Analysis method of mixed mode crack in 2D finite piezoelectric media

In this paper, the Hybrid Extended Displacement Discontinuity-Charge Simulation Method (HEDD-CSM) [1] is used to study the mixed mode cracks in two-dimensional finite piezoelectric media under combined mechanical-electrical loadings. The HEDD-CSM combines the extended displacement discontinuity method (EDDM) and the charge simulation method (CSM). The solution for an electrically impermeable crack is approximately expressed by a linear combination of fundamental solutions of the governing equations which includes the extended point force fundamental solutions with the sources placed at chosen points outside the domain of the problem under consideration and the extended Crouch fundamental solutions with the extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the conditions on the boundary of the domain and on the crack face. The center cracks in piezoelectric strips are analyzed by HEDD-CSM. The stress intensity factors and the electric displacement intensity factor are calculated. Meanwhile the effect of finite domain size on these intensity factors is studied. One of the most interesting findings is that the intensity factor K_II decouples from K₁ and K_D even in a finite piezoelectric medium.