In-Plane Wave Homogenization and the Emergent Electromomentum Tensor

Abstract

The electromomentum coupling is a macroscopic interaction between momentum density and electric field in piezoelectric composites, absent from the response of their constituents. Existing works have focused mainly on its analysis scalar mechanical settings. Here, we develop and apply homogenization scheme for the vectorial settings of in-plane motions of periodic composites, where two wave polarizations coexist. The method defines macroscopic fields by ensemble averaging and uses driving sources to obtain a unique effective model for arbitrary frequency and wavevector excitations.

Numerical examples for composites with circular and circular-sector fibers show that the homogenized model recovers the Bloch dispersion of the underlying microstructure while satisfying physical restrictions, whereas equivalent models that suppress electromomentum coupling may violate these restrictions. The structure of the effective properties distinguishes mesoscale effects, present even for axisymmetric cells at finite wavelengths, from symmetry-breaking contributions that persist in the local response of asymmetric cells. Time-domain scattering simulations further demonstrate that the local effective medium reproduces the macroscopic reflected and transmitted response of the underlying composite for the excitations considered. These results advance the modeling and analysis of electromomentum metamaterials, towards their integration in future wave-control applications.