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IssuesArchive of Issues2012-6pp.671-676

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Total articles in the database: 4725
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Yu.N. Radaev, "On Attainable Lower Boundary of the Three-Dimensional Coulomb-Tresca Invariant," Mech. Solids. 47 (6), 671-676 (2012)
Year 2012 Volume 47 Number 6 Pages 671-676
DOI 10.3103/S002565441206009X
Title On Attainable Lower Boundary of the Three-Dimensional Coulomb-Tresca Invariant
Author(s) Yu.N. Radaev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com)
Abstract An attainable lower boundary of the three-dimensional Coulomb-Tresca invariant is constructed to facilitate the search of plasticity conditions for isotropic bodies which, just as the Tresca-Saint Venant plasticity condition, ensure the hyperbolic analytic type of three-dimensional equations of the mathematical theories of plasticity based on the generalized associate flow law. The construction is performed by using the system of three "two-dimensional" tangential stresses related to the given three-dimensional stress state. It is proved that the Coulomb-Tresca invariant attains its lower bound in any plane strain state where the out-of-plane principal normal stress is intermediate (or median).
Keywords ideal plasticity, yield, yield point, Coulomb-Tresca prism, tangential stress, principal stress
References
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2.  A. Nadai, Plasticity. Mechanics of Plastic State of Material (McGraw-Hill, New York, 1931; ONTI, Moscow-Leningrad, 1936).
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8.  Yu. N. Radaev, Spatial Problem of Mathematical Theory of Plasticity (Izdat. Samara Univ., Samara, 2006) [in Russian].
9.  A. Haar and T. Karman, "To the Theory of Stress States in Plastic and Granular Materials," in Plasticity Theory, Ed. by Yu. N. Rabotnov (Izdat. Inostr. Liter., Moscow, 1948), pp. 41-56 [in Russian].
10.  M. Levy, "To the Problem of General Equations of Internal Motions Arising in Rigid Plastic Bodies beyond Elastic Limits," in Plasticity Theory, Ed. by Yu. N. Rabotnov (Izdat. Inostr. Liter., Moscow, 1948), pp. 20-23 [in Russian].
11.  Yu. N. Radaev, "To the Theory of Plane Strain of Ideally Plastic Bodies," Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser., No. 3 (62), 272-289 (2008).
12.  A. Yu. Ishlinskii, "On Equations of Body Deformation beyond the Elasticity Limit," Uch. Zap. MGU. Mekh., No. 117, 90-108 (1946).
13.  Yu. N. Radaev, "On the Ishlinskii Commutation Relations in Mathematical Theory of Plasticity," Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser., No. 6 (56), 102-114 (2007).
14.  L. Mirsky, "The Spread of a Matrix," Mathematika 3 (6), 127-130 (1956).
Received 03 August 2012
Link to Fulltext http://link.springer.com/article/10.3103/S002565441206009X
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