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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 1 Issue 3 (1998) pp 333-336
Metastability of a circular o-ring due to intrinsic curvature
T. Charitat, B. Fourcade (a)
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
Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997
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 $\alpha=C/A$ is less than $\alpha_{\rm c}(2{\rm d})=0.66$, where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that $\alpha_{\rm c}(3{\rm d})\simeq 0.9$. This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature.
PACS. 05.90.+m Other topics in statistical physics and thermodynamics - 03.40.-t Classical mechanics of continuous media: general mathematical aspects - 62.20.Dc Elasticity of solids
(a) email: fourcade@belledonne.polycnrs-gre.fr also at the Institut Universitaire de France
Online publication: February 24, 1998
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