  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
gauge-like symmetry under reptations along filament backbones. We relate force
balance to orientational geometry and assess the elastic cost of frustration in
twisted toroidal bundles.
