Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

Homogenization theories provide models that simplify the constitutive description of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain-momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green's function method predicted analogous electro-momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequencywavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Homogenization theories simplify the constitutive description of heterogeneous media, while retaining their macroscopic features; The Willis theory predicts the strain-momentum coupling in elastodynamic metamaterials; A recent theory predicts analogous electro-momentum coupling in piezoelectric metamaterials.