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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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