During my PhD studies I focus on the mechanical response of an elastic rod bent into an open trefoil knot
and submitted to an external tensile force and a torsional moment.
We also shown with B. Audoly and S. Neukirch that an instability occurs if the applied torsional moment is above a
certain threshold value (which is given by the Zajac critical value in the case of an infinitely long rod).
This work has yield to an accurate description of the rod geometry and especially the locus of self-contact
(meaning the parts of the rod which are in contact), which appears to be non trivial as it contains open regions.
We emphasize the fact that the contact-set topology is derived without any
a priori assumption.
Various experiments are presented in the references and show the accuracy of our model as long as one considers thin rod
(meaning with a length greater than its radius).
knot torsional instability
As it is now widely known it is possible to tie a knot onto a biofilament using single molecule manipulations.
Some studies have also shown that proteins are found to be knotted while the biological functions of such configurations
remain unclear. The use of our model in such cases might be useful in order to address the mechanical response of
biological objects.
References:
- B. Audoly, N. Clauvelin and S. Neukirch,
Elastic Knots, PRL,
99, 164301, 2007
- N. Clauvelin, B. Audoly and S. Neukirch,
Matched asymptotic expansions for twisted elastic knots: a self-contact problem with non-trivial contact topology,
JMPS,
57, pp 1623—1656, 2009
