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15 Plasticity Theory of Henky–Nadai–Ilyushin
Fig. 15.6 To the conclusion
of strain potential
15.6.2 Potential of Strains
Let us find the hardening curve OAB Fig. 15.6. The area of the figure OABC is
represented as
S OABC = W
−
1
2
σ 0 ,
(15.36)
where W is some function. The same area can be written otherwise:
S OABC = σ i ε i −
ε i
0
σ i dε i =
σ i
0
ε i dσ i .
(15.37)
By equating the right parts of formulas (15.36) and (15.37), we obtain
W
=
σ i
0
ε i dσ i +
1
2
σ 0 .
(15.38)
By comparing formulas (15.38) and (15.29), we note that the function W is
obtained from W , if we swap stresses σ i and strains ε i in the latter formula.
However, W is a potential for stresses. Hence it follows that the function W is a
potential for strains, e.g.
ε i =
∂W
∂σ i
, , =
∂W
∂σ 0
,
ε x =
∂W
∂σ x
, . . . , γ zx =
∂W
∂τ zx
.
(15.39)