A Discontinuous Finite Element Approximation of Quasi-static Growth of Brittle Fractures

Abstract

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.

Keywords:

• Variational models
• Energy minimization
• Free discontinuity problems
• Crack propagation
• Quasi-static evolution
• Brittle fracture
• Finite elements

Acknowledgments

The authors wish to thank Gianni Dal Maso for having proposed them the problem, and Gianni Dal Maso and Gilles A. Francfort for many helpful and interesting discussions.