Topological Defects in Twisted Bundles of Two-Dimensionally Ordered Filaments

TL;DR

This paper explores the elastic properties and defect structures in twisted filament bundles, revealing how disclinations influence stability and induce buckling, with implications for biological and material systems.

Contribution

It introduces a continuum elastic model linking twist-induced stresses to defect arrangements and predicts defect-driven buckling in filament bundles.

Findings

Elastic stresses from twist are analogous to positive curvature in elastic sheets.

Disclination defects can screen twist-induced stresses, leading to discrete energy states.

Off-center disclinations cause the entire bundle to buckle and adopt writhing configurations.

Abstract

Twisted assemblies of filaments in ropes, cables and bundles are essential structural elements in wide use in macroscopic materials as well as within the cells and tissues of living organisms. We develop the unique, non-linear elastic properties of twisted filament bundles that derive from generic properties of two-dimensional line-ordered materials. Continuum elasticity reveals a formal equivalence between the elastic stresses induced by bundle twist and those induced by the positive curvature in thin, elastic sheets. These geometrically-induced stresses can be screened by 5-fold disclination defects in lattice packing, and we predict a discrete spectrum elastic energy groundstates associated with integer numbers of disclinations in cylindrical bundles. Finally, we show that elastic-energy groundstates are extremely sensitive to defect position in the cross-section, with off-center disclinations driving the entire bundle to buckle, adopting globally writhing configurations.