12.6 Russian Mechanics in the Post-Soviet Period
157
of delay. The development of the theory of processes is described in the studies by
A.A. Ilyushin, V.G. Zubchaninov [82–84], etc.
According to the isotropy postulate, for an isotropic material, the module of stress
vector and its orientation angles in the Frenet frame are unambiguously defined by
a change in process parameters from its start to the current moment, e.g. they are
some functionalities. A complete definition of plasticity functionalities according
to experimental data is extremely complicated, and so far building methods are
proposed only to some of them. Another property of plasticity of an isotropic
material reflects the principle of delay: the values of the orientation angles of the
stress vector in the Frenet frame depend on the curvature change not along the entire
preceding trajectory of strain, but along its last part, whose length characteristic of
this material is called the trace of delay. This property made it possible to distinguish
several types of processes (simple strain, low curvature, etc. ) for which the ratios
between stresses and elastic-strain deformations are established definitively and do
not contain functionalities.
Along with strain theory, works are gradually revived, which develop other trends
in plasticity theory. Let us note the thesis by I. S. Nikitin that uses a classical model
of Batdorf and Budiansky to study deformations of layered and block media. The
classical model of sliding is supplemented by an elastic–viscous–plastic model of
the process.
Ideas of the theory of elastic–plastic processes served as a platform for a new
trend in mechanics of non-elastic deformations that are called endochronic theories.
In some theories, the dependencies between stress and strain look as functionalities.
The founder of endochronic theory is K. Valanis who published his first works [76–
78] dedicated to endochronic theory in the 1980s in collections of the American
Society of Mechanical Engineers (ASME). Apart from the new name rooted in the
global scientific literature, Valanis’s theory contains no significant development of
the theory of processes of A. A. Ilyushin, but just one of particular examples of
models within this theory. The concept of internal time introduced by the author
represents an equivalent of the internal geometry parameter of the strain trajectory,
and setting the heritage-type functionality results from Ilyushin’s principle of delay.
Among modern non-Russian publications on the endochronic theory of plasticity,
we shall indicate the monographs by T. Nakai [57], H.-Y. Fang, J.L. Daniels [12] and
the article by R.O. Davis and A.P.S. Selvadurai published at Cambridge University
[9]. All three papers are dedicated to the use of endochronic theory in geomechanics.
In Russia, the development of endochronic theory was instigated at NorthWestern universities (Saint Petersburg, Perm) and then in the center (Moscow). The
studies by Yu. I. Kadashevich and S. P. Pomytkin [27–29] formulate the endochronic
theory of a tensor-parametric type for large deformations. The variation of the
Kadashevich–Pomytkin theory takes into account the effects of time phenomena.
This distinguishes the variation from classical phenomenologic theories where
modeling of non-elastic deformations was traditionally done under flow theory.
The study of the practicability of the endochronic theory of plasticity is vastly
described in the Internet publication by B. E. Melnikov and his colleagues [47]
that discusses the possibility of using this theory for studying the deformation of
157
of delay. The development of the theory of processes is described in the studies by
A.A. Ilyushin, V.G. Zubchaninov [82–84], etc.
According to the isotropy postulate, for an isotropic material, the module of stress
vector and its orientation angles in the Frenet frame are unambiguously defined by
a change in process parameters from its start to the current moment, e.g. they are
some functionalities. A complete definition of plasticity functionalities according
to experimental data is extremely complicated, and so far building methods are
proposed only to some of them. Another property of plasticity of an isotropic
material reflects the principle of delay: the values of the orientation angles of the
stress vector in the Frenet frame depend on the curvature change not along the entire
preceding trajectory of strain, but along its last part, whose length characteristic of
this material is called the trace of delay. This property made it possible to distinguish
several types of processes (simple strain, low curvature, etc. ) for which the ratios
between stresses and elastic-strain deformations are established definitively and do
not contain functionalities.
Along with strain theory, works are gradually revived, which develop other trends
in plasticity theory. Let us note the thesis by I. S. Nikitin that uses a classical model
of Batdorf and Budiansky to study deformations of layered and block media. The
classical model of sliding is supplemented by an elastic–viscous–plastic model of
the process.
Ideas of the theory of elastic–plastic processes served as a platform for a new
trend in mechanics of non-elastic deformations that are called endochronic theories.
In some theories, the dependencies between stress and strain look as functionalities.
The founder of endochronic theory is K. Valanis who published his first works [76–
78] dedicated to endochronic theory in the 1980s in collections of the American
Society of Mechanical Engineers (ASME). Apart from the new name rooted in the
global scientific literature, Valanis’s theory contains no significant development of
the theory of processes of A. A. Ilyushin, but just one of particular examples of
models within this theory. The concept of internal time introduced by the author
represents an equivalent of the internal geometry parameter of the strain trajectory,
and setting the heritage-type functionality results from Ilyushin’s principle of delay.
Among modern non-Russian publications on the endochronic theory of plasticity,
we shall indicate the monographs by T. Nakai [57], H.-Y. Fang, J.L. Daniels [12] and
the article by R.O. Davis and A.P.S. Selvadurai published at Cambridge University
[9]. All three papers are dedicated to the use of endochronic theory in geomechanics.
In Russia, the development of endochronic theory was instigated at NorthWestern universities (Saint Petersburg, Perm) and then in the center (Moscow). The
studies by Yu. I. Kadashevich and S. P. Pomytkin [27–29] formulate the endochronic
theory of a tensor-parametric type for large deformations. The variation of the
Kadashevich–Pomytkin theory takes into account the effects of time phenomena.
This distinguishes the variation from classical phenomenologic theories where
modeling of non-elastic deformations was traditionally done under flow theory.
The study of the practicability of the endochronic theory of plasticity is vastly
described in the Internet publication by B. E. Melnikov and his colleagues [47]
that discusses the possibility of using this theory for studying the deformation of