Mechanics of Solids (about journal) Mechanics of Solids
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in January 1966
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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,,
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
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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].
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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).
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Received 03 August 2012
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