Preface
As defined by M. Ya. Leonov, “. . . the mechanics of a real solid body is not only
engineering, technology, and mathematics, but also a concentrate of rationality, a
powerful engine of social progress, and an example of classical natural science.”
A fundamental and the most complete section of the mechanics of deformations
is classical elasticity theory occupying about a quarter of the book. The subject
matter is described with an increasing complexity of topics. The existing boundaries
between the educational and scientific literature are erased. The book includes
the authors’ solutions to a number of new problems important for engineering
applications.
A quarter of the book is dedicated to principal variants of plasticity theory. It
is preceded by a short overview of plasticity theory from the first experiments of
Coulomb to endochronic variants of the theory and unconventional (synergetic)
models of our days. Primary attention in this part is paid to the theory of small
elastic–plastic deformations by Hencky–Nadai–Ilyushin, since this theory allows
solving the most important problems of engineering. It also discusses the flaws in
strain theory and the limits of its applicability.
The second part of the book is represented by the authors’ studies in the
development of the sliding conception in plasticity theory as set by M. Ya. Leonov.
The Batdorf–Budiansky sliding mechanism is taken as the basis. Solutions to some
problems eliminate primary objections against the Batdorf–Budiansky model and
rehabilitate the sliding concept in plasticity theory.
The conclusion is made that due to the complexity of this matter, it must
be admitted that creating a unified, universal, and rather complete theory of
plasticity has not been successful by using either classical methods of mechanics of
continuous media or semi-physical synergetic methods. Therefore, one must expect
xi
As defined by M. Ya. Leonov, “. . . the mechanics of a real solid body is not only
engineering, technology, and mathematics, but also a concentrate of rationality, a
powerful engine of social progress, and an example of classical natural science.”
A fundamental and the most complete section of the mechanics of deformations
is classical elasticity theory occupying about a quarter of the book. The subject
matter is described with an increasing complexity of topics. The existing boundaries
between the educational and scientific literature are erased. The book includes
the authors’ solutions to a number of new problems important for engineering
applications.
A quarter of the book is dedicated to principal variants of plasticity theory. It
is preceded by a short overview of plasticity theory from the first experiments of
Coulomb to endochronic variants of the theory and unconventional (synergetic)
models of our days. Primary attention in this part is paid to the theory of small
elastic–plastic deformations by Hencky–Nadai–Ilyushin, since this theory allows
solving the most important problems of engineering. It also discusses the flaws in
strain theory and the limits of its applicability.
The second part of the book is represented by the authors’ studies in the
development of the sliding conception in plasticity theory as set by M. Ya. Leonov.
The Batdorf–Budiansky sliding mechanism is taken as the basis. Solutions to some
problems eliminate primary objections against the Batdorf–Budiansky model and
rehabilitate the sliding concept in plasticity theory.
The conclusion is made that due to the complexity of this matter, it must
be admitted that creating a unified, universal, and rather complete theory of
plasticity has not been successful by using either classical methods of mechanics of
continuous media or semi-physical synergetic methods. Therefore, one must expect
xi