Metastability of a circular o-ring due to intrinsic curvature |
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Authors: | T. Charitat B. Fourcade |
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Affiliation: | (1) 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, FR |
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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 [#!landau!#]. 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. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997 |
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Keywords: | 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 |
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