Discrete One-dimensional Models for the Electromomentum Coupling

TL;DR

This paper introduces a simple one-dimensional discrete model demonstrating electromomentum coupling in subwavelength piezoelectric composites, elucidating its physical origins, mechanisms, and resonance effects to guide metamaterial design.

Contribution

It presents the first minimal discrete model capturing electromomentum coupling, explaining its physical basis and resonance phenomena in piezoelectric metamaterials.

Findings

Identification of local resonances enhancing coupling

Illustration of the coupling mechanism in the model

Guidelines for designing electromomentum coupling in metamaterials

Abstract

Willis dynamic homogenization theory revealed that the effective linear momentum of elastic composites is coupled to their effective strain. % This result, which is partially due to asymmetry at the subwavelength scale, implies that spatially-uniform but time-varying stress can induce temporal variations in the macroscopically observable momentum. Recent generalization of Willis' dynamic homogenization theory to the case of piezoelectric composites further revealed that their effective linear momentum is also coupled to the effective electric field. Here, we introduce the simplest possible model -- a one-dimensional discrete model -- that exhibits this so-called electromomentum coupling in subwavelength composites. We utilize our model to elucidate the physical origins of this phenomenon, illustrate its mechanism, and identify local resonances which lead to elevated Willis- and electromomentum coupling in narrow frequency bands. The results provide intuitive guidelines for the design of this coupling in piezoelectric metamaterials.