Tension-induced multistability in inextensible helical ribbons

TL;DR

This paper introduces a new model for inextensible elastic helical ribbons that predicts hysteresis and multistability, explaining experimental observations and revealing complex uncoiling behaviors relevant for nanoscale devices.

Contribution

The authors develop a novel inextensible elastic strip model that captures hysteresis and multistability in helical ribbons, extending beyond previous rod models.

Findings

Prediction of hysteresis in low-pitch ribbons

Identification of a first-order transition between helical states

Discovery of a new uncoiling scenario with sequential loop release

Abstract

We study the non-monotonic force-extension behaviour of helical ribbons using a new model for inextensible elastic strips. Unlike previous rod models our model predicts hysteresis behaviour for low-pitch ribbons of arbitrary material properties. Associated with it is a first-order transition between two different helical states as observed in experiments with cholesterol ribbons. Numerical solutions show non-uniform uncoiling with hysteresis also occurring under controlled tension. They furthermore reveal a new uncoiling scenario in which a ribbon of very low pitch shears under tension and successively releases a sequence of almost planar loops. Our results may be relevant for nanoscale devices such as force probes.