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Appendix 3: Replacing the Material Properties with Radok’s Method of Functional Equations

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Abstract

This chapter is devoted to a rigorous proof of the application procedure of the method of dimensionality reduction to contacts with elastomers. The proof is based on Radok’s principle of functional equations. It proceeds from a solution of a similar elastic problem which then is carried over to the original problem by replacing the material properties. We will show in detail how Radok’s method of functional equations is used for the replacement of the material properties.

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Notes

  1. 1.

    The mathematically sound way consists of taking the incompressibility into account in Eq. (19.29) and only then, taking the Laplace transformation. It is, however, easy to see that this procedure leads to the same result.

References

  1. J.R.M. Radok, Quart. Appl. Math. 15, 198 (1957)

    MATH  MathSciNet  Google Scholar 

  2. S. Kürschner, A.E. Filippov, Phys. Mesomech. 15, 270–274 (2012)

    Article  Google Scholar 

  3. L.D. Landau, E.M. Lifschitz, Lehrbuch der Theoretischen Physik, Band VII Elastizitätstheorie, 1st edn. (Akademie, Berlin, 1965)

    Google Scholar 

  4. L.D. Landau, E.M. Lifschitz, Lehrbuch Der Theoretischen Physik, Band VI Hydrodynamik, 5. überarb. Aufl. (Akademie Verlag, 1991)

    Google Scholar 

  5. I.N. Bronstein, K.A. Semendjajew, G. Musiol, H. Mühlig, Taschenbuch Der Mathematik, 5. überarb. u. erw. Aufl. (Harri Deutsch, 2000)

    Google Scholar 

  6. W. Yang, J. Appl. Mech. 33, 395 (1966)

    Article  Google Scholar 

  7. R.M. Christensen, Theory of Viscoelasticity: An Introduction (Academic Press, New York, 1971)

    Google Scholar 

  8. E.H. Lee, J.R.M. Radok, J. Appl. Mech. 27, 438 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Gross, Mathematical Structure of the Theories of Viscoelasticity (Hermann, Paris, 1953)

    MATH  Google Scholar 

  10. A.C. Pipkin, Lectures on Viscoelasticity Theory (Springer, Berlin, 1972)

    Book  MATH  Google Scholar 

  11. D.R. Bland, Theory of Linear Viscoelasticity (Pergamon, Oxford, 1960)

    MATH  Google Scholar 

  12. M. Vandamme, F.J. Ulm, Int. J. Solids Struct. 43, 3142 (2006)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mechanics, Technische Universität Berlin, Berlin, Germany

    Silvio Kürschner & Valentin L. Popov

  2. Abt. IC Studienkolleg, Technische Universität Berlin, Berlin, Germany

    Markus Heß

Authors
  1. Silvio Kürschner
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  2. Valentin L. Popov
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  3. Markus Heß
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Correspondence to Valentin L. Popov .

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Kürschner, S., Popov, V.L., Heß, M. (2015). Appendix 3: Replacing the Material Properties with Radok’s Method of Functional Equations. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-53876-6_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53875-9

  • Online ISBN: 978-3-642-53876-6

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