Stress and electric fields in an infinite electrostrictive plate with an elliptic inhomogeneity

The stress and electric fields in electrostrictive materials under general electric loading at infinity are obtained in this paper. It is shown that the pseudo total stresses are continuous in the whole body. The elliptic inhomogeneity problem is first discussed in this paper and its solution is also given. The results show that the stress in the inhomogeneity is not uniform which is different from the solution of Eshelby theory for elastic materials. When the inhomogeneity and matrix have the same dielectric permittivity or the matrix is a non-electrostrictive material, the stress field is uniform in the inhomogeneity. The form of stress function is simple when the inhomogeneity degenerates to a circle.