On piezoelectric inhomogeneity related problems - Part I: A close-form solution for the stress field outside a circular piezoelectric inhomogeneity

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.