Extended displacement discontinuity method for nonlinear analysis of penny-shaped cracks in three-dimensional piezoelectric media

The polarization saturation (PS) model and the dielectric breakdown (DB) model are both used, under the electrically impermeable crack assumption, to analyze penny-shaped cracks in the isotropic plane of three-dimensional (3D) infinite piezoelectric solids. Using the extended displacement discontinuity integral equation method, we obtained analytical solutions for the size of the electric yielding zone, the extended displacement discontinuities, the extended field intensity factor and the J-integral. Integrating the Green function for the point extended displacement discontinuity provided constant element fundamental solutions. These solutions correspond to an annular crack element applied with uniformly distributed extended displacement discontinuities in the transversely isotropic plane of a 3D piezoelectric medium. Using the obtained Green functions, the extended displacement discontinuity boundary element method was developed to analyze the PS model and DB model for penny-shaped cracks. The numerical method was validated by the analytical solution. Both the analytical results and numerical results show that the PS and the DB models give equivalent solutions for nonlinear fracture analysis of 3D piezoelectric materials, even though they are based on two physically different grounds.