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IssuesArchive of Issues2015-4pp.397-399

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B.D. Annin, "Nonequivalence of Some Loading Paths Obtained by Rotation in the Five-Dimensional Il'yushin Space," Mech. Solids. 50 (4), 397-399 (2015)
Year 2015 Volume 50 Number 4 Pages 397-399
DOI 10.3103/S0025654415040056
Title Nonequivalence of Some Loading Paths Obtained by Rotation in the Five-Dimensional Il'yushin Space
Author(s) B.D. Annin (Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, annin@hydro.nsc.ru)
Abstract An example illustrating the noninvariance of the coaxiality property of nonsimilar stress and strain tensors under rotations in the five-dimensional Il'yushin space is constructed.
Keywords coaxiality, rotation, five-dimensional space
References
1.  A. A. Il'yushin, Collected Papers (1946-1966), Vol. 2: Plasticity (Fizmatlit, Moscow, 2004) [in Russian].
2.  A. Yu. Ishlinskii, Applied Problems of Mechanics, Vol. 1: Mechanics of Viscoplastic and Imperfectly Elastic Bodies (Nauka, Moscow, 1986) [in Russian].
3.  A. A. Il'yushin, Continuum Mechanics (Izd-vo MGU, Moscow, 1971) [in Russian].
4.  D. D. Ivlev, Mechanics of Plastic Media, (Fizmatlit, Moscow, 2001), Vol. 2 [in Russian].
5.  V. V. Novozhilov, "On the Forms of the Stress-Strain Relation for Initially Isotropic Nonelastic Bodies (Geometric Aspect of the Question)," Prikl. Mat. Mekh. 27 (5), 794-812 (1963) [J. Appl. Math. Mech. (Engl. Transl.) 27 (5), 1219-1243 (1963)].
6.  A. A. Il'yushin, Collected Papers. Modeling of Dynamic Processes in Solids and Engineering Applications (Fizmatlit, Moscow, 2009) [in Russian].
7.  V. G. Zubchaninov, "Theory of Processes and Incomplete Plasticity of Continua and A. A. Il'yushin's Isotropy Postulate," Vestnik ChGPU im. Yakovleva, No. 1(9), 38-60 (2011).
8.  R. A. Vasin, "Several Problems of Relationship between Stresses and Strains in Complex Loading," in Elasticity and Inelasticity (Izd-vo MGU, Moscow, 1971), pp. 59-126 [in Russian].
9.  R. A. Vasin, "Theory of Elastoplastic Processes and Experimental Plasticity," Elasticity and Inelasticity (Izd-vo MGU, Moscow, 2011), pp. 44-50 [in Russian].
10.  Yu. N. Rabotnov (Editor), Theory of Plasticity (Gos. Izdat. Inostr. Lit., Moscow, 1948) [in Russian].
Received 05 March 2015
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