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Mestastability of a circular o-ring

Wednesday 9 July 2008, by mcube members

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 C/A is less than c(2d) = 0.66, where C and A are the torsion and the bending elastic constants. In three dimensions, our variational approach shows that c(3D) = 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. Numerical simulation done by D. Garrivier and B. Fourcade generalised this approach in three dimensions leading to the numerical value c(3D) = 1.2.