Stretching Instability of Helical Springs

David A. Kessler, Yitzhak Rabin

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48 Scopus citations


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 steplike 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.

Original languageEnglish
Pages (from-to)4
Number of pages1
JournalPhysical Review Letters
Issue number2
StatePublished - 2003

Bibliographical note

Funding Information:
D. A. K. and Y. R. acknowledge the support of the Israel Science Foundation.


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