Free damage propagation with memory

Abstract

We introduce a simple model for free damage propagation based on non-local potentials. The model is developed using a state based peridynamic formulation. The resulting evolution is shown to be well posed. At each instant of the evolution we identify the damage set. On this set the local strain has exceeded critical values either for tensile or hydrostatic strain and damage has occurred. For this model the damage set is nondecreasing with time and associated with damage variables defined at each point in the body. We show that energy balance hold for this evolution. For differentiable displacements away from the damage set we show that nonlocal model converges to the linear elastic model. We provide several numerical examples modeling fatigue and fracture.