A mixed electric boundary value problem for an anti-plane piezoelectric crack

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation. The crack face is partly conductive and partly impermeable. The results show that the stress intensity factor is identical with the mode III stress intensity factor independent of the conducting length. But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and axe singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.