150
12 Origin and Development of Plasticity Theory
σ 1 − σ 2
2
= f
σ 1 + σ 2
2
.
Assuming linear approximation for f in the first approximation, the author believes
that
σ 2 − σ 1
2
= K − a
σ 1 + σ 2
2
.
The further intensive development of plasticity theory took place in this period
in the papers by Hencky [16], (for Russian translation, see [14]), Prandtl [62, 63],
Reuss [66, 67], Hill [30], Nadai [56], Odquist [60], etc.
12.5 Soviet Period of Plasticity Theory Development
After the October Revolution of 1917, the development of mechanics in Soviet
Russia and then in the Soviet Union was defined for many decades by healthy
traditions of domestic science in general and by those scientists who inherited
these traditions. They made an invaluable contribution to the upbringing and
establishment of the first Soviet generations of scientists [81].
Starting from 1935, the USSR becomes the center of research activity in
plasticity theory and retains leadership for more than 10 years. In chronological
order, we will indicate the papers by S. G. Mikhlin [48] and S. L. Sobolev [73].
Fundamental papers in plasticity theory in the USSR appeared in 1936. They
are associated with the names of A. A. Ilyushin and S. A. Khristianovich [32, 33].
After the war, more than two hundred papers were published in the periodicals of
the Academy of Sciences. Their overview is given in the article by A. A. Vakulenko
and L. M. Kachanov [26, p. 79–118], and in the seventh chapter of the book by
J. Goodier and F. Hodge [15]. These papers were accompanied by developments
of efficient experimental methods for researching the plasticity of materials in a
complex stressed state basically in the case of simple loading.
The development of plasticity theory in the USSR was not isolated. Many studies
were associated with developments of foreign scientists, were noted, admitted, and
rarely criticized by Western colleagues.
At the brink of the 1950s, Prager developed the concept of a limit loading
surface of strain-hardening materials and established a link of increments of plastic
deformations with this surface in general, and also created the general Melan–Prager
theory. This area was further developed by A. Yu. Ishlinsky, V. V. Novozhilov, Yu. I.
Kadashevich [58], and other Soviet scientists.
In 1944, A. Yu. Ishlinsky studied the axisymmetric task of plasticity theory
[21] suggesting the fulfillment of the full plasticity condition of Haar–Karnan by
proving the static definability and hyperbolicity of principal equations. Using the
numerical method, the authors of the same paper solved the problem of pressing a
12 Origin and Development of Plasticity Theory
σ 1 − σ 2
2
= f
σ 1 + σ 2
2
.
Assuming linear approximation for f in the first approximation, the author believes
that
σ 2 − σ 1
2
= K − a
σ 1 + σ 2
2
.
The further intensive development of plasticity theory took place in this period
in the papers by Hencky [16], (for Russian translation, see [14]), Prandtl [62, 63],
Reuss [66, 67], Hill [30], Nadai [56], Odquist [60], etc.
12.5 Soviet Period of Plasticity Theory Development
After the October Revolution of 1917, the development of mechanics in Soviet
Russia and then in the Soviet Union was defined for many decades by healthy
traditions of domestic science in general and by those scientists who inherited
these traditions. They made an invaluable contribution to the upbringing and
establishment of the first Soviet generations of scientists [81].
Starting from 1935, the USSR becomes the center of research activity in
plasticity theory and retains leadership for more than 10 years. In chronological
order, we will indicate the papers by S. G. Mikhlin [48] and S. L. Sobolev [73].
Fundamental papers in plasticity theory in the USSR appeared in 1936. They
are associated with the names of A. A. Ilyushin and S. A. Khristianovich [32, 33].
After the war, more than two hundred papers were published in the periodicals of
the Academy of Sciences. Their overview is given in the article by A. A. Vakulenko
and L. M. Kachanov [26, p. 79–118], and in the seventh chapter of the book by
J. Goodier and F. Hodge [15]. These papers were accompanied by developments
of efficient experimental methods for researching the plasticity of materials in a
complex stressed state basically in the case of simple loading.
The development of plasticity theory in the USSR was not isolated. Many studies
were associated with developments of foreign scientists, were noted, admitted, and
rarely criticized by Western colleagues.
At the brink of the 1950s, Prager developed the concept of a limit loading
surface of strain-hardening materials and established a link of increments of plastic
deformations with this surface in general, and also created the general Melan–Prager
theory. This area was further developed by A. Yu. Ishlinsky, V. V. Novozhilov, Yu. I.
Kadashevich [58], and other Soviet scientists.
In 1944, A. Yu. Ishlinsky studied the axisymmetric task of plasticity theory
[21] suggesting the fulfillment of the full plasticity condition of Haar–Karnan by
proving the static definability and hyperbolicity of principal equations. Using the
numerical method, the authors of the same paper solved the problem of pressing a