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A three-dimensional large deformation meshfree method for arbitrary evolving cracks. (English) Zbl 1128.74051
Summary: We describe a new approach for modelling discrete cracks in meshfree particle methods in three dimensions. The cracks can be arbitrarily oriented, but their growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack topology is needed. The crack is modelled by a local enrichment of test and trial functions with a sign function (a variant of Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centered at the particles. The method is formulated for large deformations and arbitrary nonlinear and rate-dependent materials; cohesive laws govern the traction-crack opening relations. To reduce computational cost and since more accuracy around the crack tip is needed to obtain adequate results, $h$-adaptivity is incorporated in the method. The model is applied to several three-dimensional problems, some of which are compared to experimental data.

MSC:
74S30Other numerical methods in solid mechanics
74R10Brittle fracture
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[1] Armero, F.; Garikipati, K.: An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int. J. Solids struct. 33, No. 20 -- 22, 2863-2885 (1996) · Zbl 0924.73084
[2] M. Arrea, A.R. Ingraffea, Mixed-mode crack propagation in mortar and concrete, Technical Report 81-13, Department of Structural Engineering, Cornell University Ithaka, 1982.
[3] Belytschko, T.; Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. methods engrg. 45, No. 5, 601-620 (1999) · Zbl 0943.74061
[4] Belytschko, T.; Chen, H.; Xu, J.; Zi, G.: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. methods engrg. 58, No. 12, 1873-1905 (2003) · Zbl 1032.74662
[5] Belytschko, T.; Fish, J.; Englemann, B.: A finite element method with embedded localization zones. Comput. methods appl. Mech. engrg. 70, 59-89 (1988) · Zbl 0653.73032
[6] Belytschko, T.; Guo, Y.; Liu, W. K.; Xiao, S. P.: A unified stability analysis of meshfree particle methods. Int. J. Numer. methods engrg. 48, 1359-1400 (2000) · Zbl 0972.74078
[7] Belytschko, T.; Liu, W. K.; Moran, B.: Nonlinear finite elements for continua and structures. (2000) · Zbl 0959.74001
[8] Belytschko, T.; Lu, Y. Y.: Element-free Galerkin methods for static and dynamic fracture. Int. J. Solids struct. 32, 2547-2570 (1995) · Zbl 0918.73268
[9] Belytschko, T.; Lu, Y. Y.; Gu, L.: Crack propagation by element-free Galerkin methods. Engrg. fract. Mech. 51, No. 2, 295-315 (1995)
[10] Belytschko, T.; Neal, M. O.: Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int. J. Numer. methods engrg. 31, 547-572 (1991) · Zbl 0825.73984
[11] Belytschko, T.; Tabbara, M.: Dynamic fracture using element-free Galerkin methods. Int. J. Numer. methods engrg. 39, No. 6, 923-938 (1996) · Zbl 0953.74077
[12] Bonet, J.; Kulasegaram, S.: Correction and stabilization of smooth particle hydrodynamics methods with application in metal forming simulations. Int. J. Numer. methods engrg. 47, No. 6, 1189-1214 (2000) · Zbl 0964.76071
[13] Bonet, J.; Lok, T.: Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput. methods appl. Mech. engrg. 180, No. 1 -- 2, 97-115 (1999) · Zbl 0962.76075
[14] Camacho, G. T.; Ortiz, M.: Computational modeling of impact damage in brittle materials. Int. J. Solids struct. 33, 2899-2938 (1996) · Zbl 0929.74101
[15] Carey, G. F.: Computational grids: generation, adaptation and solution strategies. (1997) · Zbl 0955.74001
[16] Devloo, P.; Oden, T. J.; Pattani, P.: An h-p adaptive finite element method for the numerical simulation of compressible flow. Comput. methods appl. Mech. engrg. 70, No. 2, 203-235 (1988) · Zbl 0636.76064
[17] Dilts, G. A.: Moving least square particle hydrodynamics I: Consistency and stability. Int. J. Numer. methods engrg. 44, 1115-1155 (2000) · Zbl 0951.76074
[18] Dilts, G. A.: Moving least square particle hydrodynamics II: Conservation and boundaries. Int. J. Numer. methods engrg., 1503-1524 (2000) · Zbl 0960.76068
[19] Dolbow, J.; Moes, N.; Belytschko, T.: Discontinuous enrichment in finite elements with a partition of unity method. Finite elem. Anal. des. 36, No. 3, 235-260 (2000) · Zbl 0981.74057
[20] Etse, G.; Willam, K.: Failure analysis of elasto-viscoplastic material models. ASCE J. Engrg. mech. 125, 60-69 (1999)
[21] Falk, M. L.; Needleman, A.; Rice, J. R.: A critical evaluation of cohesive zone models of dynamic fracture. J. phys. IV 11 (PR5), 43-50 (2001)
[22] Gravouil, A.; Moes, N.; Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets -- part II: Level set update. Int. J. Numer. methods engrg. 53, 2569-2586 (2002) · Zbl 1169.74621
[23] N. Hermann, Experimentelle Erfassung des Betonverhaltens unter Schockwellen, Ph.D. thesis, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe, 2002.
