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Self-contact for rods on cylinders

G. H. M. van der Heijden·M. A. Peletier·R. Planqué
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Abstract

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.

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G. H. M. van der Heijden, M. A. Peletier, R. Planqué. 2004-11-02. Self-contact for rods on cylinders. https://arxiv.org/abs/math-ph/0411007

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