Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder

Abstract

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  [Johanns et al., "Strength of surgical knots under cyclic loading conditions," Science Advances (2023)]. 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.