A comparative analysis on variational models for quasi-static brittle crack propagation

Abstract

We consider a brittle material under displacement control with a mode III crack running in quasi-static regime along a straight line. Several definitions of propagation, based on variational criteria, have been proposed in the last decade. Our aim is a detailed study of their properties, in particular as far as energy, energy release rate and jump discontinuities is concerned. In order to make similarities and differences appear more clearly, the analysis of the evolutions follows a common structure and theoretical results are illustrated by a prototype numerical example.