Phase-field modeling of ductile fracture at finite strains: A robust variational-based numerical implementation of a gradient-extended theory by micromorphic regularization

Summary This work provides a robust variational-based numerical implementation of a phase field model of ductile fracture in elastic–plastic solids undergoing large strains. This covers a computationally efficient micromorphic regularization of the coupled gradient plasticity-damage formulation. The phase field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with geometric features rooted in fracture mechanics. It has proven immensely successful with regard to the analysis of complex crack topologies without the need for fracture-specific computational structures such as finite element design of crack discontinuities or intricate crack-tracking algorithms. The proposed gradient-extended plasticity-damage formulation includes two independent length scales that regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones or vice versa and guarantees on the computational side a mesh objectivity in post-critical ranges. The proposed setting is rooted in a canonical variational principle. The coupling of gradient plasticity to gradient damage is realized by a constitutive work density function that includes the stored elastic energy and the dissipated work due to plasticity and fracture. The latter represents a coupled resistance to plasticity and damage, depending on the gradient-extended internal variables that enter plastic yield functions and fracture threshold functions. With this viewpoint on the generalized internal variables at hand, the thermodynamic formulation is outlined for gradient-extended dissipative solids with generalized internal variables that are passive in nature. It is specified for a conceptual model of von Mises-type elasto-plasticity at finite strains coupled with fracture. The canonical theory proposed is shown to be governed by a rate-type minimization principle, which fully determines the coupled multi-field evolution problem. This is exploited on the numerical side by a fully symmetric monolithic finite element implementation. An important aspect of this work is the regularization towards a micromorphic gradient plasticity-damage setting by taking into account additional internal variable fields linked to the original ones by penalty terms. This enhances the robustness of the finite element implementation, in particular, on the side of gradient plasticity. The performance of the formulation is demonstrated by means of some representative examples. Copyright © 2016 John Wiley & Sons, Ltd.