Energetics of twisted elastic filament pairs

TL;DR

This study explores how elastic energy and torque in twisted filament pairs evolve with applied twist, revealing the dominant role of stretching energy and providing a nonlinear model that captures the filament's geometric and energetic behavior.

Contribution

The paper introduces a nonlinear elasto-geometric model that accurately describes the energy and torque evolution in twisted elastic filaments, emphasizing the importance of stretching over bending or contact energy.

Findings

Torque peaks and then decreases as filaments cross and contact.

Stretching accounts for most stored energy, increasing with separation.

Bending and contact energies are negligible compared to stretching.

Abstract

We investigate the elastic energy stored in a filament pair as a function of applied twist by measuring torque under prescribed end-to-end separation conditions. We show that the torque increases rapidly to a peak with applied twist when the filaments are initially separate, then decreases to a minimum as the filaments cross and come into contact. The torque then increases again while the filaments form a double helix with increasing twist. A nonlinear elasto-geometric model that combines the effect of geometrical nonlinearities with large stretching and self-twist is shown to capture the evolution of the helical geometry, the torque profile, and the stored energy with twist. We find that a large fraction of the total energy is stored in stretching the filaments, which increases with separation distance and applied tension. We find that only a small fraction of energy is stored in the form of bending energy, and that the contribution due to contact energy is negligible. Our study highlights the consequences of stretchablility on filament twisting which is a fundamental topological transformation relevant to making ropes, tying shoelaces, actuating robots, and the physical properties of entangled polymers.