Phase-field modeling of electromechanical fracture in piezoelectric solids: Analytical results and numerical simulations

• Published in: Computer methods in applied mechanics and engineering 2021-12, Vol.387, p.114125, Article 114125
• Main Authors: Wu, Jian-Ying, Chen, Wan-Xin
• Format: Article
• Language: English
• Subjects: Characteristic functions; Cohesive zone model; Constitutive relationships; Crack initiation; Crack sensitivity; Electric fields; Electromechanical fracture; Energy release rate; Finite element method; Fracture mechanics; Mathematical analysis; Mathematical models; Multiphysics; Nucleation; Phase-field theory; Piezoelectric ceramics; Piezoelectricity; Regularization
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114125

The optimal design, reliable manufacture and durable utilization of electromechanical systems demand objective modeling of failure under coupled electric field and mechanical actions. This is still a challenging and largely an open issue despite the large volumes of contributions from the discontinuous approach and the phase-field community for brittle fracture. In this work we propose a length scale insensitive phase-field cohesive zone model (PF-CZM) for electromechanical fracture in linear piezoelectric solids, overcoming all the issues of mesh dependence, crack tracking complexity, length scale sensitivity and crack nucleation inconsistency. More specifically, in the electromechanically coupled phase-field constitutive relations, the evolution law for the crack phase-field is established from the geometric regularization of sharp cracks and the energetic criterion in global form. In order to capture the unsymmetric mechanical and electrical fracture behavior, the mechanical energy release rate contributed from the positive cone of the effective stress in energy norm is employed as the crack driving force, resulting in a hybrid formulation. With a set of phase-field characteristic functions optimal for cohesive fracture, the critical stress upon crack nucleation and the post-peak softening regime are derived in close-form for the first time, and the experimentally observed effects of the electric field on the fracture load are predicted qualitatively. The proposed electromechanical PF-CZM is numerically implemented in the multi-field finite element method and applied to several representative examples. In all cases, as those for purely mechanical problems, the predicted crack patterns and fracture loads are insensitive to the phase-field length scale and the experimental results are well reproduced. In particular, the effect of electric field on the deflection of crack paths can be captured. These merits make the proposed PF-CZM promising in the modeling of electromechanical fracture in piezoelectric solids. •A phase-field cohesive zone model is proposed to address the electromechanical fracture in piezoelectric solids.•The evolution law for the crack phase-field is derived from the energetic equivalence of mechanical dissipations.•A hybrid formulation is employed to describe the non-symmetric fracture behavior under tension/compression.•The analytical results for the peak load and post-peak behavior under 1D electromechanical fracture are derived.•The