Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7177411 | Journal of the Mechanics and Physics of Solids | 2018 | 33 Pages |
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.
Related Topics
Physical Sciences and Engineering
Engineering
Mechanical Engineering
Authors
Derek E. Moulton, Paul Grandgeorge, Sébastien Neukirch,