforced aluminum[J]. Engineering fracture mechanics, 2004, 71(9): 1357-1378.
 
4).Belytschko T, Chen H. Singular enrichment finite element method for elastodynamic crack propagation[J]. International Journal of Computational Methods, 2004, 1(01): 1-15.
 
5).Réthoré J, Gravouil A, Combescure A. An energy‐conserving scheme for dynamic crack growth using the eXtended finite element method[J]. International Journal for Numerical Methods in Engineering, 2005, 63(5): 631-659.
 
6).Zi G, Chen H, Xu J, et al. The extended finite element method for dynamic fractures[J]. Shock and Vibration, 2005, 12(1): 9-23.
 
7).Nistor I, Pantalé O, Caperaa S. On the modeling of the dynamic crack propagation by extended finite element method: numerical implementation in dynela code[C]//VIII International Conference on Computational Plasticity COMPLAS VIII, CIMNE, Barcelona. 2005.
 
8).Chessa J, Belytschko T. A local space–time discontinuous finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(13): 1325-1343.
 
9).Song J H, Areias P, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes[J]. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868-893.
 
10).Menouillard T, Rethore J, Combescure A, et al. Efficient explicit time stepping for the eXtended Finite Element Method (X‐FEM)[J]. International Journal for Numerical Methods in Engineering, 2006, 68(9): 911-939.
 
11).Svahn P O, Ekevid T, Runesson K. Discrete crack modelling in a new X‐FEM format with emphasis on dynamic response[J]. International journal for numerical and analytical methods in geomechanics, 2007, 31(2): 261-283.
DIV style="TEXT-INDENT: 21pt"> 
12).Prabel B, Combescure A, Gravouil A, et al. Level set X‐FEM non‐matching meshes: application to dynamic crack propagation in elastic–plastic media[J]. International Journal for Numerical Methods in Engineering, 2007, 69(8): 1553-1569.
 
13).Combescure A, Gravouil A, Grégoire D, et al. X-FEM a good candidate for energy conservation in simulation of brittle dynamic crack propagation[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(5): 309-318.
 
14).Prabel B, Marie S, Combescure A. Using the X-FEM method to model the dynamic propagation and arrest of cleavage cracks in ferritic steel[J]. Engineering Fracture Mechanics, 2008, 75(10): 2984-3009.
 
15).Fagerström M, Larsson R. Approaches to dynamic fracture modelling at finite deformations[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(2): 613-639.
 
16).Menouillard T, Rethore J, Moes N, et al. Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation[J]. International Journal for Numerical Methods in Engineering, 2008, 74(3): 447-474.
DIV style="TEXT-INDENT: 21pt"> 
17).Nistor I, Pantalé O, Caperaa S. Numerical implementation of the extended finite element method for dynamic crack analysis[J]. Advances in Engineering Software, 2008, 39(7): 573-587.
 
18).Rozycki P, Moës N, Bechet E, et al. X-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(5): 349-363.
 
19).Song J H, Wang H, Belytschko T. A comparative study on finite element methods for dynamic fracture[J]. Computational Mechanics, 2008, 42(2): 239-250.
 
20).Elguedj T, Gravouil A, Maigre H. An explicit dynamics extended finite element method. Part 1: mass lumping for arbitrary enrichment functions[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(30): 2297-2317.
 
21).Rabczuk T, Song J H, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method[J]. Engineering Fracture Mechanics, 2009, 76(6): 730-741.
 
22).Duan Q, Song J H, Menouillard T, et al. Element‐local level set method for three‐dimensional dynamic crack growth[J]. International Journal for Numerical Methods in Engineering, 2009, 80(12): 1520-1543.
 
23).Gravouil A, Elguedj T, Maigre H. An explicit dynamics extended finite element method. Part 2: element-by-element stable-explicit/explicit dynamic scheme[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(30): 2318-2328.
 
24).Song J H, Belytschko T. Cracking node method for dynamic fracture with finite elements[J]. International Journal for Numerical Methods in Engineering, 2009, 77(3): 360-385.
 
25).Grégoire D, Maigre H, Combescure A. New experimental and numerical techniques to study the arrest and the restart of a crack under impact in transparent materials[J]. International Journal of Solids and Structures, 2009, 46(18): 3480-3491.
 
26).Motamedi D, Mohammadi S. Dynamic analysis of fixed cracks in composites by the extended finite element method[J]. Engineering Fracture Mechanics, 2010, 77(17): 3373-3393.
 
27).Menouillard T, Song J H, Duan Q, et al. Time dependent crack tip enrichment for dynamic crack propagation[J]. International Journal of Fracture, 2010, 162(1-2): 33-49.
 
28).Menouillard T, Belytschko T. Smoothed nodal forces for improved dynamic crack propagation modeling in XFEM[J]. International Journal for Numerical Methods in Engineering, 2010, 84(1): 47-72.
 
29).Motamedi D, Mohammadi S. Dynamic crack propagation analysis of orthotropic media by the extended finite element method[J]. International Journal of Fracture, 2010, 161(1): 21-39.
 
30).Aubertin P, Réthoré J, De Borst R. A coupled molecular dynamics and extended finite element method for dynamic crack propagation[J]. International journal for numerical methods in engineering, 2010, 81(1): 72-88.
 
31).Menouillard T, Belytschko T. Dynamic fracture with meshfree enriched XFEM[J]. Acta Mechanica, 2010, 213(1-2): 53-69.
 
32).Xu J, Li Y, Chen X, et al. Characteristics of windshield cracking upon low-speed impact: numerical simulation based on the extended finite element method[J]. Computational Materials Science, 2010, 48(3): 582-588.
 
33).Zamani A, Eslami M R. Implementation of the extended finite element method for dynamic thermoelastic fracture initiation[J]. International Journal of Solids and Structures, 2010, 47(10): 1392-1404.
 
34).Natarajan S, Baiz P M, Bordas S, et al. Natural frequencies of cracked functionally graded material plates by the extended finite element method[J]. Composite Structures, 2011, 93(11): 3082-3092.
 
