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Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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Since 2018, translations of PMM's articles have been published in special issues of the journals Mechanics of Solids and Fluid Dynamics:

Total articles in the database: 1969
In Russian (ÏÌÌ): 1170
In English (J. Appl. Math. Mech.): 799

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"Aleksei Antonovich Il’yushin: on the 100th anniversary of his birth," J. Appl. Math. Mech. 75 (1), 1-4 (2011)
Year 2011 Volume 75 Issue 1 Pages 1-4
Title Aleksei Antonovich Il’yushin: on the 100th anniversary of his birth
Abstract January 20, 2011 marks the 100th anniversary of the birth of Aleksei Antonovich Il’yushin, an outstanding applied mathematician, a Corresponding Member of the Russian Academy of Sciences,Honoured Professor of the M.V. Lomonosov Moscow State University and a member of the editorial board of Prikladnaya Matematika i Mekhanika for almost half a century.

He was born in Kazan. On leaving school, he worked as a machine operator at the ship repair yard, and in 1929 he entered the Physics and Mathematics Faculty of Kazan University. In 1930 he transferred to the Physics and Mathematics Faculty of Moscow State University (MGU). On graduation in 1933 he pursued his postgraduate studies at the Institute of Mechanics of the MGU and at the same time became an assistant in the Elasticity Theory Department of the Mechanics and Mathematics Faculty. Although he had numerous important responsibilities elsewhere, he worked in this department (as a professor from 1939 and as its head from 1942) for the rest of his life.

A thirst for knowledge, an unusual willingness to work hard, an aptitude for theoretical research and at the same time a desire to tackle "live" technical problems were his outstanding traits even in his student and postgraduate days. It will suffice to list some of his extracurricular activities, which included:

Work in 1932-1934 as a senior technician and then as an engineer in the Central Aerohydrodynamics Institute (TsAGI) (in the Flight Testing Section he proposed a method for the experimental determination of aircraft centring and moments of inertia; in the Special Structures Department he was involved in the design of autogyro rotor blades, and wrote the first research paper on a refined procedure for airscrew blade design); he always looked back on his work at the TsAGI - the principal centre for aviation science in the country - with warmth and obvious pride.

The design of a simulator prototype for astronauts that was built in 1934 at the Moscow attraction "Paraboloid of Wonders".

The management, from 1935, of the Materials Testing Laboratory at the MGU, where, under his leadership, systematic experimental research began into the viscoplastic flows and dynamical properties of materials on specially developed testing units (including the legendary high-velocity pneumatic driver - the first in a series of linear mechanical accelerators he developed).

The start of work in the just founded Institute of Mechanics of the USSR Academy of Sciences (in 1935 he became a senior research fellow, and in 1936 head of the Strength Department).

In fact, by 1938, he had laid the foundations of viscoplastic flow theory - he had formulated the variational principle of minimum power of internal forces and established its equivalence to differential equations of viscoplastic flows; he had formulated and developed methods for solving initial-boundary-value problem; the concept of stability of viscoplastic flow had been introduced and problems relating to the stability had been solved (in relation to boundary layer pertuobations); systematic investigations had been conducted to determine the viscoplastic properties of different materials. On the basis of the results of these investigations, in 1937 he defended his Candidate's Dissertation, and at the end of 1938 his Doctoral Dissertation.

In the pre-war years, as a highly qualified specialist in the field of complex dynamical processes, he began to advise scientific research establishments attached to the People's Commissariat of Ammunition. At the very start of World War II he was engaged on the most important problem facing the State Defence Committee (GKO) of the USSR - increasing artillery shell production, chiefly by making the shell manufacturing technology as simple as possible while guaranteeing reliable firing safety. He is known to have made an invaluable contribution to solving this problem - he was the first to provide a correct description of the process of simultaneous deformations of the gun barrel and of the shell moving within it, and, by an expert analysis of firing, he explained the admissibility of plastic strains of the shell (before this, the design and the strength analysis of shells were carried out solelyby methods of elasticity theory). This outstanding work resulted in fundamentally new standards for the design and for deformability and strength analysis of shells, and in the considerable simplification of shell production technology (in particular,complex heat treatment of shells after stamping was no longer necessary, and less scarce metal could be used). This led to a sharp increase in shell production and to the gradual eradication of acute shell shortage at the front. Recalling this period of his life in the autobiographical paper ‘Dynamics’ (see his Collected papers, Vol. 1), Il’yushin wrote:

Literally within two months, the building blocks of the theory of small elastoplastic deformations (TSEPD) had been put in place, and it had been demonstrated that all versions of the constitutive relations of plasticity theory under simple loadings (the concept of SLs had been introduced) were consistent, and that the simplest deformation theory was the only physically reliable theory for SLs.

This excerpt not only contains the argument concerning the choice of model - TSEPD - for shell design but also mentions two concepts he introduced that affected the development of plasticity theory as a whole.

