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On the Analytical Approach to Galin’s Stick-Slip Problem. A Survey

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Abstract

Galin’s classical work (PMM J Appl Math Mech 9:413–424, 1945) on the contact of a rigid flat-ended indenter with an elastic half-plane with partial slip was the first successful attempt to take into account friction in the problem of normal contact. As Galin was unable to find an exact solution of the formulated problem, the problem of contact with partial slip of a rigid punch with an elastic half-plane was challenged by many researchers. At the same time Galin’s seminal work stimulated development of solutions for other contact problems with friction that feature different punch geometries and different material responses. This paper presents an overview of the developments in the area of elastic contact with partial slip. In the spirit of Galin’s work the focus is placed on contributions with substantial analytical merit.

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References

  1. Antipov, Y.A.: Galin’s problem for a periodic system of stamps with friction and adhesion. Int. J. Solids Struct. 37, 2093–2125 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Antipov, Y.A., Arutyunyan, N.K.: Contact problems of the theory of elasticity with friction and adhesion. PMM J. Appl. Math. and Mech. 55(6), 887–901 (1991)

    Article  MathSciNet  Google Scholar 

  3. Galin, L.A.: Pressure of a punch with friction and cohesion domains. PMM J. Appl. Math. and Mech. 9, 413–424 (1945)

    MATH  MathSciNet  Google Scholar 

  4. Galin, L.A.: Contact problems of the theory of elasticity. Gostehizdat, Moscow (1953) Translated from Russian edition by Moss H., in: Sneddon, I.N. (ed.), North Carolina State University at Raleigh

  5. Goodman, L.E.: Contact stress analysis of normally loaded rough spheres. Trans. ASME J. Appl. Mech. 29(9), 515–522 (1962)

    MATH  Google Scholar 

  6. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    MATH  Google Scholar 

  7. Hills, D.A., Sackfield, A.: The stress field induced by normal contact between dissimilar spheres. Trans. ASME, J. Appl. Mech. 54, 8–14 (1987)

    Article  Google Scholar 

  8. Mossakovskii, V.I.: The fundamental general problem of the theory of elasticity for a half-space with a circular curve determining boundary conditions. PMM J. Appl. Math. and Mech. 18(2), 187–196 (1954)

    MathSciNet  Google Scholar 

  9. Mossakovskii, V.I.: Compression of elastic bodies under conditions of adhesion (axisymmetric case). PMM J. Appl. Math. and Mech. 27(3), 418–427 (1963)

    Google Scholar 

  10. Mossakovskii, V.I., Biskup, A.G.: Pressing-in of die when friction and cohesion are present. Dokl. Akad. Nauk SSSR. 206(5), 1068–1070 (1972)

    Google Scholar 

  11. Mossakovskii, V.I., Biskup, A.G., Mossakovskaia, L.V.: Further development of Galin’s problem with dry friction and adhesion. Dokl. Akad. Nauk SSSR. 271(1), 60–64 (1983)

    Google Scholar 

  12. Mossakovskii, V.I., Biskup, A.G., Mossakovskaia, L.V.: On one method of solution of two-dimensional contact problems with dry friction and adhesion. Dokl. Akad. Nauk SSSR. 308(3), 561–564 (1989)

    Google Scholar 

  13. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen, The Netherlands (1963)

    MATH  Google Scholar 

  14. Nehari, Z.: Conformal Mapping. McGraw-Hill, New York (1952)

    MATH  Google Scholar 

  15. Ronveaux, A.: Heun’s Differential Equations. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  16. Spence, D.A.: Self-similar solutions to adhesive contact problems with incremental loading. Proc. R. Soc. Lond. A. 305, 81–92 (1968)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Spence, D.A.: An egenvalue problem for elastic contact with finite friction. Proc. Camb. Phil. Soc. 73, 249–268 (1973)

    MATH  MathSciNet  Google Scholar 

  18. Spence, D.A.: The Hertz contact problem with finite friction. J. Elast. 5, 297–319 (1975)

    Article  MATH  Google Scholar 

  19. Storakers, B., Biwa, S., Larsson, P.L.: Similarity analysis of inelastic contact. Int. J. Solids Struct. 34, 3061–3083 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhupanska, O.I., Ulitko, A.F.: Contact with friction of a rigid cylinder with an elastic half-space. J. Mech. Phys. Solids, 53, 975–999 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Zhupanska, O.I. On the Analytical Approach to Galin’s Stick-Slip Problem. A Survey. J Elasticity 90, 315–333 (2008). https://doi.org/10.1007/s10659-007-9145-x

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