Thermoelectroelastic solution for elliptic inclusions and application to crack–inclusion problems

Abstract

The thermoelectroelastic solution for an elliptic piezoelectric inclusion embedded in an infinite matrix and its application to crack–inclusion problems are investigated in this paper. By combining the method of Stroh's formalism, the technique of conformal mapping, the concept of perturbation and the method of analytical continuation, a general analytical thermoelectroelastic solution for an elliptic piezoelectric inclusion embedded in an infinite piezoelectric matrix subjected to thermal loading is obtained. The loading may be point heat source, temperature discontinuity, or uniform remote heat flow. Special cases when the inclusion becomes rigid or a hole are also investigated. As an application of the proposed solution, a system of singular integral equations is derived for analyzing crack–inclusion interactions. Numerical results for a piezoelectric plate with an elliptic inclusion and an inclined crack are given to illustrate the application of the proposed formulation.