POSTE Numerical modelling of tight knots (PhD or Post-Doc)

Advisors

Thibaut Métivet (INRIA Rhône-Alpes, ELAN) thibaut.metivet@inria.fr

Florence Bertails-Descoubes (INRIA Rhône-Alpes, ELAN) florence.descoubes@inria.fr

Mélina Skouras (INRIA Rhône-Alpes, IMAGINE) melina.skouras@inria.fr

Hosting Laboratory

ELAN team (INRIA and LJK, Grenoble), https://team.inria.fr/elan/

Practical details

PhD thesis (3 years) or post-doctoral position (1 year renewable), salary as defined in Inria scales. Start in fall 2020.

http://elan.inrialpes.fr/people/bertails/SujetsThesePostDoc2020/sujetNoeuds.pdf

Context:

Knots are fascinating and widely spread structures which combine the seeming simplicity of a thread with some intricate topology to obtain many different properties. As such, they have been mathematically studied since the 18th century and knot theory closely developed along the early foundations of mathematical topology until the modern use of algebraic topology, which eventually allowed to classify knots using simple polynomial functions. However, while the geometry of knots is now well understood, their mechanical properties is still vague and the choice of a particular knot for some task is most of the time governed by empiricism. From the numerical perspective, some recent works have focused on reduced models for the simulation of threads [1, 8, 9, 2], thereby efficiently accounting for the nonlinear behaviour of this slender structures. However, the challenging case of tight and self-locking knots, where both the knot topology and the thread mechanical behaviour come into play, have been poorly studied despite their intensive and crucial use in many fields such as surgery or rock-climbing, or their appearance in many biological phenomena [5].

Objectives:

The goal of the project is to develop numerical models for the study of tight knots. To this end, various approaches will be considered, ranging from full ab-initio finite-element models to reduced physical models, and the numerical aspects will be built upon tools developed by researchers from the ELAN team [6, 4, 7].

The project will also involve collaborations with physicists to develop and validate the model.

Keywords:

Numerical modelling, analysis and simulation, mechanics of thin elastic rods, dry frictional contact, physics of knots