Untangling the mechanics of elastic knots*

In surgery, knots are used as ligatures to bind surgical thread during suturing. Even if breakage or unraveling of knotted configurations can be disastrous, suturing guidelines are mostly empirical. Knot theory, a well-established field of mathematics, tends to focus on idealized, non-elastic knots. Moreover, analytical models based on Kirchhoff’s theory for elastic rods are limited to simple knots in loose configurations. However, functioning knots are in general tight and involve elastic deformation of the thread, self-contact and nontrivial frictional interactions. We tackle this problem by performing high precision experiments to acquire unprecedented experimental data on the geometry and deformation of simple open-knots. We make use of X-ray micro computed tomography to acquire volumetric information of knotted configurations on homogeneous elastomeric rods. Emphasis is placed on systematically exploring how the mechanical properties of the rod, friction, and the externally applied loads, all conspire to dictate the mechanical performance of knotted structures. We hope that the physical insight gained from this experimental characterization will form the bases for future predictive models for physical knots.