Gradient damage models coupled with plasticity and nucleation of cohesive cracks

In the framework of rate-independent systems, a family of elastic-plastic-damage models is proposed through a variational formulation. Since the goal is to account for softening behaviors until the total failure, the dissipated energy contains a gradient damage term in order to limit localization effects. The resulting model owns a great flexibility in the possible coupled responses, depending on the constitutive parameters. Moreover, considering the one-dimensional quasi-static problem of a bar under simple traction and constructing solutions with localization of damage, it turns out that in general a cohesive crack appears at the center of the damage zone before the rupture. The associated cohesive law is obtained in a closed form in terms of the parameters of the model.