Method of potential functions in fundamental problems for piezoelectric materials of class six

The problem of the transversely isotropic piezoelectric material of class 6 symmetry under the action of point force and point charge is addressed utilizing the methods of potential functions. The solution of the infinite space is found and used to generate the Greens' function of the material. The stress fields and electric displacements constructed for the infinite space are then modified to create the necessary boundary value problems to solve the infinite half-space condition. The half space is chosen where the plane of transverse isotropy is aligned. These results of the infinite half-space are then utilized to show the displacements and stresses under the action of indenters of various geometries. The results of these are valuable to discuss the sensitivity of indenter depth in regards to the piezoelectric properties of a given material in relation to a solely elastic material, which may aide in the calibration of scanning probe microscopy.