An adaptive algorithm for cohesive zone model and arbitrary crack propagation

Authors

  • Vincent Chiaruttini Onera – the French Aerospace Lab, Chatillon, France
  • Dominique Geoffroy Laboratoire de Mécanique des Solides (UMR 7649 CNRS), Ecole Polytechnique, Palaiseau, France
  • Vincent Riolo Onera – the French Aerospace Lab, Chatillon, France; and Laboratoire de Mécanique des Solides (UMR 7649 CNRS), Ecole Polytechnique, Palaiseau, France
  • Marc Bonnet POems (UMR 7231 CNRS-ENSTA-INRIA), ENSTA, Paris, France

DOI:

https://doi.org/10.13052/17797179.2012.744544

Keywords:

cohesive zone model, mixed mode crack propagation, remeshing; field transfer

Abstract

This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading.

Downloads

Download data is not yet available.

References

Alfano, G., & Crisfield, M.A. (2001). Finite element interface models for the delamination analysis of

laminated composites: mechanical and computational issues. International Journal of Numerical

Methods in Engineering, 50, 1701–1736.

Barenblatt, G.I. (1962). The mathematical theory of equilibrium cracks in brittle failure. Advances in

Applied Mechanics, 7, 55–129.

Bechet, E., Minnebo, H., Moes, N., & Burgardt, B. (2005). Improved implementation and robustness

study of the X-FEM for stress analysis around cracks. International Journal of Numerical Methods

in Engineering, 64, 1033–1056.

Bonnet, M. (1999). Stability of crack fronts under Griffith criterion: a computational approach using

integral equations and domain derivatives of potential energy. Computer Methods in Applied

Mechanics and Engineering, 173, 337–364.

Chessa, J., Smolinski, P., & Belytschko, T. (2002). The extended finite element method (XFEM) for

solidification problems. International Journal of Numerical Methods in Engineering, 53, 1959–1977.

Chiaruttini, V., Feyel, F., & Chaboche, J.L. (2010). A robust meshing algorithm for complex 3D crack

growth simulation. European Conference on Computational Mechanics, Paris, France.

Chiaruttini, V., Feld-Payet, S., & Rannou, J. (2012). Some recent advances in remeshing techniques for

complex 3D crack growth simulation. ODAS meeting, DLR, Braunschweig, Germany.

Destuynder, P., Lescure, S., & Djaoua, M. (1983). Some remarks on elastic fracture mechanics. Journal

de Mécanique Théorique et Appliquée, 2, 113–135.

Dugdale, D.S. (1960). Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of

Solids, 8, 100–104.

Geißler, G., & Kaliske, M. (2010). Discrete crack path prediction by an adaptive cohesive crack model.

Engineering Fracture Mechanics, 77, 3541–3557.

Gosz, M., Dolbow, J., & Moran, B. (1998). Domain integral formulation for stress intensity factor

computation along curved three-dimensional interface cracks. International Journal of Solids and

Structures, 35, 1763–1783.

Levy, S., Seagraves, A., Molinari, J-F., & Radovitzky, R. (2009). Discontinuous Galerkin method

applied to fragmentation of heterogeneous materials. 9e Colloque en calcul des structures, Giens,

France, M. Raous et al. Eds., II, 145–150.

Mergheim, J., Kuhl, E., & Steinmann, P. (2004). A hybrid discontinuous Galerkin/interface method for

the computational modelling of failure. Communications in Numerical Methods in Engineering, 20,

–519.

Mi, Y., Crisfield, M.A., Davies, G.A.O., & Hellweg, H.B. (1998). Progressive delamination using

interface elements. Journal of Composite Materials, 32, 1246–1272.

Moes, N., Dolbow, J., & Belytschko, T. (1999). A finite element method method for crack growth

without remeshing. International Journal of Numerical Methods in Engineering, 46, 131–150.

Nitsche, J.A. (1971). On a variational principle for solving Dirichlet problems less boundary conditions

using subspaces (in German). Abhandlungen aus dem Mathematischen Seminar der Universität

Hamburg, 36, 9–15.

Zi, G., & Belytschko, T. (2003). New crack-tip elements for XFEM and applications to cohesive cracks.

International Journal of Numerical Methods in Engineering, 57, 2221–2240.

Downloads

Published

2012-06-06

How to Cite

Chiaruttini, V. ., Geoffroy, D. ., Riolo, V. ., & Bonnet, M. (2012). An adaptive algorithm for cohesive zone model and arbitrary crack propagation. European Journal of Computational Mechanics, 21(3-6), 208–218. https://doi.org/10.13052/17797179.2012.744544

Issue

Section

Original Article