Punch problem for piezoelectric ceramic half-plane

Abstract

Based on the theory of linear piezoelectricity, this study presents an exact solution for a two dimensional indentation on a piezoelectric ceramic half-plane with different contact conditions. The flat-ended indenters are assumed to be rigid. Besides, they can either be insulating or conducting. In addition, different contact conditions, including frictionless, frictional, and adhesive punches are investigated. Lekhnitskii's formulism and Fourier transforms are used to obtain the Green's function of a piezoelectric ceramic half-plane subjected to a point loading. Utilizing Green's half-plane function, we obtain the three integral equations by connecting generalized displacement gradients at the surface and surface loading. Both uncoupled and coupled integral equations can be transformed into a Fredholm integral equation. The analytical closed form solutions of the contact forces and the electric charges under the indenter can be derived by solving the Fredholm integral equations. Once the distributions of the contact forces and the electric charges on the surface are known, the electroelastic response in the half-plane can also be obtained.