Stretching Instability of Helical Spring

TL;DR

This paper investigates the nonlinear stretching behavior of helical springs, revealing multiple discontinuous transitions and hysteresis phenomena under tensile forces, with implications for understanding their mechanical stability.

Contribution

It introduces a theoretical analysis of stretching instabilities in helical springs, identifying critical conditions and transition behaviors not previously characterized.

Findings

Multiple discontinuous stretching transitions observed

Hysteresis during force decrease demonstrated

Number of transitions increases with helix length

Abstract

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur, and propose experimental tests of our predictions.