Electrostrictive stresses around an elliptical hole

By using the complex variable theory combined with the conformal method, this paper studies the electro-strictive stress around an elliptical hole in an infinite uniform plane subjected to a remote electric field. Emphasis is focused on the discussion about the effect of Maxwell´ stresses inside the elliptical hole on the stress field around the elliptical hole. Firstly, through using electric boundary conditions and calculating the Cauchy integral along the boundary of the elliptical hole, the complex functions are obtained. Then, the stress fields for the plane stress problem are presented in the analytical form. Finally, the effect of Maxwell´ stresses on the stress field around the elliptical hole is discussed. The curves of the stress around the elliptical hole and along the line ahead the right point of the ellipse are also given under different size of the hole, respectively. It is found that when the hole degenerates into a crack, the stress field at the crack tip is not singular, and the stress is uniform everywhere in the infinite matrix.