Diffuse cohesive energy in plasticity and fracture

In this paper we anticipate some results of a work in progress, in which the phenomena of fracture and yielding are described by a cohesive energy model, and fracture is regarded as a consequence of an extreme localization of the inelastic deformation. We first study a local model, which is successful in describing a number of aspects of the experimentally observed response, but fails to describe the phenomenon of strain softening. Indeed the model's prediction is that, just after its appearance, the inelastic deformation localizes, growing in an uncontrolled way and determining a catastrophic rupture. A more gradual growth is obtained by introducing a non-local energy term. Some numerical experiments show the great flexibility of the improved model: depending on the analytical shape assumed for the cohesive energy, the non-local model describes different types of response, such as yielding without fracture, ductile fracture with and without strain softening, and brittle fracture.