General Solution Technique for Electroelastic Problems in Green Materials

Abstract

In view of the engineering significance of piezoelectric bodies with D ∞ symmetry, such as bulk wood and film or fibers made of poly-L-lactic acid, an analytical technique is constructed for general solutions to electroelastic problems in these bodies. First, the constitutive equations which describe the symmetry are presented. Then, the displacement and electric field are expressed in terms of two types of displacement potential functions and the electric potential function, and their governing equations are obtained using the fundamental equations for the electroelastic field. As a result, the electroelastic field quantities are found to be expressed in terms of three functions, namely an elastic displacement potential functions and two piezoelastic displacement potential functions, and the former is found to satisfy a fourth-order differential equation and the latter to satisfy a Laplace equation with respect to the appropriately transformed spatial coordinates.