Remarks on a basic law for dynamic crack propagation

Abstract

A basic law of motion for a dynamic crack propagating in a brittle material is derived in the case of two space dimensions. The only basic assumptions for this purpose are the energy conservation law and a variational inequality following the well known Hamilton's principle. Our study is developed within Griffith's framework, that is under the assumption that crack surface energy is proportional to crack length. It is shown that the speed and direction of the crack can be found without further assumptions. Moreover, the corresponding law is local, and if expressed in terms of the stress intensity factors yields the principle of local symmetry previously proposed for quasi-static evolution.