A variational approach of homogenization of piezoelectric composites towards piezoelectric and flexoelectric effective media

The effective piezoelectric properties of heterogeneous materials are evaluated in the context periodic homogenization, whereby a variational formulation is developed, articulated with extended Hill macrohomogeneity condition. entire set homogenized moduli obtained as volumetric averages microscopic individual constituents weighted by displacement and polarization localization operators. This framework second part paper to computation flexoelectric properties, thereby accounting for higher gradient effects that may be induced strong contrast composite constituents. inclusion-based composites numerically an illustration general homogenization theory respective effect volume fraction relative tensile modulus reinforcement assessed numerically.