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The simple asymptotic problem of an impermeable crack in an electrostrictive ceramic under electric loading is analyzed. Closed form solutions of elastic fields are obtained by using the complex function theory. It is found that the K I -dominant region is very small compared to the electric saturation zone. A fracture parameter for an electrostrictive material subjected to electric loading is discussed. In order to investigate the influence of the transverse electric displacement on fracture behavior under the small-scale conditions, we also consider the modified boundary layer problem of a crack in an electrostrictive material. Analytic solutions of electric displacement fields for the asymptotic problem are obtained based on the nonlinear dielectric theory from a modified boundary layer analysis. The shape of the electric displacement saturation zone is shown to depend on the transverse electric displacement. Stress intensity factors induced by the electrostrictive strains are evaluated using the nonlinear solution of the electric displacements. It is found that the transverse electric displacement affects strongly the variation of the mode mixity.

a b s t r a c tProperties of the J integral for a conductive tubular channel embedded in a dielectric material are examined. It is shown that the J integral can be interpreted as the energy release per unit length of the channel due to the channel growth. In order to investigate the effect of a conductive defect on the dielectric breakdown, the asymptotic problem of a conductive hemispheroid on an electrode sheet is considered. The J integral for the hemispheroidal defect is obtained in the closed form from the electrostatic solution. The J integral for a tubular channel with a hemispheroidal head is calculated numerically through the finite element analysis. It is found that the breakdown strength is sensitive to the length and head shape of the channel. The variation of the apparent breakdown strength for the dielectric material with the conductive hemispheroidal defect is also discussed.

a b s t r a c tThe 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.