Elliptical Inclusion Problem in Antiplane Piezoelectricity: Stress Concentrations and Energy Release Rates

An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of antiplane piezoelectricity. The stress distribution patterns for different elliptical inclusion and cavity shapes with different material constants are discussed based on the closed-form solution obtained by the authors. It is found that the stress concentration at the interface of the inclusion and the matrix becomes significantly high when piezoelectric constants of the inclusion and matrix have opposite sign. The variation in the energy release rates of selfsimilarly expanding and rotating defects, expressed by the M-and L-integrals, respectively, are discussed as a function of the applied electric field. Information on the stress concentration and the energetics of such a system can be quite useful in predicting failures, hence, aid in properly designing piezoelectric electromechanical systems.