Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy

Abstract

We consider a family of vectorial models for cohesive fracture, which may incorporate SO(n)-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an openingdependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional can be naturally obtained as Γ-limit of an appropriate phase-field model. The energy densities entering the limiting functional can be expressed, in a partially implicit way, in terms of those appearing in the phase-field approximation.