The electromomentum effect in piezoelectric Willis scatterers

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