Archive for Rational Mechanics and Analysis

, Volume 168, Issue 1, pp 35–82

Euler-Lagrange Equations for Nonlinearly Elastic Rods with Self-Contact

  • Friedemann Schuricht
  • Heiko von der Mosel

DOI: 10.1007/s00205-003-0253-x

Cite this article as:
Schuricht, F. & Mosel, H. Arch. Rational Mech. Anal. (2003) 168: 35. doi:10.1007/s00205-003-0253-x

Abstract.

 We derive the Euler-Lagrange equations for nonlinearly elastic rods with self-contact. The excluded-volume constraint is formulated in terms of an upper bound on the global curvature of the centre line. This condition is shown to guarantee the global injectivity of the deformation of the elastic rod. Topological constraints such as a prescribed knot and link class to model knotting and supercoiling phenomena as observed, e.g., in DNA-molecules, are included by using the notion of isotopy and Gaussian linking number. The bound on the global curvature as a nonsmooth side condition requires the use of Clarke's generalized gradients to obtain the explicit structure of the contact forces, which appear naturally as Lagrange multipliers in the Euler-Lagrange equations. Transversality conditions are discussed and higher regularity for the strains, moments, the centre line and the directors is shown.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Friedemann Schuricht
    • 1
  • Heiko von der Mosel
    • 2
  1. 1.Mathematisches Institut Universität zu Köln Weyertal 86-90 D-50931 Köln, Germany e-mail: fs@math.uni-koeln.de DE
  2. 2.Mathematisches Institut Universität Bonn Beringstraße 1 D-53115 Bonn, Germany e-mail: heiko@math.uni-bonn.deDE

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