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G.L. Brovko, D.L. Bykov, R.A. Vasin, D.V. Georgievskii, I.A. Kiiko, I.N. Molodtsov, and B.E. Pobedrya, "A. A. Il'yushin's Scientific Heritage and Development of His Ideas in Mechanics," Mech. Solids. 46 (1), 3-14 (2011)
Year 2011 Volume 46 Number 1 Pages 3-14
DOI 10.3103/S002565441101002X
Title A. A. Il'yushin's Scientific Heritage and Development of His Ideas in Mechanics
Author(s) G.L. Brovko (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, glb@dataforce.net)
D.L. Bykov (Central Scientific Research Institute for Engineering (TsNIIMash), Pionerskaya 4, Korolev, Moscow oblast, 141070 Russia)
R.A. Vasin (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192 Russia, prof.vasin@mail.ru)
D.V. Georgievskii (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, georgiev@mech.math.msu.su)
I.A. Kiiko (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, 66krok@rambler.ru)
I.N. Molodtsov (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, mechmathmsu@mail.ru)
B.E. Pobedrya (Lomonosov Moscow State University, GSP-2, pobedria@tochka.ru, pob@mail.ru)
Abstract We present a survey of the main results and scientific ideas due to the 20th century prominent scientist Aleksey Antonovich Il'yushin, which can be regarded today, at his hundredth birthday anniversary, as his scientific heritage. The survey material is arranged (mainly, chronologically) in the key directions of Il'yushin's activities such as the theory of viscoplastic flow, hydrodynamic stability, dynamics of deformable media, supersonic aerodynamics and related flatter problems, theory of elastoplastic processes, theory of plastic flow, thermoviscoelasticity and thermodynamics, strength of polymer bodies and structures, general theory of constitutive relations in classical continuum mechanics, and nonclassical models of continuum.
References
1.  A. A. Il'yushin, "To the Problem of Viscoplastic Flow of Materials," in Proc. Conf. in Plastic Strains, December 1936 (Izd-vo AN SSSR, Moscow-Leningrad, 1938), pp. 5-18 [in Russian].
2.  A. A. Il'yushin, "Deformation of Viscoplastic Bodies," Uchen. Zap. MGU. Mekh. No. 39, 3-81 (1940).
3.  A. Yu. Ishlinskii, "Stability of Viscoplastic Flow of a Circular Plate," Prikl. Mat. Mekh. 7 (6), 405-412 (1943) [J. Appl. Math. Mech. (Engl. Transl.)].
4.  A. Yu. Ishlinskii, "Stability of Viscoplastic Flow of a Plate and a Circular Rod," Prikl. Mat. Mekh. 7 (2), 109-130 (1943) [J. Appl. Math. Mech. (Engl. Transl.)].
5.  A. A. Il'yushin, "On Tests of Metals at Large Velocities," Inzh. Sb., No. 1, 13-26 (1941).
6.  I. V. Keppen and S. Yu. Rodionov, "Tension and Compression of a Band Made of a Nonlinearly Viscoplastic Material," in Elasticity and Inelasticity (Izd-vo Mosk. Univ., Moscow, 1987), pp. 97-105 [in Russian].
7.  P. M. Ogibalov and A. Kh. Mirzadzhanzade, Nonstationary Motions of Viscoplastic Media (Izd-vo MGU, Moscow, 1977) [in Russian].
8.  I. A. Kiiko, "Plastic Flow of Metals," in Scientific Principles of Progressive Techniques and Technology (Mashinostroenie, Moscow, 1985), pp. 102-133 [in Russian].
9.  E. A. Leonova, "Invariant Properties of Thermo-Viscoplasticity Equations with Incomplete Information about the Medium Properties," in Elasticity and Inelasticity, Part 1 (Izd-vo MGU, Moscow, 1993), pp. 55-87 [in Russian].
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11.  A. A. Il'yushin, On the Use of Multilayer Metallic Armors and Methods for Calculations of Their Puncture Resistance, Manuscript of Postgraduate Report (Institute of Mechanics MGU, Moscow, 1935) [in Russian].
12.  A. A. Il'yushin and P. M. Ogibalov, "New Pneumatic High-Speed Impact Machine," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 57-65 (1957).
13.  A. A. Il'yushin and T. Rashidov, "Simplified Equations of Seismic Dynamics of Complex Systems of Underground Constructions," Izv. Akad. Nauk Uzbek. SSR. Ser. Tekhn. Nauk, No. 2, 20-30 (1970).
