The electromomentum effect in piezoelectric Willis scatterers

Materials with asymmetric microstructure can constitutively couple macroscopic fields from different physics. Examples include piezoelectric materials that couple mechanical and electric fields and Willis materials that anomalously couple dynamic and elastic fields, for example velocity and stress. Recently, it was shown that anomalous coupling between the elastodynamic and electric field emerges when piezoelectricity is incorporated into Willis materials. Here, we investigate one-dimensional asymmetric piezoelectric Willis elements using heuristic homogenization, long-wavelength asymptotic analysis and numerical experiments. We show that in order to describe the heterogeneous scatterer using a homogenized description that respects reciprocity and energy conservation, anomalous electromomentum moduli must be included. Our findings elucidate the origins of this electromomentum coupling and provide insight for the future design of this new class of coupled-field metamaterials.