Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Murashkin E. V., Radayev Y. N. Two-dimensional Nye figures for hemitropic micropolar elastic solids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 109-122. DOI: 10.18500/1816-9791-2024-24-1-109-122, EDN: FKFRHA

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.03.2024
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2024-24-1-109-122
EDN: 
FKFRHA

Two-dimensional Nye figures for hemitropic micropolar elastic solids

Autors: 
Murashkin Evgenii Valeryevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Radayev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Abstract: 

The paper is devoted to a wide range of problems related to the two-dimensional Nye figures for micropolar continua. The method of two-dimensional matrix representation of fourth-rank tensors is well known from monographs on crystallography. Such representations are used to simplify tensor notation of the equations of anisotropic solids. This method allows us to represent the asymmetric constitutive tensors and pseudotensors of the fourth, third and second ranks in the form of specific two-dimensional figures. The Nye figures for the constitutive hemitropic tensors of the fourth and second ranks are given. The matrix form of the constitutive equations of a hemitropic micropolar solid in the athermal case is obtained. The transformation of the pseudotensor governing equations of the micropolar theory to a formulation in terms of absolute tensors is carried out via the  pseudoscalar units and their integer powers. The study is carried out in terms of absolute tensors in a Cartesian rectangular coordinate system.

Key words: 
elastic energy potential
constitutive tensor
pseudotensor unit
hemitropic micropolar continuum
Nye figure
matrix notation
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 23-21-00262 “Coupled thermomechanics of micropolar semi-isotropic media”).
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Received: 
18.08.2023
Accepted: 
11.09.2023
Published: 
01.03.2024
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