Cylinder morphology of a stretched and twisted ribbon

TL;DR

This paper investigates the shape transitions of a stretched and twisted elastic ribbon, focusing on the cylindrical form that emerges at high tension and twist, combining theoretical modeling with experimental validation.

Contribution

It introduces a simple theoretical description for the cylindrical shape and maps its stability region on the phase diagram, advancing understanding of elastic ribbon morphologies.

Findings

The cylindrical shape is predicted to occur at high tension and twist.

Theoretical predictions match experimental observations.

A phase diagram delineates shape stability regions.

Abstract

A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a transverse instability of the helicoid. Here, we propose a simple description for this cylindrical shape. By comparing its energy to the energy of other configurations, we are able to determine its location on the phase diagram. The theoretical predictions are in good agreement with our experimental results.