Mechanics of metric frustration in contorted filament bundles: From local symmetry to columnar elasticity

TL;DR

This paper develops a nonlinear geometric framework to understand how filament bundles deform under frustration, revealing the mechanical effects of combined bending and twisting in complex structures.

Contribution

It introduces a gauge-like formalism for bundle mechanics, linking force balance to filament orientation and quantifying frustration effects in twisted toroidal bundles.

Findings

Derived a nonlinear formalism for filament bundle mechanics.

Linked force balance to filament orientation geometry.

Quantified elastic costs of frustration in twisted bundles.

Abstract

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.