A discontinuous finite element approximation of quasi-static growth of brittle fractures

We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith's criterion. We restrict our analysis to the case of anti-planar shear and we consider discontinuous displacements which are piecewise affine with respect to a regular triangulation.Comment: 34 pages, 4 figure

A GammaGamma-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications

We prove a stability result for a large class of unilateral minimality properties which arise naturally in the theory of crack propagation proposed by Francfort and Marigo (JMPS, 1999). Then we give an application to the quasistatic evolution of cracks in composite materials