35).Coon E T, Shaw B E, Spiegelman M. A Nitsche-extended finite element method for earthquake rupture on complex fault systems[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(41): 2859-2870.
 
36).Haboussa D, Grégoire D, Elguedj T, et al. X‐FEM analysis of the effects of holes or other cracks on dynamic crack propagations[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 618-636.
 
37).Larsson R, Mediavilla J, Fagerström M. Dynamic fracture modeling in shell structures based on XFEM[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 499-527.
 
38).Liu Z L, Menouillard T, Belytschko T. An XFEM/Spectral element method for dynamic crack propagation[J]. International Journal of Fracture, 2011, 169(2): 183-198.
 
39).Kroon M. Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method[J]. Computational Mechanics, 2012, 49(1): 73-86.
 
40).Tran V X, Geniaut S, Galenne E, et al. A modal analysis for computation of stress intensity factors under dynamic loading conditions at low frequency using eXtended Finite Element Method[J]. Engineering Fracture Mechanics, 2013, 98: 122-136.
 
41).Zhang S, Wang G, Yu X. Seismic cracking analysis of concrete gravity dams with initial cracks using the extended finite element method[J]. Engineering Structures, 2013, 56: 528-543.
 
42).Mostofizadeh S, Fagerström M, Larsson R. Dynamic crack propagation in elastoplastic thin‐walled structures: Modelling and validation[J]. International Journal for Numerical Methods in Engineering, 2013, 96(2): 63-86.
 
43).Xu D, Liu Z, Liu X, et al. Modeling of dynamic crack branching by enhanced extended finite element method[J]. Computational Mechanics, 2014, 54(2): 489-502.
 
44).Saksala T, Brancherie D, Harari I, et al. Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials[J]. International Journal for Numerical Methods in Engineering, 2015, 101(3): 230-250.
 
45).Wang G, Wang Y, Lu W, et al. XFEM based seismic potential failure mode analysis of concrete gravity dam–water–foundation systems through incremental dynamic analysis[J]. Engineering Structures, 2015, 98: 81-94.
 
46).Broumand P, Khoei A R. X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model[J]. Finite Elements in Analysis and Design, 2015, 99: 49-67.
 
47). Sachin Kumar, I.V. Singh, B.K. Mishra, Akhilendra Singh. New enrichments in XFEM to model dynamic crack response of 2-D elastic solids. International Journal of Impact Engineering,2016, 87:198–211.
 
48). Marko Bendezu, Celso Romanel, Deane Roehl. Finite element analysis of blast-induced fracture propagation in hard rocks. Computers and Structures 182 (2017) 1–13.
 
49). X. Peng, S. Kulasegaram, S.C. Wu, S.P.A. Bordas. An extended finite element method (XFEM) for linear elastic fracture with smooth nodal stress. Computers and Structures 179 (2017) 48–63.
 
50). Xuan Nam Do, Adnan Ibrahimbegovic, Delphine Brancherie. Dynamics framework for 2D anisotropic continuum-discrete damage model for progressive localized failure of massive structures. Computers and Structures 183 (2017) 14–26.
 
51). Longfei Wen, Rong Tian.Improved XFEM: Accurate and robust dynamic crack growth Simulation. Comput. Methods Appl. Mech. Engrg. 308 (2016) 256–285.
 
52). Timothy Crump, Guilhem Ferté, Andrey Jivkov, Paul Mummery, Van-Xuan Tran. Dynamic fracture analysis by explicit solid dynamics and implicit crack propagation. International Journal of Solids and Structures 110–111 (2017) 113–126 .
 
53). Xiaoqing Xu, Jun Xu, Jingjing Chen, Penghui Li, Bohan Liu, Yibing Li. Investigation of dynamic multi-cracking behavior in PVB laminated glass plates. International Journal of Impact Engineering 100(2017)62-74.
 
 
40.Error estimation,convergence analysis
 
1).Strouboulis T, Zhang L, Wang D, et al. A posteriori error estimation for generalized finite element methods[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(9): 852-879.
 
2).Chahine E, Laborde P, Renard Y. A quasi-optimal convergence result for fracture mechanics with XFEM[J]. Comptes Rendus Mathematique, 2006, 342(7): 527-532.
 
3).Bordas S, Duflot M. Derivative recovery and a posteriori error estimate for extended finite elements[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(35): 3381-3399.
 
4).Duflot M, Bordas S. A posteriori error estimation for extended finite elements by an extended global recovery[J]. International Journal for Numerical Methods in Engineering, 2008, 76(8): 1123-1138.
 
5).Bordas S, Duflot M, Le P. A simple error estimator for extended finite elements[J]. Communications in Numerical Methods in Engineering, 2008, 24(11): 961-971.
 
6).Ródenas J J, González‐Estrada O A, Tarancón J E, et al. A recovery‐type error estimator for the extended finite element method based on singular+ smooth stress field splitting[J]. International Journal for Numerical Methods in Engineering, 2008, 76(4): 545-571.
 
7).Waisman H, Belytschko T. Parametric enrichment adaptivity by the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2008, 73(12): 1671-1692.
 
8).Pannachet T, Sluys L J, Askes H. Error estimation and adaptivity for discontinuous failure[J]. International Journal for Numerical Methods in Engineering, 2009, 78(5): 528-563.
 
9).Hild P, Lleras V, Renard Y. A residual error estimator for the XFEM approximation of the elasticity problem[J]. Computational Mechanics, 2010: 1-28.
 
10).Ródenas J J, González-Estrada O A, Díez P, et al. Accurate recovery-based upper error bounds for the extended finite element framework[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37): 2607-2621.
 
11).Shen Y, Lew A. Stability and convergence proofs for a discontinuous-Galerkin-based extended finite element method for fracture mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37): 2360-2382.
 
12).Shen Y, Lew A. An optimally convergent discontinuous Galerkin‐based extended finite element method for fracture mechanics[J]. International journal for numerical methods in engineering, 2010, 82(6): 716-755.
 
