A further investigation of Greenʹs functions for a piezoelectric material with a cavity or a crack

In this paper, the Greenʹs functions of an in®nite two-dimensional piezoelectric material containing an elliptical cavity are re-investigated by introducing exact electric boundary conditions on the hole boundary, and the corresponding modi®ed solutions are obtained. By setting E0, the dielectric constant in the cavity, to be zero, the modi®ed Greenʹs functions are returned to the conventional ones (Lu and Williams, 1998). Furthermore, the hoop stresses along the hole boundary under the action of a set of generalized concentrated forces are obtained. When the hole is reduced to a slit crack, the expressions of generalized stress intensity factors are also provided.