Interacting circular inclusions in antiplane piezoelectricity

The problem of multiple piezoelectric circular inclusions, which are perfec tly bonded to a piezoelectric matrix, is analyzed in the framework of linea r piezoelectricity. Both the matrix and the inclusions are assumed to posse ss the symmetry of a hexagonal crystal in the 6 mm class and subject to ele ctromechanical loadings (singularities) which produce in-plane electric fie lds and out-of-plane displacement. Based upon the complex variable theory a nd the method of successive approximations, the solution of electric field and displacement field either in the inclusions or in the matrix is express ed in terms of explicit series form. Stress and electric field concentratio ns are studied in detail which are dependent on the mismatch in the materia l constants, the distance between two circular inclusions, and the magnitud e of electromechanical loadings. It is shown that, when the two inclusions approach each other, the oscillatory behavior of the stress and electric fi eld can be induced in the inclusion as the matrix and the inclusions are po led in the opposite directions. This important phenomenon can be utilized t o build a very sensitive sensor in a piezoelectric composite material syste m. The present derived solution can also be applied to the inclusion proble m with straight boundaries. The problem associated with three-material medi a under electromechanical sources is also considered. (C) 1999 Elsevier Sci ence Ltd. All rights reserved.