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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)