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IssuesArchive of Issues2011-3pp.357-367

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M.Ya. Brovman, "On the Choice of Coordinates in the Analysis of Plane Plastic Strain," Mech. Solids. 46 (3), 357-367 (2011)
Year 2011 Volume 46 Number 3 Pages 357-367
DOI 10.3103/S0025654411030034
Title On the Choice of Coordinates in the Analysis of Plane Plastic Strain
Author(s) M.Ya. Brovman ("Module-Engineering" LTD, Sadovnicheskaya 20-1, Moscow, 115035 Russia, brovman@mail.ru)
Abstract The plane strain of an ideal rigid-plastic medium is studied in curvilinear coordinates. The methods used to solve the equations of plasticity were considered in [1-3]. Curvilinear orthogonal coordinates with the introduction of a metric function were used in [4, 5].

In the present paper, specific features of the choice of a coordinate system in which the coordinate lines are the slip lines or the principal stress lines are studied and solutions containing coordinate functions determined by the metric tensor for the two-dimensional space are obtained.
Keywords plastic strain, curvilinear coordinates, equilibrium equations
References
1.  V. V. Sokolovskii, The Theory of Plasticity (Vysshaya Shkola, Moscow, 1969) [in Russian].
2.  D. D. Ivlev, Theory of Perfect Plasticity (Nauka, Moscow, 1966) [in Russian].
3.  R. Hill, The Mathematical Theory of Plasticity (Clarendon press, Oxford, 1950; Gostekhizdat, Moscow, 1956).
4.  M. Ya. Brovman, "Solution of Equations of a Plastic Flow in Curvilinear Coordinates," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 86-97 (2004) [Mech. Solids (Engl. Transl.) 39 (4), 68-76 (2004)].
5.  M. Ya. Brovman, "Solution of the Plastic Flow Equations under Axisymmetric Deformation," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 137-146 (2007) [Mech. Solids (Engl. Transl.) 42 (2), 283-290 (2007)].
6.  L. I. Golovina, Linear Algebra and Some Applications (Nauka, Moscow, 1971) [in Russian].
7.  M. Ya. Brovman, Application of the Theory of Plasticity in Rolling (Metallurgiya, Moscow, 1991) [in Russian].
Received 15 October 2008
Link to Fulltext http://www.springerlink.com/content/p60g75157q18734n/
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