Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 87

The ratio E R / E U is often used to compare viscoelastic materials. If
it is equal to one, the material is fully elastic. The smaller this ratio is,
the more viscous behavior is seen, so the more viscoelastic the material
is considered. The ratio has a value of approximately 0.95 for cortical
bone but only approximately 0.2 for articular cartilage, for strains within
physiologic limits. Thus, we tend to think of cartilage as a viscoelastic
material and bone as an essentially elastic material.

Hysteresis

Viscous deformation produces an additional important difference in
mechanical behavior between elastic-plastic and viscoelastic materials.
If an elastic material is stressed to a point below the proportional limit
and then the load is removed, the stress-strain curve will be retraced and
the elastic energy, the area below the curve to ε p , will be fully recovered.
However, if the same experiment is performed on a standard linear vis-
coelastic material by applying an instantaneous stress, the results will
be as shown in Figure 4.11. Although the strain can be recovered, in a
fully constrained arrangement, the stress-strain curve is not retraced.
The area under the curves may be divided into two regions: region 1, the
area between the curves, and region 2, the area under the unload portion
of the curve. Region 1 represents the portion of the energy of deforma-
tion that is lost, whereas region 2 represents the recoverable portion. The
unrecoverable energy is dissipated as heat, which can be appreciated
by the increase in temperature of clay or bread dough during kneading
(repeated deformation).
This phenomenon, the loss of strain energy despite the full recovery
of strain, is called hysteresis . It will occur in any viscoelastic material
in which either internal creep or stress relaxation has been permitted to
occur during a load-unload cycle. For a specific model, the area between
the load and unload curves will be a function of strain rate.
It is interesting to inquire into the connection between energy dis-
sipation and permanent set (unrecoverable strain). In an elastic-plastic

σ

1

2

ε

FIGUre 4.11 hysteresis.