# Topology, geometry and mechanics of strongly stretched and twisted filaments

## TL;DR

This paper investigates the complex morphologies of soft elastic filaments under stretch and twist, using simulations and topology to understand their structures and behaviors relevant to artificial muscles.

## Contribution

It combines numerical simulations with topological analysis to map filament morphologies and explain the link between topology, geometry, and mechanics in practical fiber-based systems.

## Key findings

- Identified various filament morphologies like plectonemes and knots.
- Mapped phase diagram of structures based on extension and twist.
- Linked topological transformations to mechanical behaviors in experiments.

## Abstract

Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical simulations of soft elastic filaments that account for geometric nonlinearities and self-contact to map out these structures in a phase diagram that is a function of extension and twist density, consistent with previous experimental observations. By using ideas from computational topology, we also track the interconversion of link, twist and writhe in these geometrically complex physical structures. This allows us to explain recent experiments on fiber-based artificial muscles that use the conversion of writhe to extension or contraction, exposing the connection between topology, geometry and mechanics in an everyday practical setting.