Penny-shaped cracks in three-dimensional piezoelectric semiconductors via Green's functions of extended displacement discontinuity

In this article, a penny-shaped crack in the isotropic plane of three-dimensional transversely isotropic piezoelectric semiconductors is analyzed via the displacement discontinuity boundary element method. The general solutions are derived based on the generalized Almansi's theorem and the operator theory. Green's functions are derived using the Hankel transformation under uniformly distributed extended displacement discontinuities (including displacement discontinuities, potential discontinuity, and electron density discontinuity) on a penny-shaped crack in the isotropic plane of three-dimensional transversely isotropic piezoelectric semiconductors. Using the extended displacement discontinuity boundary element method, penny-shaped cracks in transversely isotropic plane of three-dimensional piezoelectric semiconductors are studied, and the stress, electric displacement, and electric current intensity factors under uniform mechanical-electric-current loads applied on the penny-shaped crack surface are calculated. The fracture behaviors of piezoelectric semiconductors are studied.