13).Panetier J, Ladeveze P, Chamoin L. Strict and effective bounds in goal‐oriented error estimation applied to fracture mechanics problems solved with XFEM[J]. International Journal for Numerical Methods in Engineering, 2010, 81(6): 671-700.
 
14).Shibanuma K, Utsunomiya T. Evaluation on reproduction of priori knowledge in XFEM[J]. Finite Elements in Analysis and Design, 2011, 47(4): 424-433.
 
15).Stein E, Gerasimov T, Rüter M. Explicit and implicit residual-type goal-oriented error estimators for XFEM in LEFM[C]//International Conference on Adaptive Modeling and Simulation, ADMOS. 2011.
 
16).Nicaise S, Renard Y, Chahine E. Optimal convergence analysis for the extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2011, 86(4‐5): 528-548.
 
17).Gerasimov T, Rüter M, Stein E. An explicit residual‐type error estimator for Q1‐quadrilateral extended finite element method in two‐dimensional linear elastic fracture mechanics[J]. International Journal for Numerical Methods in Engineering, 2012, 90(9): 1118-1155.
 
18).Loehnert S, Prange C, Wriggers P. Error controlled adaptive multiscale XFEM simulation of cracks[J]. International journal of fracture, 2012, 178(1-2): 147-156.
 
19).Prange C, Loehnert S, Wriggers P. Error estimation for crack simulations using the XFEM[J]. International Journal for Numerical Methods in Engineering, 2012, 91(13): 1459-1474.
 
20).Andrés González-Estrada O, José Ródenas J, Pierre Alain Bordas S, et al. On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods[J]. Engineering Computations, 2012, 29(8): 814-841.
 
21).Rodenas J J, González-Estrada O A, Fuenmayor F J, et al. Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM[J]. Computational Mechanics, 2013, 52(2): 321-344.
 
22).Rüter M, Gerasimov T, Stein E. Goal-oriented explicit residual-type error estimates in XFEM[J]. Computational Mechanics, 2013, 52(2): 361-376.
 
23).Ferté G, Massin P, Moës N. Convergence analysis of linear or quadratic X-FEM for curved free boundaries[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 278: 794-827.
 
24).González-Estrada O A, Ródenas J J, Bordas S P A, et al. Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method[J]. Computers & Structures, 2015, 152: 1-10.
 
25). Y. Jin, O. A. González-Estrada, O. Pierard, and S. P.A. Bordas. Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation. Comput. Methods Appl. Mech. Engrg. (2017), http://dx.doi.org/10.1016/j.cma.2016.12.016
 
 
41.Interface problem
 
1).Sukumar N, Chopp D. L, Moës N. modeling holes and inclusions by level sets in the xfem. 2001,6183-6200.
 
2).Moës N, Cloirec M, Cartraud P, et al. A computational approach to handle complex microstructure geometries[J]. Computer methods in applied mechanics and engineering, 2003, 192(28): 3163-3177.
 
3).Belytschko T, Parimi C, Moës N, et al. Structured extended finite element methods for solids defined by implicit surfaces[J]. International journal for numerical methods in engineering, 2003, 56(4): 609-635.
 
4).Hettich T, Ramm E. Interface material failure modeled by the extended finite-element method and level sets[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(37): 4753-4767.
 
5).Gracie R, Ventura G, Belytschko T. A new fast finite element method for dislocations based on interior discontinuities[J]. International Journal for Numerical Methods in Engineering, 2007, 69(2): 423-441.
 
6).Li S, Ghosh S. Modeling interfacial debonding and matrix cracking in fiber reinforced composites by the extended Voronoi cell FEM[J]. Finite elements in analysis and design, 2007, 43(5): 397-410.
 
7).Belytschko T, Gracie R. On XFEM applications to dislocations and interfaces[J]. International Journal of Plasticity, 2007, 23(10): 1721-1738.
 
8).Gracie R, Oswald J, Belytschko T. On a new extended finite element method for dislocations: core enrichment and nonlinear formulation[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(1): 200-214.
 
9).Anahid M, Khoei A R. New development in extended finite element modeling of large elasto‐plastic deformations[J]. International Journal for Numerical Methods in Engineering, 2008, 75(10): 1133-1171.
 
10).Khoei A R, Anahid M, Shahim K. An extended arbitrary Lagrangian–Eulerian finite element method for large deformation of solid mechanics[J]. Finite Elements in Analysis and Design, 2008, 44(6): 401-416.
 
11).Dolbow J, Mosso S, Robbins J, et al. Coupling volume-of-fluid based interface reconstructions with the extended finite element method[J]. Computer methods in applied mechanics and engineering, 2008, 197(5): 439-447.
 
12).Khoei A R, Biabanaki S O R, Anahid M. Extended finite element method for three-dimensional large plasticity deformations on arbitrary interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(9): 1100-1114.
 
13).Yvonnet J, He Q C, Toulemonde C. Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface[J]. Composites Science and Technology, 2008, 68(13): 2818-2825.
 
14).Dolbow J, Harari I. An efficient finite element method for embedded interface problems[J]. International journal for numerical methods in engineering, 2009, 78(2): 229-252.
 
15).Zhang H H, Li L X. Modeling inclusion problems in viscoelastic materials with the extended finite element method[J]. Finite Elements in Analysis and Design, 2009, 45(10): 721-729.
 
16).Oswald J, Gracie R, Khare R, et al. An extended finite element method for dislocations in complex geometries: Thin films and nanotubes[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(21): 1872-1886.
 
17).Bedrossian J, Von Brecht J H, Zhu S, et al. A second order virtual node method for elliptic problems with interfaces and irregular domains[J]. Journal of Computational Physics, 2010, 229(18): 6405-6426.
 
18).Harari I, Dolbow J. Analysis of an efficient finite element method for embedded interface problems[J]. Computational Mechanics, 2010, 46(1): 205-211.
 
19).Dréau K, Chevaugeon N, Moës N. Studied X-FEM enrichment to handle material interfaces with higher order finite element[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(29): 1922-1936.
 
