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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 2, Pages 246–255 (Mi vsgtu1669)  

Mechanics of Solids

Asymmetric tensor representations in micropolar continuum mechanics theories

Yu. N. Radayev

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 107045, Russian Federation

Abstract: 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, force stress, couple stress, asymmetric tensor, eigenvalue, eigenvector, asymptotic direction

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation AAAA-A17-117021310381-8
Russian Foundation for Basic Research 18-01-00844_а
This study was in part financially supported by the Ministry of Science and Higher Education (State Registration Number AAAA–A17–117021310381–8) and by the Russian Foundation for Basic Research (project no. 18–01–00844_a).


DOI: https://doi.org/10.14498/vsgtu1669

Full text: PDF file (834 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 539.3
MSC: 74A60, 74F05
Received: January 14, 2019
Revised: April 8, 2019
Accepted: April 29, 2019
First online: April 30, 2019
Language:

Citation: Yu. N. Radayev, “Asymmetric tensor representations in micropolar continuum mechanics theories”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 246–255

Citation in format AMSBIB
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\paper Asymmetric tensor representations in micropolar continuum mechanics theories
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 2
\pages 246--255
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\crossref{https://doi.org/10.14498/vsgtu1669}
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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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