A Priori Inequalities between Energy Release Rate and Energy Concentration for 3D Quasistatic Brittle Fracture Propagation.

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. [ABSTRACT FROM PUBLISHER]