Odd Elasticity in Disordered Chiral Active Materials

Chiral active materials generate motion with a preferred helical or rotational direction, generally due to the presence of local torques fueled by local energy consumption. These materials are abundant in nature, including cytoskeleton twisted by motor proteins, rotary clusters of bacteria, and self-spinning starfish embryos. Due to broken mirror-image symmetry, chiral active materials may exhibit `odd’ elasticity. Odd elasticity non-reciprocally couples two different modes of shear strain with shear stress and hence shows unusual intriguing mechanics. The current search for odd elasticity focused on ordered structures, e.g., lattice designs of metamaterials. It still remains less explored how odd elasticity can emerge in disordered elastic materials, which are ubiquitous in biological and synthetic systems. In this theoretical work, we propose a minimal generic model for disordered `odd solids’, using micropolar/Cosserat elasticity with local active torques, and apply to a two-dimensional system. We find that odd elasticity emerges from the nonlinear elasticity. We further study the viscoelasticity of this solid by immersing it in active self-spinning solvent (`odd fluid'). We discover a new type of propagating waves and new unreported instability regions in the dynamic phase diagram.