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.

• Received 7 May 2021
• Revised 17 August 2021
• Accepted 22 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.218002