Some half-space problems of cubic piezoelectric materials

Half-space problems of a cubic piezoelectric material subjected to anti-plane deformation and in-plane electric field are studied. A general solution in terms of the integration of the boundary data prescribed over the surface of the semi-infinite domain is derived. Based on the general solution, the problem of a concentrated line force acting on the surface is treated and ensuing electromechanical response is determined. The solution to the problem of a screw dislocation in the half-space is also obtained, and the result is exploited to study a sub-surface crack problem by simulating the crack as a continuous distribution of dislocations.