Analysis of an arbitrarily oriented crack in a finite piezoelectric plane via the hybrid extended displacement discontinuity-fundamental solution method

In this paper, we analyze an arbitrarily oriented crack in a finite two-dimensional piezoelectric medium with the polarization saturation model near the crack tip. We first derive the extended Green’s functions corresponding to the extended point-displacement discontinuities of an arbitrarily oriented crack based on the Green’s functions of the extended point forces and the Somigliana identity. Then, the extended field intensity factors and the local J-integral near the crack tip are expressed in terms of the extended displacement discontinuity on crack faces. Finally, the nonlinear hybrid extended displacement discontinuity-fundamental solution method is proposed to analyze an electrically nonlinear crack in a finite piezoelectric medium. Numerical examples are carried out for both linear and nonlinear fracture models of the crack under electrically impermeable boundary conditions. The influence of the crack orientation and geometric size on the fracture behaviors of the crack is investigated.