 | | 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
|
| In English (Mech. Solids): | | 3212 |
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| S.E. Aleksandrov and E.A. Lyamina, "Riemann Method for the Plane Strain of a Homogeneous Porous Plastic Material," Mech. Solids. 50 (2), 171-175 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
2 |
Pages |
171-175 |
| DOI |
10.3103/S0025654415020065 |
| Title |
Riemann Method for the Plane Strain of a Homogeneous Porous Plastic Material |
| Author(s) |
S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, sergei_alexandrov@yahoo.com)
E.A. Lyamina (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, lyamina@inbox.ru) |
| Abstract |
The system of static equations describing the stress state in a homogeneous porous plastic material obeying the pyramidal yield criterion is studied under plane strain conditions. It is shown that determining the curvature radii of the characteristics amounts to solving the telegraph equation. Thus, it is expedient to construct the net of characteristics by the Riemann method, which is widely used to solve boundary value problems in the classical theory of plasticity of incompressible materials. These solutions can directly be generalized to the considered porous material model. |
| Keywords |
characteristics, Riemann method, porous material, plane strain state, ideal plasticity |
| References |
| 1. | L. M. Kachanov,
Foundations of the Theory of Plasticity
(Gostekhizdat, Moscow, 1956)
[in Russian]. |
| 2. | R. Hill,
The Mathematical Theory of Plasticity
(Clarendon Press, Oxford, 1950; Gostekhizdat, Moscow, 1956). |
| 3. | J. Chakrabarty,
Theory of Plasticity
(McGraw-Hill, New York, 1987). |
| 4. | B. A. Druyanov and R. I. Nepershin,
Theory of Technological Plasticity
(Mashinostroenie, Moscow, 1990)
[in Russian]. |
| 5. | R. Hill, E. H. Lee, and S. J. Tupper,
"A Method of Numerical Analysis of Plastic Flow in Plane Strain and Its Application
to the Compression of a Ductile Material between Rough Plates,"
J. Appl. Mech.
18 (1), 46-52 (1951). |
| 6. | B. A. Druyanov,
Applied Plasticity Theory for Porous Bodies
(Mashinostroenie, Moscow, 1989)
[in Russian]. |
|
| Received |
03 March 2014 |
| Link to Fulltext |
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