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
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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998