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The Strength of Adhesion

  • Genady P. CherepanovEmail author
Chapter
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Abstract

A series of most significant problems concerning the motion of a sharp punch on an adhesive, elastic foundation, plate, or membrane are studied using the invariant integral of adhesion of different materials. A film covered most of the bodies is also taken into account. This is, in fact, a new contact mechanics accounting for the adhesion and predicting the resistance forces. Also, in this chapter, the basic mathematical problem of stick and slip on the contact area was, at last, solved after many unsuccessful attempts of such great individuals as Hertz, Prager, Muskhelishvili, and others; the solution of this nonlinear problem appeared to depend on six dimensionless parameters! This chapter is a must for mechanical engineers.

Literature

  1. 1.
    G.P. Cherepanov, The contact problem of the mathematical theory of elasticity with stick-and-slip areas. The theory of rolling and tribology. J. Appl. Math. Mech. (JAMM) 79(1), 81–101 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G.P. Cherepanov, Fracture Mechanics, (Moscow-Izhevsk, IKI Publ., 2012), pp. 1–840Google Scholar
  3. 3.
    G.P. Cherepanov, Some new applications of the invariant integrals in mechanics. J. Appl. Math. Mech. (JAMM) 76(5), 519–536 (2012)CrossRefGoogle Scholar
  4. 4.
    G.P. Cherepanov, Singular solutions in the theory of elasticity. In: Problems of Solid Mechanics, (Leningrad, Sudpromgiz, 1970), pp 380–398Google Scholar
  5. 5.
    G. P. Cherepanov, Stresses in an inhomogeneous plate with cuts. Izvestia Acad. Nauk SSSR, OTN Mekh. Mash. 1, 131–139 (1962)Google Scholar
  6. 6.
    G.P. Cherepanov, On propagation of cracks in compressed bodies. J. Appl. Math. Mech. (JAMM) 30(1), 76–86 (1966)zbMATHGoogle Scholar
  7. 7.
    G.P. Cherepanov, Mechanics of Brittle Fracture (McGraw-Hill, New York, 1978), pp. 1–952Google Scholar
  8. 8.
    G.P. Cherepanov (ed.), Fracture. A Topical Encyclopedia of Current Knowledge, (Malabar, Krieger, 1998), pp. 1–890Google Scholar
  9. 9.
    G.P. Cherepanov, Methods of Fracture Mechanics: Solid Matter Physics (Kluwer, Dordrecht, 1997), pp. 1–312CrossRefGoogle Scholar
  10. 10.
    G.P. Cherepanov, Theory of rolling: Solution of the Coulomb problem. J. Appl. Mech. Tech. Phys. (JAMTP) 55(1), 182–189 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    G.P. Cherepanov, The laws of rolling. Phys. Mesomech. 21(5), 435–451 (2018)Google Scholar
  12. 12.
    H. Hertz, Uber die Beruhrung Fester Elastischer Korper. Zeitschrift fur Reine Angew. Math. 92, 156–180 (1882)zbMATHGoogle Scholar
  13. 13.
    F.D. Gakhov, Boundary Value Problems (Dover, New York, 1990), pp. 1–490Google Scholar
  14. 14.
    L.A. Galin, Contact Problems of Elasticity Theory (Gostekhizdat, Moscow, 1953), pp. 1–280Google Scholar
  15. 15.
    N.I. Glagolev, The resistance to the rolling of cylindrical bodies. Prikl. Mat. Mekh. (PMM) 9(4), 318–332 (1945)MathSciNetGoogle Scholar
  16. 16.
    N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Groningen, Amsterdam, 1958), pp. 1–720Google Scholar
  17. 17.
    M.A. Sadowsky, Zweidimensionale Probleme der Elastizitatstheorie. Zeitschrift fur Angewandte Math und Mech. 8, 107–127 (1928)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MiamiUSA

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