Cascade unlooping of a low-pitch helical spring under tension

TL;DR

This paper investigates the complex force-extension behavior of low-pitch helical springs made from anisotropic elastic rods, revealing non-monotonic responses due to hockle formation and pop-out events, with implications for nanoscale devices.

Contribution

It introduces a detailed analysis of the force-extension behavior of low-pitch helical springs, highlighting the non-unfolding and pop-out phenomena in anisotropic elastic rods.

Findings

Hockle formation prevents unwinding in certain springs.

Force-extension curve exhibits non-monotonic behavior with pop-out events.

Planar elastica solutions accurately describe the behavior between pop-outs.

Abstract

We study the force vs extension behaviour of a helical spring made of a thin torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to unwind when pulled but rather to form hockles that pop-out one by one and lead to a highly non-monotonic force-extension curve. Between abrupt loop pop-outs this curve is well described by the planar elastica whose relevant solutions are classified. Our results may be relevant for tightly coiled nanosprings in future micro- and nano(electro)mechanical devices.