Boundary integral–differential equations and boundary element method for interfacial cracks in three-dimensional piezoelectric media

Abstract Using the method of Ding et al. [Int. J. Solids Struct. 34 (1997) 3041], the fundamental solutions for three-dimensional two-phase transversely isotropic piezoelectric media are re-derived. Based on the fundamental solutions, the displacements and the electric potential at any point for an internal crack parallel to the interface in a two-phase transversely isotropic piezoelectric medium are expressed in terms of the displacement and electric potential discontinuities across the crack surfaces. The hyper-singular boundary integral–differential equations of the displacement and electric potential discontinuities are obtained for arbitrarily shaped planar interfacial cracks in three-dimensional two-phase transversely isotropic piezoelectric media. A boundary element formulation to solve the boundary integral–differential equations is presented. Numerical results of stress and electric displacement intensity factors and energy release rate of penny shaped and elliptical cracks are presented to illustrate the application, accuracy and efficiency of the proposed method in analyzing interfacial cracks in three-dimensional transversely isotropic piezoelectric bimaterials.