14.  A. A. Il'yushin, "Riddles of Mechanics of Deformable Solids," in Unsolved Problems of Mechanics and Applied Mathematics (Izd-vo MGU, Moscow, 1977), pp. 68-73 [in Russian].
15.  A. A. Il'yushin, "Dynamics," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 3, 227-240 (1994) [Moscow Univ. Math. Bull. (Engl. Transl.)].
16.  A. A. Il'yushin, "Law of Plane Sections in Supersonic High-Speed Aerodynamics," Prikl. Mat. Mekh. 20 (6), 733-755 (1956) [J. Appl. Math. Mech. (Engl. Transl.)].
17.  A. A. Movchan, Several Problems of Oscillations of a Plate Moving in a Gas, in Proc. of Institute of Mechanics, AN SSSR, No. 1 (1955).
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19.  A. A. Il'yushin and I. A. Kiiko, "A New Formulation of the Problem of the Flutter of a Hollow Shell," Prikl. Mat. Mekh. 58 (3), 167-171 (1994) [J. Appl. Math. Mech. (Engl. Transl.) 58 (3), 545-549 (1994)].
20.  S. D. Algazin and I. A. Kiiko, Flutter of Plates and Shells (Nauka, Moscow, 2006) [in Russian].
21.  G. S. Larionov, "Nonlinear Flutter in an Elastic-Viscous Plate," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 95-100 (1974) [Mech. Solids (Engl. Transl.) 9 (4), 85-89 (1974)].
22.  V. I. Matyash, "Flutter of a Viscoelastic Plate," Mekh. Polim., No. 6, 1077-1083 (1971) [Polimer Mech. (Engl. Transl.) 7 (6), 957-961 (1971)].
23.  I. A. Kiiko, "Flutter of a Viscoelastic Plate," Prikl. Mat. Mekh. 60 (1), 172-175 (1996) [J. Appl. Math. Mech. (Engl. Transl.) 60 (1), 167-170 (1996)].
24.  I. A. Kiiko and V. V. Pokazeev, "Vibrations and Stability of a Viscoelastic Strip Placed into Gas Flow," Dokl. Ross. Akad. Nauk 401 (3), 342-344 (2005) [Dokl. Phys. (Engl. Transl.) 50 (3), 158-160 (2005)].
25.  A. A. Il'yushin, Plasticity, Part 1: Elastoplastic Strains (OGIZ GITTL, Moscow-Leningrad, 1948) [in Russian].
26.  A. A. Il'yushin, Plasticity, Part 1: Elastoplastic Strains in Classical University Manual (Logos, Moscow, 2004), Reprint of 1948 edition [in Russian].
27.  A. A. Il'yushin, "Mechanics of Elastic and Plastic Strains of Solids," in Collection of Works, Vol. 1 (1935-1945) (Fizmatlit, Moscow, 2003), pp. 232-272 [Manuscript, November 1942; the work is published completely as "Several Problems of Plasticity," Prikl. Mat. Mekh. 7 (4), (1943)] [in Russian].
28.  A. A. Il'yushin, "On the Relation between Stresses and Small Strains in Continuum Mechanics," Prikl. Mat. Mekh. 18 (6), 641-666 (1954) [J. Appl. Math. Mech. (Engl. Transl.)].
29.  A. A. Il'yushin, Plasticity. Foundations of Mathematical Theory (Izd-vo AN SSSR, Moscow, 1963) [in Russian].
30.  R. A. Vasin, A. A. Il'yushin, and P. A. Mossakovskii, "Investigation of Constitutive Equations and Fracture Criteria Using Solid and Thick-Walled Tubular Cylindrical Specimens," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 177-184 (1994) [Mech. Solids (Engl. Transl.)].
31.  I. S. Bogatyrev, A. A. Il'yushin, V. S. Lenskii, and V. M. Panferov, "SN-Machine for Studies of Plastic Strain of Metals under Complex Loading," Inzh. Zh., No. 2, 182-193 (1961).
32.  V. G. Zubchaninov, N. L. Okhlopkov, and V. V. Garanikov, Experimental Plasticity, Processes of Complex Strain, Book 1 (TGTU, Tver, 2003) [in Russian].
33.  V. G. Zubchaninov, N. L. Okhlopkov, and V. V. Garanikov, Experimental Plasticity, Processes of Complex Stressing, Book 2 (TGTU, Tver, 2003) [in Russian].
