An iterative approach for analyzing cracks in two-dimensional piezoelectric media with exact boundary conditions

An iterative approach is proposed for analyzing cracks in two-dimensional piezoelectric media based on the sub-region boundary element formulation with exact boundary conditions on the crack face. In this approach, the opening crack cavity is treated as one of the sub-regions governed by the Poisson equation of electric potential. The real crack opening, the crack cavity region, and the field in the cavity region are determined for the geometrically nonlinear problem. The widely used approximate crack models corresponding to three approximate boundary conditions are evaluated based on the proposed approach. The proposed approach is implemented efficiently to analyze problems with very thin domains, such as the crack opening cavity, and employing the intelligent adaptive algorithms in the Mathematica software means that nearly singular integrals require no special treatment.