4.5 Generalized-Maxwell Model
191
d m = π m (˙ v m ) + π
∗
m (σ v m ) ≥ 0.
(4.241)
The generic Generalized-Maxwell model is summarized in Table 4.15.
Table 4.15 Summary of the generic Generalized-Maxwell model
(1) Strain
= em + vm
(2) Energy ψ m = ψ m ( − vm )
ψ =
M
m=1 ψ m
(3) Stress
σ m = ∂ ψ m ≡ σ
m
≡ −σ
vm
σ =
M
m=1 σ m
(4) Potential π m = π m (˙ vm )
π =
M
m=1 π m
(5) Stress
σ vm = ∂ ˙
v m π m ≡ σ
vm
σ v =
M
m=1 σ vm
or
(4) Potential π ∗
m = π ∗
m (σ vm )
π ∗ =
M
m=1 π ∗
m
(5) Evolution ˙
vm = ∂ σv m π ∗
m