Self-contact for rods on cylinders

G.H.M. van der Heijden, M.A. Peletier & R. Planqué

We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a second-order functional of a single scalar variable, and the self-contact constraint is written as an integral inequality. Using techniques from ode theory (comparison principles) and variational calculus (cut-and-paste arguments) we fully characterize the structure of constrained minimizers. An important auxiliary result states that the set of self-contact points is continuous, a result that contrasts with known examples from contact problems in free rods.

keywords: elastic rods, calculus of variations, constrained minimization, self-contact, comparison principle

Arch. Rat. Mech. Anal. 182, 471-511 (2006)