20).Nouy A, Clement A. eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces[J]. International journal for numerical methods in engineering, 2010, 83(10): 1312-1344.
 
21).Tran A B, Yvonnet J, He Q C, et al. A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM[J]. International Journal for Numerical Methods in Engineering, 2011, 85(11): 1436-1459.
 
22).Khoei A R, Haghighat E. Extended finite element modeling of deformable porous media with arbitrary interfaces[J]. Applied Mathematical Modelling, 2011, 35(11): 5426-5441.
 
23).Hiriyur B, Waisman H, Deodatis G. Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM[J]. International Journal for Numerical Methods in Engineering, 2011, 88(3): 257-278.
 
24).Soghrati S, Geubelle P H. A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 217: 46-57.
 
25).Nielsen C V, Legarth B N, Niordson C F. Extended FEM modeling of crack paths near inclusions[J]. International Journal for Numerical Methods in Engineering, 2012, 89(6): 786-804.
 
26).Soghrati S, Aragón A M, Armando Duarte C, et al. An interface‐enriched generalized FEM for problems with discontinuous gradient fields[J]. International Journal for Numerical Methods in Engineering, 2012, 89(8): 991-1008.
 
27).Sousa F S, Ausas R F, Buscaglia G C. Numerical assessment of stability of interface discontinuous finite element pressure spaces[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 63-74.
 
28).Kramer R, Bochev P, Siefert C, et al. An extended finite element method with algebraic constraints (XFEM-AC) for problems with weak discontinuities[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 266: 70-80.
 
29).Sadeghirad A, Brannon R M, Guilkey J E. Second‐order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces[J]. International Journal for Numerical Methods in Engineering, 2013, 95(11): 928-952.
 
30).Zunino P. Analysis of backward Euler/extended finite element discretization of parabolic problems with moving interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 258: 152-165.
 
31).Joulaian M, Düster A. Local enrichment of the finite cell method for problems with material interfaces[J]. Computational Mechanics, 2013, 52(4): 741-762.
 
32).Benvenuti E, Ventura G, Ponara N, et al. Variationally consistent eXtended FE model for 3D planar and curved imperfect interfaces[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 267: 434-457.
 
33).Benvenuti E. XFEM with equivalent eigenstrain for matrix–inclusion interfaces[J]. Computational Mechanics, 2014, 53(5): 893-908.
 
34).Ferté G, Massin P, Moës N. Interface problems with quadratic X‐FEM: design of a stable multiplier space and error analysis[J]. International Journal for Numerical Methods in Engineering, 2014, 100(11): 834-870.
 
35).Liu J T, Gu S T, Monteiro E, et al. A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM[J]. Computational Mechanics, 2014, 53(4): 825-843.
 
36).Bouhala L, Koutsawa Y, Makradi A, et al. An advanced numerical method for predicting effective elastic properties of heterogeneous composite materials[J]. Composite Structures, 2014, 117: 114-123.
 
37).Savvas D, Stefanou G, Papadrakakis M, et al. Homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by XFEM[J]. Computational Mechanics, 2014, 54(5): 1221-1235.
 
38).Jiang W, Annavarapu C, Dolbow J E, et al. A robust Nitsche's formulation for interface problems with spline‐based finite elements[J]. International Journal for Numerical Methods in Engineering, 2015, 104(7): 676-696.
 
39).Zhao J, Li Y, Liu W K. Predicting band structure of 3D mechanical metamaterials with complex geometry via XFEM[J]. Computational Mechanics, 2015, 55(4): 659-672.
 
40). A.S.Shedbale, I.V.Singh, B.K.Mishra, S.K.Singh. Numerical prediction of indentation behavior of metal matrix composites using XFEM. Procedia Engineering 2017;173:1071-1078.
 
41). Jifeng Zhao, Oleg Y. Kontsevoi, Wei Xiong, Jacob Smith. Simulation-aided constitutive law development –Assessment of low triaxiality void nucleation models via extended finite element method. Journal of the Mechanics and Physics of Solids 102 (2017) 30–45.
 
42). Benoît Lé, Grégory Legrain, Nicolas Moës. Mixed dimensional modeling of reinforced structures. Finite Elements in Analysis and Design 128 (2017) 1–18.
 
43). Nana Duan, Weijie Xu, Shuhong Wang, and Jianguo Zhu. Accuracy analysis of structure with nearby interfaces within XFEM. AIP ADVANCES 7, 056011 (2017).
 
44). Bernard Sonon and Thierry J. Massart. A Level-Set Based Representative Volume Element Generator and XFEM Simulations for Textile and 3D-Reinforced Composites. Materials 2013, 6, 5568-5592; doi:10.3390/ma6125568.
 
 
42.Fluids & fluid–structure interaction
 
1).Wagner G J, Moës N, Liu W K, et al. The extended finite element method for rigid particles in Stokes flow[J]. International Journal for Numerical Methods in Engineering, 2001, 51(3): 293-313.
 
2).Jack Chessa, Ted Belytschko. Extended Finite Element and Level Set Methods for free surface and phase interface problems. 2001.
 
3).Chessa J, Belytschko T. An enriched finite element method and level sets for axisymmetric two‐phase flow with surface tension[J]. International Journal for Numerical Methods in Engineering, 2003, 58(13): 2041-2064.
 
4).Wagner G J, Ghosal S, Liu W K. Particulate flow simulations using lubrication theory solution enrichment[J]. International Journal for Numerical Methods in Engineering, 2003, 56(9): 1261-1289.
 
5).Chessa J, Belytschko T. An extended finite element method for two-phase fluids[J]. Journal of Applied Mechanics, 2003, 70(1): 10-17.
 
6).Legay A, Chessa J, Belytschko T. An Eulerian–Lagrangian method for fluid–structure interaction based on level sets[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(17): 2070-2087.
 
7).Marchandise E, Remacle J F. A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows[J]. Journal of Computational Physics, 2006, 219(2): 780-800.
 
8).Groß S, Reusken A. An extended pressure finite element space for two-phase incompressible flows with surface tension[J]. Journal of Computational Physics, 2007, 224(1): 40-58.
 
