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

Article type: Research Article

Authors: Shen, Shengping^{a; *} | Kuang, Zhen-Bang^a

Affiliations: [a] Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P. R. China

Correspondence: [*] Corresponding author: Dr. Shengping Shen, Department of Engineering Mechanics, Shanghai Jiaotong University, 1954 Hua Shan Road, Shanghai 200030, P. R. China. E-mail: spshen@online.sh.cn.

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 \sigma_{ij} and electric field E_i or displacement {\bf u} and electric displacement D_i. E_i is expressed with an antisymmetric electric field tensor V_{ij}, and D_i is expressed with an antisymmetric electric displacement tensor P_{ij} which can be expressed with ‘induction potential’ \psi_i. Then stress equilibrium and electric field equations can be described by a second order canonical differential equation system of u_i and \psi_i. 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.

DOI: 10.3233/JAE-1999-146

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 10, no. 4, pp. 279-292, 1999