Interfaces and Free Boundaries
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Published online: 2007-09-30
Numerical implementation of the variational formulation for quasi-static brittle fractureBlaise Bourdin (1) Louisiana State University, Baton Rouge, United States
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 $\Gamma$--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.
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Bourdin Blaise: Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound. 9 (2007), 411-430. doi: 10.4171/IFB/171