On a ordering of area tensor elements orientations in a micropolar continuum immersed in an external plane space

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Abstract

The paper deals with the problems of ordering the reper orientations for a micropolar continuum immersed in an external plane space. Based on the concept of an elementary tensor volume (area) \(M\)-cells, an algorithm for comparing and matching external spatial orientations of \(M\)-cells is proposed. The process of continuous transfer of reper directions associated with a \(M\)-cell is considered. As a result, we can talk about the orientation of micropolar continuum itself and its boundary. The oriented continuum plays an important role in micropolar elasticity. This is especially true for the theory of hemitropic elastic media. The pseudotensor formulation of Stokes' theorem is discussed.

About the authors

Evgenii V. Murashkin

Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Author for correspondence.
Email: evmurashkin@gmail.com
ORCID iD: 0000-0002-3267-4742
SPIN-code: 4022-4305
Scopus Author ID: 12760003400
ResearcherId: F-4192-2014
http://www.mathnet.ru/person53045

Cand. Phys. & Math. Sci., PhD, MD; Senior Researcher; Lab. of Modeling in Solid Mechanics

101–1, pr. Vernadskogo, Moscow, 119526, Russian Federation

Yuri N. Radayev

Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Email: y.radayev@gmail.com
ORCID iD: 0000-0002-0866-2151
SPIN-code: 5886-9203
Scopus Author ID: 6602740688
ResearcherId: J-8505-2019
http://www.mathnet.ru/person39479

D.Sc. (Phys. & Math. Sci.), Ph.D., M.Sc., Professor; Leading Researcher; Lab. of Modeling in Solid Mechanics

101–1, pr. Vernadskogo, Moscow, 119526, Russian Federation

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