34.  A. A. Il'yushin, R. A. Vasin, and P. A. Mossakovskii, "Theory of Elastoplastic Processes under Large Plastic Strains," in Applied Problems of Mechanics of Thin-Walled Structures (Izd-vo Mosk. Univ., Moscow, 2000), pp. 128-137 [in Russian].
35.  A. A. Il'yushin, "CL-Computer Method in the Theory of Plasticity," in Problems of Applied Mathematics and Mechanics (Nauka, Moscow, 1971), pp. 166-178 [in Russian].
36.  M. Lucchesi and P. Podio-Guidugli, "Equivalent Dissipation Postulates in Classical Plasticity," Meccanica 25, 26-31 (1990).
37.  G. A. Maugin, The Thermomechanics of Plasticity and Fracture (Cambridge Univ. Press, Cambridge, New York, Port Chester, Melbourne, Sydney, 1992).
38.  I. A. Kiiko, M. Sh. Israilov, and G. L. Brovko (Editors), Elasticity and Inelasticity, Materials of International Scientific Symposium on Problems of Mechanics of Deformable Bodies on the Occasion of A. A. Il'yushin Nineteenth Birthday (Moscow, January 22-23, 2001) (Izd-vo Mosk. Univ., Moscow, 2001) [in Russian].
39.  A. A. Il'yushin, "Several Problems of the Theory of Plastic Flow," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 64-86 (1958).
40.  A. A. Il'yushin, "Problems of the Theory of Flow of Plastic Matters on Surfaces," Prikl. Mat. Mekh. 18 (3), 265-288 (1954) [J. Appl. Math. Mech. (Engl. Transl.)].
41.  A. A. Il'yushin, "Total Plasticity in Processes of Flow between Rigid Surfaces, Analogy with Sand Fill and Several Applications," Prikl. Mat. Mekh. 19 (6), 693-713 (1955) [J. Appl. Math. Mech. (Engl. Transl.)].
42.  I. A. Kiiko, "Theory of Viscoplastic Flows," in Elasticity and Inelasticity (Lenand, Moscow, 2006), pp. 12-26 [in Russian].
43.  I. A. Kiiko, "Anisotropy in the Flow Processes of a Thin Plastic Layer," Prikl. Mat. Mekh. 70 (2), 344-351 (2006) [J. Appl. Math. Mech. (Engl. Transl.) 70 (2), 311-317 (2006)].
44.  V. V. Moskvitin, Resistance of Viscoplastic Materials with Regard to Charges of Solid-Propellant Rocket Engines (Nauka, Moscow, 1972) [in Russian].
45.  A. A. Il'yushin and B. E. Pobedrya, Foundations of Mathematical Theory of Thermoviscoelasticity (Nauka, Moscow, 1970) [in Russian].
46.  A. A. Il'yushin, Continuum Mechanics (Izd-vo MGU, Moscow, 1990; Izd-vo MGU, Moscow, 1971 and 1978) [in Russian].
47.  V. S. Lenskii, "Experimental Verification of Laws of Isotropy and Retardation under Complex Loading," Izv. Akad. Nauk SSSR. OTN. Mekh. Mashinostr., No. 11, 15-24 (1958).
48.  A. A. Il'yushin and V. S. Lenskii, "On Relations and Methods of Modern Theory of Plasticity," in Progress in Mechanics of Deformable Media (Nauka, Moscow, 1975), pp. 240-255 [in Russian].
49.  V. S. Lenskii, "Physical Adequacy in Modern Theory of Plasticity," in Elasticity and Inelasticity, Part 1 (Izd-vo MGU, Moscow, 1993), pp. 95-119 [in Russian].
50.  A. A. Il'yushin and V. S. Lenskii, Strength of Materials (Fizmatgiz, Moscow, 1959) [in Russian].
51.  A. A. Il'yushin, V. A. Lomakin, and A. P. Shmakov, Problems and Exercises in Continuum Mechanics (Izd-vo Mosk. Univ., Moscow, 1959) [in Russian].
52.  B. E. Pobedrya and D. V. Georgievskii, Foundations of Continuum Mechanics (Fizmatlit, Moscow, 2006) [in Russian].
53.  A. A. Il'yushin, "On the Increments of Plastic Deformations and the Yield Surface," Prikl. Mat. Mekh. 24 (4), 663-666 (1960) [J. Appl. Math. Mech. (Engl. Transl.) 24 (4), 987-992 (1960)].
