Skip to main content
SpringerLink
Log in

Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

Analogies between elastic and viscous contact problems are used to apply boundary element algorithms and the method of reduction of dimensionality respectively to the problem of normal contact between a rigid body and a viscous half space. Some basic examples are examined in order to compare both methods and their results to each other.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V.L. Popov and S.G. Psakhie, Numerical simulation methods in tribology, Tribol. Int., 40, No. 6 (2007) 916.

    Article  Google Scholar 

  2. T. Geike and V.L. Popov, Mapping of three-dimensional contact problems into one dimension, Phys. Rev. E, 76, No. 3 (2007) 036710.

    Article  ADS  Google Scholar 

  3. T. Geike and V.L. Popov, Reduction of three-dimensional contact problems to one-dimensional ones, Tribol. Int., 40, No. 6 (2007) 924.

    Article  Google Scholar 

  4. V.L. Popov, Contact Mechanics and Friction, Physical Principles and Applications, Springer-Verlag, Berlin, 2010.

    Book  MATH  Google Scholar 

  5. E.H. Lee, Stress analysis in visco-elastic bodies, Quart. Appl. Math., 13, No. 2 (1955) 183.

    MathSciNet  MATH  Google Scholar 

  6. J.R.M. Radok, Visco-elastic stress analysis, Quart. Appl. Math., 15, No. 2 (1957) 198.

    MathSciNet  MATH  Google Scholar 

  7. L.D. Landau and E.M. Lifschitz, Lehrbuch der Theoretischen Physik, Band 7: Elastizitätstheorie, Akademie-Verlag, Berlin, 1965.

    Google Scholar 

  8. L.D. Landau and E.M. Lifschitz, Lehrbuch der Theoretischen Physik, Band 6: Hydrodynamik, Akademie-Verlag, Berlin, 1991.

    Google Scholar 

  9. T Geike, Theoretische Grundlagen eines schnellen Berechnungsver-fahrens für den Kontakt rauer Oberflächen, Dissertation, TU Berlin, Berlin, 2008.

    Google Scholar 

  10. V.L. Popov and A.E. Filippoy, Force of friction between fractal rough surface and elastomer, Tech. Phys. Lett., 36, No. 6 (2010) 525.

    Article  ADS  Google Scholar 

  11. V.L. Popov and A.V. Dimaki, Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties, Tech. Phys. Lett., 37, No. 1 (2011).

    Google Scholar 

  12. R. Pohrt and V.L. Popov, Normal contact stiffness of elastic solids with fractal rough surfaces, Phys. Rev. Lett., 108 (2012) 104301.

    Article  ADS  Google Scholar 

  13. C.H. Vernier and A.A. Lubrecht, Multilevel Methods in Lubrication, Elsevier, Amsterdam, 2000.

    Google Scholar 

  14. I.A. Polonsky and L.M. Keer, A numerical method for solvingrough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear, 231, No. 2 (1999) 206.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Berlin University of Technology, Berlin, 10623, Germany

    Silvio Kürschner

  2. Donetsk Institute for Physics and Engineering of NASU, Donetsk, 83114, Ukraine

    A. E. Filippov

Authors
  1. Silvio Kürschner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. E. Filippov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Silvio Kürschner.

Additional information

Original Text © S. Kürschner, A.E. Filippov, 2012, published in Fiz. Mezomekh., 2012, Vol. 15, No. 4, pp. 25–30.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kürschner, S., Filippov, A.E. Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media. Phys Mesomech 15, 270–274 (2012). https://doi.org/10.1134/S1029959912030046

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959912030046

Keywords

Search

Navigation