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arXiv · 1806.06968

Shape of an elastica under growth restricted by friction

Marcell G. Horváth·András Á. Sipos·Péter L. Várkonyi
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Abstract

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure-8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions.

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Marcell G. Horváth, András Á. Sipos, Péter L. Várkonyi. 2018-06-18. Shape of an elastica under growth restricted by friction. https://arxiv.org/abs/1806.06968

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