zbMATH — the first resource for mathematics

An extended finite element method for modeling crack growth with frictional contact. (English) Zbl 1033.74042
The authors propose a new technique for finite element modeling of crack growth with frictional contact on crack faces. The extended finite element method is used to discretize the equations. Because the geometry of cracks is independent of the finite element mesh, no remeshing of the domain is required to model the crack growth. The frictional contact conditions are formulated as a non-smooth constitutive law on crack faces. An iterative scheme is implemented in the LATIN method. Several benchmark problems are solved in order to illustrate the robustness of the method and to examine the convergence. The results are compared to analytical and experimental results.

74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
Full Text: DOI
[1] Alart, P.; Curnier, A., A mixed formulation for frictional contact problems prone to Newton-like solution methods, Comput. methods appl. mech. engrg., 92, 353-375, (1991) · Zbl 0825.76353
[2] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. numer. methods engrg., 45, 5, 601-620, (1999) · Zbl 0943.74061
[3] L. Champaney, Une nouvelle approche modulaire pour l’analyse d’assemblages de structures tridimensionnelles, Ph.D. Thesis, Ecole Normale Superieure de Cachan, 1996
[4] Champaney, L.; Cognard, J.; Dureisseix, D.; Ladevèze, P., Large scale applications on parallel computers of a mixed domain decomposition method, Comput. mech., 19, 253-263, (1997) · Zbl 0894.73211
[5] Cotterell, B., Brittle fracture in compression, Int. J. fract. mech., 8, 2, 195-208, (1972)
[6] Daux, C.; Moës, N.; Dolbow, J.; Sukumar, N.; Belytschko, T., Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. numer. methods engrg., 48, 1741-1760, (2000) · Zbl 0989.74066
[7] J. Dolbow, An extended finite element method with discontinuous enrichment for applied mechanics, Ph.D. thesis, Northwestern University, USA, 1999
[8] Dolbow, J.; Moës, N.; Belytschko, T., Discontinuous enrichment in finite elements with a partition of unity method, Finite elements anal. des., 36, 235-260, (2000) · Zbl 0981.74057
[9] Duarte, C.A.; Hamzeh, O.N.; Liszka, T.J.; Tworzydlo, W.W., A generalized finite element method for the simulation of three-dimensional dynamic crack propagation, Comput. methods appl. mech. engrg., 190, 2227-2262, (2001) · Zbl 1047.74056
[10] Erdogan, F.; Sih, G., On the crack extension in plates under plane loading and transverse shear, J. basic engrg., 85, 519-527, (1963)
[11] J. Fish, Finite element method for localization analysis, Ph.D. thesis, Northwestern University, USA, 1989
[12] Fleming, M.Y.; Chu, A.; Moran, B.; Belytschko, T., Enriched element-free Galerkin methods for singular fields, Int. J. numer. methods engrg., 40, 1483-1504, (1997)
[13] Hoek, E.; Bieniawski, Z.T., Brittle fracture propagation in rock under compression, Int. J. fract. mech., 1, 139-155, (1965)
[14] Ingraffea, A.R.; Heuze, F.E., Finite element models for rock fracture mechanics, Int. J. numer. anal. methods geomech., 4, 25-43, (1980) · Zbl 0418.73094
[15] Ladevèze, P., Nonlinear computational structural mechanics, (1998), Springer New York
[16] Laursen, Private Communication, 2000
[17] Melenk, J.M.; Babuška, I., The partition of unity finite element method: basic theory and applications, Comput. methods appl. mech. engrg., 39, 289-314, (1996) · Zbl 0881.65099
[18] Moës, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Int. J. numer. methods engrg., 46, 131-150, (1999) · Zbl 0955.74066
[19] Nemat-Nasser, S.; Horii, H., Compression-induced nonplanar crack extension with application to splitting, exfoliation and rockburst, J. geophys. res., 87, B8, 6805-6821, (1982)
[20] Rashid, M.M., The arbitrary local mesh refinement method: an alternative to remeshing for crack propagation analysis, Comput. methods appl. mech. engrg., 154, 133-150, (1998) · Zbl 0939.74071
[21] Shih, C.; Asaro, R., Elastic – plastic analysis of cracks on bimaterial interfaces: part I - small scale yielding, J. appl. mech., 55, 299-316, (1988)
[22] Simo, J.; Laursen, T., An augmented Lagrangian treatment of contact problems involving friction, Comput. struct., 42, 97-116, (1992) · Zbl 0755.73085
[23] Simo, J.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by softening solutions in rate-independent solids, J. comput. mech., 12, 277-296, (1993) · Zbl 0783.73024
[24] Sumi, Y., Computational crack path prediction, Theoret. appl. fract. mech., 4, 149-156, (1985)
[25] Yau, J.; Wang, S.; Corten, H., A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity, J. appl. mech., 47, 335-341, (1980) · Zbl 0463.73103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.