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IssuesArchive of Issues2012-1pp.57-70

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O.A. Kilikovskaya and N.V. Ovchinnikova, "Influence of the Material Hardening and Compressibility on the Solution of Elastoplastic Deformation Problems for a Space with a Cylindrical Cavity," Mech. Solids. 47 (1), 57-70 (2012)
Year 2012 Volume 47 Number 1 Pages 57-70
DOI 10.3103/S0025654412010050
Title Influence of the Material Hardening and Compressibility on the Solution of Elastoplastic Deformation Problems for a Space with a Cylindrical Cavity
Author(s) O.A. Kilikovskaya (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192 Russia)
N.V. Ovchinnikova (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192 Russia, ovch-n@yandex.ru)
Abstract The present paper deals with plane deformation problems (εz=0) concerned with elastoplastic deformation of a space with a cylindrical cavity in the case where the load is given either at infinity or on the cavity surface. It is assumed that the material obeys the relations of the theory of flow with isotropic hardening and the von Mises plasticity condition. The effects of the elastic compressibility (Poisson's ratio) and the coefficient of linear hardening on the stress-strain state are studied. The influence of the linear hardening is shown to be small, while that of the elastic compressibility is shown to be quite significant.
Keywords plane deformation, plasticity, Poisson's ratio, finite-element method
References
1.  A. A. Il'yushin, Plasticity (Gostechizdat, Moscow, 1948) [in Russian].
2.  V. V. Sokolovskii, "Elastoplastic Equilibrium of a Cylindrical Tube in the Case of the Material Strengthening," Prikl. Mat. Mekh. 7 (4), 273-292 (1943) [J. Appl. Math. Mech. (Engl. Transl.)].
3.  R. Hill, The Mathematical Theory of Plasticity (Oxford Univ. Press, Oxford, 1950; Gostekhizdat, Moscow, 1956).
4.  W. Prager and P. Hodge, Theory of Perfectly Plastic Solids (Wiley, New York, 1951; Izd-vo Inostr. Lit., Moscow, 1956).
5.  L. A. Galin, "Plane Elastoplastic Problem. Plastic Domains for Circular Holes in Plates and Beams," Prikl. Mat. Mekh. 10 (3), 367-386 (1946) [J. Appl. Math. Mech. (Engl. Transl.)].
6.  V. V. Sokolovskii, The Theory of Plasticity (Vysshaya Shkola, Moscow, 1969) [in Russian].
7.  D. D. Ivlev, Theory of Ideal Plasticity (Nauka, Moscow, 1966) [in Russian].
8.  V. G. Zadorozhnyi, A. V. Kovalev, and A. N. Sporykhin, "Analyticity of the Solution of a Plane Elastoplastic Problem," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 138-146 (2008) [Mech. Solids (Engl. Transl.) 43 (1), 117-123 (2008)].
9.  D. D. Ivlev and L. V. Ershov, Perturbation Method in the Theory of Elastoplastic Body (Nauka, Moscow, 1978) [in Russian].
10.  D. D. Ivlev, E. V. Makarov, and Yu. M. Marushkei, "On Conditions of Plasticity of Compressible Elastoplastic Material in Plane Deformation," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 80-87 (1978) [Mech. Solids (Engl. Transl.)].
11.  A. Nadai, Plasticity (McGraw-Hill, New York, 1931; ONTI, Moscow-Leningrad, 1936).
Received 10 April 2009
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