 | | 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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| D. V. Georgievskii, "On the linearization of the constitutive relations for tensorially nonlinear isotropic media," Mech. Solids. 36 (5), 14-17 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
14-17 |
| Title |
On the linearization of the constitutive relations for tensorially nonlinear isotropic media |
| Author(s) |
D. V. Georgievskii (Moscow) |
| Abstract |
The boundary value problem of stability of the deformation process
in an arbitrary tensorially nonlinear isotropic medium is considered.
This problem is closed by the linearized relation between the
increments of the stress deviator and the strain rate tensor. It is
shown that the structure of this relation is similar to that for a
linear but anisotropic material, the type of anisotropy being
defined by the kinematics of the unperturbed process. The form of
this relation is specified for quasilinear materials and
Shvedov-Bingham-Il'yushin body, and also for the cases where the
unperturbed process is the one-dimensional shear or plane
tension-compression. |
| References |
| 1. | B. E. Pobedrya, Lectures on Tensor Analysis [in Russian],
Izd-vo MGU, Moscow, 1986. |
| 2. | D. V. Georgievskii, "Isotropic nonlinear tensor functions
in the theory of constitutive relations," in Achievements in Science and Technology.
Ser. Modern Mathematics and its Application. Volume 83 [in
Russian], VINITI, Moscow, 2001. |
| 3. | M. Reiner, Rheology [Russian translation], Nauka, Moscow, 1965. |
| 4. | E. Lainé, C. Vallée, and D. Fortuné, "Nonlinear isotropic
constitutive laws: choice of the three invariants, convex
potentials and constitutive inequalities," Intern. J. Engng. Sci.,
Vol. 3, No. 15, pp. 1927-1941, 1999. |
| 5. | D. V. Georgievskii, Stability of Processes of Deformation of
Viscoplastic Bodies [in Russian], URSS, Moscow, 1998. |
| 6. | A. A. Il'yushin, "Deformation of a viscoplastic body,"
Uchen. Zap. MGU. Mekhanika, No 39, pp. 3-81, 1940. |
| 7. | I. V. Keppen and S. Yu. Rodionov, "Tension and
compression of a strip made of a nonlinear viscoplastic material,"
in Elasticity and Inelasticity [in Russian], pp. 97-105, Izd-vo MGU,
Moscow, 1987. |
|
| Received |
06 May 2001 |
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