Curved Odd Elasticity

TL;DR

This paper develops a covariant theory to study how curvature influences active solids, revealing effects on spectral properties, defect modes, and activity patterns, with implications for biological tissues and active metamaterials.

Contribution

It introduces a covariant effective theory for active solids on curved manifolds, linking curvature to non-reciprocal elasticity and spectral phenomena.

Findings

Curvature patterns activity distribution.

Gaps in the spectral response due to curvature.

Emergence of non-Hermitian defect modes.

Abstract

Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference configuration. These materials often live in complex and curved manifolds, yet most descriptions of active solids are flat. Here, we explore the interplay between curvature and non-reciprocal elasticity via a covariant effective theory on curved manifolds in combination with numerical simulations. We find that curvature spatially patterns activity, gaps the spectrum, modifies exceptional points and introduces non-Hermitian defect modes. Together these results establish a foundation for hydrodynamic and rheological models on curved manifolds, with direct implications for living matter and active metamaterials.