A priori inequalities between energy release rate and energy concentration for 3D quasistatic brittle fracture propagation

Abstract

We study the properties of absolute minimal and equilibrium states of generalized Mumford-Shah functionals, with applications to models of quasistatic brittle fracture propagation. The main results, theorems 7.3, 8.4 and 9.1, concern a priori inequalities between energy release rate and energy concentration for 3D cracks with complex shapes, seen as outer measures living on the crack edge. ©The Author(s) 2011.