On piezoelectric inhomogeneity related problem—part I: a close-form solution for the stress field outside a circular piezoelectric inhomogeneity

Abstract

The stress investigation for a circular piezoelectric fiber sensor embedded in a non-piezoelectric elastic material has been carried out. During the formulation procedure, the inhomogeneity problem is partially decoupled into an elastic problem and a dielectric inhomogeneity problem connected via some eigenstrain and eigen-electric field. The stress field inside the piezoelectric fiber sensor (the inhomogeneity) is evaluated based on Eshelby’s equivalent inclusion method. While the explicit close-form solution for the stress distribution outside the inhomogeneity is obtained through Tanak–Mura’s superposition process. The analytical solutions presented in this paper have been checked and confirmed by finite element analysis results.