 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.A.Markin, M.Yu. Sokolova, and D.V. Khristich, "A. A. Il'yushin's Postulate for Anisotropic Materials and a Version of Constitutive Relations," Mech. Solids. 46 (1), 30-35 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
1 |
Pages |
30-35 |
| DOI |
10.3103/S0025654411010055 |
| Title |
A. A. Il'yushin's Postulate for Anisotropic Materials and a Version of Constitutive Relations |
| Author(s) |
A.A.Markin (Tula State University, pr-t Lenina 92, Tula, 300600 Russia, markin@tsu.tula.ru)
M.Yu. Sokolova (Tula State University, pr-t Lenina 92, Tula, 300600 Russia, sokolova@tula.net)
D.V. Khristich (Tula State University, pr-t Lenina 92, Tula, 300600 Russia, dmitro@tula.net) |
| Abstract |
The particular isotropy postulate proposed by A. A. Il'yushin permits stating and implementing programs for construction and experimental justification of relations determining the thermomechanical properties of initially isotropic materials for trajectories of various degree of complexity.
In the present paper, we propose an extended statement of the isotropy postulate, which takes into account the initial elastic anisotropy as well as possible dilatation effects for initially isotropic materials. The construction is based on the consideration (following the approach proposed by Ya. K. Rykhlevskii) of eigensubspaces of the linear elasticity operator. The strain and stress tensors in the eigensubspaces are similar, and their vector images in the six-dimensional space are coaxial and do not vary under orthogonal transformations within the eigensubspace. The form of the particular postulate generalized to nonlinear operators takes into account the fact that the vector images of stresses can leave the eigensubspace in which the strain trajectories are located. In this case, the process image must be invariant under rotations and reflections of the strain trajectory within the eigensubspace.
In the framework of the extended isotropy postulate, we consider a version of the constitutive relations of physically nonlinear thermoelasticity in which the effects of multimodulus behavior of materials, as well as dilatation and thermodynamic effects, are taken into account. |
| Keywords |
particular postulate, anisotropy, thermoelasticity, nonlinearity, strain trajectory, vector images of processes |
| References |
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|
| Received |
02 June 2010 |
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