78
4 Visco-Elasticity
4.1 Newton Model
The Newton model of a viscous fluid (in short the Newton model) consists of a
viscous dashpot (see the sketch of the specific Newton model in Fig. 4.1).
The basic kinematic assumption of the Newton model is the equality of the total
strain and the viscous strain v (representing the elongation of the viscous dashpot),
i.e.
≡ v .
(4.1)
Note that the set of internal variables is empty for the Newton model, i.e. α = ∅.
Sir Isaac Newton [b. 4.1.1643, Woolsthorpe,
England, d. 31.3.1727, London, England] was
Lucasian Professor of Mathematics at the Trinity
College in Cambridge. He laid the foundations
of classical mechanics in his landmark treatise
“Philosophiae Naturalis Principia Mathematica”
from 1687. Likewise he is the co-founder of differential and integral calculus (as the opponent
to Leibniz) and greatly contributed to optics. The
Newton model of viscous fluids is named after
him.
4.1.1 Specific Newton Model: Formulation
The specific Newton model, displayed in Fig. 4.1, consists of a linear viscous dashpot
with viscosity η.
Direct Representation
Since there is no energy storage for the specific Newton model the free energy density
ψ vanishes identically
ψ( ≡ 0.
(4.2)
Fig. 4.1 Specific Newton
model
σ
σ
v
η