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IssuesArchive of Issues2003-4pp.121-128

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D. D. Ivlev, "A. Yu. Ishlinskii's ideas and results in the theory of plasticity," Mech. Solids. 38 (4), 121-128 (2003)
Year 2003 Volume 38 Number 4 Pages 121-128
Title A. Yu. Ishlinskii's ideas and results in the theory of plasticity
Author(s) D. D. Ivlev (Moscow)
Abstract The creative work of A. Yu. Ishlinskii in mechanics of solids is extensive and diverse. It covers the theory of elasticity, static and dynamic stability of elastic bodies, imperfect elasticity, vibrations and fracture of inelastic bodies, viscoplastic flows, impacts, dynamics of soils and sand, fracture mechanics, and other areas. The present paper is devoted to Ishlinskii's ideas and results in the field of plasticity theory and applications.
References
1.  B. Saint-Venant, "On establishing equations of internal motions occurring in plastic solids beyond the elastic limit," in Plasticity [Russian translation], pp. 11-19, Izd-vo Inostr. Lit-ry, Moscow, 1948.
2.  A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity [in Russian], Fizmatlit, Nauka, 2001.
3.  T. Thomas, Plastic Flow and Fracture in Solids [Russian translation], Mir, Moscow, 1964.
4.  D. D. Ivlev and G. I. Bykovthsev, Theory of a Hardening Plastic Body [in Russian], Nauka, Moscow, 1971.
5.  A. Yu. Ishlinskii, "Forming strength hypothesis," Uchenye Zapiski MGU. Mekhanika, No. 46, pp. 117-124, 1940.
6.  A. Yu. Ishlinskii, "On the stability of the viscoplastic flow of a strip and a round rod," PMM [Applied Mathematics and Mechanics], Vol. 7, No. 2, pp. 109-130, 1943.
7.  A. Yu. Ishlinskii, "On the stability of the viscoplastic flow of a round plate," PMM [Applied Mathematics and Mechanics], Vol. 7, No. 6, pp. 405-412, 1943.
8.  A. Yu. Ishlinskii, "The axially symmetric problem of plasticity and the Brinell test," PMM [Applied Mathematics and Mechanics], Vol. 8, No. 3, pp. 201-224, 1944.
9.  H. Henky, "On some statically determinate cases of equilibrium in plastic bodies," in Plasticity [Russian translation], pp. 80-101, Izd-vo Inostr. Lit-ry, Moscow, 1948.
10.  A. Haar and T. Karman, "To the theory of stress states in plastic and loose media," in Plasticity [Russian translation], pp. 41-56, Izd-vo Inostr. Lit-ry, Moscow, 1948.
11.  A. Yu. Ishlinskii, "Spatial deformation of incompletely elastic and viscoplastic bodies," Izv. AN SSSR. OTN, No. 3, pp. 250-260, 1945.
12.  A. Yu. Ishlinskii, "Fracture of incompletely elastic materials," Uchenye Zapiski MGU. Mekhanika, Vol. 1, No. 117, pp. 109-126, 1946.
13.  D. D. Ivlev, Theory of Perfect Plasticity [in Russian], Nauka, Moscow, 1966.
14.  A. Yu. Ishlinskii, "General theory of plasticity with linear hardening," Ukr. Mat. Zh., Vol. 6, No. 3, pp. 314-325, 1954.
15.  A. Yu. Ishlinskii, "Tension of an infinitely long perfectly plastic strip of variable cross-section," Doklady AN UkrSSR, No. 1, pp. 12-15, 1958.
16.  D. D. Ivlev, A. Yu. Ishlinskii, and L. A. Maksimova, "On the properties of flow of an isotropic medium," Doklady AN, Vol. 375, No. 2, pp. 191-194, 2000.
17.  D. D. Ivlev, A. Yu. Ishlinskii, and L. A. Maksimova, "On the flow of isotropic media," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 5-12, 2000.
18.  D. D. Ivlev, A. Yu. Ishlinskii, and R. I. Nepershin, "On the characteristic relationships between the stresses and displacement rates in 3D problem for a perfectly plastic body in the case of complete plasticity," Doklady AN, Vol. 381, No. 5, pp. 616-622, 2001.
19.  D. D. Ivlev, A. Yu. Ishlinskii, and R. I. Nepershin, "On the characteristic relationships between the stresses in 3D problem for a loose medium in the case of complete limit equilibrium," Doklady AN, Vol. 383, No. 5, pp. 638-642, 2002.
20.  D. D. Ivlev, A. Yu. Ishlinskii, and R. I. Nepershin, "On the characteristic relationships between the displacement rates in 3D problem of complete limit equilibrium for a loose medium," Doklady AN, Vol. 384, No. 1, pp. 57-62, 2002.
21.  D. D. Ivlev, A. Yu. Ishlinskii, and R. I. Nepershin, "Indentation of a pyramid into a perfectly plastic half-space," Doklady AN, Vol. 385, No. 6, pp. 766-769, 2002.
22.  D. D. Ivlev, A. Yu. Ishlinskii, and R. I. Nepershin, "On indentation of a rigid pyramid into a perfectly plastic half-space," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 57-62, 2002.
Received 05 March 2003
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