Interacting circular inclusions in antiplanepiezoelectricity

The problem of multiple piezoelectric circular inclusions, which are perfectly bondedto a piezoelectric matrix, is analyzed in the framework of linear piezoelectricity. Both the matrixand the inclusions are assumed to possess the symmetry of a hexagonal crystal in the 6 mm classand subject to electromechanical loadings (singularities) which produce in-plane electric fieldsand out-of-plane displacement. Based upon the complex variable theory and the method ofsuccessive approximations, the solution of electric field and displacement field either in theinclusions or in the matrix is expressed in terms of explicit series form. Stress and electric fieldconcentrations are studied in detail which are dependent on the mismatch in the materialconstants, the distance between two circular inclusions, and the magnitude of electromechanicalloadings. It is shown that, when the two inclusions approach each other, the oscillatory behaviorof the stress and electric field can be induced in the inclusion as the matrix and the inclusions arepoled in the opposite directions. This important phenomenon can be utilized to build a verysensitive sensor in a piezoelectric composite material system. The present derived solution canalso be applied to the inclusion problem with straight boundaries. The problem associated withthree-material media under electromechanical sources is also considered.