On the Interaction of Two Piezoelectric Fibers Embedded in an Intelligent Material

Abstract

In this paper we are concerned with the problem of two circular piezoelectric fibers of different radii and distinct material properties, perfectly bonded to a host intelligent material, of infinite extent. The matrix material may be piezoelectric or nonpiezoelectric but, together with the fibers' materials, it possesses the symmetry of a hexagonal crystal in the 6 mm class. The system is subjected to electromechanical loadings (singularities) which produce out-of-plane displacement and in-plane electric fields, but are otherwise arbitrary. Within the framework of the procedure of heterogenization, recently developed by the authors, the solution is sought as a transformation applied to the solution of the corresponding homogeneous problem (i.e., the problem of the host material occupying the full space and subjected to the same sources). The solution is formulated in a manner which leads to some exact results. Universal formulae are derived for the electromechanical field at the point of contact of two piezoelectric fibers. Some quantities which are invariant under the transformation, i.e., quantities which take the same values in the heterogeneous as in the corresponding homogeneous problems, are also discovered. The ramifications of this discovery are investigated. Moreover, the asymptotic behavior of the electromechanical field at the closest points of two plated circular holes or rigid conductors, approaching each other in an intelligent matrix material is also studied and given by universal formulae, i.e., formulae which are independent of the electromechanical sources. The interaction of the fibers with host-material microdefects, such as dislocations, electric line charges and microvoids, is scrutinized. The possibility of manipulating the electrical potential to reduce the high stress level is also discussed.