On double circular inclusion problem in antiplane piezoelectricity

Abstract

In this paper, an analytical solution in series form for the problem of double circular piezoelectric inclusions embedded in an infinite piezoelectric matrix is presented within the framework of linear theory of piezoelectricity. The matrix is subjected to remote electro-mechanical loading, and the three phase system is also subjected to the action of arbitrary singularities. The solution is obtained by applying complex potential approach in conjunction with the techniques of conformal mapping, analytical continuation, singularity analysis, Laurent's series expansion in an annular ring region and Cauchy integral formulae, etc. Based on the obtained complex potentials, explicit expressions for the stress and electric displacement in the matrix and the two circular inclusions are also derived. A numerical investigation for the case of remote loading is performed to illustrate the influence of a third phase on the system's electroelastic coupling behavior and also to verify the correctness and usefulness of the solution.