# Symmetry Breaking Creates Electro-Momentum Coupling in Piezoelectric Metamaterials

## TL;DR

This paper introduces a homogenization method revealing new electro-momentum couplings in piezoelectric metamaterials caused by symmetry breaking, enabling advanced active wave control through external stimuli.

## Contribution

It develops a rigorous homogenization framework to identify symmetry-breaking induced couplings in responsive metamaterials, specifically unveiling electro-momentum interactions in piezoelectric systems.

## Key findings

- Discovered Willis-like couplings in piezoelectric metamaterials.
- Developed a homogenization method for responsive metamaterials.
- Demonstrated potential for active wave control via external stimuli.

## Abstract

Metamaterials posses microstructure designed to acquire properties not found in nature. An epitome in acoustics and solid mechanics is Willis coupling, which refers to the particle velocity-stress coupling, and of great significance since it controls mechanical waves. We here reveal new couplings, analogous to Willis coupling, when considering patterns of materials that mechanically interact with magnetic, electric or thermal fields. To this end, we develop a rigorous homogenization method for the effective properties of such responsive metamaterials. As an example, we apply the scheme to piezoelectric materials, and unveil coupling of the velocity and electric fields. Hence, Willis-like couplings in responsive metamaterials open new avenues for active wave control by modulation of external stimuli.