Numerical analysis of an electrode embedded between dissimilar electrostrictive materials

The asymptotic problem of an electrode that is embedded between dissimilar electrostrictive materials and subjected to electric loading is numerically analyzed by using the finite element method. Electrostatic analysis for the asymptotic problem is conducted under the small-scale saturation condition on the basis of the mathematical equivalence between anti-plane shearing and electrostatics. The distribution of the electric displacement fields is obtained. It is shown that the shapes of the saturation zones are affected by the ratios of the permittivities and the saturated electric displacements between the dissimilar electrostrictive materials. Stress fields that are generated for matching incompatible strains, which are induced by non-uniform electric displacement fields, are numerically calculated for various combinations of the material properties. Also, stress intensity factors for arbitrary small cracks that are initiated from the edge of an electrode are evaluated. Behaviors of cracking that may take place at the edge of an electrode are discussed.