MEchanics GAthering -MEGA- Seminar: Untangling the mechanics of elastic knots and not-knots
Event details
| Date | 20.12.2018 |
| Hour | 16:15 › 17:30 |
| Speaker | Paul Johanns & Paul Grandgeorge, fleXLab, EPFL |
| Location | |
| Category | Conferences - Seminars |
Abstract
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. 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. Such descriptions are too abstract for practical settings. Realistic physical knots are in general tight, with no separation of length scales; the overall size of the knot, the diameter of the rod, and its characteristic radii of curvature are all of the same order of magnitude. In addition, functioning knots 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, focusing specifically on the overhand and the figure-of-eight knots.Furthermore, in order to gain better insight into this complex class of problems, we also study the ‘not-knot’; a simpler model system that comprises the clasp of two bent elastic rods brought together into mechanical contact. We believe that considering complex tight knots as assemblies of simple not-knots will provide a solid foundation to develop much needed predictive models for knotted structures. We make use of X-ray micro computed tomography (micro-CT) to acquire volumetric information of knotted configurations on homogeneous elastomeric rods. More specifically, we focus on the centerline geometry and the regions of self-contact. Systematic exploration of parameter space enables us to construct a family of solutions of not-knot configurations. We envision that the physical insight gained from this experimental characterization will form the basis for future predictive models for physical 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. 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. Such descriptions are too abstract for practical settings. Realistic physical knots are in general tight, with no separation of length scales; the overall size of the knot, the diameter of the rod, and its characteristic radii of curvature are all of the same order of magnitude. In addition, functioning knots 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, focusing specifically on the overhand and the figure-of-eight knots.Furthermore, in order to gain better insight into this complex class of problems, we also study the ‘not-knot’; a simpler model system that comprises the clasp of two bent elastic rods brought together into mechanical contact. We believe that considering complex tight knots as assemblies of simple not-knots will provide a solid foundation to develop much needed predictive models for knotted structures. We make use of X-ray micro computed tomography (micro-CT) to acquire volumetric information of knotted configurations on homogeneous elastomeric rods. More specifically, we focus on the centerline geometry and the regions of self-contact. Systematic exploration of parameter space enables us to construct a family of solutions of not-knot configurations. We envision that the physical insight gained from this experimental characterization will form the basis for future predictive models for physical knots.
Practical information
- General public
- Free
Organizer
- MEGA.Seminar Organizing Committee