Odd Cosserat elasticity in active materials

TL;DR

This paper extends Cosserat elasticity to include chiral active components and odd elasticity, analyzing static properties, wave dispersion, and surface wave polarization, revealing exceptional points and distinct wave regimes.

Contribution

It introduces a novel odd Cosserat elasticity model incorporating chiral active effects and analyzes its static and dynamic properties, including wave behavior and surface wave polarization.

Findings

Static response depends on Cosserat and odd elasticity

Presence of exceptional points in wave dispersion

Distinct regimes of wave attenuation and propagation

Abstract

Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modelled using Cosserat (also called micropolar) elasticity. In this paper, we explore the phenomenology for a natural extension of Cosserat materials that includes chiral active components and odd elasticity. We calculate static elastic properties of such a solid, where we show that static response to rotational stresses leads to strains that depend on both Cosserat and odd elasticity. We then compute the dispersion of linear solutions in these odd Cosserat materials in the overdamped regime and find the presence of \emph{exceptional points} in the dispersion relation. We discover that these exceptional points create a sharp boundary between a Cosserat-dominated regime of complete wave attenuation and an odd-elasticity-dominated regime of propagating waves. We conclude by showing the effect of Cosserat and odd elastic terms on the polarization of Rayleigh surface waves.