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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsLiterature
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)
G.P. Cherepanov, Fracture Mechanics, (Moscow-Izhevsk, IKI Publ., 2012), pp. 1–840
G.P. Cherepanov, Some new applications of the invariant integrals in mechanics. J. Appl. Math. Mech. (JAMM) 76(5), 519–536 (2012)
G.P. Cherepanov, Singular solutions in the theory of elasticity. In: Problems of Solid Mechanics, (Leningrad, Sudpromgiz, 1970), pp 380–398
G. P. Cherepanov, Stresses in an inhomogeneous plate with cuts. Izvestia Acad. Nauk SSSR, OTN Mekh. Mash. 1, 131–139 (1962)
G.P. Cherepanov, On propagation of cracks in compressed bodies. J. Appl. Math. Mech. (JAMM) 30(1), 76–86 (1966)
G.P. Cherepanov, Mechanics of Brittle Fracture (McGraw-Hill, New York, 1978), pp. 1–952
G.P. Cherepanov (ed.), Fracture. A Topical Encyclopedia of Current Knowledge, (Malabar, Krieger, 1998), pp. 1–890
G.P. Cherepanov, Methods of Fracture Mechanics: Solid Matter Physics (Kluwer, Dordrecht, 1997), pp. 1–312
G.P. Cherepanov, Theory of rolling: Solution of the Coulomb problem. J. Appl. Mech. Tech. Phys. (JAMTP) 55(1), 182–189 (2014)
G.P. Cherepanov, The laws of rolling. Phys. Mesomech. 21(5), 435–451 (2018)
H. Hertz, Uber die Beruhrung Fester Elastischer Korper. Zeitschrift fur Reine Angew. Math. 92, 156–180 (1882)
F.D. Gakhov, Boundary Value Problems (Dover, New York, 1990), pp. 1–490
L.A. Galin, Contact Problems of Elasticity Theory (Gostekhizdat, Moscow, 1953), pp. 1–280
N.I. Glagolev, The resistance to the rolling of cylindrical bodies. Prikl. Mat. Mekh. (PMM) 9(4), 318–332 (1945)
N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Groningen, Amsterdam, 1958), pp. 1–720
M.A. Sadowsky, Zweidimensionale Probleme der Elastizitatstheorie. Zeitschrift fur Angewandte Math und Mech. 8, 107–127 (1928)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cherepanov, G.P. (2019). The Strength of Adhesion. In: Invariant Integrals in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-28337-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-28337-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-28336-0
Online ISBN: 978-3-030-28337-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)