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We investigate the quasi-static growth of elastic fibers in the presence ofdry or viscous friction. An unusual form of destabilization beyond a criticallength is described. In order to characterize this phenomenon, a new definitionof stability against infinitesimal perturbations over finite time intervals isproposed and a semi-analytical method for the determination of the criticallength is developed. The post-critical behavior of the system is studied byusing an appropriate numerical scheme based on variational methods. We findpost-critical shapes for uniformly distributed as well as for concentratedgrowth and demonstrate convergence to a figure-8 shape for large lengths whenself-crossing is allowed. Comparison with simple physical experiments yieldsreasonable accuracy of the theoretical predictions.

Shape of an elastica under growth restricted by friction