3.9 Viscoelastic Materials
65
Fig. 3.9 Mechanical models
for viscoelasticity. Top: A
Kelvin-Voigt material;
Middle: A Maxwell material;
and Bottom: A ‘Standard
linear’ viscoelastic material
S = Y σ + η
dσ
dt
,
(3.27)
where S is the stress and σ is the strain.
3.9.2 Maxwell Model
A ‘Maxwell’ viscoelastic material behaves as a spring in series with a damper, i.e.
viscous for slow changes in stress but elastic for rapid changes. Using the fact that
the displacements of the spring and the damper add to the displacement overall, δx,
and that the force F between the spring and the damper must match with the external
force F , the displacement of the material will satisfy δx = (1/k)δF +(1/η)
δF dt.
As a stress-strain relation, the Maxwell model has
σ =
1
Y
S +
1
η
S dt .
(3.28)
A Maxwell viscoelastic material is also called a ‘rheid’. (Rheos means flow in
Greek. Rheology is the study of material flow.) Maxwell viscoelastic materials can