9).Cirak F, Deiterding R, Mauch S P. Large-scale fluid–structure interaction simulation of viscoplastic and fracturing thin-shells subjected to shocks and detonations[J]. Computers & Structures, 2007, 85(11): 1049-1065.
 
10).Zhang L T, Gay M. Immersed finite element method for fluid-structure interactions[J]. Journal of Fluids and Structures, 2007, 23(6): 839-857.
 
11).Gerstenberger A, Wall W A. An extended finite element method/Lagrange multiplier based approach for fluid–structure interaction[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(19): 1699-1714.
 
12).Zilian A, Legay A. The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction[J]. International Journal for Numerical Methods in Engineering, 2008, 75(3): 305-334.
 
13).Dolbow J, Mosso S, Robbins J, et al. Coupling volume-of-fluid based interface reconstructions with the extended finite element method[J]. Computer methods in applied mechanics and engineering, 2008, 197(5): 439-447.
 
14).Tezaur R, Zhang L, Farhat C. A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(19): 1680-1698.
 
15).Fries T P. The intrinsic XFEM for two‐fluid flows[J]. International Journal for Numerical Methods in Fluids, 2009, 60(4): 437-471.
 
16).Van der Bos F, Gravemeier V. Numerical simulation of premixed combustion using an enriched finite element method[J]. Journal of Computational Physics, 2009, 228(10): 3605-3624.
 
17).Mayer U M, Gerstenberger A, Wall W A. Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction[J]. International journal for numerical methods in engineering, 2009, 79(7): 846-869.
 
18).Zlotnik S, Díez P. Hierarchical X-FEM for n-phase flow (n> 2)[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(30): 2329-2338.
 
19).Sauerland H, Fries T P. Free-surface flows with the XFEM: A comparison with interface tracking in the classical FEM[J]. 2009.
 
20).Zilian A, Netuzhylov H. Hybridized enriched space–time finite element method for analysis of thin-walled structures immersed in generalized Newtonian fluids[J]. Computers & structures, 2010, 88(21): 1265-1277.
 
21).Bertakis E, Groß S, Grande J, et al. Validated simulation of droplet sedimentation with finite-element and level-set methods[J]. Chemical Engineering Science, 2010, 65(6): 2037-2051.
 
22).Zhou J M, Qi L H. Treatment of discontinuous interface in liquid-solid forming with extended finite element method[J]. Transactions of Nonferrous Metals Society of China, 2010, 20: s911-s915.
 
23).Gracie R, Craig J R. Modelling well leakage in multilayer aquifer systems using the extended finite element method[J]. Finite Elements in Analysis and Design, 2010, 46(6): 504-513.
 
24).Rabczuk T, Gracie R, Song J H, et al. Immersed particle method for fluid-structure interaction[J]. International Journal for Numerical Methods in Engineering, 2010, 22(1): 48.
 
25).Ausas R F, Sousa F S, Buscaglia G C. An improved finite element space for discontinuous pressures[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(17): 1019-1031.
 
26).Choi Y J, Hulsen M A, Meijer H E H. An extended finite element method for the simulation of particulate viscoelastic flows[J]. Journal of Non-Newtonian Fluid Mechanics, 2010, 165(11): 607-624.
 
27).Esser P, Grande J, Reusken A. An extended finite element method applied to levitated droplet problems[J]. International journal for numerical methods in engineering, 2010, 84(7): 757-773.
 
28).Noble D R, Newren E P, Lechman J B. A conformal decomposition finite element method for modeling stationary fluid interface problems[J]. International Journal for Numerical Methods in Fluids, 2010, 63(6): 725-742.
 
29).Sauerland H, Fries T P. 3D two-phase flow simulations with the extended finite element method (XFEM)[C]. V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, J. C. F. Pereira and A. Sequeira (Eds), Lisbon, Portugal,14-17 June 2010
 
30).Mayer U M, Popp A, Gerstenberger A, et al. 3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach[J]. Computational Mechanics, 2010, 46(1): 53-67.
 
31).Shahmiri S, Gerstenberger A, Wall W A. An XFEM‐based embedding mesh technique for incompressible viscous flows[J]. International Journal for Numerical Methods in Fluids, 2011, 65(1‐3): 166-190.
 
32).Baltussen M, Choi Y J, Hulsen M A, et al. Weakly-imposed Dirichlet boundary conditions for non-Newtonian fluid flow[J]. Journal of Non-Newtonian Fluid Mechanics, 2011, 166(17): 993-1003.
 
33).Sauerland H, Fries T P. The extended finite element method for two-phase and free-surface flows: a systematic study[J]. Journal of Computational Physics, 2011, 230(9): 3369-3390.
 
34).Rasthofer U, Henke F, Wall W A, et al. An extended residual-based variational multiscale method for two-phase flow including surface tension[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(21): 1866-1876.
 
35).Craig J R, Gracie R. Using the extended finite element method for simulation of transient well leakage in multilayer aquifers[J]. Advances in Water Resources, 2011, 34(9): 1207-1214.
 
36).Kalashnikova I, Tezaur R, Farhat C. A discontinuous enrichment method for variable‐coefficient advection–diffusion at high Péclet number[J]. International Journal for Numerical Methods in Engineering, 2011, 87(1‐5): 309-335.
 
37).Juhnke D, Tobiska L. A local projection type stabilization with exponential enrichments applied to one-dimensional advection–diffusion equations[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 201: 179-190.
 
38).Cheng K W, Fries T P. XFEM with hanging nodes for two-phase incompressible flow[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 290-312.
 
39).Sousa F S, Ausas R F, Buscaglia G C. Numerical assessment of stability of interface discontinuous finite element pressure spaces[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 63-74.
 
40).Bernauer M K, Herzog R. Implementation of an X-FEM solver for the classical two-phase Stefan problem[J]. Journal of Scientific Computing, 2012, 52(2): 271-293.
 
41).Sauerland H, Fries T P. The stable XFEM for two-phase flows[J]. Computers & Fluids, 2013, 87: 41-49.
 
