A variationally consistent phase-field anisotropic damage model for fracture

• Published in: Computer methods in applied mechanics and engineering 2020-01, Vol.358, p.112629, Article 112629
• Main Authors: Wu, Jian-Ying, Nguyen, Vinh Phu, Zhou, Hao, Huang, Yuli
• Format: Article
• Language: English
• Subjects: Anisotropic damage; Anisotropy; Boundary conditions; Brittle fracture; Cohesive zone model; Crack propagation; Damage assessment; Exact solutions; Field theory; Finite element method; Flux density; Fracture mechanics; Free energy; Internal energy; Locking; Mathematical models; Parameters; Phase-field theory; Strain localization; Unilateral effects; Variational approach to fracture
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112629

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. •A variationally and thermodynamically consistent phase-field anisotropic damage model is presented.•Unilateral effects are dealt with by a positive/negative projection of the effective stress in energy norm.•A rounded-Rankine criterion is obtained to describe localized failure in brittle and quasi-brittle solids.•A mixed-mode cohesive zone model is recovered from strain localization for a vanishing length scale.•Representative numerical examples are presented to validate the mesh and length scale independence.