Optimization in constrained crack problems

Abstract

Following the optimization approach to brittle fracture, we consider the evolution of a crack in a domain as solution of the global problem of constrained minimization of the total potential energy with respect to both state variables (the displacement vector) and shape variables (parameters of the crack shape). This formulation describes the initiation of a crack in a homogeneous body and its stable as well as unstable propagation, which allows also a kink (topology change) of the crack during the evolution process. By this we assume that contact can occurs between the opposite crack faces.