Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
e-mail: sebastien.neukirch (-atat-) upmc.fr

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Elastic knots

Basile Audoly, Nicolas Clauvelin and Sébastien Neukirch

Physical Review Letters, 99 (2007) 164301

Abstract : We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equilibrium are compared to experiments. The extension of the theory to tight knots is discussed.

PACS numbers : 46.25.-y, 46.70.Hg

Key words : elastic rods, self-contact, matched asymptotic expansion, boundary layer approach

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