Shape of an elastica under growth restricted by friction
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.
Cite
@article{arxiv.1806.06968,
title = {Shape of an elastica under growth restricted by friction},
author = {Marcell G. Horváth and András Á. Sipos and Péter L. Várkonyi},
journal= {arXiv preprint arXiv:1806.06968},
year = {2018}
}