Exotic elastodynamics in thin structures

In this talk I will discuss two recent projects in theoretical, thin-structure elasticity. The first concerns inextensible rods that can flex and sustain axial forces and torques within an Euler-Bernoulli description, also known as the worm-like chain model. Surprisingly, the dynamics of such rods are isomorphic to the dynamics of a minimally coupled quantum particle in 1D, including de Broglie and uncertainty relations. When one of these rods is formed into a ring, its vibrations give rise to quantized orbital angular momentum and a “twist quantum” that is analogous to the magnetic flux quantum. In the second part of the talk I will introduce an exciting new area of continuum mechanics called “odd elasticity,” relevant to active, driven, or otherwise out-of-equilibrium systems that feature non-reciprocal interactions. I will then show how the mathematical hallmark of odd elasticity – major anti-symmetry in an elastic response tensor – can also be realized in purely conservative, equilibrium systems by tuning anisotropic prestresses. The tuning recipe that does this can be used to derive lattice spring models that function as unique elastic waveguides, and I will discuss several such models along with their novel acoustic and transport properties.