An alternative expression of piezoelectric representation and its application in inclusion problem

Abstract

This paper intends to conform the mathematical correspondence between electric and mechanical variables to the physical correspondence in electroelastic problem when a piezoelectric material is subjected to stress field σij and electric field Ei or displacement u and electric displacement Di. Ei is expressed with an antisymmetric electric field tensor Vij , and Di is expressed with an antisymmetric electric displacement tensor Pij which can be expressed with ‘induction potential’ ψi. Then stress equilibrium and electric field equations can be described by a second order canonical differential equation system of ui and ψi. As an example, the coupled electroelastic fields in an inclusion or inhomogeneity embedded in an infinite matrix are obtained in a manner directly analogous to Eshelby’s classical elastic solution. The electroelastic fields inside the ellipsoidal inclusion or inhomogeneity and just outside the ellipsoidal inclusion or inhomogeneity are also given. In addition, we analyze the energies of the inclusion. The results in this paper are the backbone in the development of the electric damage theory and ferroelectric constitutive theory.