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 simulations of a traction experiment on a fiber-reinforced matrix, and of the propagation of cracks in a perforated sample under mode-I loading. © European Mathematical Society 2007.
Publication Source (Journal or Book title)
Interfaces and Free Boundaries
Bourdin, B. (2007). Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces and Free Boundaries, 9 (3), 411-430. https://doi.org/10.4171/IFB/171