Comparison of phase-field models of fracture coupled with plasticity

In the last few years, several authors have proposed different phase-field models aimed at describing ductile fracture phenomena. Most of these models fall within the class of variational approaches to fracture proposed by Francfort and Marigo [13]. For the case of brittle materials, the key concept due to Griffith consists in viewing crack growth as the result of a competition between bulk elastic energy and surface energy. For ductile materials, however, an additional contribution to the energy dissipation is present, related to plastic deformations. Of crucial importance, for the performance of the modeling approaches, is the way the coupling is realized between plasticity and phase field evolution. Our aim is a critical revision of the main constitutive choices underlying the available models and a comparative study of the resulting predictive capabilities.