Metastability of a circular o-ring due to intrinsic curvature

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(c)(2d) = 0.66, where C and A are the torsion and the bending elastic constants [1]. In three dimensions, our variational approach shows that alpha(c)(3d) similar or equal to 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.