Complete damage evolution based on energies and stresses

Abstract

The rate-independent damage model recently developed in Bouchitté, Mielke, Roubícek ``A complete-damage problem at small strains" allows for complete damage, such that the deformation is no longer well-defined. The evolution can be described in terms of energy densities and stresses. Using concepts of parametrized Gamma convergence, we generalize the theory to convex, but non-quadratic elastic energies by providing Gamma convergence of energetic solutions from partial to complete damage under rather general conditions