Chemistry Reference
In-Depth Information
(a)
(b)
FIGURE 4.18
Simple mechanical models of viscoelastic behavior. (a) Voigt or Kelvin element and (b)
Maxwell element.
A mechanical model for such response would include a parallel arrangement
of a spring for elastic behavior and a dashpot for the viscous component. (A dash-
pot is a piston inside a container filled with a viscous liquid.) This model, shown
in
Fig. 4.18a
, is called a Kelvin or a Voigt element. When a force is applied
across such a model, the stress is divided between the two components and the
elongation of each is equal.
Another way to combine the responses of
Eqs. (4-39) and (4-57)
is to add the
strains. Then
γ 5γ
elastic
1γ
viscous
d
dt
5
d
γ
elastic
d
γ
elastic
d
dt
1
τ
(4-59)
1
G
kt
1
dt
5
η
The mechanical analog for this behavior is a spring and dashpot in series. This
body, called a Maxwell element, is shown in
Fig. 4.18b
.
Mechanical models are useful tools for selecting appropriate mathematical
functions to describe particular phenomena. The models have no physical relation
to real materials, and it should be realized that an infinite number of different
models can be used to represent a given phenomenon. Two models are mentioned
here to introduce the reader to such concepts, which are widely used in studies of
viscoelastic behavior.
The Maxwell body is appropriate for the description of stress relaxation, while
the Voigt element is more suitable for creep deformation. It is worth noting that
