Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance. In this paper, a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle. Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations. A staggered algorithm is used to simulate the crack propagation. The polynomial splines over hierarchical T-meshes (PHT-splines) are adopted as the basis function, which owns the C1 continuity. Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials. The electric boundary conditions may influence crack paths and fracture loads significantly. The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.