Transient dynamic response of a cracked piezoelectric solid under impact loading

In this paper, a time-domain boundary integral equation method is presented for transient dynamic crack analysis in linear piezoelectric solids. A finite crack in an infinite linear piezoelectric solid subjected to an impact crack-face loading is considered. The corresponding initial-boundary value problem is formulated as a set of hypersingular time-domain boundary integral equations, with the crack-opening-displacement and the electric-potential-discontinuity as unknown boundary quantities. A numerical solution procedure is developed for solving the hypersingular time-domain BIEs, which uses a convolution quadrature formula for approximating the temporal convolution and a Galerkin method for the spatial discretization of the time-domain BIEs.