[24] Krongauz, Y.; Belytschko, T.: Consistent pseudo derivatives in meshless methods. Comput. methods appl. Mech. engrg. 146, 371-386 (1997) · Zbl 0894.73156
[25] Krysl, P.; Belytschko, T.: The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks. Int. J. Numer. methods engrg. 44, No. 6, 767-800 (1999) · Zbl 0953.74078
[26] Lemaitre, J.: Evaluation of dissipation and damage in metal submitted to dynamic loading. Proc. ICM 1 (1971)
[27] Loehner, R.: Applied CFD techniques: an introduction based on finite element methods. (2001)
[28] Lu, H.; Chen, J. S.: Adaptive Galerkin particle method. Lect. notes comput. Sci. engrg. 26, 251-267 (2002) · Zbl 1090.65547
[29] Lu, Y. Y.; Belytschko, T.; Tabbara, M.: Element-free Galerkin method for wave-propagation and dynamic fracture. Comput. methods appl. Mech. engrg. 126, No. 1 -- 2, 131-153 (1995) · Zbl 1067.74599
[30] Moes, N.; Dolbow, J.; Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. methods engrg. 46, No. 1, 133-150 (1999) · Zbl 0955.74066
[31] Moes, N.; Gravouil, A.; Belytschko, T.: Non-planar 3-D crack growth by the extended finite element method and level sets, part i: Mechanical model. Int. J. Numer. methods engrg. 53, No. 11, 2549-2568 (2002) · Zbl 1169.74621
[32] J. Ockert, Ein Stoffgesetz fuer die Schockwellenausbreitung in Beton, Ph.D. thesis, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe, 1997.
[33] Ortiz, M.; Leroy, Y.; Needleman, A.: Finite element method for localized failure analysis. Comput. methods appl. Mech. engrg. 61, No. 2, 189-214 (1987) · Zbl 0597.73105
[34] 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
[35] Rabczuk, T.; Belytschko, T.: Application of meshfree particle methods to static fracture of reinforced concrete structures. Int. J. Fract. 137, No. 1 -- 4, 19-49 (2006) · Zbl 1197.74175
[36] Rabczuk, T.; Belytschko, T.: Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. methods engrg. 61, No. 13, 2316-2343 (2004) · Zbl 1075.74703
[37] Rabczuk, T.; Belytschko, T.: Adaptivity for structured meshfree particle methods in 2D and 3D. Int. J. Numer. methods engrg. 63, No. 11, 1559-1582 (2005) · Zbl 1145.74041
[38] Rabczuk, T.; Belytschko, T.; Xiao, S. P.: Stable particle methods based on Lagrangian kernels. Comput. methods appl. Mech. engrg. 193, 1035-1063 (2004) · Zbl 1060.74672
[39] Rabczuk, T.; Eibl, J.: Simulation of high velocity concrete fragmentation using sph/mlsph. Int. J. Numer. methods engrg. 56, 1421-1444 (2003) · Zbl 1106.74428
[40] Randles, P. W.; Libersky, L. D.: Recent improvements in sph modeling of hypervelocity impact. Int. J. Impact engrg. 20, 525-532 (1997)
[41] Randles, P. W.; Libersky, L. D.: Normalized sph with stress points. Int. J. Numer. methods engrg. 48, 1445-1462 (2000) · Zbl 0963.74079
[42] E. Samaniego, X. Oliver, A. Huespe, Contributions to the continuum modelling of strong discontinuities in two-dimensional solids, Ph.D. thesis, International Center for Numerical Methods in Engineering, Monograph CIMNE No. 72, Barcelona, Spain, 2003. · Zbl 1038.74645
[43] H. Schuler, Experimentelle und numerische Untersuchungen zur Schaedigung von stossbeanspruchtem Beton, Ph.D. thesis, Universitaet der Bundeswehr Mnchen, 2004.
[44] Swegle, L. W.; Hicks, D. A.: Smooth particle hydrodynamics stability analysis. J. comput. Phys. 116, 123-134 (1995) · Zbl 0818.76071
[45] Unosson, M.; Nilsson, L.: Projectile penetration and perforation of high performance concrete: experimental results and macroscopic modelling. Int. J. Impact engrg. 32, No. 7, 1068-1085 (2006)
[46] Vila, L. P.: On particle weighted methods and smooth particle hydrodynamics. Math. models methods appl. Sci. 9, No. 2, 161-209 (1999) · Zbl 0938.76090
[47] Xu, X. -P.; Needleman, A.: Void nucleation by inclusion debonding in a crystal matrix. Modell. simul. Mater. sci. Engrg. 1, 111-132 (1993)
[48] Xu, X. -P.; Needleman, A.: Numerical simulations of fast crack growth in brittle solids. J. mech. Phys. solids 42, 1397-1434 (1994) · Zbl 0825.73579
[49] You, Y.; Chend, J. S.; Lu, H.: Filters, reproducing kernel and adaptive meshfree method. Comput. mech. 31, 316-326 (2003) · Zbl 1038.74681
[50] Zhou, F.; Molinari, J. F.: Dynamic crack propagation with cohesive elements: a methodology to address mesh dependence. Int. J. Numer. methods engrg. 59, No. 1, 1-24 (2004) · Zbl 1047.74074