 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| V. G. Grinchenko and A. F. Ulitko, "The role of the loading history in mechanics of contact interaction allowing for friction in the contact zone," Mech. Solids. 37 (4), 10-18 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
10-18 |
| Title |
The role of the loading history in mechanics of contact interaction allowing for friction in the contact zone |
| Author(s) |
V. G. Grinchenko (Kiev)
A. F. Ulitko (Kiev) |
| Abstract |
In mechanics of contact interaction of solids with friction
in the contact zone (commonly accounted for
by Amonton-Coulomb dry friction law), the loading history
is frequently not given due attention [1,2]. On the other hand,
even in the case of purely elastic deformation of the contacting
bodies it is impossible to separate the true distribution
of contact stresses from among theoretically possible ones
without considering the loading history [3, 4]. Proceeding
from the general theoretical principles, one can account for
the dependence of the solutions of contact problems with friction
on the loading history
by the fact that the loading/unloading process cannot be perfectly
elastic because of irreversible energy loss in slip zones. At the same
time, it is well known that when departing from the model of a perfectly
elastic body, it is necessary to take into account the loading history.
This observation is clearly illustrated by Il'yushin's remarkable works
on the theory of plasticity [5, 6].
In the present paper, we illustrate the role of the loading
history in contact problems with friction for the classical
problem of compression of two identical elastic disks loaded
by additional torsion moments [7]. Note that in [7], the loading
history of compressed disks performing constrained rotations
with constant angular velocities is taken into account
by introducing a restrained strain. In terms of the restrained
strain, one can find an elastic slip region in the contact zone
and account for a difference between the angular velocities of
the driving and driven disks. This difference is observed
in experiments (the angular velocity of the driven disk is always
higher than that of the driving disk). |
| References |
| 1. | L. A. Galin, Contact Problems of Elasticity and Viscoelasticity
[in Russian], Nauka, Moscow, 1980. |
| 2. | I. Ya. Shtaerman. Contact Problems of Elasticity [in Russian],
Gostekhizdat, Moscow, 1949. |
| 3. | A. Yu. Ishlinskii, "The rolling friction,"
PMM [Applied Mathematics and Mechanics], Vol. 2,
No. 2, pp. 245-260, 1938. |
| 4. | L. Föppl, Die strenge Lösung für die rollende Reibung,
Leibniz Verlag, München, 1947. |
| 5. | A. A. Il'yushin. Plasticity. Elastoplastic Strains
[in Russian], Gostekhizdat, Moscow, Leningrad, 1948. |
| 6. | A. A. Il'yushin and B. E. Pobedrya, Fundamentals
of Mathematical Theory of Thermoviscoelsticity
[in Russian], Nauka, Moscow, 1970. |
| 7. | H. Fromm, "Berechnung des Schlupfes beim Rollen
deformierberer Scheiben,"
Z. Angew. Math. Mech., B. 7, No. 1, S. 27-58, 1927. |
| 8. | A. F. Ulitko, Exakte Lösung des Kontaktproblems
für zwei Zylinder under Berücksichtigung der Reibung,"
Z. Angew. Math. Mech., B. 80, No. 7, S. 435-455, 2000. |
| 9. | H. Hertz, "Über die Beruhrung fester elastischer
Korper,"
J. Reine Angew. Math., B. 92, S. 156-171, 1881. |
| 10. | C. Catteneo, "Sul contatto di due corpi elastici:
distribuzione locate degli sforzi,"
Rend. Acad. Nar. Lincei, Ser. 6, S. 27, 342-348, 434-436, 474-478,
1938. |
| 11. | R. D. Mindlin, " Compliance of elastic bodies in contact,"
Trans. ASME. J. Appl. Mech., Vol. 16, pp. 259-268, 1949. |
| 12. | D. A. Spence, "Self-similar solution to adhesive contact problems
with incremental loading," Proc. Roy. Soc., Vol. A305, pp. 55-80, 1968. |
| 13. | K. L. Johnson, Contact Mechanics [Russian translation], Mir,
Moscow, 1989. |
| 14. | F. D. Gakhov, Boundary Value Problems [in Russian],
Fizmatgiz, Moscow, 1963. |
|
| Received |
20 December 2000 |
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