 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Y.N. Radayev, "Tensors with Constant Components in the Constitutive Equations of a Hemitropic Micropolar Solids," Mech. Solids. 58 (5), 1517-1527 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
5 |
Pages |
1517-1527 |
| DOI |
10.3103/S0025654423700206 |
| Title |
Tensors with Constant Components in the Constitutive Equations of a Hemitropic Micropolar Solids |
| Author(s) |
Y.N. Radayev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com) |
| Abstract |
The present paper is devoted to elastic potentials and the constitutive equations of mechanics of anisotropic micropolar solids, the kinematics of which can be specified by two independent vector fields: a contravariant field of translational displacements and a contravariant pseudovector field of microrotations of weight +1. The quadratic stress potential is represented by three constitutive tensors of the fourth rank, two of which are pseudotensor in nature and can be assigned weights −2 and −1. Such a solid is completely specified by the 171st micropolar elastic modulus. The main attention is focused on the model of a hemitropic (half-isotropic, demitropic) micropolar elastic solid characterized by nine constitutive constants. The components of the constitutive pseudo-tensor of weight −1 turn out to be sensitive to mirror reflection transformations in three-dimensional space. A peculiar algebraic structure of the constitutive tensors of a hemitropic solid, more precisely, their absolute analogues obtained by multiplying by integer powers of a pseudoscalar unity, is studied. It is shown that these tensors can always be constructed from isomers (isomer) of a tensor with constant components (generally insensitive to any transformations of the coordinate system) and one additional fourth-rank tensor constructed, in turn, from the components of the metric tensor. |
| Keywords |
micropolar solid, stress potential, semi-isotropic solid, constitutive tensor, mirror reflection, isomer |
| Received |
13 March 2023 | Revised |
06 April 2023 | Accepted |
21 April 2023 |
| Link to Fulltext |
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