Skip to main content

A uniqueness criterion for the Signorini problem with Coulomb friction

  • Chapter
Analysis and Simulation of Contact Problems

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 27))

Abstract

Some optimal a priori estimates are given for the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem) and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have been presented in the continuous framework. It is proven, here, that if a solutions satisfies an hypothesis on the tangential displacement and if the friction coefficient is small enough, it is the unique solution to the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.A. Adams. Sobolev spaces. Academic Press, 1975.

    Google Scholar 

  2. L.-E. Andersson. Existence results for quasistatic contact problems with Coulomb friction. Applied Mathematics and Optimisation, 42 (2): pp 169–202, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Duvaut. Problémes unilatéraux en mécanique des milieux continus. in: Actes du congrés international des mathématiciens (Nice 1970), Tome 3, Gauthier-Villars, Paris, pages pp 71–77, 1971.

    Google Scholar 

  4. G. Duvaut, J.L. Lions. Les inéquations en mécanique et en physique. Dunod Paris, 1972.

    Google Scholar 

  5. R. Hassani, P. Hild, I. lonescu, N.-D. Sakki. A mixed finite element method and solution multiplicity for Coulomb frictional contact. Comput. Methods Appl. Mech. Engrg., pages 4517–4531, 192 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Hild. An example of nonuniqueness for the continuous static unilateral contact model with Coulomb friction. C. R. Acad. Sci. Paris, pages 685–688, 337 (2003).

    MATH  MathSciNet  Google Scholar 

  7. P. Hild. Non-unique slipping in the Coulomb friction model in two-dimensional linear elasticity. Q. Jl. Mech. Appl. Math., pages 225–235, 57 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Kikuchi, J.T. Oden. Contact problems in elasticity. SIAM, 1988.

    Google Scholar 

  9. P. Laborde, Y. Renard. Fixed points strategies for elastostatic frictional contact problems, submitted.

    Google Scholar 

  10. V.G. Maz’ya, T.O. Shaposhnikova. Theory of multipliers in spaces of differentiate functions. Pitman, 1985.

    Google Scholar 

  11. Y. Renard. A uniqueness criterion for the Signorini problem with Coulomb friction, submitted.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

Renard, Y. (2006). A uniqueness criterion for the Signorini problem with Coulomb friction. In: Wriggers, P., Nackenhorst, U. (eds) Analysis and Simulation of Contact Problems. Lecture Notes in Applied and Computational Mechanics, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31761-9_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-31761-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31760-9

  • Online ISBN: 978-3-540-31761-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics