Quasi Static Fracture – Global Minimizer of the Regularized Energy
Fracture mechanics has been revisited aimed at modeling brittle fracture based on Griffith viewpoint. The purpose of this work is to present a numerical computational method for solving the quasi static crack propagation based on the variational theory. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. At the numerical level, we use a standard linear (P1) Lagrange finite element method for space discretization. We perform numerical simulations of a piece of brittle material without initial crack. We show also the necessity of adding the backtracking algorithm to alternate minimizations algorithm to ensure the convergence of the alternate minimizations algorithm to a global minimizer.
H. Hentati et al., "Quasi Static Fracture – Global Minimizer of the Regularized Energy", Applied Mechanics and Materials, Vol. 232, pp. 97-101, 2012