54.  A. A. Il'yushin, "On Foundations of General Mathematical Theory of Plasticity," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 3, 31-36 (1961).
55.  A. A. Il'yushin, "Functionals and Measures of Irreversibility on the Sets of Processes in Continuum Mechanics (CM)," Dokl. Ross. Akad. Nauk 337 (1), 48-50 (1994) [Dokl. Phys. (Engl. Transl.)].
56.  G. A. Il'yushina, "On Certain Consequences of the Macroscopic Definability Postulate in Continuum Mechanics," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 1, 84-88 (1978) [Moscow Univ. Math. Bull. (Engl. Transl.)].
57.  A. A. Il'yushin and G. A. Il'yushina, "Problems of Thermodynamics of Irreversible Processes," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 3, 73-80 (1983) [Moscow Univ. Math. Bull. (Engl. Transl.)].
58.  G. A. Il'yushina, "The Non-Uniqueness of the Solutions of the Basic Thermodynamic Equation of the Mechanics of Continuous Media in Classes of Continuous Functionals," Zh. Vychisl. Mat. Mat. Fiz. 36 (5), 784-787 (1995) [Comput. Math. Math. Phys. (Engl. Transl.) 35 (5), 619-621 (1995)].
59.  G. A. Il'yushina, "On Solutions of Thermodynamical Equation for the Functional of Reaction in the Space of Continuously Differentiable Processes," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 2, 75-79 (1996) [Moscow Univ. Math. Bull. (Engl. Transl.)].
60.  G. L. Brovko and A. A. Il'yushin, "Models and Constitutive Experiments in the Theory of Elastoplastic Processes under Finite Strains," in A. A. Il'yushin Collection of Works, Vol. 4: Modeling of Dynamical Processes in Rigid Bodies and Engineering Applications (Fizmatlit, Moscow, 2009), pp. 148-159 [in Russian].
61.  G. L. Brovko, "Material and Spatial Representations of the Constitutive Relations of Deformable Media," Prikl. Mat. Mekh. 54 (5), 814-824 (1990) [J. Appl. Math. Mech. (Engl. Transl.) 54 (5), 668-677 (1990)].
62.  A. A. Il'yushin and V. A. Lomakin, "Moment Theories in Mechanics of Rigid Deformable Bodies," in Strength and Plasticity (Nauka, Moscow, 1971), pp. 54-61 [in Russian].
63.  A. A. Il'yushin, "Unsymmetry of Strain and Stress Tensors in Continuum Mechanics," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 5, 6-14 (1996) [Moscow Univ. Math. Bull. (Engl. Transl.)].
64.  G. L. Brovko, "Modeling of Inhomogeneous Media of Complex Structure and Cosserat Continuum," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 5, 55-63 (1996) [Moscow Univ. Math. Bull. (Engl. Transl.)].
65.  I. N. Molodtsov, "Mathematical Modeling of Structure Variations in Materials under Large Strains," Izv. TulGU. Ser. Mat. Mekh. Inf. 9 (2), 158-167 (2002).
66.  G. L. Brovko, "A Model of Inhomogeneous Liquid-Gas-Saturated Medium with a Deformable Solid Frame," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 5, 45-52 (1998) [Moscow Univ. Math. Bull. (Engl. Transl.) 53 (5), 19-26 (1998)].
67.  P. M. Ogibalov, E. P. Tambovtsev, and I. N. Molodtsov, "Dynamic Calibration of Dissipation in Composite Nonlocal Media," Mekh. Komp. Mater., No. 2, 217-224 (1985).
68.  G. L. Brovko and A. A. Il'yushin, "On a Plane Model of Perforated Plates," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 2, 83-91 (1993) [Moscow Univ. Math. Bull. (Engl. Transl.)].
69.  G. L. Brovko, "On one Structural Model of the Cosserat Medium," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 75-91 (2002) [Mech. Solids (Engl. Transl.) 37 (1), 60-73 (2002)].
70.  V. A. Lomakin, Statistical Problems of the Mechanics of Deformable Solids (Nauka, Moscow, 1970) [in Russian].
71.  V. A. Lomakin, Theory of Elasticity of Inhomogeneous Bodies (Izd-vo Mosk. Univ., Moscow, 1976) [in Russian].
Received 16 September 2010
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