Shape of an elastica under growth restricted by friction

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:156

Article

Horvath, Marcell G.¹  Sipos, Andras A.^1,2  Varkonyi, Peter L.¹ 

[1] Budapest Univ Technol & Econ, Dept Mech Mat & Struct, Muegyet Rkp 1-3,K261, H-1111 Budapest, Hungary

[2] MTA BME Morphodynam Res Grp, Budapest, Hungary

关键词: Friction;    Buckling;    Elastica;    Growth;   

DOI  :  10.1016/j.ijsolstr.2018.08.009

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Ltd. All rights reserved.

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