Rods coiling about a rigid constraint: Helices and perversions

TL;DR

This paper develops a mathematical model for elastic rods constrained by a rigid support, revealing how they can form helices and perversions under axial forces, with theoretical predictions validated by experiments.

Contribution

It introduces a novel model for constrained elastic rods that predicts complex shapes like helices and perversions, supported by experimental validation.

Findings

Rod can form multiple perversions under certain conditions

Model accurately predicts buckled configurations and shape transitions

Energy landscape explains the formation of complex shapes

Abstract

Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite. Using both theoretical and computational techniques, we characterize the bifurcations of such a mechanical system, in which the axial force and the natural curvature of the beam are used as control parameters. We show that, in the presence of a straight support, the rod can deform into shapes exhibiting helices and perversions, namely transition zones connecting together two helices with opposite chirality. The mathematical predictions of the proposed model are also compared with some experiments, showing a good quantitative agreement. In particular, we find that the buckled configurations may exhibit multiple perversions and we propose a possible explanation for this phenomenon based on the energy landscape of the mechanical system.