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Interface material failure modeled by the extended finite-element method and level sets. (English) Zbl 1154.74386
Summary: Multi-phase materials are characterized by the fact that they possess a specific heterogeneous microstructure. This feature often necessitates complex formulations in order to obtain realistic mechanical behavior with macroscopic material models. Furthermore, such complex models cause substantial difficulties when the corresponding material parameters need to be identified and their physical meaning interpreted. In multiscale analyses, usually the microstructure of a material point is resolved directly. Thus, the material behavior at the material point can be modeled in an elegant, natural and simple way. The present contribution aims at a detailed geometric modeling of multi-phase materials, as well as at a local mechanical modeling of material interfaces and interfacial failure. The geometry of the material distribution within the microstructure is described through level set functions. The mechanical modeling of material interfaces and interfacial cracks is accomplished by the extended finite-element method (X-FEM). The combination of both, the level set method and the X-FEM, allows one to model such internal features of the microstructure without the adaptation of the mesh. Thus, expensive meshing procedures can be avoided and considerable flexibility is obtained with respect to the variation of the material design. In the X-FEM, the finite-element approximation is enriched by appropriate functions through the concept of partition of unity. Remarkably, the level set method cannot only be applied to describe the geometry of the material interfaces and cracks, respectively, but also to support and even to develop the corresponding enrichment function.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74R10 Brittle fracture
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[1] Osher, S.; Sethian, J., Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. comput. phys., 79, 12-49, (1988) · Zbl 0659.65132
[2] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Int. J. numer. methods engrg., 45, 601-620, (1999) · Zbl 0943.74061
[3] Babuška, J.; Melenk, J., The partition of unity method, Int. J. numer. methods engrg., 40, 727-758, (1997) · Zbl 0949.65117
[4] Schellekens, J.; de Borst, R., On the numerical integration of interface elements, Int. J. numer. methods engrg., 36, 43-66, (1993) · Zbl 0825.73840
[5] Simone, A., Partition of unity-based discontinuous elements for interface phenomena: computational issues, Commun. numer. methods engrg., 20, 465-478, (2004) · Zbl 1058.74082
[6] Karihaloo, B.; Xiao, Q., Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review, Comput. struct., 81, 119-129, (2003)
[7] 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
[8] 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
[9] Nagashima, T.; Omoto, Y.; Tani, S., Stress intensity factor analysis of interface cracks using X-FEM, Int. J. numer. methods engrg., 56, 1151-1173, (2003) · Zbl 1078.74662
[10] Liu, X.; Xiao, Q.; Karihaloo, B., XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, Int. J. numer. methods engrg., 59, 1103-1118, (2004) · Zbl 1041.74543
[11] Sukumar, N.; Huang, Z.; Prévost, J.-H.; Suo, Z., Partition of unity enrichment for bimaterial interface cracks, Int. J. numer. methods engrg., 59, 1075-1102, (2004) · Zbl 1041.74548
[12] Wells, G.; Sluys, L., A new method for modelling cohesive cracks using finite elements, Int. J. numer. methods engrg., 50, 2667-2682, (2001) · Zbl 1013.74074
[13] Moës, N.; Belytschko, T., Extended finite element method for cohesive crack growth, Engrg. fract. mech., 69, 813-833, (2002)
[14] Krongauz, Y.; Belytschko, T., EFG approximation with discontinuous derivatives, Int. J. numer. methods engrg., 41, 1215-1233, (1998) · Zbl 0906.73063
[15] Belytschko, T.; Moës, N.; Usui, S.; Parimi, C., Arbitrary discontinuities in finite elements, Int. J. numer. methods engrg., 50, 993-1013, (2001) · Zbl 0981.74062
[16] Sukumar, N.; Chopp, D.; Moës, N.; Belytschko, T., Modeling holes and inclusions by level sets in the extended finite element method, Comput. methods appl. mech. engrg., 190, 6183-6200, (2001) · Zbl 1029.74049
[17] Belytschko, T.; Parimi, C.; Moës, N.; Sukumar, N.; Usui, S., Structured extended finite element methods for solids defined by implicit surfaces, Int. J. numer. methods engrg., 56, 609-635, (2003) · Zbl 1038.74041
[18] Moës, N.; Cloirec, M.; Cartraud, P.; Remacle, J.-F., A computational approach to handle complex microstructure geometries, Comput. methods appl. mech. engrg., 192, 3163-3177, (2003) · Zbl 1054.74056
[19] Osher, S.; Fedkiw, R., Level set methods and dynamic implicit surfaces, () · Zbl 1026.76001
[20] Remmers, J.; de Borst, R.; Needleman, A., A cohesive segments method for the simulation of crack growth, Comput. mech., 31, 69-77, (2003) · Zbl 1038.74679
[21] de Borst, R.; Remmers, J.; Needleman, A.; Abellan, M.-A., Discrete vs smeared crack models for concrete failure: bridging the gap, Int. J. numer. anal. meth. geomech., 28, 583-607, (2004) · Zbl 1086.74044
[22] Budyn, E.; Zi, G.; Moës, N.; Belytschko, T., A method for multiple crack growth in brittle materials without remeshing, Int. J. numer. methods engrg., 61, 1741-1770, (2004) · Zbl 1075.74638
[23] Duarte, C.; Oden, J., H-p clouds: an h-p meshless method, Numer. methods partial diff. equations, 12, 673-705, (1996) · Zbl 0869.65069
[24] Zi, G.; Belytschko, T., New crack-tip elements for XFEM and applications to cohesive cracks, Int. J. numer. methods engrg., 57, 2221-2240, (2003) · Zbl 1062.74633
[25] Wells, G.; Sluys, L., Three-dimensional embedded discontinuity model for brittle fracture, Int. J. solid struct., 38, 897-913, (2001) · Zbl 1004.74065
[26] Ortiz, M.; Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Int. J. numer. methods engrg., 44, 1267-1282, (1999) · Zbl 0932.74067
[27] Coleman, B.D.; Noll, W., The thermodynamics of elastic materials with heat conduction and viscosity, Arch. rat. mech. anal., 13, 167-178, (1963) · Zbl 0113.17802
[28] Coleman, B.D.; Gurtin, M.E., Thermodynamics with internal variables, J. chem. phys., 47, 2, 597-613, (1967)
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