Tension-induced multistability in inextensible helical ribbons

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.

11 pages, 6 figures

References in corpus (2)

• Stretching Instability of Helical Spring
• Stretching helical nano-springs at finite temperature

Cited by in corpus (6)

• "Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods
• A non-linear rod model for folded elastic strips
• Force and moment balance equations for geometric variational problems on curves
• Bistability and equilibria of creased annular sheets and strips
• Cascade unlooping of a low-pitch helical spring under tension
• Effective extensional-torsional elasticity and dynamics of helical filaments under distributed loads