Analysis of a Partially Debonded Conducting Rigid Elliptical Inclusion in a Piezoelectric Matrix

A closed-form full-field solution for the problem of a partially debonded conducting rigid elliptical inclusion embedded in a piezoelectric matrix is obtained by employing the eight-dimensional Stroh formula in conjunction with the techniques of conformal mapping, analytical continuation and singularity analysis. Some new identities and sums for anisotropic piezoelectric media are also derived, through which real-form expressions for the stresses and electric displacements along the interface as well as the rotation of the rigid inclusion can be obtained. As is expected, the stresses and electric displacements at the tips of the debonded part of the interface exhibit the same singular behavior as in the case of a straight Griffith interface crack between dissimilar piezoelectric media. Some numerical examples are presented to validate the correctness of the obtained solution and also to illustrate the generality of the exact solution and the effects of various electromechanical loading conditions, geometry parameters and material constants on the distribution of stresses and electric displacements along the interface.