A cohesive zone model which is energetically equivalent to a gradient-enhanced coupled damage-plasticity model

Modeling the fracture of a material can take two different approaches. A first solution consists in using models which preserve a continuous description of the material throughout the fracture process. These models are often regularized in order to deal with the softening part of the material’s behavior properly. Another solution consists in introducing discontinuity surfaces into the structure along with the possibility of taking into account cohesive forces between the two sides of the discontinuity. Many works have been devoted to the establishment of a relation between these two families of models. The present work is based on the equivalent crack concept, which states that a localized damage zone can be replaced by a crack as long as the energy dissipated by the structure is preserved when switching models. In a first paper, we introduced a method of construction of a cohesive law based on an elastic-damageable reference model. For a given test case, the cohesive model was built incrementally from the known solution given by the continuous reference model. There was no prerequisite assumption on the form of the cohesive law. In that work, the presence of plastic strains in the structure had not been taken into account, which limited the range of applicability of the method to elastic-damageable models. The objective of this paper is to eliminate this limitation by extending the method to the more general class of elastic–plastic damageable models.