Nonlinear solution of the PS model for a semi-permeable crack in a 3D piezoelectric medium

By considering the electric field in the crack cavity, the polarization saturation (PS) model of a penny-shaped crack under electrically semi-permeable boundary condition in a three-dimensional piezoelectric medium is studied via both the extended displacement discontinuity boundary integral equation method and the boundary element method. An approximate analytical solution is derived, and the electric displacement in the crack cavity, the electric yielding zone and the local J-integral are obtained. The extended displacement discontinuity boundary element method with double iterative approaches is adapted to numerically simulate the electrically semi-permeable crack and to validate the analytical solution. The effects of different boundary conditions on the electric yielding zone and the local J-integral are also investigated.