Firstly, he proposed the classical concept, which still stands, of simple loading. Emphasizing the dependence of the mechanical behaviour of a material on the type (form) of loading process, i.e, on the history of thermomechanical action on the material, he introduced a clear division of loading processes into simple and complex processes. The other concept he addressed was the physical reliability constitutive equations. His solution to the problem of the physical reliability of the TSEPD was so exhaustive that it remains exemplary to this day. Within the framework of the TSEPD, setting out the theory of plate and shell equilibrium beyond the elastic limit, he provided (and applied in specific cases) formulations and methods for solving problems of the bearing capacity and stability of plates and shells. To solve boundary-value problems of the theory of small elastoplastic deformations, he proposed an effective iteration method that he called “the method of elastic solutions”. Convergence of the method was guaranteed by the experimentally observed properties of the "Il’yushin function" which occured in the expression for the equivalent stress in terms of the equivalent strain. This method not only enabled serious elastoplastic problems to be solved, even at a time when computers were not existing but also influenced the development of numerical methods for solving physically non-linear boundary-value problems in the mechanics of solids.

Work on developing and applying the TSEPD resulted in his monograph Plasticity. Part 1. Elastoplastic Deformations (1948), which for many years formed the basis of analyses of strength, deformability and stability beyond the elastic limit in different sectors of engineering and was a rich source of new ideas, approaches and methods for specialists in the field of plasticity theory. For his work on plasticity, he was awarded the Stalin Prize (first order) in 1948.

For his scientific and applied research in the war years, he was the recipient of high government awards. In 1943 he was made a Corresponding Member of the USSR Academy of Sciences, and in 1947 a Full Member of the Academy of Artillery Sciences of the Ministry of the Armed Forces (MVS) of the USSR (now the Russian Academy of Rocket and Artillery Sciences (RARAN)).

From 1947 onwards, the subject matter of his research changed - he was appointed deputy head of science at NII-88 (now the Central Scientific Research Institute of the Engineering Industry (TsNIIMASh), Korolev, Moscow Region). Along with tremendous and vital scientific and organizational work (the setting up of departments engaged in experimental and theoretical research in all areas of mechanics pertinent to the rocket centre and the development of a unique specialized experimental base), Il’yushin - an aircraft designer by university education - turned to questions of supersonic aerodynamics. In 1947 he proposed a brilliant solution to the problem of the aerodynamic design of aircraft at high Mach numbers (there was no equipment in the country for the experimental determination of the aerodynamic coefficients of forces and moments of rockets at M>3) - he formulated the law of plane sections in the aerodynamics of high supersonic velocities. This law reduced the three-dimensional problem of the flow about a thin elongated body to a two-dimensional problem, gave a method for the experimental determination of the aerodynamic coefficients for up to M=6 on supersonic tubes with M<3 and led to the "piston theory"-based panel flutter theory. The law of plane sections was used subsequently in the development of the theory of penetration of rigid bodies into various media (the theory of armour piercing and the development of the corresponding technology); the theory of panel flutter was developed on the basis of new formulations refining "piston theory".

In 1950, he became rector of Leningrad University; much effort was spent on protecting and supporting the Leningrad School of Genetics at a difficult time for this science. His research interests again included problems of plastic flow - the problem of modelling high-temperature and high-velocity processes. In the spring of 1952 he was made deputy scientific head and chief designer of the Design Bureau of the Ministry of Medium Machine Construction (Arzamas-16, Sarov), and he took an active part in implementing the nuclear project.

From 1953 to 1960, he was director of the Institute of Mechanics of the USSR Academy of Sciences. In this period, a computer centre and new laboratories were set up, new testing units were commissioned and the Inzhenernyi Sbornik - the precursor of the journal Izvestiya AN SSSR. Mekhanika Tverdogo Tela - began to be published. He initiated the creation and was permanent manager of the Scientific Council of the USSR Academy of Sciences for Strength and Plasticity Problems. His scientific research in these years involved the study of the dynamic properties of metals, the development of methods for modelling dynamic processes, the development and special purpose use of linear mechanical accelerators (accelerators were built with a linear field of constant acceleration of 100 g and 1000 g). In particular, on the high-velocity pneumatic driver and the LMU-100 linear accelerator, models of different structures were tested, and effects of underground explosions and the explosive transfer of rock were investigated. Simultaneously with these investigations, he took an active part in the forming of the strength cycle in the MGU Institute of Mechanics under construction, and in the setting up at the Institute of Mechanics of a modern testing unit room for testing the large components of structures, and a dynamic laboratory with a hydraulic reservoir and vacuum chambers for explosive work.

