Journal of Elasticity

, Volume 117, Issue 1, pp 1–20 | Cite as

Contact with a Corner for Nonlinearly Elastic Rods

Article

Abstract

In elastic contact problems it is usually required that the contact force has to be directed normally to the contact surface in the absence of friction. For an obstacle with nonsmooth surface this gives infinitely many normal directions at an edge or at a corner. For the case where a nonlinearly elastic rod under terminal loads is hanging over a needle, it is shown that the balance equations supplemented with such a normality condition have a continuum of solutions. Moreover, an additional contact condition is derived from a corresponding variational problem by means of special inner variations that preserve the shape of the rod. This way one is finally lead to a unique solution at least locally.

Keywords

Elastic rods Contact problems Nonlinear elasticity Variational methods 

Mathematics Subject Classification

34A34 49J52 74B20 74K10 

References

  1. 1.
    Antman, S.S.: Nonlinear Problems of Elasticity. Springer, New York (1995) CrossRefMATHGoogle Scholar
  2. 2.
    Konz, V.: Ein spezielles Kontaktproblem für nichtlinear elastische Stäbe. Diploma thesis, Universität zu Köln (2006) Google Scholar
  3. 3.
    Schuricht, F.: A variational approach to obstacle problems for shearable nonlinearly elastic rods. Arch. Ration. Mech. Anal. 140, 103–159 (1997) CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Schuricht, F.: Regularity for shearable nonlinearly elastic rods in obstacle problems. Arch. Ration. Mech. Anal. 145, 23–49 (1998) CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Schuricht, F., Werner, B.: Paradoxical bending behavior of shearable nonlinearly elastic rods. J. Elast. 50, 27–48 (1998) CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Saarland University and MPI InformatikSaarbrückenGermany
  2. 2.Fachrichtung MathematikTechnische Universität DresdenDresdenGermany

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