Electro-momentum coupling tailored in piezoelectric metamaterials with resonant shunts

TL;DR

This paper demonstrates how to tune electro-momentum coupling in piezoelectric metamaterials using RLC shunts, enabling control over wave propagation and nonreciprocal wave phenomena for advanced applications.

Contribution

It provides a closed-form expression for electro-momentum coupling in shunted piezoelectric metamaterials and shows how to tailor wave responses via electrical stimuli.

Findings

Electro-momentum coupling can be effectively tuned using RLC shunts.

Tailored coupling controls wave amplitudes and phases, enabling asymmetric wave responses.

The approach offers potential for nonreciprocal and programmable metamaterials.

Abstract

Local microstructural heterogeneities of elastic metamaterials give rise to non-local macroscopic cross-coupling between stress-strain and momentum-velocity, known as Willis coupling. Recent advances have revealed that symmetry breaking in piezoelectric metamaterials introduces an additional macroscopic cross-coupling effect, termed electromomentum coupling, linking electrical stimulus and momentum and enabling the emergence of exotic wave phenomena characteristic of Willis materials. The electro-momentum coupling provides an extra degree of freedom for controlling elastic wave propagation in piezoelectric composites through external electrical stimuli. In this study, we present how to tune the electro-momentum coupling arising in 1-D periodic piezoelectric metamaterials with broken inversion symmetry through shunting the inherent capacitance of the individual piezoelectric layers with a resistor and inductor in series forming an RLC (resistor-inductor-capacitor) circuit. Guided by the effective elastodynamic theory and homogenization method for piezoelectric metamaterials, we derived a closed-form expression of the electro-momentum coupling in shunted piezoelectric metamaterials. Moreover, we demonstrate the ability to tailor the electro-momentum coupling coefficient and control the amplitudes and phases of the forward and backward propagating waves, yielding tunable asymmetric wave responses. The results of our study hold promising implications for applications involving nonreciprocal wave phenomena and programmable metamaterials.