Archive for Rational Mechanics and Analysis

, 182:471

Self-Contact for Rods on Cylinders


  • G. H. M. van der Heijden
    • Centre for Nonlinear DynamicsUniversity College London
  • M. A. Peletier
    • Dept. of Mathematics and Computing ScienceTechnical University Eindhoven
    • Department of Computer ScienceUniversity of Bristol

DOI: 10.1007/s00205-006-0011-y

Cite this article as:
van der Heijden, G.H.M., Peletier, M.A. & Planqué, R. Arch Rational Mech Anal (2006) 182: 471. doi:10.1007/s00205-006-0011-y


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 ordinary differential equation 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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© Springer-Verlag 2006