Publications on the XFEM

We have gathered some of the most important publications on the XFEM and related methods. For easier access we have sorted them into the following categories:

XFEM for cracks

1 P.M.A. Areias, T. Belytschko: Analysis of three-dimensional crack initiation and propagation using the extended finite element method, Internat. J. Numer. Methods Engrg., 63, 760–788, 2005.
2 A. Asadpoure, S. Mohammadi: Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method, Internat. J. Numer. Methods Engrg., 69, 2150–2172, 2007.
3 A.O. Ayhan, H.F. Nied: Stress intensity factors for three-dimensional surface cracks using enriched finite elements, Internat. J. Numer. Methods Engrg., 54, 899–921, 2002.
4 E. Béchet, H. Minnebo, N. Moës, B. Burgardt: Improved implementation and robustness study of the X-FEM for stress analysis around cracks, Internat. J. Numer. Methods Engrg., 64, 1033–1056, 2005.
5 T. Belytschko, T. Black: Elastic crack growth in finite elements with minimal remeshing, Internat. J. Numer. Methods Engrg., 45, 601–620, 1999.
6 T. Belytschko, N. Moës, S. Usui, C. Parimi: Arbitrary discontinuities in finite elements, Internat. J. Numer. Methods Engrg., 50, 993–1013, 2001.
7 T. Belytschko, H. Chen, J. Xu, G. Zi: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, Internat. J. Numer. Methods Engrg., 58, 1873–1905, 2003.
8 É. Budyn, G. Zi, N. Moës, T. Belytschko: A method for multiple crack growth in brittle materials without remeshing, Internat. J. Numer. Methods Engrg., 61, 1741–1770, 2004.
9 E. Chahine, P. Laborde, Y. Renard: Crack tip enrichment in the XFEM using a cutoff function, Internat. J. Numer. Methods Engrg., DOI: 10.1002/nme.2265, 2008.
10 D.L. Chopp, N. Sukumar: Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method, Int. J. Engrg. Sci., 41, 845–869, 2003.
11 C. Comi, S. Mariani: Extended finite element simulation of quasi-brittle fracture in functionally graded materials, Comp. Methods Appl. Mech. Engrg., 196, 4013–4026, 2007.
12 C. Daux, N. Moës, J. Dolbow, N. Sukumar, T. Belytschko: Arbitrary branched and intersecting cracks with the extended finite element method, Internat. J. Numer. Methods Engrg., 48, 1741–1760, 2000.
13 J. Dolbow, N. Moës, T. Belytschko: Discontinuous enrichment in finite elements with a partition of unity method, Finite Elem. Anal. Des., 36, 235–260, 2000.
14 J. Dolbow, N. Moës, T. Belytschko: An extended finite element method for modeling crack growth with frictional contact, Comp. Methods Appl. Mech. Engrg., 190, 6825–6846, 2001.
15 M. Duflot: The extended finite element method in thermoelastic fracture mechanics, Internat. J. Numer. Methods Engrg., 74, 827–847, 2008.
16 T. Elguedj, A. Gravouil, A. Combescure: Appropriate extended functions for X-FEM simulation of plastic fracture mechanics, Comp. Methods Appl. Mech. Engrg., 195, 501–515, 2006.
17 A. Gravouil, N. Moës, T. Belytschko : Non-planar 3D crack growth by the extended finite element and level sets, part II: level set update, Internat. J. Numer. Methods Engrg., 53, 2569–2586, 2002.
18 P.A. Guidault, O. Allix, L. Champaney, C. Cornuault: A multiscale extended finite element method for crack propagation, Comp. Methods Appl. Mech. Engrg., 197, 381–399, 2008.
19 T. Hettich, E. Ramm: Interface material failure modeled by the extended finite-element method and level sets, Comp. Methods Appl. Mech. Engrg., 195, 4753–4767, 2006.
20 T. Hettich, A. Hund, E. Ramm: Modeling of failure in composites by X-FEM and level sets within a multiscale framework, Comp. Methods Appl. Mech. Engrg., 197, 414–424, 2008.
21 P.R. Heyliger, R.D. Kriz: Stress intensity factors by enriched mixed finite elements, Internat. J. Numer. Methods Engrg., 28, 1461–1473, 1989.
22 R. Huang, N. Sukumar, J.H. Prévost: Modeling quasi-static crack growth with the extended finite element method, part II: numerical applications, J. Solids Struct., 40, 7539–7552, 2003.
