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Method of Dimensionality Reduction in Contact Mechanics and Friction pp 239–243Cite as

Appendix 2: Exact Solutions in Three Dimensions for the Tangential Contact of Axially-Symmetric Bodies

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Abstract

In this chapter, the proof of validity of the method of dimensionality to tangential contacts with friction between axially-symmetric bodies is given. The proof is based on the close relationship between normal and tangential contacts found in the works by Cattaneo, Mindlin, Jäger, and Ciavarella.

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Notes

  1. 1.

    Elastically similar materials are characterized by \( \beta_{D} = 0 \).

  2. 2.

    Let it be emphasized that in the special case of non-differentiable profiles, only the first integral expression in (18.18) may be used.

References

  1. C, Cattaneo, Sul contatto di due corpi elastici: distribuzione locale degli sforzi. Rendiconti dell’Accademia nazionale dei Lincei. 27, pp. 342–348, 434–436, 474–478 (1938)

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  2. R.D. Mindlin, Compliance of elastic bodies in contact. J. Appl. Mech. 16(3), 259–268 (1949)

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  4. R.L. Munisamy, D.A. Hills, D. Nowell, Static axisymmetric hertzian contacts subject to shearing forces. ASME J. Appl. Mech. 61, 278–283 (1994)

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  5. J. Jäger, Axi-symmetric bodies of equal material in contact under torsion or shift. Arch. Appl. Mech. 65, 478–487 (1995)

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  6. I.N. Sneddon, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47–57 (1965)

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  7. M. Ciavarella, Tangential loading of general three-dimensional contacts. J. Appl. Mech. 65, 998–1003 (1998)

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  8. M. Ciavarella, Indentation by nominally flat or conical indenters with rounded corners. Int. J. Solids Struct. 36, 4149–4181 (1999)

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  9. J. Boussinesq, Application des Potentiels a L’etude de L’equilibre et du Mouvement des Solides Elastiques (1885)

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  10. V. Cerruti, Ricerche Intorno all’Equilibrio dei Corpie Elastici Isotropi. Atti della Reale Accademia dei Lincei, Memoriae della Classe de Scienze Fisiche, Matematiche e Naturali. 13 (1882)

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Authors and Affiliations

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

    Markus Heß

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

    Valentin L. Popov

Authors
  1. Markus Heß
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  2. Valentin L. Popov
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Correspondence to Valentin L. Popov .

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Heß, M., Popov, V.L. (2015). Appendix 2: Exact Solutions in Three Dimensions for the Tangential Contact of Axially-Symmetric Bodies. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-53876-6_18

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  • Print ISBN: 978-3-642-53875-9

  • Online ISBN: 978-3-642-53876-6

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