Variational framework for phase field modeling of ductile fracture in porous solids at finite strains

This work outlines a rigorous variational‐based framework for the phase field modeling of fracture in isotropic and anisotropic porous solids undergoing small elastic but large plastic deformations. It extends the recent work [1] to a formulation of porous plasticity with particulate microstructures characterized by spherical pores or by ellipsoidal voids, which additionally undergo a change in size and orientation. A gradient plasticity model for isotropic and anisotropic porous plasticity is developed, and linked to a failure criterion in terms of the local elastic‐plastic work density that drives the fracture phase field [2]. It is shown that this approach is able to model phenomena of ductile failure such as cup‐cone failure surfaces. The proposed model is governed by a rate‐type minimization principle, which describes the coupled multifield evolution problem of plasticity‐damage. Another aspect is the regularization towards a micromorphic gradient plasticity‐damage setting which enhances the robustness of the finite element formulation. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)