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

Abstract

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 plasticitydamage. Another aspect is the regularization towards a micromorphic gradient plasticity-damage setting which enhances the robustness of the finite element formulation.

An anisotropic cohesive phase field model for quasi-brittle fractures in thin fibre-reinforced composites

“…The primary advantage of PFM lies in its capability of automatically predicting mesh-independent curvilinear crack patterns including branching and merging; this motivates its application to the simulation of complex intra-laminar composite failure mechanisms. The current applications of PFM include brittle fractures [38,39,40,41,42,43], quasibrittle fractures [44,45], ductile fractures [46,47,48,49], hydraulic fractures [50,51], and hydrogen assisted fractures [52]. PFM has also been implemented in the commercial software Abaqus [53,54,55,56] within user-element (UEL) and usermaterial (UMAT) subroutines.…”