Mechanics of Metric Frustration in Contorted Filament Bundles: From Local Symmetry to Columnar Elasticity.

Bundles of filaments are subject to geometric frustration: certain deformations (e.g., bending while twisted) require longitudinal variations in spacing between filaments. While bundles are common-from protein fibers to yarns-the mechanical consequences of longitudinal frustration are unknown. We derive a geometrically nonlinear formalism for bundle mechanics, using a gaugelike symmetry under reptations along filament backbones. We relate force balance to orientational geometry and assess the elastic cost of frustration in twisted-toroidal bundles.