The work outlined above proceeded in parallel with the development of a new direction in the theory of plastic metal working - the theory of flow of a plastic matter over surfaces, and with the preparation of his most outstanding publication on plasticity theory - the paper "On the relation between stresses and small strains in continuum mechanics" (1954) in the journal Prikladnaya Matematika i Mekhanika. (It should be mentioned out that for almost half a century he was a member of the editorial board of the journal, and that all his important papers on plasticity theory were published in this journal).

The paper mentioned above was the direct development of ideas expressed in his book Plasticity (1948) in the form of clear definitions and postulates, explicit allocation of the role of the loading process, and the specific principle of the classification of loading processes. In fact, whereas in the TSEPD the term “complex loading” was introduced only qualitatively, as a designation of processes differing appreciably from simple processes (i.e., processes not described by the TSEPD), in this new paper a measure of process complexity was proposed. It must be stressed that the Basic postulates of the theory of elastoplastic processes, unlike other directions of the development of plasticity theory, allow of a direct experimental check.

The idea of the classification of elastoplastic processes according to their degree of complexity made it possible to distinguish production processes (for example, metal forming process) according to the types of characteristic deformation trajectory in them, and laid down the principles of the theory of experiments under complex loading (investigation of the mechanical properties and the evolution of the structure of material on certain classes of thermomechanical processes).

From 1960 onwards, his permanent principal place of work was the Department of Elasticity Theory of the MGU. At the start of the 1960 s he continued research on developing the theory of elastoplastic processes and comparing it with the flow theory, and showed the admissibility of differential non-linearity of the constitutive equations. He formulated the gradients condition in flow theory, taking deformation anisotropy into account, and proposed a plasticity postulate that was less restrictive than Drucker's postulate. His book Plasticity. The Principles of General Mathematical Theory, with its exposition of the theory of elastoplastic processes, its corollaries and a description of the idea of the original Complex Loading-Computer numerical-experimental method for solving boundary-value problems of plasticity theory under arbitrary complex loading, was published in 1963. In this method, the successive approximation algorithm provides for the combination of computer calculations with the testing of standard specimens on a complex loading unit according to special (calculated) programs. For his work on the theory of elastoplastic processes, in 1995 he was awarded the Lomonosov Prize (first order).

In 1964, he headed work on the strength of solid fuel charges (from 1964 to 1994 he was a scientific consultant of TsNIIMASh) and made a key contribution not only to the development of corresponding strength standards but also to the construction of a general theory of thermoviscoplasticity. He developed the thermodynamics of viscoelastic media, created the phenomenological theory of damage accumulation and long-term strength, devised a fairly accurate and simple quasi-linear theory of viscoelasticity, and proposed a new effective method for solving problems of the linear theory of viscoelasticity - the so-called "method of approximations", which was widely used in engineering calculations. Some of these results were reflected in the monograph Principles of the Mathematical Theory of Thermoviscoelasticity (A.A. Il’yushin and B.Ye. Pobedrya, 1970).

In the field of the dynamics of viscoelastic structures, he developed a new scientific direction based on the application of averaging methods of the corresponding systems of integro-differential equations; this immediately found use in calculations of different installations. The model of interaction of installations with the earth that he proposed was directly designed for calculations of installations for seismic stability; after extensive experimental investigations, it led to the creation of the applied theory of seismic stability of underground installations.

An important cycle of investigations he made was devoted to general problems of continuum mechanics. He extended the plasticity postulate to continuum mechanics as the postulate of the irreversibility of thermodynamic processes and formulated the main thermodynamic identity. This identity, interpreted as a functional equation for the reaction of material during a given process, can be regarded as the basic identity for the theory of constitutive equations.

In 1990's, he made a tremendous contribution to solving the problem of guaranteeing the strength of the steam generators collectors of nuclear power stations - by ascertaining the reasons for stress concentration in these structures it became possible to improve their reliability.

This brief enumeration of the outstanding scientific results he obtained indicates not only the originality and depth of his ideas but also the highest scientific level of his research, which was always aimed at solving the most important problems facing the country.

Professor Il’yushin invested a great deal of effort in and paid great attention to his teaching and the creation of original courses and textbooks. His textbooks The Resistance of Materials (coauthor V.S. Lenskii) and Continuum Mechanics (in three editions) are widely known. Indeed, the seminar of the MGU Department of Elasticity Theory, which he managed until the end of his life (Il’yushin died on 31 May 1998), was famous throughout the Soviet Union. For many years he was a member of the Higher Certification Commission of the USSR, a Member of the Presidium of the USSR National Committee on Theoretical and Applied Mechanics and a Member of the General Assembly of the International Union of Theoretical and Applied Mechanics.

His scientific work and his participation in artillery, space rocket and nuclear projects was recognized by ten orders of merit, numerous medals and honorary titles. In the words of one of his students, his highest accolade was and remains his name. And the best memory of him is the scientific school that he founded and that is continuing to develop successfully.
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