Shape of an elastica under growth restricted by friction

Horváth, Marcell G. and Sipos, András Árpád and Várkonyi, Péter László (2019) Shape of an elastica under growth restricted by friction. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 156-15. pp. 137-147. ISSN 0020-7683

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Abstract

We investigate the quasi-static growth of elastic fibers in the presence of isotropic 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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