Let me spin you a yarn: fiber geometry and the elasticity of twisted filaments

Flexible bundles of twisted filaments are found in myriad materials across lengthscales, from biopolymers like DNA to more familiar yarns and cables. Ordered ground states in filament bundles, however, are highly geometrically constrained, and we show that only two families of filament textures permit equidistance between the constituent filaments---the developable domains, which can bend, but not twist, and the helical domains, which can twist uniformly, but not bend. Because of this, the spacing between filaments varies along their length when twisted bundles bend, and so two dimensional descriptions, like those used to describe columnar liquid crystals, are inadequate. To better describe the elasticity of non-equidistant bundles, we must account for invariance under reptations: continuous zero energy deformations corresponding to displacements along the filaments. The resulting force balance equations show that constant spacing plays an essential role in the mechanics of filament bundles, with deviations from equidistance generating forces along the filament tangents. We use this gauge-theoretic description of filaments' elasticity to describe the low energy configurations of weakly curved twisted toroidal bundles, showing that this longitudinal frustration leads to an effective bending stiffness which is independent of the filaments' flexibility, and instead determined by the bundle's twist.