42).Legay A. An extended finite element method approach for structural‐acoustic problems involving immersed structures at arbitrary positions[J]. International Journal for Numerical Methods in Engineering, 2013, 93(4): 376-399.
 
43).Mohammadnejad T, Khoei A R. An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies[J]. Computational Mechanics, 2013, 51(3): 327-345.
 
44).Diez P, Cottereau R, Zlotnik S. A stable extended FEM formulation for multi‐phase problems enforcing the accuracy of the fluxes through Lagrange multipliers[J]. International Journal for Numerical Methods in Engineering, 2013, 96(5): 303-322.
 
45).Shadi Mohamed M, Seaid M, Trevelyan J, et al. A partition of unity FEM for time‐dependent diffusion problems using multiple enrichment functions[J]. International Journal for Numerical Methods in Engineering, 2013, 93(3): 245-265.
 
46).Schott B, Wall W A. A new face-oriented stabilized XFEM approach for 2D and 3D incompressible Navier–Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering, 2014, 276: 233-265.
 
47).Park J M, Hulsen M A, Anderson P D. An extended finite element method for a diffuse-interface model[J]. Journal of Computational and Applied Mathematics, 2014, 272: 25-40.
 
48).Shao Q, Fernández-González R, Mikdam A, et al. Influence of heat transfer and fluid flow on crack growth in multilayered porous/dense materials using XFEM: Application to Solid Oxide Fuel Cell like material design[J]. International Journal of Solids and Structures, 2014, 51(21): 3557-3569.
 
49).Legay A. The extended finite element method combined with a modal synthesis approach for vibro‐acoustic problems[J]. International Journal for Numerical Methods in Engineering, 2015, 101(5): 329-350.
 
50).Cattaneo L, Formaggia L, Iori G F, et al. Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces[J]. Calcolo, 2015, 52(2): 123-152.
 
51).Foucard L C, Vernerey F J. An X‐FEM‐based numerical–asymptotic expansion for simulating a Stokes flow near a sharp corner[J]. International Journal for Numerical Methods in Engineering, 2015, 102(2): 79-98.
 
52).Ladubec C, Gracie R, Craig J. An extended finite element method model for carbon sequestration[J]. International Journal for Numerical Methods in Engineering, 2015, 102(3-4): 316-331.
 
53).Kamran K, Rossi R, Oñate E. A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 294: 1-18.
 
54).Wang K G, Lea P, Farhat C. A computational framework for the simulation of high‐speed multi‐material fluid–structure interaction problems with dynamic fracture[J]. International Journal for Numerical Methods in Engineering, 2015, 104(7): 585-623.
 
55). N.O. Jaensson, M.A. Hulsen, P.D. Anderson. A comparison between the XFEM and a boundary-fitted mesh method for the simulation of rigid particles in Cahn–Hilliard fluids. Computers and Fluids 148 (2017) 121–136.
 
 
43.GFEM
 
1).Duarte C A, Babuška I, Oden J T. Generalized finite element methods for three-dimensional structural mechanics problems[J]. Computers & Structures, 2000, 77(2): 215-232.
 
2).Strouboulis T, Babuška I, Copps K. The design and analysis of the generalized finite element method[J]. Computer methods in applied mechanics and engineering, 2000, 181(1): 43-69.
 
3).Strouboulis T, Copps K, Babuska I. The generalized finite element method: an example of its implementation and illustration of its performance[J]. International Journal for Numerical Methods in Engineering, 2000, 47(8): 1401-1417.
 
4).Duarte C A, Hamzeh O N, Liszka T J, et al. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(15): 2227-2262.
 
5).Strouboulis T, Copps K, Babuška I. The generalized finite element method[J]. Computer methods in applied mechanics and engineering, 2001, 190(32): 4081-4193.
 
6).Babuška I, Banerjee U, Osborn J E. On principles for the selection of shape functions for the generalized finite element method[J]. Computer methods in applied mechanics and engineering, 2002, 191(49): 5595-5629.
 
7).Duarte C A, Babuška I. Mesh‐independent p‐orthotropic enrichment using the generalized finite element method[J]. International Journal for Numerical Methods in Engineering, 2002, 55(12): 1477-1492.
 
8).Plaks A, Tsukerman I, Friedman G, et al. Generalized finite-element method for magnetized nanoparticles[J]. IEEE transactions on magnetics, 2003, 39(3): 1436-1439.
 
9).Strouboulis T, Zhang L, Babuška I. Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28): 3109-3161.
 
10).彭自强, 李小凯, 葛修润. 广义有限元法对动态裂纹扩展的数值模拟[J]. 岩石力学与工程学报, 2004, 23(18): 3132-3137.
 
11).Babuška I, Banerjee U, Osborn J E. Generalized finite element methods—main ideas, results and perspective[J]. International Journal of Computational Methods, 2004, 1(01): 67-103.
 
12).Barros F B, Proenca S P B, de Barcellos C S. Generalized finite element method in structural nonlinear analysis–a p-adaptive strategy[J]. Computational Mechanics, 2004, 33(2): 95-107.
 
13).Barros F B, Proença S P B, de Barcellos C S. On error estimator and p‐adaptivity in the generalized finite element method[J]. International journal for numerical methods in engineering, 2004, 60(14): 2373-2398.
 
14).Strouboulis T, Zhang L, Babuška I. p‐version of the generalized FEM using mesh‐based handbooks with applications to multiscale problems[J]. International Journal for Numerical Methods in Engineering, 2004, 60(10): 1639-1672.
 
15).Mourad H M, Dolbow J, Harari I. A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces[J]. Int. J. Numer. Meth. Engng, 2006, 69: 1-21.
 
16).Simone A, Duarte C A, Van der Giessen E. A generalized finite element method for polycrystals with discontinuous grain boundaries[J]. International Journal for Numerical Methods in Engineering, 2006, 67(8): 1122-1145.
 
17).Tian R, Yagawa G, Terasaka H. Linear dependence problems of partition of unity-based generalized FEMs[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(37): 4768-4782.
 
