Variational bounds of the effective moduli of piezoelectric composites

Abstract

The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric materials. The auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic medium. The electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields. A closed-form solution can be obtained for the disturbance fields, which is convenient for the manipulation of the energy functional. As an application, a two-phase piezoelectric composite with nonpiezoelectric matrix is considered. Expressions of upper and lower bounds for the overall electromechanical moduli of the composite can be developed. These bounds are shown better than the Voigt-Reuss type ones.