Solution of an elliptic inclusion in an electrostrictive solid

This paper presents the theoretical and numerical results for the plane problem of an elliptic inclusion in an infinite electrostrictive solid subjected to remote electric fields based on the Faber series method. Firstly, the general solutions are obtained for the electric fields inside the elliptical inclusion and the complex potentials in the solid, respectively. Secondly, the complex potentials in the elliptic inclusion in the form of Faber series with unknown coefficients are expressed and then they are inserted into the boundary condition on the interface. Finally, numerical results of stresses around the inclusions are given for different permittivity and electrostrictive coefficients. It is found that as the ratio of permittivity and electrostrictive coefficients increases, the absolute value of the hoop stress increases.