A variationally consistent phase-field anisotropic damage model for fracture

In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model within the framework of the unified phase-field theory for brittle fracture and quasi-brittle failure Wu [1,2]. Consistent with the variational approach to fracture, the positive/negative projection of the effective stress in energy norm Wu and Cervera [3] is adopted, minimizing the tensile part of the stored energy that drives crack evolution. A rounded-Rankine criterion naturally emerges to realistically characterize localized failure of brittle and quasi-brittle solids, with no need of ad hoc assumptions. A mixed-mode cohesive zone model is recovered upon strain localization, with the involved parameters determined from the analytical solution of a softening bar under constrained stretching. Representative numerical examples show that the proposed model can capture arbitrary cracks propagation in solids independently of the mesh discretization and length scale parameter. Remarkably, the spurious stress locking, which is notoriously accompanied with classical anisotropic damage models, is not exhibited. (C) 2019 Elsevier B.V. All rights reserved.