Extended displacement discontinuity method for analysis of penny-shaped cracks in three-dimensional thermal piezoelectric semiconductors

In this paper, the extended displacement discontinuity (EDD) boundary element method is developed to analyze a penny-shaped crack in the isotropic plane of a three-dimensional (3D) transversely isotropic thermal piezoelectric semiconductor (PSC). The generalized Almansi's theorem and the operator theory are used to obtain the general solutions under generalized loading. The fundamental solutions for extended displacement discontinuities (EDDs) applied on the penny-shaped crack surface, which include the displacement, electric potential, carrier density, and temperature discontinuities, are derived. By using the EDD boundary element method, the EDD under mechanical, electrical and heat loading near the edge of a penny-shaped crack is calculated. The stress and heat flux intensity factors of the crack are obtained. The influence of uniform and non-uniform heat loadings on the fracture of 3D transversely isotropic thermal PSCs is investigated.