Odd elasticity and topological waves in active surfaces

Abstract

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components appear in the elastic tensor. In this work, we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. We find that a free-standing moderately thick, isotropic plate can exhibit two odd-elastic moduli, both of which are related to shear deformations of the plate. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism: the finite thickness of the sample gaps the shear modes and the odd elasticity endows them with chirality.

13 pages, 6 figures

References in corpus (6)

• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Odd Viscosity and Odd Elasticity
• How Does A Porous Shell Collapse? Delayed Buckling And Guided Folding Of Inhomogeneous Capsules
• Fluctuating shells under pressure
• Theory of nematic and polar active fluid surfaces
• Dynamics, scaling behavior, and control of nuclear wrinkling

Cited by in corpus (4)

• Symmetry-driven Phononic Metamaterials
• Classifying topological floppy modes in the continuum
• Odd elasticity in disordered chiral active materials
• Irreversibility of stochastic state transitions in Langevin systems with odd elasticity