Piezoelectric study for a three-phase composite containing arbitrary inclusion

This paper analyzes a coated inclusion of arbitrary shape embedded in an infinite plate subjected to anti-plane mechanical and in-plane electrical loadings. Based on the methods of complex variable, conformal mapping, Faber series and Laurent series, the complex potential for each component can be expressed in series form with unknown coefficients. The continuity conditions of the interfaces are used to build up a set of linear equations to determine the unknown coefficients. The exact solutions are obtained after the complex potentials are solved. By truncating the infinite system of linear equations at finite N terms, some numerical examples are provided to show the effect of the material mismatch and the shape of inclusion on the interfacial stress and elastic field. The accuracy of the linear systems is also discussed in the article.