Chapter 14
On the Plasticity Conditions of an
Isotropic Body
14.1 General Considerations
Conditions that must be satisfied by stresses corresponding to the appearance of
plastic strains are usually called plasticity conditions.
In the case of uniaxial elongation–compression, the plasticity condition looks as
follows:
|σ | = σ s ,
(14.1)
where σ s is the plasticity limit for elongation–compression.
In the case of pure shift, the plasticity condition is as follows:
τ max = τ s ,
(14.2)
where τ s is the shear yield stress (torsion of a thin-wall tube).
Setting plasticity conditions for a complex stressed state is still a complicated
task. It is solved by various hypotheses, assumptions, and idealizations. Before
describing plasticity conditions, let us note as follows.
14.2 General Notes
Physical representations result in a number of requirements that the plasticity
condition must satisfy. Let us consider these requirements.
The plasticity conditions of an initially isotropic body must not depend on
selecting the coordinate system. Consequently, it can be represented in a general
form by the following equation:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_14
181
On the Plasticity Conditions of an
Isotropic Body
14.1 General Considerations
Conditions that must be satisfied by stresses corresponding to the appearance of
plastic strains are usually called plasticity conditions.
In the case of uniaxial elongation–compression, the plasticity condition looks as
follows:
|σ | = σ s ,
(14.1)
where σ s is the plasticity limit for elongation–compression.
In the case of pure shift, the plasticity condition is as follows:
τ max = τ s ,
(14.2)
where τ s is the shear yield stress (torsion of a thin-wall tube).
Setting plasticity conditions for a complex stressed state is still a complicated
task. It is solved by various hypotheses, assumptions, and idealizations. Before
describing plasticity conditions, let us note as follows.
14.2 General Notes
Physical representations result in a number of requirements that the plasticity
condition must satisfy. Let us consider these requirements.
The plasticity conditions of an initially isotropic body must not depend on
selecting the coordinate system. Consequently, it can be represented in a general
form by the following equation:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_14
181