 | | 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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| << Previous article | Volume 46, Issue 1 / 2011 | Next article >> |
| E.V. Lomakin and A.M. Mel'nikov, "Plane Stress State Problems for Notched Bodies Whose Plastic Properties Depend on the Form of the Stress State," Mech. Solids. 46 (1), 62-69 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
62-69 |
| DOI |
10.3103/S0025654411010092 |
| Title |
Plane Stress State Problems for Notched Bodies Whose Plastic Properties Depend on the Form of the Stress State |
| Author(s) |
E.V. Lomakin (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, evlomakin@yandex.ru)
A.M. Mel'nikov (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, m_andrew_m@mail.ru) |
| Abstract |
We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed. |
| Keywords |
plasticity, form of the stress state, limit load, velocity field, stress field |
| References |
| 1. | E. V. Lomakin,
"Dependence of the Limit State of Composite and
Polymer Materials on the Type of the Stress State. Part 1.
Experimental Dependencies and Constitutive Relations,"
Mekh. Komp. Mater.,
No. 1, 3-9 (1988)
[Mech. Comp. Mater. (Engl. Transl.)
24 (1), 1-7 (1988)]. |
| 2. | E. V. Lomakin,
"Constitutive Relations of Deformation Theory for Dilatant Materials,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 66-75 (1991)
[Mech. Solids (Engl. Transl.)
26 (6), 64 (1991)]. |
| 3. | E. V. Lomakin,
"Plastic Flow of a Dilatant Medium under Plane Strain Conditions,"
Izv. Akad. Nauk, Mekh. Tverd. Tela,
No. 6, 58-68 (2000)
[Mech. Solids (Engl. Transl.)
35 (6), 46-54 (2000)]. |
| 4. | E. V. Lomakin and A. M. Mel'nikov,
"Plane Stress State of Media with Plastic Properties
Sensitive to the Type of Stress,"
Vych. Mekh. Sploshn. Sred
2 (2), 48-64 (2009). |
| 5. | Yu. N. Rabotnov,
Creep of Construction Elements
(Nauka, Moscow, 1966)
[in Russian]. |
| 6. | A. M. Freudenthal and H. Geiringer,
Mathematical Theories of Nonelastic Continuum
(Springer, Berlin, 1958; Fizmatlit, Moscow, 1962). |
| 7. | L. M. Kachanov,
Foundations of the Theory of Plasticity
(Nauka, Moscow, 1969; North-Holland, Amsterdam, 1971). |
| 8. | E. V. Lomakin and E. S. Sorvirog,
"Axially Symmetric Plastic Flow of
Materials Whose Resistance Depends on the Form of the Stress State,"
Vestnik Moskov. Univ. Ser. I. Mat. Mekh.,
No. 6, 61-66 (1991)
[Moscow Univ. Math. Bull. (Engl. Transl.)]. |
|
| Received |
06 June 2010 |
| Link to Fulltext |
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