Calculus of Variations and Geometric Measure Theory

A. Giacomini - M. Ponsiglione

Discontinuous finite element approximation of quasistatic crack growth in finite elasticity

created on 27 Jan 2004
modified by giacomini on 15 Dec 2006


Published Paper

Inserted: 27 jan 2004
Last Updated: 15 dec 2006

Journal: Math. Models. and Methods Appl. Sci
Volume: 16
Number: 1
Pages: 77-118
Year: 2006


We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed in 13 by G. Dal Maso, G.A. Francfort, and R. Toader, which takes into account body forces and surface loads. We employ adaptive triangulations and prove convergence results for the total, elastic and surface energies. In the case in which the elastic energy is strictly convex, we prove also a convergence result for the deformations.

Keywords: variational models, Crack propagation, energy minimization, finite elements, brittle fractures, quasistatic growth