Fundamental solutions and numerical modeling of an elliptical crack with polarization saturation in a transversely isotropic piezoelectric medium

In this paper, we first derive the fundamental solutions for uniformly distributed extended displacement discontinuities on triangular and rectangular elements in the isotropic plane of a three-dimensional transversely piezoelectric medium. Based on these solutions, we propose the extended displacement discontinuity boundary element method to analyze numerically an elliptical crack with polarization saturation. The size of the electric yielding zone and the stress intensity factors are presented and some interesting features are discussed. Furthermore, when both semi-axes are the same, our results for the elliptical crack can be reduced to the existing ones associated with the penny-shaped crack.