Singular Problems of Spherically Uniform Anisotropic Piezoelectric Solids

Abstract

A material is radially anisotropic piezoelectric when its generalized Hooke’s law at each material point referred to a spherical coordinate system is the same everywhere. In a recent paper by Ting, the remarkable nature at the center of a sphere has been shown when a spherically uniform linear anisotropic elastic material is subjected to a uniform traction at the surface of the sphere. This paper extends elastic material for piezoelectric material, and shows that the singular problems also prevail in piezoelectric material. When a sphere of piezoelectric material is subjected to a uniform traction and electric potential at the surface of the sphere, for a certain range of material parameter, the stress, the electric field and the electric potential at the center of the sphere are infinite. When the sphere is subjected to a uniform tension, a cavitation occurs at the center of the sphere. If the applied traction is a uniform pressure, a black hole occurs at the center of the sphere. The singular problems depend only on one non-dimensional material parameter and the direction of the applied traction, while is independent of the magnitude of the traction.