6.1 Bingham Model
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Table 6.2 Algorithmic update for the specific Bingham model. (Note the different input and output
arguments for either strain or stress control!)
Input
n (or ¯
σ n ) n−1
vp
σ k−1
vp
Trial Strain
vp = n−1
vp
Trial Stress
σ
vp = σ k−1
vp
σ = σ
vp − E [
vp − n ]
Trial Yield
φ = |σ | − σ y
Loading Check IF φ < 0 THEN
λ = 0
ELSE
λ =
φ
E + η//t n
ENDIF
Update Strain
n
vp =
vp + λ
σ
|σ |
Constraint Check IF | n − n
vp | ≥ tol THEN
Update Multiplier
σ k
vp = σ
vp + E [ n − n
vp ]
if stress control n = n
vp + [ ¯
σ n − σ k
vp ]/E
k = k + 1
goto Trial Stress
ELSE
Update Stress
σ n = σ
vp
ENDIF
Output
σ n (or n ) n
vp σ k−1
vp