Determination of dynamic intensity factors and time-domain BEM for interfacial cracks in anisotropic piezoelectric materials

In this paper, a universal matrix-form displacement extrapolation formula and the explicit form are derived to determine the dynamic intensity factors of an interface crack in general anisotropic piezoelectric bi-materials. It is very feasible for numerical methods, especially for boundary element method (BEM) which can directly present the unknown boundary values. Using the explicit extrapolation formula, the transient response of interfacial cracks in piezoelectric bi-materials under electro-mechanical impacts is studied by time-domain BEM together with a sub-domain technique. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at the tips of the interface cracks. General cases for the poling axis of each piezoelectric component unparallel to the Cartesian coordinate axes are studied. Numerical examples are presented and discussed the effects of the poling direction, material combination and the load combination on dynamic intensity factors.