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Elastic knots N. Clauvelin, and S. Neukirch

Summary: Elastic knots
B. Audoly,
N. Clauvelin, and S. Neukirch
Institut Jean le Rond d'Alembert,
UMR 7190: CNRS & Universit´e Pierre et Marie Curie, Paris, France
(Dated: September 28, 2007)
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,
Knots have long been considered mainly from a math-
ematical perspective but this topic has today spread to
different areas in science. Fishermen and sailors know
that tying a knot on a rope severely reduces its tensile
strength [1]. More recently knots have been tied on bio-
logical molecules [2], micrometric silica wires [3], or lipid-
bilayer nanotubes [4] and their properties were compared
to unknotted configurations. Sufficiently long polymers


Source: Audoly, Basile - Institut Jean Le Rond D'Alembert, Université Pierre-et-Marie-Curie, Paris 6


Collections: Materials Science; Physics