 | | 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
|
| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 51, Issue 5 / 2016 | Next article >> |
| D.V. Georgievskii, "Potentiality of Isotropic Nonlinear Tensor Functions Relating Two Deviators," Mech. Solids. 51 (5), 619-622 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
5 |
Pages |
619-622 |
| DOI |
10.3103/S0025654416050162 |
| Title |
Potentiality of Isotropic Nonlinear Tensor Functions Relating Two Deviators |
| Author(s) |
D.V. Georgievskii (Lomonosov Moscow State University, Moscow, 119992 Russia; Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, georgiev@mech.math.msu.ru) |
| Abstract |
In the theory of constitutive relations, isotropic quadratic nonlinear tensor functions modeling media with second-order effects, in particular, with misalignment of the force and kinematic tensors, are considered. It is very interesting to consider tensor functions with a scalar potential relating two symmetric deviators of rank two. In this case, the potentiality conditions are integrated, and it is shown that the first integral contains two arbitrary functions of the quadratic invariant of the tensor argument and one arbitrary function of the cubic invariant. A tensorially nonlinear generalization of the rigid-viscoplastic model (a two-contact Bingham solid) is carried out. |
| Keywords |
tensor function, scalar potential, constitutive relations, material function, invariant, rigid-viscoplastic model |
| References |
| 1. | R. S. Rivlin and J. L. Ericksen,
"Stress-Deformation Relations for Isotropic Materials,"
J. Rat. Mech. Anal.
4, 323-425 (1955). |
| 2. | M. A. Brutyan and P. L. Krapivskii,
"Hydrodynamics of Newtonian Fluids,"
in Ser. Complex and Special Fields of Mechanics, Vol. 4
(VINITI, Moscow, 1991),
pp. 3-98
[in Russian]. |
| 3. | B. E. Pobedrya,
Numerical Methods in Elasticity and Plasticity Theory
(Izd-vo MGU, Moscow, 1995)
[in Russian]. |
| 4. | D. V. Georgievskii,
"Tensor Nonlinear Effects in Isothermal Deformation of Continuous Media,"
Uspekhi Mekh.
1 (2), 150-176 (2002). |
| 5. | D. V. Georgievskii,
"Tensor-Nonlinear Shear Flows: Material Functions and Diffusion-Vortex Solutions,"
Nelin. Din.
7 (3), 451-463 (2011). |
| 6. | D. V. Georgievskii,
"On "Orthogonal Effects" of Stress-Strain State in Continuum Mechanics,"
Vestnik Kiev Nats. Un-tu, Ser. Fiz.-Mat. Nauki,
No. 3, 114-116 (2013). |
| 7. | D. V. Georgievskii,
"The Angle between the Stress Deviator and the Strain-Rate Deviator
in a Tensor Nonlinear Isotropic Medium,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh.,
No. 6, 63-66 (2013)
[Moscow Univ. Mech. Bull. (Engl. Transl.)
68 (6), 149-151 (2013)]. |
| 8. | D. V. Georgievskii, W. H. Müller, and B. E. Abali,
"Establishing Experiments to Find Material Functions
in Tensor Nonlinear Constitutive Relations,"
Izv. Ross. Akad. Nauk. Ser. Fiz.
76 (12), 1534-1537 (2012)
[Bull. Russ. Acad. Sci. Phys. (Engl. Transl.)
76 (12), 1374-1377 (2012)]. |
| 9. | D. V. Georgievskii,
"Establishing Experiments in Tensor Nonlinear Theories of Continuum Mechanics,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh.,
No. 2, 66-68 (2016)
[Moscow Univ. Mech. Bull. (Engl. Transl.)
71 (2), 49-50 (2016)]. |
| 10. | R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko,
"Pointing Effect for Cylindrically Anisotropic Nano/Microtubes,"
Fiz. Mezomekhanika
19 (1), 5-14 (2016). |
|
| Received |
03 April 2016 |
| Link to Fulltext |
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