Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid

Abstract

Stress and electric field concentration around two arbitrarily-shaped holes in a finite electrostrictive solid subjected to uniform remote electric field are studied. The edge of the solid and the shapes of the holes are defined via several conformal mappings. The electro-elastic field of the solid as well as the electric fields both outside the solid and inside the holes are obtained on using conformal mapping techniques, Faber series and Fourier expansion method. Extensive numerical results are shown for elliptical, triangular, square, oval and rectangular holes in a square electrostrictive plane. The exact external electric field near the edge of the solid is found to be essentially non-uniform and its maximum appears to be much larger than the uniform remote electric field, while it is shown that the hoop stress nearby the point of maximum curvature on the hole's boundary increases rapidly as the point of maximum curvature approaches either the edge of the solid or the other hole. On the other hand, for a single centrally-located hole, the finite electrostrictive plane can be approximately treated as an infinite plane if the size of the finite plane is not less than six times the size of the hole, while for two interacting holes, the interaction between them is negligible when the distance between the two holes is larger than three times the size of the holes.