 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| D.V. Georgievskii, "An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus," Mech. Solids. 53 (4), 381-384 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
4 |
Pages |
381-384 |
| DOI |
10.3103/S0025654418040039 |
| Title |
An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119992 Russia; Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, georgiev@mech.math.msu.su) |
| Abstract |
A class of constitutive relations is considered that connect symmetric stress and small strain tensors in three-dimensional space using an isotropic potential tensor nonlinear function of a rather general form. Various definitions of tensor nonlinearity are given and their equivalence is shown. From the standpoint of the mathematical apparatus of the theory of tensor nonlinear functions, the interpretation of the Poynting effect known in experimental mechanics and similar phenomena has been carried out. It is proved that these effects are not necessarily the result of the tensor nonlinearity of the defining relations, but may be due to the dependence on one of the material functions on the quadratic invariant, which is absent, for example, in the physically linear case. From here conclusions are drawn about the order of smallness of these effects. The possibility of modeling the Poynting effect by tensor-linear defining relations is discussed. |
| Keywords |
tensor nonlinearity, scalar nonlinearity, stress, deformation, defining relation, material function, invariant, Poynting effect |
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|
| Received |
27 March 2018 |
| Link to Fulltext |
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