Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack

Based on the complex potential approach\ the two!dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied[ The explicit\ closed!form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole[ When the elliptic hole degenerates into a crack\ the _eld intensity factors are obtained[ It is shown that the stress intensity factors are the same as that of isotropic material\ while the electric displacement intensity factor depends on both the material properties and the mechanical loads\ but not on the electric loads[ In other words\ the uniform electric loads have no in~uence on the _eld singularities[ It is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials