Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2008-1pp.124-130

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K. F. Komkov, "Description of anisotropy of isotropic materials caused by plastic strain," Mech. Solids. 43 (1), 124-130 (2008)
Year 2008 Volume 43 Number 1 Pages 124-130
DOI 10.3103/S0025654408010123
Title Description of anisotropy of isotropic materials caused by plastic strain
Author(s) K. F. Komkov (Military Technical University, Russian Federal Service of Special Construction, Karbysheva 8, Balashiha, Moscow oblast, 143911, Russia,
Abstract Many materials are polycrystalline media or hardened mechanical mixtures of complicated structure. For small elastic strains, they behave as isotropic media. But under stresses exceeding the elastic limit, these materials exhibit effects related to strain anisotropy. The problem of quantitatively estimating this phenomenon still remains open.

In the present paper, without any assumptions, we reduce the nonlinear Novozhilov equations to a form typical of the constitutive relations for orthotropic media. We obtain expressions for generalized nonlinear elasticity characteristics by choosing a specific expression for the strain potential. We derive working formulas for calculating the elasticity coefficients in the principal directions and of all coefficients of the transverse strains and shear moduli in the principal planes of elastic symmetry. We describe methods for determining them from the results of extension-compression tests.

We also analyze several results of tests published on this subject. We show that the effect related to the anomalous behavior of the transverse strain coefficient, which is observed both under compression and under tension, can be explained completely if the fact that the plastic strain is accompanied with strain anisotropy effects is taken into account.
1.  V. V. Novozhilov, On the Relation between Stresses and Strains in Nonlinearly Elastic Medium, Prikl. Mat. Mekh. 15(2), 183-194 (1951) [J. Appl. Math. Mech. (Engl. Transl.)].
2.  K. F. Komkov, Use of Nonlinear Tensor Equations in the Mechanics of Deformable Bodies, Prikl. Mekh. 27(7), 36-41 (1991) [Int. Appl. Mech. (Engl. Transl.) 27 (7), 654-659 (1991)].
3.  S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, Moscow, 1977) [in Russian].
4.  N. N. Malinin, Applied Theory of Plasticity and Creep (Mashinostroenie, Moscow, 1975) [in Russia].
5.  A. Nadai, Plasticity and Destruction of Solid Bodies, Vol. 2 (Izd-vo Inosr. Liter., Moscow, 1969) [in Russian].
6.  K. F. Komkov, The Calculation of the Lode Parameters when Processing the Results of Experiments, Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 126-135 (2005) [Mech. Solids (Engl. Transl.) 40 (2), 104-112 (2005)].
Received 21 February 2005
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