80
4 Visco-Elasticity
−1
−0.5
0
0.5
1
−1
0.5
0
0.5
1
˙
π( ˙)
1
2
η ˙
2
−1
−0.5
0
0.5
1
−1
−0.5
0
0.5
1
˙
σ( ˙)
η ˙
−1
−0.5
0
0.5
1
−1
0.5
0
0.5
1
σ
π
∗ (σ)
1
2
σ
2
/η
−1
−0.5
0
0.5
1
−1
−0.5
0
0.5
1
σ
˙(σ)
σ/η
Fig. 4.2 Specific Newton model: Smooth dissipation potential π(˙ together with resulting smooth
σ = σ(˙ and smooth dual dissipation potential π ∗ (σ) together with resulting smooth ˙
= ˙
Table 4.1 Summary of the specific Newton model
(1) Strain
≡ v
(2) Potential π =
1
2 η |˙ 2
(3) Stress
σ = η ˙
≡ σ
or
(2) Potential π ∗ =
1
2
1
η
|σ|
2
(3) Evolution ˙
=
1
η
σ