18).Strouboulis T, Zhang L, Wang D, et al. A posteriori error estimation for generalized finite element methods[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(9): 852-879.
 
19).Strouboulis T, Babuška I, Hidajat R. The generalized finite element method for Helmholtz equation: theory, computation, and open problems[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(37): 4711-4731.
 
20).Duarte C A, Kim D J, Babuška I. A global-local approach for the construction of enrichment functions for the generalized FEM and its application to three-dimensional cracks[M]//Advances in meshfree techniques. Springer Netherlands, 2007: 1-26.
 
21).Duarte C A, Liszka T J, Tworzydlo W W. Clustered generalized finite element methods for mesh unrefinement, non‐matching and invalid meshes[J]. International journal for numerical methods in engineering, 2007, 69(11): 2409-2440.
 
22).Strouboulis T, Zhang L, Babuška I. Assessment of the cost and accuracy of the generalized FEM[J]. International journal for numerical methods in engineering, 2007, 69(2): 250-283.
 
23).Srinivasan K R, Matouš K, Geubelle P H. Generalized finite element method for modeling nearly incompressible bimaterial hyperelastic solids[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(51): 4882-4893.
 
24).Strouboulis T, Hidajat R, Babuška I. The generalized finite element method for Helmholtz equation. Part II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(5): 364-380.
 
25).Babuška I, Nistor V, Tarfulea N. Generalized finite element method for second-order elliptic operators with Dirichlet boundary conditions[J]. Journal of Computational and Applied Mathematics, 2008, 218(1): 175-183.
 
26).Aquino W, Brigham J C, Earls C J, et al. Generalized finite element method using proper orthogonal decomposition[J]. International Journal for Numerical Methods in Engineering, 2009, 79(7): 887-906.
 
27).Pereira J P, Duarte C A, Guoy D, et al. hp‐Generalized FEM and crack surface representation for non‐planar 3‐D cracks[J]. International Journal for Numerical Methods in Engineering, 2009, 77(5): 601-633.
 
28).Park K, Pereira J P, Duarte C A, et al. Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems[J]. International Journal for Numerical Methods in Engineering, 2009, 78(10): 1220-1257.
 
29).Payre G M J. Consistency conditions for the influence graphs generalized finite difference method[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(33): 2565-2575.
 
30).Pereira J P, Duarte C A, Jiao X. Three-dimensional crack growth with hp-generalized finite element and face offsetting methods[J]. Computational Mechanics, 2010, 46(3): 431-453.
 
31).Benson D J, Bazilevs Y, De Luycker E, et al. A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM[J]. International Journal for Numerical Methods in Engineering, 2010, 83(6): 765-785.
 
32).Pereira J P, Duarte C A, Jiao X. Three-dimensional crack growth with hp-generalized finite element and face offsetting methods[J]. Computational Mechanics, 2010, 46(3): 431-453.
 
33).Aragón A M, Duarte C A, Geubelle P H. Generalized finite element enrichment functions for discontinuous gradient fields[J]. International Journal for Numerical Methods in Engineering, 2010, 82(2): 242-268.
 
34).Dias-da-Costa D, Alfaiate J, Sluys L J, et al. A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements[J]. International journal of fracture, 2010, 161(1): 97-119.
 
35).Kim D J, Pereira J P, Duarte C A. Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes[J]. International Journal for Numerical Methods in Engineering, 2010, 81(3): 335-365.
 
36).Paulo de Tarso R M, De Barcellos C S, Torres D A F. Analysis of anisotropic Mindlin plate model by continuous and non-continuous GFEM[J]. Finite elements in Analysis and Design, 2011, 47(7): 698-717.
 
37).Gupta V, Kim D J, Duarte C A. Analysis and improvements of global–local enrichments for the generalized finite element method[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 47-62.
 
38).Soghrati S, Geubelle P H. A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 217: 46-57.
 
39).Kim D J, Duarte C A, Proença S P. A generalized finite element method with global-local enrichment functions for confined plasticity problems[J]. Computational Mechanics, 2012, 50(5): 563-578.
 
40).Soghrati S, Aragón A M, Armando Duarte C, et al. An interface‐enriched generalized FEM for problems with discontinuous gradient fields[J]. International Journal for Numerical Methods in Engineering, 2012, 89(8): 991-1008.
 
41).Babuška I, Banerjee U. Stable generalized finite element method (SGFEM)[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 201: 91-111.
 
42).Ebrahimi S H, Mohammadi S, Kani I M. A local PUFEM modeling of stress singularity in sliding contact with minimal enrichment for direct evaluation of generalized stress intensity factors[J]. Engineering Fracture Mechanics, 2013, 105: 16-40.
 
43).Tian R. Extra-dof-free and linearly independent enrichments in GFEM[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 266: 1-22.
 
44).Gupta V, Duarte C A, Babuška I, et al. A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 266: 23-39.
 
45).Garzon J, O'Hara P, Duarte C A, et al. Improvements of explicit crack surface representation and update within the generalized finite element method with application to three‐dimensional crack coalescence[J]. International Journal for Numerical Methods in Engineering, 2014, 97(4): 231-273.
 
46).Meschke G, Leonhart D. A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 290: 438-465.
 
47).Soghrati S, Duarte C A, Geubelle P H. An adaptive interface‐enriched generalized FEM for the treatment of problems with curved interfaces[J]. International Journal for Numerical Methods in Engineering, 2015, 102(6): 1352-1370.
 
48).Gupta V, Duarte C A, Babuška I, et al. Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 289: 355-386.
 
49).Sillem A, Simone A, Sluys L J. The Orthonormalized Generalized Finite Element Method–OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 112-149.
 
50). M. Komijani, R. Gracie. An enriched finite element model for wave propagation in fractured media. Finite Elements in Analysis and Design 125 (2017) 14–23.
 
51). J. Garzon, V. Gupta, A. Simone, C.A. Duarte. Bridging Scales with a Generalized Finite Element Method. Procedia IUTAM 3 ( 2012 ) 172 – 191.
 
