12.5 Soviet Period of Plasticity Theory Development
151
solid ball into an ideally plastic medium. The solution of A. Yu. Ishlinsky caused
critical comments of R. Hill and others [36, 68, 75]. In particular, Hill believed that
“. . . such calculations had a low and no value, since the Haar–Karman hypothesis for
metals is physically unreal and it introduces an error of unknown magnitude.” Hill
based his objections on the impossibility to define the distribution of stresses within
the Levi–Mises theory, which would satisfy the condition of full plasticity due to
the overdetermination of the system of kinematic ratios. Hill’s objection was later
eliminated by Ishlinsky by substituting [22] the Levi–Mises law with the generalized
flow law associated with the Coulomb–Tresca plasticity condition.
In these years, A. A. Ilyushin introduced the notions of director tensors, simple
and complex loading, and theoretically proved the identity of primary plasticity
theories existing at that time in the case of simple loading using the single
general theory of low elastic–plastic deformations. Searching for ways to create
the general plasticity theory in complex loading led A. A. Ilyushin to introducing
linear coordinate Euclidian 5D spaces into the theory of plasticity, introducing the
concepts of process image, isotropy postulate, and the principle of delay.
The need to check the isotropy postulate in complex trajectories of deformation
led to the creation of automated test stations at MSU, the Institute of Mechanics
of the Academy of Sciences of the USSR, and the Institute of Mechanics of the
National Academy of Sciences of Ukraine. Systematic experiments for checking
the isotropy postulate and the principle of delay were conducted by V. S. Lensky.
A huge contribution to the development of the new area in plasticity theory called
the theory of processes was made by V. S. Lensky [38, 39], V. G. Zubchaninov [81],
V. V. Moskvitin [54], and others. A significant contribution to the development of
ideal plasticity theory and limit states was made by D. D. Ivlev, S. L. Khristianovich,
A. Yu. Ishlinsky, V. V. Sokolovsky, E. I. Shemyakin, V. D. Klushnikov, etc.
In the 1990s, V. G. Zubchaninov [83, 84] developed a general theory of determinant ratios of the process theory. He guided (with the participation of A. A. Ilyushin)
the project and built an SN-EVM automated test station used to conduct important
systematic tests at complex loading of samples of structural materials.
Another area that originated in the West [6] and later actively developed [33, 34,
40, 42, 44, 46], [43, 53] in the USSR was the sliding concept in plasticity theory.
Researchers intended to build determinant ratios which are true at arbitrary loading
beyond the yield strength. The most successful results in the development of the
sliding concept were obtained by M. Ya. Leonov and his school. An undeniable
advantage of their results is the rehabilitation of the sliding concept by eliminating
the flaw found by Cicala [8] and Iosimura [20] in the Batdorf and Budiansky model.
151
solid ball into an ideally plastic medium. The solution of A. Yu. Ishlinsky caused
critical comments of R. Hill and others [36, 68, 75]. In particular, Hill believed that
“. . . such calculations had a low and no value, since the Haar–Karman hypothesis for
metals is physically unreal and it introduces an error of unknown magnitude.” Hill
based his objections on the impossibility to define the distribution of stresses within
the Levi–Mises theory, which would satisfy the condition of full plasticity due to
the overdetermination of the system of kinematic ratios. Hill’s objection was later
eliminated by Ishlinsky by substituting [22] the Levi–Mises law with the generalized
flow law associated with the Coulomb–Tresca plasticity condition.
In these years, A. A. Ilyushin introduced the notions of director tensors, simple
and complex loading, and theoretically proved the identity of primary plasticity
theories existing at that time in the case of simple loading using the single
general theory of low elastic–plastic deformations. Searching for ways to create
the general plasticity theory in complex loading led A. A. Ilyushin to introducing
linear coordinate Euclidian 5D spaces into the theory of plasticity, introducing the
concepts of process image, isotropy postulate, and the principle of delay.
The need to check the isotropy postulate in complex trajectories of deformation
led to the creation of automated test stations at MSU, the Institute of Mechanics
of the Academy of Sciences of the USSR, and the Institute of Mechanics of the
National Academy of Sciences of Ukraine. Systematic experiments for checking
the isotropy postulate and the principle of delay were conducted by V. S. Lensky.
A huge contribution to the development of the new area in plasticity theory called
the theory of processes was made by V. S. Lensky [38, 39], V. G. Zubchaninov [81],
V. V. Moskvitin [54], and others. A significant contribution to the development of
ideal plasticity theory and limit states was made by D. D. Ivlev, S. L. Khristianovich,
A. Yu. Ishlinsky, V. V. Sokolovsky, E. I. Shemyakin, V. D. Klushnikov, etc.
In the 1990s, V. G. Zubchaninov [83, 84] developed a general theory of determinant ratios of the process theory. He guided (with the participation of A. A. Ilyushin)
the project and built an SN-EVM automated test station used to conduct important
systematic tests at complex loading of samples of structural materials.
Another area that originated in the West [6] and later actively developed [33, 34,
40, 42, 44, 46], [43, 53] in the USSR was the sliding concept in plasticity theory.
Researchers intended to build determinant ratios which are true at arbitrary loading
beyond the yield strength. The most successful results in the development of the
sliding concept were obtained by M. Ya. Leonov and his school. An undeniable
advantage of their results is the rehabilitation of the sliding concept by eliminating
the flaw found by Cicala [8] and Iosimura [20] in the Batdorf and Budiansky model.