Quasistatic fracture evolution using a nonlocal cohesive model

We introduce a nonlocal model of peridynamic type for fracture evolution in the quasistatic regime. Nonlocal quasistatic fracture evolution is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationary and fixed point methods. Here a smooth cohesive force-strain model is used. Initially the force increases with strain then softens and decreases to zero. It is proved that the fracture evolution decreases stored elastic energy with each displacement step as the cracks advance; provided the displacement increments are chosen sufficiently small. These results apply to any system of multiple cracks. This is also seen in the numerical examples. The numerical examples include evolution of a straight crack, a crack propagating inside an L-shaped domain, and two offset inward propagating cracks.