Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866918434711797760 |
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| author | Sabater, Javier Park, Ji-Sung Crassous, Jérôme Neukirch, Sébastien Reis, Pedro M. |
| author_facet | Sabater, Javier Park, Ji-Sung Crassous, Jérôme Neukirch, Sébastien Reis, Pedro M. |
| contents | We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments' axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [1]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from $π/4$ to $4π$ yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder Sabater, Javier Park, Ji-Sung Crassous, Jérôme Neukirch, Sébastien Reis, Pedro M. Soft Condensed Matter Applied Physics We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments' axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [1]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from $π/4$ to $4π$ yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies. |
| title | Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder |
| topic | Soft Condensed Matter Applied Physics |
| url | https://arxiv.org/abs/2604.06962 |