Variational and microstructure-independent relations for piezoelectric composites

The Hill-Mandel lemma is first extended to piezoelectricity. It is then shown that, when the macroscopic variable couple is fixed and when the local piezoelectric tensor field is subjected to a variation, the variation of the macroscopic energy is equal to the volume average of the variations of the microscopic energy. This variational relation is finally used to derive microstructure-independent relations.