Author
Moulton, D
Neukirch, S
Grandgeorge, P
Journal title
Journal of the Mechanics and Physics of Solids
DOI
10.1016/j.jmps.2018.03.019
Volume
116
Last updated
2024-02-26T22:35:03.427+00:00
Page
33-53
Abstract
We study an elastic rod bent into an open trefoil knot and clamped at both ends. The question we consider is whether there are stable configurations for which there are no points of self-contact. This idea can be fairly easily replicated with a thin strip of paper, but is more difficult or even impossible with a flexible wire. We search for such configurations within the space of three tuning parameters related to the degrees of freedom in a simple experiment. Mathematically, we show, both within standard Kirchhoff theory as well within an elastic strip theory, that stable and contact-free knotted configurations can be found, and we classify the corresponding parametric regions. Numerical results are complemented with an asymptotic analysis that demonstrates the presence of knots near the doubly-covered ring. In the case of the strip model, quantitative experiments of the region of good knots are also provided to validate the theory.
Symplectic ID
831682
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Publication type
Journal Article
Publication date
27 Mar 2018
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