Prestress-induced odd elasticity

Previous work has suggested that the presence of prestress induced by active components can lead to non-vanishing odd elastic coefficients [1], although the conditions for prestresses to do so are not clear. Symmetry and conservation laws indicate that equilibrium prestresses should not be sufficient, but what are the minimal set of active or driven components that are needed to achieve odd elastic behavior? Work from 20^th century elasticity theory teaches us that perturbing around a prestressed reference configuration requires working with the nonlinear strain tensor; this also reveals that the rank 4 tensor appearing in the prestressed energy density has fewer symmetries than the usual elastic modulus tensor [2,3]. We show how these symmetry conditions can be exploited to yield a recipe for dynamically stable, prestress-induced odd elasticity. We then use this recipe to derive a minimal lattice model – a 2D triangular lattice with a mixture of positive and negative stiffness bonds under biaxial prestress – that functions as an odd elastic waveguide.



[1] M. Fruchart, C. Scheibner, & V. Vitelli, Odd viscosity and odd elasticity, Annu. Rev. Condens. Matter Phys. 14, 471-510 (2023).

[2] K. Huang, On the atomic theory of elasticity, Proc. R. Soc. Lond. A 203, 178-194 (1950).

[3] T. H. K. Barron & M. L. Klein, Second-order elastic constants of a solid under stress. Proc. Phys. Soc. 85, 523-532 (1965).