Section: New Results

Static simulation of thin elastic ribbons

Participants : Raphaël Charrondière, Florence Bertails-Descoubes, Victor Romero.

In collaboration with Sébastien Neukirch (Sorbonne Université, Institut Jean le Rond d'Alembert), we have proposed a robust and efficient numerical model to compute stable equilibrium configurations of thin elastic ribbons featuring arbitrarily curved natural shapes. Our spatial discretization scheme relies on elements characterized by a linear normal curvature and a quadratic geodesic torsion with respect to arc length. Such a high-order discretization allows for a great diversity of kinematic representations, while guaranteeing the ribbon to remain perfectly inextensible. Stable equilibria are calculated by minimizing gravitational and elastic energies of the ribbon, under a developability constraint. This work is currently under review in a journal of Mechanics. Some preliminary results have already been communicated about in two French congresses, one in Mechanics [6] and one in Computer Graphics [7] (best paper award).