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Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. (English) Zbl 1054.74724
Summary: Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. Three different crack growth criteria and the respective crack paths prediction for several test cases are compared. The maximal circumferential stress criterion, the strain energy density fracture criterion and the criterion of the maximal strain energy release rate are implemented using advanced finite element techniques. A fully automatic remesher enables to deal with multiple boundaries and multiple materials. The propagation of the crack is calculated with both remeshing and nodal relaxation. Several examples are presented to check for the robustness of the numerical techniques, and to study specific features of each criterion.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
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[1] Inglis, C.E., Stresses in a plate due to the presence of cracks and sharp corners, Proc. inst. naval architects, 60, 219-241, (1913)
[2] Griffith, A.A., The phenomena of rupture and flow in solid, Phil. trans. roy. soc. London A, 221, 163-197, (1920)
[3] Irwin, G.R.; Washington, D.C., Analysis of stresses and strains near the end of a crack traversing a plate, J. appl. mech., 361-364, (1957)
[4] Belytschko, T.; Lu, Y.Y.; Gu, L., Element free Galerkin methods, Int. J. numer. methods engrg., 37, 229-256, (1994) · Zbl 0796.73077
[5] Simo, J.C.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by strain softening in rate dependent inelastic solids, Int. J. numer. methods engrg., 12, 277-296, (1993) · Zbl 0783.73024
[6] K. Garikipati, On strong discontinuities in inelastic solids and their numerical simulations, Ph.D. Thesis, Stanford University, 1996
[7] J. Oliver, Continuum material failure in strong discontinuity settings, in: E. Oñate, D.R. Owen (Eds.), COMPLAS 2003, VII International Conference on Computational Plasticity, CIMNE, Barcelona, 2003
[8] 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
[9] 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
[10] N. Moës, E. Bechet, Modeling stationary and evolving discontinuities with finite elements, in: E. Oñate, D.R. Owen (Eds.), COMPLAS 2003, VII International Conference on Computational Plasticity, CIMNE, Barcelona, 2003
[11] Babuska, I.; Melenk, J.M., The partition of unity method, Int. J. numer. methods engrg., 40, 727-758, (1997) · Zbl 0949.65117
[12] Bittencourt, T.; Wawrzynek, P.; Sousa, J.; Ingraffea, A., Quasi-automatic simulation of crack propagation for 2D LEFM problems, Engrg. fract. mech., 55, 2, 321-334, (1996)
[13] Carter, B.J.; Wawrzynek, P.A.; Ingraffea, A.R., Automated 3D crack growth simulation, Gallagher special issue of int. J. numer. methods engrg., 47, 229-253, (2000) · Zbl 0988.74079
[14] Bouchard, P.O.; Bay, F.; Chastel, Y.; Tovena, I., Crack propagation modelling using an advanced remeshing technique, Comput. methods appl. mech. engrg., 189, 723-742, (2000) · Zbl 0993.74060
[15] Chastel, Y.; Magny, C.; Bay, F., An elastic – viscoplastic finite element model for multimaterials, Engrg. comput., 15, 1, 139-149, (1998) · Zbl 0918.73253
[16] Barsoum, R.S., On the use of isoparametric finite elements in linear fracture mechanics, Int. J. numer. methods engrg., 10, 25-37, (1976) · Zbl 0321.73067
[17] Destuynder, P.; Djaoua, M.; Lescure, S., Quelques remarques sur la mécanique de la rupture élastique, J. Méca. théo. appl., 2, 1, 113-135, (1983) · Zbl 0529.73081
[18] Hellen, T.K., On the method of virtual crack extentions, Int. J. numer. methods. engrg., 9, 187-207, (1975) · Zbl 0293.73049
[19] Erdogan, F.; Sih, G.C., On the crack extension in plane loading and transverse shear, J. basic engrg., 85, 519-527, (1963)
[20] Sih, G.C.; Macdonald, B., Fracture mechanics applied to engineering problems–strain energy density fracture criterion, Engrg. fract. mech., 6, 361-386, (1974)
[21] Maiti, S.K.; Smith, R.A., Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress – strain field. part II: pure shear and uniaxial compressive loading, Int. J. fract., 24, 5-22, (1984)
[22] M.A. Hussain, S.L. Pu, J.H. Underwood, Strain energy release rate for a crack under combined Mode I and Mode II, Fract. Analysis, ASTM STP 560, Philadelphia, 1974, pp. 2-28
[23] Könke, K.; Schmid, G., (), 431-441
[24] van Vroonhoven, J.C.W.; de Borst, R., Combination of fracture and damage mechanics for numerical failure analysis, Int. J. solids and structures, 36, 1169-1191, (1999) · Zbl 0949.74061
[25] Könke, C., Damage evolution in ductile materials: from micro- to macro-damage, Comp. mech., 15, 497-510, (1995) · Zbl 0825.73535
[26] P.O. Bouchard, Contribution à la modélisation numérique en mécanique de la rupture et structures multimatériaux, Thèse de doctorat de l’Ecole Nationale Supérieure des Mines de Paris, Septembre 2000
[27] H.B. Bui, Dualité entre les intégrales de contour, Compte Rendu Acad. Sciences, vol. 276, Paris, Mai 1973
[28] X.B. Zhang, Etude numérique de la propagation de fissures par la mécanique de la rupture, Thèse de doctorat de l’universitéde Clermont-Ferrand II, Juin 1992
[29] Rice, J.R., A path independent integral and the approximate analysis of strain concentrations by notches and cracks, J. appl. mech., 35, 379-386, (1968)
[30] Li, F.Z.; Shih, C.F.; Needleman, A., A comparison of methods for calculating energy release rate, Engrg. fract. mech., 21, 2, 405-421, (1985)
[31] Parks, D.M., A stiffness derivative finite element technique for determination of crack tip stress intensity factors, Int. J. fract., 10, 4, 487-502, (1974)
[32] de Lorenzi, H.G., Energy release rate calculations by the finite element method, Engng fract. mech., 21, 1, 129-143, (1985)
[33] Lin, S.C.; Abel, J.F., Variational approach for a new direct-integration form of the virtual crack extension method, Int. J. fract., 38, 217-235, (1988)
[34] Ph. Gilles, Ph. Mourgue, M. Rochette, Précision de calcul de la force d’extension de fissure G: effets du maillage et avantage de la méthode G-θ, in: Hermès et INRIA (Ed.), Acte du Colloque National en Calcul de Structures, vol. 2, 1993, pp. 639-670
[35] J. Wang, Development and application of a micromechanics-based numerical approach for the study of crack propagation in concrete, Ph.D. Thesis from Ecole Polytechnique Fédérale de Lausanne, 1994
[36] Flemming, M.; Chu, Y.A.; Moran, B.; Belytschko, T., Enriched element-free Galerkin methods for crack tip fields, Int. J. numer. methods engrg., 40, 1483-1504, (1997)
[37] Belytschko, T.; Lu, Y.Y.; Gu, L., Element free Galerkin methods, Int. J. numer. methods engrg., 37, 229-256, (1994) · Zbl 0796.73077
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