Analytical solution of a semi-permeable crack in a 2D piezoelectric medium based on the PS model

This paper considers a straight but nonlinear crack in a two-dimensional piezoelectric plane. Different to the existing theoretical solution of the well-known polarization saturation (PS) model, we assume the crack to be semi-permeable. By introducing the dislocation density along the crack line, we derive the analytical solution for the field quantities. Numerical results show that the effect of different boundary conditions on the electric yielding zone and the stress intensity factor is significant and should not be ignored. The influence of the saturated electric displacement on the stress intensity factor and the electric displacement in the crack cavity is also demonstrated.