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Oliveira, H. L.; Leonel, E.D.;

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This paper addresses to analysis of crack growth in quasi-brittle materials using the boundary element method (BEM) and cohesive models. BEM has been widely used to solve many complex engineering problems, especially those where its mesh dimension reduction includes advantages on the modelling. The non-linear formulations developed are based on the dual BEM, in which singular and hyper-singular integral equations are adopted. The first formulation uses the concept of constant operator, in which all corrections on the nonlinear system of equations are performed only by applying appropriate tractions along the crack surfaces. The second proposed BEM formulation is an implicit technique based on the use of a tangent operator. This formulation is accurate, stable and always requires less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Examples of problems of crack growth are shown to illustrate the performance of these two formulations.

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Palavras-chave: Cohesive crack growth, Non-linear BEM formulation, Tangent operator,


DOI: 10.5151/meceng-wccm2012-18399

Referências bibliográficas
  • [1] Barenblatt, G.I. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics. 7:55–129, 1962.
  • [2] Carpinteri, A. Post-peak and post-bifurcation analysis of cohesive crack propagation. Engineering Fracture Mechanics. 32:265–278, 1989.
  • [3] Dugdale, D.S. Yelding of steel sheets containing slits. Journal of Mechanics and Physics of Solids. 8:100–104, 1960.
  • [4] Hillerborg, A; Modeer, M; Peterson, P.E. Analysis of crack formation and crack growth in concrete by mean of failure mechanics and finite elements. Cement Concrete Research. 6:773–782, 1976.
  • [5] Bouchard, P.O; Bay, F; Chastel, Y. Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Computer Methods in Applied Mechanics and Engineering. 192:3887–3908, 2002.
  • [6] Patzak, B; Jirasek, M. Adaptive resolution of localized damage in quasi-brittle materials. Journal of Engineering Mechanics. 130:720–732, 2004.
  • [7] Moes, N; Dolbow, J; Belytschko, T. A finite element method for crack growth without remeshing, Int J Numer Meth Eng. 46, pp. 131–150, 1999.
  • [8] Belytschko, T; Liu, Y.Y. Element free Galerkin methods. Int J Numer Meth Eng. 37, pp. 229–256, 1994.
  • [9] Cruse, T.A. Boundary Element Analysis in computational fracture mechanics. Dordrecht: Kluwer Academic Publishers; 1988.
  • [10] Crouch, S. L. Solution of plane elasticity problems by the displacement discontinuity method. International Journal of Numerical Methods in Engineering. 10:301-343, 1976.
  • [11] Portela, A; Aliabadi, M.H; Rooke, D.P. Dual Boundary element method: efficient implementation for crack problems. International Journal of Numerical Methods in Engineering. 33:1269-1287, 1992.
  • [12] Yan, X. Microdefect interacting with a finite main crack. Journal of Strain Analysis Engineering Design. 40:421–430, 2005.
  • [13] Kebir, H; Roelandt, J.M; Chambon, L. Dual boundary element method modelling of aircraft structural joints with multiple site damage. Engineering Fracture Mechanics. 73:418- 434, 2006.
  • [14] Leonel, E.D; Venturini, W.S. Dual boundary element formulation applied to analysis of multi-fractured domains. Engineering Analysis with Boundary Elements. 34: 1092-1099, 2010.
  • [15] Leonel, E.D; Venturini, W.S. Multiple random crack propagation using a boundary element formulation, Engineering Fracture Mechanics, 78, 1077–1090, 2011.
  • [16] Leonel, E.D; Beck, A.T; Venturini, W.S. On the performance of response surface and direct coupling approaches in solution of random crack propagation problems. Structural Safety. 33 (4-5), pp. 261-274, 2011.[17 ] Leonel, E.D; Venturini, W.S; Chateauneuf, A. A BEM model applied to failure analysis of multi-fractured structures. Engineering Failure Analysis, 18, (6) 1538-1549, 2011.[18 ]Kumar, V; Mukherjee, S. Boundary-integral equation formulation for time-dependent inelastic deformation in metals. International Journal of Mechanical Sciences. 19(12):713– 724, 1977.
  • [17] Leonel, E.D; Venturini, W.S. Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials. Engineering Analysis with Boundary Elements. 34:122–129, 2010.
  • [18] Poon, H; Mukherjee S; Bonnet, M. Numerical implementation of a CTO-based implicit approach for solution of usual and sensitivity problems in elasto-plasticity. Engineering Analysis with Boundary Elements. 22:257–269, 1998.
  • [19] Saleh, A.L; Aliabadi, M.H. Crack-growth analysis in concrete using boundary element method. Engineering Fracture Mechanics. 51(4):533–545, 1995.
  • [20] Botta, A.S; Venturini, W.S; Benallal, A. BEM applied to damage models emphasizing localization and associated regularization techniques. Engineering Analysis with Boundary Elements. 29:814–827, 2005.
  • [21] Galvez, J.C; Elices, M; Guinea, G.V; Planas, J. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture. 94: 267-284, 1998.
Como citar:

Oliveira, H. L.; Leonel, E.D.; "COHESIVE CRACK PROPAGATION ANALYSIS USING A NON-LINEAR BOUNDARY ELEMENT FORMULATION", p. 1363-1381 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18399

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