The variational formulation of brittle fracture: numerical implementation and extensions

This paper presents the implementation of a variational formulation of brittle fracture mechanics proposed by G.A. Francfort and J.-J. Marigo in 1998. The essence of the model relies on successive global minimizations of an energy with respect to any crack set and any kinematically admissible displacement field. We briefly present the model itself, and its variational approximation in the sense of Gamma–convergence. We propose a globally convergent and monotonically decreasing numerical algorithm. We introduce a backtracking algorithm whose solution satisfy a global optimality criterion with respect to the time evolution. We illustrate this algorithm with three dimensional numerical experiments. Then we present an extension of the model to crack propagation under thermal load and its numerical application to the quenching of glass.