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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. Recently, it was shown anomalous coupling between the elastodynamic and electric field emerges when piezoelectricity is incorporated into Willis materials. Here, we investigate such one-dimensional piezoelectric Willis elements using heuristic homogenization, long-wavelength asymptotic analysis and numerical experiments. We show that an anomalous electromomentum coupling is necessary to explain the scattering properties of the asymmetric piezoelectric media by a macroscopic description that respects reciprocity and energy conservation. Our findings elucidate the origins of the electromomentum coupling and provide insight for the future design of this new class of coupled-field metamaterials.