Eur. Phys. J. B 1, 333-336 (1998)
https://doi.org/10.1007/s100510050191

Metastability of a circular o-ring due to intrinsic curvature

Institut Laue-Langevin, and Université Joseph Fourier, Maison des Magistères J. Perrin, LPNSC, CNRS, 25 avenue des Martyrs, BP 166, 38042 Grenoble Cedex 09, France

Corresponding author: ^a fourcade@belledonne.polycnrs-gre.fr

Received: 27 August 1997
Revised: 23 October 1997
Accepted: 12 November 1997
Published online: 15 February 1998

Abstract

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [CITE]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature.