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Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. (English) Zbl 1222.74041
Summary: The extended finite element method (X-FEM) was used with success in the past few years for linear elastic fracture mechanics (LEFM). In the case of elastic–plastic fracture mechanics (EPFM), this method cannot be used without adequate asymptotic solutions to enrich the shape function basis. In this paper, we propose to use the well-known Hutchinson–Rice–Rosengren (HRR) fields to represent the singularities in EPFM. The analysis we are presenting is done in the context of confined plasticity, and shall be used to predict fatigue crack growth without remeshing. A Fourier analysis of the HRR fields is done in order to extract a proper elastic–plastic enrichment basis. Several strategies of enrichment, based on the Fourier analysis results, are compared and a six-enrichment-functions basis is proposed. This new tip enrichment basis is coupled with a Newton like iteration scheme and a radial return method for plastic flow. Numerical comparisons with and without unloading of fracture parameters are made with classical finite element results and show good agreements.

74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage
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[1] Babuška, I.; Melenk, J.M., The partition of unity method, Int. J. numer. methods engrg., 40, 727-758, (1997) · Zbl 0949.65117
[2] Black, T.; Belytschko, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. numer. methods engrg., 45, 601-620, (1999) · Zbl 0943.74061
[3] Moës, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Int. J. numer. methods engrg., 46, 1, 133-150, (1999) · Zbl 0955.74066
[4] Sukumar, N.; Moës, N.; Moran, B.; Belytschko, T., Extended finite element method for three-dimensional crack modelling, Int. J. numer. methods engrg., 48, 1549-1570, (1999) · Zbl 0963.74067
[5] Huang, R.; Prévost, J.H.; Huang, Z.Y.; Suo, Z., Channel-cracking of thin films with the extended finite element method, Engrg. fracture mech., 70, 2513-2526, (2003)
[6] Mariano, P.M.; Stazi, F.L., Strain localization due to crack-microcrack interactions: X-FEM for a multified approach, Comput. methods appl. mech engrg., 193, 5035-5062, (2004) · Zbl 1112.74529
[7] Wells, G.N.; de Borst, R.; Sluys, L.J., A consistent geometrically non-linear approach for delamination, Int. J. numer. methods engrg., 54, 1333-1355, (2002) · Zbl 1086.74043
[8] Ji, H.; Chopp, D.; Dolbow, J.E., A hybrid finite element/level set method for modelling phase transformation, Int. J. numer. methods engrg., 54, 1209-1233, (2002) · Zbl 1098.76572
[9] Hutchinson, J.W., Singular behavior at the end of a tensile crack in a hardening material, J. mech. phys. solids, 16, 13-31, (1968) · Zbl 0166.20704
[10] Rice, J.R.; Rosengren, G.F., Plane strain deformation near a crack tip in a power-law hardening material, J. mech. phys. solids, 16, 1-12, (1968) · Zbl 0166.20703
[11] O’Dowd, N.P.; Shih, C.F., Family of crack-tip fields characterized by a triaxiality parameter: part I—structure of fields, J. mech. phys. solids, 39, 8, 989-1015, (1991)
[12] O’Dowd, N.P.; Shih, C.F., Family of crack-tip fields characterized by a triaxiality parameter: part II—fracture applications, J. mech. phys. solids, 40, 5, 939-963, (1992)
[13] Fleming, M.; Chu, Y.U.; Moran, B.; Belytschko, T., Enriched element-free Galerkin methods for crack tip fields, Int. J. numer. methods engrg., 40, 1483-1504, (1997)
[14] Rao, B.N.; Rahman, S., An enriched meshless method for non-linear fracture mechanics, Int. J. numer. methods engrg., 50, 197-223, (2004) · Zbl 1047.74082
[15] Pan, J., Asymptotic analysis of a crack in a power-law material under combined in-plane and out-of-plane shear loading conditions, J. mech. phys. solids, 38, 2, 133-159, (1990) · Zbl 0706.73066
[16] Pan, J.; Shih, C.F., Elastic-plastic analysis of combined mode I, II and III crack-tip fields under small-scale yielding conditions, Int. J. solids struct., 29, 22, 2795-2814, (1992) · Zbl 0793.73078
[17] G. Pluvinage, Mécanique élasto-plastique de la rupture—Critères d’amorçage, Cepadues Editions, 1989. · Zbl 0725.73066
[18] Mariani, S.; Perego, U., Extended finite element method for quasi-brittle fracture, Int. J. numer. methods engrg., 58, 103-126, (2003) · Zbl 1032.74673
[19] Duarte, C.A.; Babuška, I.; Oden, J.T., Generalized finite element methods for three-dimensional structural mechanics problems, Comput. struct., 77, 215-232, (2000)
[20] P. Laborde, J. Pommier, Y. Renard, M. Salaün, High order extended finite element method for cracked domains, Int. J. Numer. Methods Engrg., submitted. · Zbl 1181.74136
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