UNIVERSAL RELATIONS IN PIEZOELECTRIC COMPOSITES WITH EIGENSTRESS AND POLARIZATION-FIELDS .2. MULTIPHASE MEDIA - EFFECTIVE BEHAVIOR

We consider heterogeneous piezoelectric media in general and multiphase piezoelectric composites in particular. A distribution of statistically homogeneous eigenstress and spontaneous polarization fields is admitted in the solid which is itself statistically homogeneous, and the effective eigenstress and spontaneous polarization is sought. The method here is based on the use of virtual work theorems in piezoelectric media and therefore differs from the approach used in the companion paper (Benveniste, 1993). We show that the effective eigenstress and polarization follow from a knowledge of the influence functions related to an electromechanical loading of the composite aggregate in which no eigenstresses and polarizations are present. When applied to the special case of binary systems with constant eigenstress and polarization fields in the phases, the above result implies that the effective eigenstress and polarization can be determined in terms of the effective elastic, piezoelectric, dielectric tensors of the medium, the constituent properties, and the individual eigenstresses and polarizations.