6.5 Summary of the Equations

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The following equations result:

1. Hyperelasticity equation

S = pJC

−1 + μDEV(C

p−1

). (6.132)

2. von Mises yield condition

(a) For plastic materials:

_ − _23

h1(_peq) ≤ 0. (6.133)

(b) For viscoplastic materials:

_ − _23

h1(_peq) = _23

f (˙_ peq) for _ ≥ _23

h1(_peq) (6.134)

where

_ := DEV(S +Q2). (6.135)

3. Flow rule

−J

−2/3μDEV(˙C

p−1

) = 2γ˙μN (6.136)

μ := μ + 13

J

−2/3TRQ2 (6.137)

μ := 13

μJ

−2/3TRCp−1 (6.138)

N := DEV_

DEV_ (6.139)

TR( ˙C

p−1

) = 0. (6.140)

4. Kinematic hardening law

−J

−2/3DEV( ˙Q2) =

_h

eq’

2 (_peq)

3μ

_

2γ˙μN (6.141)

TR( ˙Q2) = 0. (6.142)

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