 | | 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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| << Previous article | Volume 57, Issue 6 / 2022 | Next article >> |
| D.V. Georgievskii, "Isotropic Tensor Functions with Quasipolynomial Scalar Potential in Nonlinear Elasticity Theory," Mech. Solids. 57 (6), 1359-1364 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
6 |
Pages |
1359-1364 |
| DOI |
10.3103/S0025654422060231 |
| Title |
Isotropic Tensor Functions with Quasipolynomial Scalar Potential in Nonlinear Elasticity Theory |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Moscow, 119991 Russia; Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, 119991 Russia, georgiev@mech.math.msu.su) |
| Abstract |
Based on the apparatus of tensor functions of one tensor arg ument, a multilevel family of scalar stress potentials with respect to deformations of isotropic elastic media is proposed, in which the elements of each level include elements of all previous levels. This potential generates a multilevel family of tensorially nonlinear constitutive relations in which each term, regardless of the level, has the first order of smallness in terms of the tendency of the deformation norm to zero. The number of material constants included in the multilevel constitutive relations is found. A system of installation experiments is proposed for finding four material constants in direct and inverse ratios of the second level. The questions of the reciprocity of tensor functions and the positive definiteness of the second-level potential, which leads to a tensor-linear dependence of stresses on strains, are discussed. |
| Keywords |
multilevel elastic potential, stress tensor, strain tensor, constitutive relation, quasi-polynomial, isotropic tensor function |
| Received |
10 January 2022 | Revised |
04 February 2022 | Accepted |
07 February 2022 |
| Link to Fulltext |
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