Not-knots as the building block of elastic knots*

Knots are key for a wide variety of applications such as mooring ships to docks, ensuring the safety of a falling climber or fastening surgical suture threads. Even if knots have been used in hundreds of configurations for millennia, the understanding of their mechanical behavior remains mainly empirical. Past fundamental studies on knots include ideal knots, purely based on geometry and one-dimensional reduced elasticity models. For tight knots, intricate three-dimensional geometries, large deformations, and friction between rod strands are all present in setting a highly nonlinear and coupled behavior. To gain better insight into this complex class of problems, we study the ‘not-knot’; a simpler model system composed of a clasp of two bent elastic rods brought together in mechanical contact. We use X-ray computed tomography to probe the geometry of not-knots, as well as precise force-displacement measurements to quantify the interplay of bending curvature, elasticity, and friction. We believe that regarding complex tight knots as assemblies of simple not-knots will provide a solid foundation to develop much needed predictive models for knotted structures.