Piezoelectric properties of multiphase fibrous composites: Some theoretical results

A number of exact results are established for overall moduli of a piezoelectric composite medium consisting of many perfectly-bonded transversely isotropic phases of cylindrical shape and arbitrary transverse geometry. It is shown that for three-phase media of this type three universal relationships, which are independent of geometry at given volume fractions, connect six of these effective physical constants. When the phases have equal transverse rigidities in shear, exact values of certain overall moduli can be derived for multiphase systems. The explicit formulae depend solely on the concentrations and phase moduli and are unaffected by the transverse geometry of the inclusions. Specifically, seven out of a total of 10 overall moduli of a transversely isotropic composite can be found. The remaining three constants p, e₁₅ and k₁₁ are shown to obey an exact relation, which also applies to other physical phenomena, such as magnetoelectric and thermoelectric effects. The result is a generalization of the relations found by Hill [J. Mech. Phys. Solids 12, 199 (1964)] for purely elastic media and by Mendelson [J. Appl. Phys. 46, 917 (1975)] for the purely dielectric problem.