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IssuesArchive of Issues2015-2pp.171-175

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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 http://link.springer.com/article/10.3103/S0025654415020065
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