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12 Origin and Development of Plasticity Theory
construction materials and soils. The authors see the attractiveness of endochronic
theory in the fact that in building determinant ratios, the theory abandons one of the
basic principles of classical plasticity theory—the concept of flow surface. A link
between stresses and strains in this theory is provided based on implementing new
functions of a heritage type, which allows describing loading and unloading using
a unified equation system. A conclusion is made that using the theory abstaining
from the concept of loading (flow) surface is efficient in describing the deformation
of geo-materials and construction materials, since building such a surface with any
tolerance is rather complicated for these materials.
12.7 Abstract
To end this short overview, we shall conclude that currently, there are several various
approaches to formulating the determinant laws of plasticity theory resulting in
the division of plasticity theory into flow type theories, deformation type theories,
sliding theories, statistical plasticity theories, endochronic theories of plasticity,
etc. Approaches are also suggested to describe the processes of low non-elastic
deformations of initially isotropic materials (synergetics).
The existing situation was differently assessed by representatives of various
scientific schools: from the most optimistic: “Principal variants of the theory of
plastic deformations differ in the completeness and perfection of mathematical
formulations” A. A. Ilyshin, [17, p. 5], to the pessimistic one: “Both sliding theory
and consideration of the simplest model lead to pessimistic conclusions as to the
possible progress of plasticity theory” Yu. N. Rabotnov, [64, p. 104].
In any way, it should be admitted that a desire to describe the entire scope
of non-elastic properties of a real body by a unified system of equations has not
resulted in sufficiently definitive results. One should pay serious attention to noncompetent (but ambitious) assertions about an allegedly created “. . . expansion of
the unified theory of strength in plasticity theory leading to the unified processing of
metal plasticity and plasticity of geo-materials in general” [80]. For many decades,
the development of mechanics of non-elastic deformations will be represented
by various simplified models suitable for describing principal phenomena in the
deformation of a specific class of materials.
References
1. N. Adigamov, Protsessy neobratimogo deformirovaniya i rezervy prochnosti materialov
(Processes of irreversible deformation and reserves of strength of materials). Dr. philos.
sci. diss. KRSU Publ., Bishkek (2004), 210 p. PhD thesis, Bishkek, KRSU Publ.
fizmathim/com/protsessy-neobratimogo-deformirovanija-i-rezervy-prochnosti-materialov.
Accessed 20 Oct 2014
12 Origin and Development of Plasticity Theory
construction materials and soils. The authors see the attractiveness of endochronic
theory in the fact that in building determinant ratios, the theory abandons one of the
basic principles of classical plasticity theory—the concept of flow surface. A link
between stresses and strains in this theory is provided based on implementing new
functions of a heritage type, which allows describing loading and unloading using
a unified equation system. A conclusion is made that using the theory abstaining
from the concept of loading (flow) surface is efficient in describing the deformation
of geo-materials and construction materials, since building such a surface with any
tolerance is rather complicated for these materials.
12.7 Abstract
To end this short overview, we shall conclude that currently, there are several various
approaches to formulating the determinant laws of plasticity theory resulting in
the division of plasticity theory into flow type theories, deformation type theories,
sliding theories, statistical plasticity theories, endochronic theories of plasticity,
etc. Approaches are also suggested to describe the processes of low non-elastic
deformations of initially isotropic materials (synergetics).
The existing situation was differently assessed by representatives of various
scientific schools: from the most optimistic: “Principal variants of the theory of
plastic deformations differ in the completeness and perfection of mathematical
formulations” A. A. Ilyshin, [17, p. 5], to the pessimistic one: “Both sliding theory
and consideration of the simplest model lead to pessimistic conclusions as to the
possible progress of plasticity theory” Yu. N. Rabotnov, [64, p. 104].
In any way, it should be admitted that a desire to describe the entire scope
of non-elastic properties of a real body by a unified system of equations has not
resulted in sufficiently definitive results. One should pay serious attention to noncompetent (but ambitious) assertions about an allegedly created “. . . expansion of
the unified theory of strength in plasticity theory leading to the unified processing of
metal plasticity and plasticity of geo-materials in general” [80]. For many decades,
the development of mechanics of non-elastic deformations will be represented
by various simplified models suitable for describing principal phenomena in the
deformation of a specific class of materials.
References
1. N. Adigamov, Protsessy neobratimogo deformirovaniya i rezervy prochnosti materialov
(Processes of irreversible deformation and reserves of strength of materials). Dr. philos.
sci. diss. KRSU Publ., Bishkek (2004), 210 p. PhD thesis, Bishkek, KRSU Publ.
fizmathim/com/protsessy-neobratimogo-deformirovanija-i-rezervy-prochnosti-materialov.
Accessed 20 Oct 2014