52). M. Malagu`, E. Benvenuti, C.A. Duarte, A. Simone.One-dimensional nonlocal and gradient elasticity: Assessment of high order approximation schemes. Comput. Methods Appl. Mech. Engrg. 275 (2014) 138–158.
 
53). J. Kim1, A. Simone, and C. A. Duarte.Mesh refinement strategies without mapping of non-linear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures. Int. J. Numer. Meth. Engng 2015; 00:1–26.
 
54). Dorival Piedade Neto, Sergio Persival Baroncini Proenca, (2016) "Generalized Finite Element Method in linear and nonlinear structural dynamic analyses", Engineering Computations, Vol. 33 Issue: 3, pp.806-830..
 
55). Seyed Abolfazl Hosseini, Naser Vosoughi. Development of two-dimensional, multigroup neutron diffusion computer code based on GFEM with unstructured triangle elements. Annals of Nuclear Energy 51 (2013) 213–226.
 
56). P. O’Hara,J. Hollkamp,C. A. Duarte,T. Eason. A two-scale generalized finite element method for fatigue crack propagation simulations utilizing a fixed, coarse hexahedral mesh. Comput Mech (2016) 57:55–74.
 
 
44.Thesis & report
 
1).Dolbow J E. An extended finite element method with discontinuous enrichment for applied mechanics. Northwestern university, 1999.
 
2).Wells G N. Discontinuous modelling of strain localisation and failure. Delft University of Technology, 2001.
 
3).Stéphane Bordas. An extended finite element method for elastic and elastic-plastic cracks in complex components. Northwestern university, 2001.
 
4).Stéphane Bordas. Extended finite element and level set methods with applications to growth of cracks and biofilms. Northwestern university, 2003.
 
5).NGUYEN VINH PHU. An object-oriented approach to the extended finite element method with applications to fracture mechanics. M. Sc. Thesis, Dep’t of Mech. Eng., Hochiminh City Univ. of Tech, 2005.
 
6).Mergheim J. Computational modeling of strong and weak discontinuities. Techn. Univ., Lehrstuhl für Techn. Kaiserslautern, März 2006
 
7).Jesper L. Asferg. Modleing of Concrete Fracture Applying the eXtended Finite Element Method. Technical University of Denmark, 2006.
 
8).Geniaut S. Approche X-FEM pour la fissuration sous contact des structures industrielles. École Centrale de Nantes, 2006.
 
9).Truong Quang Tri. Extended Finite Element Method for multi-material fracture mechanics. Hochiminh City University of Technology, 2006.
 
10).David NOËL. Crack simulation with eXtended Finite Element Methods. University of Glasgrow, 2008.
 
11).Bryan G. Smith. The Extended Finite Element Method for Special Problems with Moving Interfaces. Northwestern university, 2008.
 
12).Song J H. Computations of the dynamic fracture of quasi-brittle plane and shell structures by the extended finite element method. Northwestern university, 2008.
 
13).Lara Vigneron. FEM/XFEM-Based modeling of brain shift, resection, and retraction for image-guided surgery. UNIVERSITÉ DE LIÈGE, 2009.
 
14).Awais Ahmed. Extended finite element method (XFEM)-modeling arbitrary discontinuities and failure analysis. Istituto Universitario di Studi Superiori di Pavia, Università degli Studi di Pavia, 2009.
 
15).Michael James McNary. Implementation of the extended finite element method (XFEM) in the abaqus software package. Georgia Institute of Technology, 2009.
 
16).Taleghani A D. Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures. The university of Texas, USA, 2009.
 
17).Matthew Jon Pais. Accurate integration of fatigue crack growth models through kriging and reanalysis of the extended finite element method. University of Florida, 2010.
 
18).Ethan T. Coon. Nitsche Extended Finite Element Methods for Earthquake Simulation. Columbia University, 2010.
 
19).Lim Shi Yee. Numerical Modeling of Multi-phase flow with surface tension using a level set description and X-FEM.2010.
 
20).Saeid Mojiri. Numerical Analysis of Cohesive Crack Growth Using Extended Finite Element Method (X-FEM). Ecole Centrale de Nantes,2010.
 
21).Hannes Schumann. A two-phase navier-stokes flow with surface tension modeled in X-FEM. Universitat Politècnica de catalunya, Barcelona Swansea university, Swansea, 2010.
 
22).Young Joon Choi. Modeling particulate complex flows using XFEM. Technische Universiteit Eindhoven, 2011.
 
23).Menk A. Simulation of complex microstructural geometries using X-FEM and the application to solder joint lifetime prediction. University of Glasgow, 2011.
 
24).Pais M J. Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis. University of Florida, 2011.
 
25).Estruch i Tena C. DG-XFEM formulation for the unsteady incompressible Navier-Stokes equations. Universitat Politècnica de catalunya, Barcelona, 2011.
 
26).Villanueva C H, Yu Kai. A complete methodology for the implementation of XFEM inclusive models. University of Colorado Boulder, 2013.
 
27).Santiago Giraldo. HIGH ORDER X-FEM: IMPROVING THE NUMERICAL INTEGRATION. école centrale de Nantes, Nantes, 2011.
 
28).HAZIZA F. The Extended Finite Element Method and Its Implementation in 2D in the Aster Code. Royal Institute of Technology, Sweden,2006.
 
29).Simon Arnesson. XFEM-Analysis and Implementation. Lund University, Sweden, 2014.
 
30).Ferdinando Auricchio. Alternativa al Metodo degli Elementi Finitinella Meccanica della Frattura: gli X-FEM. Università degli Studi di Pavia,2010-2011.
 
31).Elham Maghsoudi. Multi-phase Navier-Stokes FE solver with level set description and XFEM.Universitat Politècnica de Catalunya & Swansea University
 
32).Reza Keshavarzi. Numerical Modeling of Hydraulic Fracturing Propagation in Naturally Fractured Reservoirs: Interaction between Hydraulic and Natural Fractures. Islamic Azad University, 2011.