Geodesic
Asymmetric tensor representations in micropolar continuum mechanics theories
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 246-255.

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In this paper, new representations of three-dimensional asymmetric stress tensor and the corresponding form of the differential equilibrium equations are given. Asymmetric theories of solid mechanics continues to attract attention in connection with the necessity of mathematical modelling of the mechanical behaviour of the advanced materials. The study is restricted to such asymmetric second rank tensors, for which it is still possible to keep the notion of real eigenvalues, but not to accept the mutual orthogonality of the directors of the principal trihedron. The exact algebraic formulation of these asymmetry conditions is discussed. The study extends the dyadic tensor representations of the symmetric stress tensor based on the notion of asymptotic directions. The obtained results are a clear evidence in favor of algebraic hyperbolicity both the symmetric and asymmetric second rank tensors in three-dimensional space.
Keywords: micropolar continuum, couple stress, asymmetric tensor, eigenvalue, eigenvector, asymptotic direction.
Mots-clés : force stress 
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Yu. N. Radayev. Asymmetric tensor representations in micropolar continuum mechanics theories. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 246-255. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_2_a2/

[1] Nowacki W., Theory of Asymmetric Elasticity, Pergamon Press, Oxford, New York, etc., 1986, viii+383 pp. | MR | Zbl

[2] Radayev Y. N., “The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci., 22:3 (2018), 504–517 (In Russian) | DOI | Zbl

[3] Nowacki W., Theory of Elasticity, Mir Publ., Moscow, 1975, 872 pp. (In Russian) | MR

[4] Sushkevich A. K., Foundations of Higher Algebra, ONTI, Moscow, Leningrad, 1937, 476 pp. (In Russian)

[5] Radayev Y. N., Three-dimensional Problem of the Mathematical Theory of Plasticity, Samara University Publ., Samara, 2006, 240 pp. (In Russian)

[6] Radayev Y. N., “Asymptotic axes of stress tensors and strain increment tensors in mechanics of compressible continua”, Mech. Solids, 48:5 (2013), 546–552 | DOI

[7] Radayev Y. N., “Instantaneously not Elongated Directors in Three-Dimensional Kinematics of the Coulomb–Mohr Medium”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 18:4 (2018), 467–483 (In Russian) | DOI

[8] Radayev Y. N., “Hyperbolic theories and applied problems of solid mechanics”, Actual Problems of Mechanics. Int. Conf., devoted to L. A. Galin 100th Anniversary (September, 20–21, 2012, Moscow), Book of Abstracts, IPMech RAS, Moscow, 2012, 75–76