Numerical implementation of the variational formulation for quasi-static brittle fracture
Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 411-430
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This paper presents the analysis and implementation of the variational formulation of quasi-static brittle fracture mechanics proposed by G.A. Francfort and J.-J. Marigo in 1998. We briefly present the model itself, and its variational approximation in the sense of Γ-convergence. We propose a numerical algorithm based on Alternate Minimizations and prove its convergence under restrictive assumptions. We establish a new necessary condition for optimality for the entire time evolution from which we derive the Backtracking algorithm. We give some elements of analysis of the Backtracking algorithm on a simple problem. We present realistic numerical simulation of a traction experiment on a fiber-reinforced matrix, and of the propagation of cracks in a perforated sample under mode-I loading.
Classification :
35-XX, 65-XX, 76-XX, 92-XX
Affiliations des auteurs :
Blaise Bourdin 1
Blaise Bourdin. Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 411-430. doi: 10.4171/ifb/171
@article{10_4171_ifb_171,
author = {Blaise Bourdin},
title = {Numerical implementation of the variational formulation for quasi-static brittle fracture},
journal = {Interfaces and free boundaries},
pages = {411--430},
year = {2007},
volume = {9},
number = {3},
doi = {10.4171/ifb/171},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/171/}
}
TY - JOUR AU - Blaise Bourdin TI - Numerical implementation of the variational formulation for quasi-static brittle fracture JO - Interfaces and free boundaries PY - 2007 SP - 411 EP - 430 VL - 9 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/171/ DO - 10.4171/ifb/171 ID - 10_4171_ifb_171 ER -
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