12.6 Russian Mechanics in the Post-Soviet Period
155
12.6.2 Plasticity Theory in Russia in the Post-Soviet Period
The first half of the period after the USSR collapse was occupied by articles, monographs, study books, and training aids in the theory of plasticity that summarized the
results of authors’ work for many years of the described developments and results
achieved in the Soviet times. This situation was expected and foreseeable since
irrespective of political events, the 1970s saw a stagnation in the development of
plasticity theory [41, p. 3]. As M. Ya. Leonov believes, the reason for the stagnation
was an extreme complexity of the problem of creating a general mathematical
theory of plasticity and traditional disregard of taking into account the physical
mechanisms of the non-elastic deformation process. In these conditions, a danger
was predicted that the mechanics of a deformable solid body would lose the nature
of a classical natural science and will become [41] “. . . rather abstract, on the one
hand (elasticity theory), and strictly concrete on the other hand (particular problems
of plasticity theory and destruction).”
These concerns were doomed not to become reality partially because the classical
mechanics of deformations was born along with a new science—mesomechanics
(for example, [45, 61, 72] )—that studies the phenomenon of non-elastic deformation balancing between continuum mechanics and microcosm physics, more
inclined, however, to solid body physics. Without diminishing the usefulness
of mesomechanics methods, we should admit that in terms of usefulness for
engineering, the most perspective trend in developing non-elasticity theory is an
approach based on the continuum theory of dislocations [10, 51].
Here we will give only some most prominent Russian publications of this halfperiod.
First of all, we must note a two-volume edition of collections by A.A. Ilyushin
[18, 19] that will allow newcomer researchers to get familiar with the original works
of the scientist from a single source for over 30 years of his career.
A monument of the ideal plasticity theory was the publication of a two-volume
book by D. D. Ivlev [23, 24]. Volume 1 includes the author’s articles dedicated
to building and studying general ratios of the ideal plasticity theory based on a
statically definable system of equations of a hyperbolic type. The general theory is
described for compressible and anisotropic media, solutions are given for a number
of applied problems (pressing-in of indenters, implementation of rigid bodies, etc.).
Along with studies of problems of an ideal elastic–plastic body, the second volume
also studies models of a hardening plastic body and other complex media.
In terms of developing the theory, let us note the works by D. D. Ivlev together
with A. Yu. Ishlinskiy [25], and works with M. A. Artemov [4]. In all the above
works, the theory of ideal plasticity is developed. The publications by A. V. Kuptsov
[37] and N. D. Vereyko [79] are dedicated to the same problem. Unlike these
works, a 3D anisotropic state is considered in the article by Yu. N. Radayev and
S. Murakami [55].
Among experimental studies, the monograph by B. D. Annin and V. M. Zhigalkin
[3] published in 1999 represents special interest. The book presents experimental
155
12.6.2 Plasticity Theory in Russia in the Post-Soviet Period
The first half of the period after the USSR collapse was occupied by articles, monographs, study books, and training aids in the theory of plasticity that summarized the
results of authors’ work for many years of the described developments and results
achieved in the Soviet times. This situation was expected and foreseeable since
irrespective of political events, the 1970s saw a stagnation in the development of
plasticity theory [41, p. 3]. As M. Ya. Leonov believes, the reason for the stagnation
was an extreme complexity of the problem of creating a general mathematical
theory of plasticity and traditional disregard of taking into account the physical
mechanisms of the non-elastic deformation process. In these conditions, a danger
was predicted that the mechanics of a deformable solid body would lose the nature
of a classical natural science and will become [41] “. . . rather abstract, on the one
hand (elasticity theory), and strictly concrete on the other hand (particular problems
of plasticity theory and destruction).”
These concerns were doomed not to become reality partially because the classical
mechanics of deformations was born along with a new science—mesomechanics
(for example, [45, 61, 72] )—that studies the phenomenon of non-elastic deformation balancing between continuum mechanics and microcosm physics, more
inclined, however, to solid body physics. Without diminishing the usefulness
of mesomechanics methods, we should admit that in terms of usefulness for
engineering, the most perspective trend in developing non-elasticity theory is an
approach based on the continuum theory of dislocations [10, 51].
Here we will give only some most prominent Russian publications of this halfperiod.
First of all, we must note a two-volume edition of collections by A.A. Ilyushin
[18, 19] that will allow newcomer researchers to get familiar with the original works
of the scientist from a single source for over 30 years of his career.
A monument of the ideal plasticity theory was the publication of a two-volume
book by D. D. Ivlev [23, 24]. Volume 1 includes the author’s articles dedicated
to building and studying general ratios of the ideal plasticity theory based on a
statically definable system of equations of a hyperbolic type. The general theory is
described for compressible and anisotropic media, solutions are given for a number
of applied problems (pressing-in of indenters, implementation of rigid bodies, etc.).
Along with studies of problems of an ideal elastic–plastic body, the second volume
also studies models of a hardening plastic body and other complex media.
In terms of developing the theory, let us note the works by D. D. Ivlev together
with A. Yu. Ishlinskiy [25], and works with M. A. Artemov [4]. In all the above
works, the theory of ideal plasticity is developed. The publications by A. V. Kuptsov
[37] and N. D. Vereyko [79] are dedicated to the same problem. Unlike these
works, a 3D anisotropic state is considered in the article by Yu. N. Radayev and
S. Murakami [55].
Among experimental studies, the monograph by B. D. Annin and V. M. Zhigalkin
[3] published in 1999 represents special interest. The book presents experimental