23 R. Larsson, M. Fagerström: A framework for fracture modelling based on the material forces concept with XFEM kinematics, Internat. J. Numer. Methods Engrg., 62, 1763–1788, 2005.
24 S.H. Lee, J.H. Song, Y.C. Yoon, G. Zi, T. Belytschko: Combined extended and superimposed finite element method for cracks, Internat. J. Numer. Methods Engrg., 59, 1119–1136, 2004.
25 G. Legrain, N. Moës, E. Verron: Stress analysis around crack tips in finite strain problems using the eXtended finite element method, Internat. J. Numer. Methods Engrg., 63, 290–314, 2005.
26 S. Li, S. Ghosh: Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials, Internat. J. Numer. Methods Engrg., 65, 1028–1067, 2006.
27 X.Y. Liu, Q.Z. Xiao, B.L. Karihaloo: XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, Internat. J. Numer. Methods Engrg., 59, 1103–1118, 2004.
28 S. Mariani, U. Perego: Extended finite element method for quasi-brittle fracture, Internat. J. Numer. Methods Engrg., 58, 103–126, 2003.
29 P.M. Mariano, F.L. Stazi: Strain localization due to crack-microcrack interactions: X-FEM for a multifield approach, Comp. Methods Appl. Mech. Engrg., 193, 5035–5062, 2004.
30 G. Meschke, P. Dumstorff: Energy-based modeling of cohesive and cohesionless cracks via X-FEM, Comp. Methods Appl. Mech. Engrg., 196, 2338–2357, 2007.
31 N. Moës, J. Dolbow, T. Belytschko: A finite element method for crack growth without remeshing, Internat. J. Numer. Methods Engrg., 46, 131–150, 1999.
32 N. Moës , A. Gravouil, T. Belytschko : Non-planar 3D crack growth by the extended finite element and level sets, part I: mechanical model, Internat. J. Numer. Methods Engrg., 53, 2549–2568, 2002.
33 I. Nistor, O. Pantalé, S. Caperaa: Numerical implementation of the eXtended finite element method for dynamic crack analysis, Adv. Eng. Softw, DOI: 10.1016/j.advengsoft.2007.06.003, 2007.
34 D. Rabinovich, D. Givoli, S. Vigdergauz: XFEM-based crack detection scheme using a genetic algorithm, Internat. J. Numer. Methods Engrg., 71, 1051–1080, 2007.
35 J. Réthoré, A. Gravouil, A. Combescure: An energy-conserving scheme for dynamic crack growth using the eXtended finite element method, Internat. J. Numer. Methods Engrg., 63, 631–659, 2005.
36 M. Stolarska, D.L. Chopp, N. Moës, T. Belytschko: Modelling crack growth by level sets in the extended finite element method, Internat. J. Numer. Methods Engrg., 51, 943–960, 2001.
37 M. Stolarska, D.L. Chopp: Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method, Int. J. Engrg. Sci., 41, 2381–2410, 2003.
38 N. Sukumar, N. Moës, B. Moran, T. Belytschko: Extended finite element method for three-dimensional crack modelling, Internat. J. Numer. Methods Engrg., 48, 1549–1570, 2000.
39 N. Sukumar, D.L. Chopp, B. Moran: Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, Eng. Fract. Mech., 70, 29–48, 2003.
40 N. Sukumar, D.J. Srolovitz, T.J. Baker, J.H. Prévost: Brittle fracture in polycrystalline microstructures with the extended finite element method, Internat. J. Numer. Methods Engrg., 56, 2015–2037, 2003.
41 N. Sukumar, J.H. Prévost: Modeling quasi-static crack growth with the extended finite element method, part I: computer implementation, J. Solids Struct., 40, 7513–7537, 2003.
42 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, Internat. J. Numer. Methods Engrg., DOI: 10.1002/nme.2344, 2008.
43 Q.Z. Xiao, B.L. Karihaloo: Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery, Internat. J. Numer. Methods Engrg., 66, 1378–1410, 2006.
44 Q.Z. Xiao, B.L. Karihaloo, X.Y. Liu: Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM, Internat. J. Numer. Methods Engrg., 69, 2606–2635, 2007.
45 Q.Z. Xiao, B.L. Karihaloo: Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM, Comp. Methods Appl. Mech. Engrg., 196, 1864–1873, 2007.
46 G. Zi, T. Belytschko: New crack-tip elements for XFEM and applications to cohesive cracks, Internat. J. Numer. Methods Engrg., 57, 2221–2240, 2003.

Thomas-Peter Fries (fries@tugraz.at)