Elastic knots.
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.
Audoly
B
B
Institut Jean le Rond d'Alembert, UMR 7190, CNRS, Paris, France.
Clauvelin
N
N
Neukirch
S
S