402
6 Visco-Plasticity
Table 6.13 Summary of the generic Perzyna hardening model
(1) Strain
= e + vp
(2) Energy ψ = ψ( − vp , ε h )
(3) Stress
σ = ∂ ψ ≡ σ ≡ −σ
vp
(4) Stress
σ h = ∂ εh ψ
(5) Potential π = π(˙ vp , ˙
ε h )
(6) Stress
σ vp ∈ d ˙
vp π σ
vp
(7) Stress
σ h ∈ d ˙
εh π σ
h
or
(5) Potential π ∗ =
1
2 φ(σ vp , σ h ) 2 /η
(6) Evolution ˙
vp = λ ∂ σvp φ
(7) Evolution ˙
ε h = λ ∂ σh φ with λ : = =φ(σ vp , σ h )/η