 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| E.I. Ryzhak, "Idea of a Device for Modeling Localization Phenomena in Domains of Arbitrary Shape and a Generalized Localization Theory," Mech. Solids. 47 (1), 40-56 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
1 |
Pages |
40-56 |
| DOI |
10.3103/S0025654412010049 |
| Title |
Idea of a Device for Modeling Localization Phenomena in Domains of Arbitrary Shape and a Generalized Localization Theory |
| Author(s) |
E.I. Ryzhak (Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, B. Gruzinskaya 10, Moscow, 123995 Russia, e_i_ryzhak@mail.ru) |
| Abstract |
A conceptual diagram of a testing device is proposed where
the medium filling a domain of a given (practically arbitrary) shape is subjected to a homogeneous simple shear until the medium becomes unstable. The diagram is based on that of a working prototype. It is proved that the instability occurs immediately after Hadamard's inequality for the medium plastic response is violated. It is also proved that the onset of instability is necessarily accompanied by a localization of incremental plastic strains; the proof relies on the new theory of generalized localization developed in the present paper. The theoretical results obtained fill in significant logical gaps in the traditional strain localization theory suggested by Rice and his scientific school. |
| Keywords |
localization phenomena, plate shear device, elastoplastic medium, stability, instability, Hadamard inequality, localized instability, generalized strain localization |
| References |
| 1. | A. F. Revuzhenko, S. B. Stazhevskii, and E. I. Shemyakin,
"Mechanism of Deformation of a Granular Material under High Shear,"
Phyz.-Tekh. Probl. Razrab. Polez. Ispokaemykh,
No. 3, 130-133 (1974)
[J. Mining Sci. (Engl. Transl.)
10 (3), 374-377 (1974)]. |
| 2. | J. W. Rudnicki and J. R. Rice,
"Conditions for the Localization of Deformation in Pressure-Sensitive Dilatant Materials,"
J. Mech. Phys. Solids
23 (6), 371-394 (1975). |
| 3. | J. R. Rice,
"The Localization of Plastic Deformation,"
in Theoretical and Applied Mechanics.
Proc. 14th IUTAM Congr.
(North-Holland, Amsterdam, 1976),
pp. 207-220. |
| 4. | E. I. Ryzhak,
"Kink Folds as Bending Localization. The Simplest Model,"
Dokl. Akad. Nauk SSSR
289 (1), 67-71 (1986)
[Sov. Phys. Dokl. (Engl. Transl.)]. |
| 5. | E. I. Ryzhak,
"Necessity of Hadamard Conditions for Stability of Elastic-Plastic Solids,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 4, 101-104 (1987)
[Mech. Solids (Engl. Transl.)
22 (4), 99-102 (1987)]. |
| 6. | E. I. Ryzhak,
"To the Problem of Realizability of Homogeneous Postcritical Deformation
in a Rigid Triaxial Testing Machine,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 1, 111-127 (1991)
[Mech. Solids (Engl. Transl.)]. |
| 7. | E. I. Ryzhak,
"On Stable Deformation of `Unstable' Materials in a Rigid Triaxial Testing Machine,"
J. Mech. Phys. Solids
41 (8), 1345-1356 (1993). |
| 8. | E. I. Ryzhak,
"Investigation of Modes of Constitutive Instability Manifestation in a One-Dimensional Model,"
ZAMM
73 (12), 380-383 (1993). |
| 9. | E. I. Ryzhak,
"On Stable Postcritical Deformation in a Nonrigid Triaxial Testing Machine,"
Dokl. Ross. Akad. Nauk
330 (2), 197-199 (1993).
[Dokl. Phys. (Engl. Transl.)]. |
| 10. | E. I. Ryzhak,
"On Stability of Homogeneous Elastic Bodies under Boundary Conditions
Weaker Than Displacement Conditions,"
Quart. J. Mech. Appl. Math.
47 (4), 663-672 (1994). |
| 11. | E. I. Ryzhak,
"A Case of Indispensable Localized Instability in Elastic-Plastic Solids,"
Int. J. Solids Struct.
36 (30), 4669-4691 (1999). |
| 12. | E. I. Ryzhak,
Stability Conditions and Modes of Instability Manifestation
in Softening Elastoplastic Bodies,
Doctoral Dissertation in Mathematics and Physics
(Moscow, 2002)
[in Russian]. |
| 13. | R. Hill,
"Acceleration Waves in Solids,"
J. Mech. Phys. Solids
10 (1), 1-16 (1962). |
| 14. | R. Hill,
"Some Basic Principles in the Mechanics of Solids without a Natural Time,"
J. Mech. Phys. Solids
7 (2), 209-225 (1959). |
| 15. | Z. P. Bazant and F. B. Lin,
"Stability against Localization of Softening into Ellipsoids and Bands;
Parameter Study,"
Int. J. Solids Struct.
25 (12), 1483-1498 (1989). |
| 16. | E. I. Ryzhak,
"On Simplest Localization Potentials,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 114-121 (1983)
[Mech. Solids (Engl. Transl.)]. |
| 17. | A. P. Bobryakov and A. F. Revuzhenko,
"Complex Loading of Free-Flowing Materials with Breaks in the Trajectory.
Procedure and Experimental Results,"
Phyz.-Tekh. Probl. Razrab. Polez. Ispokaemykh,
No. 5, 48-56 (1994)
[J. Mining Sci. (Engl. Transl.)
30 (5), 456-462 (1994)]. |
| 18. | A. F. Revuzhenko,
Mechanics of Granular Media
(Izdat. "OFSET", Novosibirsk, 2003)
[in Russian]. |
| 19. | A. F. Revuzhenko,
Mechanics of Granular Media
(Springer, Berlin, 2006). |
| 20. | C. A. Truesdell,
A First Course in Rational Continuum Mechanics
(The Johns Hopkins University Press, Baltimore, Maryland, 1972; Mir, Moscow, 1975). |
| 21. | W. Noll,
"A New Mathematical Theory of Simple Materials,"
Arch. Rat. Mech. Anal.
48 (1), 1-50 (1972). |
|
| Received |
24 June 2009 |
| Link to Fulltext |
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