12.3 Early Development Stages of Plasticity Theory
147
primary concepts, methods, and results, whose originality and distinction allowed
the collection editor in 1948 to assert as follows: “This theory that is often called
plasticity theory (in a narrow sense) can’t be deemed final; however, the studies
of recent years have definitely explored some principal laws that permit regarding
many results as truly valid.”
The below history of the origin and early stage of development of plasticity
theory is mostly based on the materials of that collection.
As indicated above, the subject of research of plasticity theory is currently metals
and their alloys, though it can be applied to such materials as rocks, soils, ice, etc .
The tasks of plasticity theory are rather diverse. All static and dynamic tasks
of elasticity must be set for areas of plastic deformations. The thing is that in
many structures of modern engineering, such deformations are inevitable, permitted,
or desirable. Taking into account plastic deformations and creep, the problems
of rigidity, stability, and strength must be solved, and the issues of the synthesis
of structures of minimal weight, etc. must be raised. Plasticity theory must give
methods to solve many problems of metalworking by pressure and permit raising
the issues of quality.
12.3 Early Development Stages of Plasticity Theory
Plastic properties of various materials have been known for a long time and were
studied by Coulomb (C. A. Coulomb, 1776) in the 1770s. An overview of these
studies can be found in a book by S. P. Timoschenko [74]. It is notable that in
the report of the French Academy of Science in 1773, Coulomb stated that the
destruction of a prismatic specimen in compression occurred by sliding of one
of its parts relative to the other one on a plane making an angle of 45 ◦ with
the compression direction. Coulomb also found that sliding occurred when the
tangential stress in the sliding plane reached a magnitude sufficient to overcome
shear resistance along this plane.
After Coulomb, there were almost no experiments in plastic deformation for
a long time, which was one of the reasons for the retarded birth of plasticity
theory. The insufficiency of experimental capability has been typical of plasticity
theory since its birth until now. The difference is that in the eighteenth–nineteenth
centuries, there were few experiments, then there were too many experiments, with
their results frequently not matching each other, or the same results being interpreted
differently. This situation caused multiple versions of plasticity theory to appear,
which sometimes contradicted each other.
Almost a 100 years after Coulomb’s experiments, H. Tresca carried out systematic research of the plastic yield of metals and used Coulomb’s idea to formulate a
historically first condition of yield.
We have already said (p. 146) that the development history of plasticity theory
starting with the fundamental works by Saint-Venant and M. Levy (1871) can be
147
primary concepts, methods, and results, whose originality and distinction allowed
the collection editor in 1948 to assert as follows: “This theory that is often called
plasticity theory (in a narrow sense) can’t be deemed final; however, the studies
of recent years have definitely explored some principal laws that permit regarding
many results as truly valid.”
The below history of the origin and early stage of development of plasticity
theory is mostly based on the materials of that collection.
As indicated above, the subject of research of plasticity theory is currently metals
and their alloys, though it can be applied to such materials as rocks, soils, ice, etc .
The tasks of plasticity theory are rather diverse. All static and dynamic tasks
of elasticity must be set for areas of plastic deformations. The thing is that in
many structures of modern engineering, such deformations are inevitable, permitted,
or desirable. Taking into account plastic deformations and creep, the problems
of rigidity, stability, and strength must be solved, and the issues of the synthesis
of structures of minimal weight, etc. must be raised. Plasticity theory must give
methods to solve many problems of metalworking by pressure and permit raising
the issues of quality.
12.3 Early Development Stages of Plasticity Theory
Plastic properties of various materials have been known for a long time and were
studied by Coulomb (C. A. Coulomb, 1776) in the 1770s. An overview of these
studies can be found in a book by S. P. Timoschenko [74]. It is notable that in
the report of the French Academy of Science in 1773, Coulomb stated that the
destruction of a prismatic specimen in compression occurred by sliding of one
of its parts relative to the other one on a plane making an angle of 45 ◦ with
the compression direction. Coulomb also found that sliding occurred when the
tangential stress in the sliding plane reached a magnitude sufficient to overcome
shear resistance along this plane.
After Coulomb, there were almost no experiments in plastic deformation for
a long time, which was one of the reasons for the retarded birth of plasticity
theory. The insufficiency of experimental capability has been typical of plasticity
theory since its birth until now. The difference is that in the eighteenth–nineteenth
centuries, there were few experiments, then there were too many experiments, with
their results frequently not matching each other, or the same results being interpreted
differently. This situation caused multiple versions of plasticity theory to appear,
which sometimes contradicted each other.
Almost a 100 years after Coulomb’s experiments, H. Tresca carried out systematic research of the plastic yield of metals and used Coulomb’s idea to formulate a
historically first condition of yield.
We have already said (p. 146) that the development history of plasticity theory
starting with the fundamental works by Saint-Venant and M. Levy (1871) can be