Coupled gradient damage - Viscoplasticty model for ductile materials: Phase field approach

The framework of coupled nonlocal damage model through phase field method and viscoplasticity in continuum scale is developed in this work. It is shown that the recently proposed non local gradient type damage model through the phase field method can be coupled to a viscoplastic model to capture the inelastic behavior of the rate dependent material. Free energy functional of the system containing two main parts including damage propagation as a phase transformation and viscoplastic deformation is proposed. Analogous to conventional viscoplastic models, two terms are incorporated in the viscoplastic free energy functional to appropriately address dissipation and the von Mises type viscoplastic surface. In this framework it is assumed that the damage variable covers summation of evolution of microcracks density in elastic and plastic region and the total strain represents the summation of the elastic and viscoplastic counterparts. It is shown that a material constant plays an important role to capture the ductile failure through the proposed model by means of numerical examples.