Cascade unlooping of a low-pitch helical spring under tension

E.L. Starostin & G.H.M. van der Heijden

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.

keywords: thin anisotropic elastic rod, helical spring, cascade unlooping, planar elastica, force-extension response, loop pop-out, hysteresis

Journal of the Mechanics and Physics of Solids 57, 959-969 (2009)