Chapter 18
Theories of Plastic Yield
18.1 General Ratios
We have already said that plasticity theories of the strain type take the non-linear
elasticity theory as the reference point and represent its generalization in the case of
a non-elastic material. The link between stresses and strains is usually represented
by finite ratios. Unlike it, the theories of plastic yield set links between infinitely
low gains of strains and stresses, the stresses themselves, and some parameters of
plastic condition.
The following initial provisions are taken in most variants of yield theory.
1. The body is deemed initially isotropic.
2. The volumetric strain is deemed elastic (14.30)
ε 0 =
σ 0
3K
,
or
dd =
dσ 0
K
,
where
= ε ii ; ε 0 =
1
3
σ 0 =
1
3
σ ii ; K =
E
3(1 − 2ν)
.
3. The gains of the full strain components are presented by the sums of gains of the
respective components of elastic and plastic strain
dε ij = dε
y
ij + dε
p
ij .
(18.1)
© 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_18
267