Odd Cosserat elasticity in active materials

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.

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Cited by in corpus (7)

• Probe particles in odd active viscoelastic fluids: how activity and dissipation determine linear stability
• Generalizing odd elasticity theory to odd thermoelasticity for planar materials
• Engineering active motion in quantum matter
• Molecular modelling of odd viscoelastic fluids
• A geometric formulation of Schaefer's theory of Cosserat solids
• Nonclassical heat flow in passive chiral solids is third rank, not odd
• Odd elasticity in disordered chiral active materials