Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots
We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to quantify the dependence of the mechanical res...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/98481 https://orcid.org/0000-0003-3984-828X https://orcid.org/0000-0003-4661-1408 |
| Summary: | We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to quantify the dependence of the mechanical response of the knot as a function of the geometry of the self-contacting region, and for different topologies as measured by their crossing number. An analytical model based on the nonlinear theory of thin elastic rods is then developed to describe how the physical and topological parameters of the knot set the tensile force required for equilibrium. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers. |
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