Biomedical Engineering Reference
In-Depth Information
4. Linear-Elastic Ideal-Plastic Materials. If a material does not exhibit distinct
hardening behaviour, the stress-strain response can be approximated by a
linear-elastic curve path (curve #2) and an ideal-plastic path (curve #4). Thus,
materials that begin to yield after reaching a certain stress limit can be
approximated.
5. Rigid-Plastic Materials. If the elastic strain is negligibly small compared to
the plastic strain, the material behaviour can be described assuming a rigid-
plastic repose whereby the material behaves as rigid up to a certain stress
limit (curve #1) and then begins to yield (curve #5).
6. Plastic Hardening Materials. Such materials are characterized by permanent
deformation after unloading, and under additional loading cycles, loading
and unloading follow the same linear paths.
• Viscous material behaviour is basically characterized through a time-
dependent deformation at stresses r
0
\r
y
;
i.e. stresses below the yield stress r
y
:
)
The following three cases can be distinguished:
7. Viscous Materials—Creep (r(t) = r
0
= const., e = e(t). If for instance,
plastomers (PVC, PU etc.) as well as biologic structures (e.g. human soft
tissue, hair, etc.) are exposed to a constant load r
0
, the material begins to
'yield'. This is known as creep.
8. Viscous Materials--Relaxation (e(t) = e
0
= const., r = r(t)). If plastomers
(PVC, PU etc.) or biologic structures (e.g. human soft tissue, hair, etc.) are
exposed to a constant deformation e
0
;
a time-dependent decrease of stress can
be observed. This phenomenon is known as stress relaxation or relaxation.
9. Viscous Materials--Deformation-Relaxation. If plastomers (PVC, PU etc.)
or biologic structures (e.g. human soft tissue, hair, etc.) are exposed to sudden
unloading
(r
ð
t
Þ¼
0),
the
deformation
decreases.
This
phenomenon
is
referred to as deformation-relaxation, backward creep or retardation.
If the stress-strain response initially follows the elastic path 0A (cf. Fig.
3.5
)
and then from point A the curve path #7, a combination of elastic and viscous
material behavior exists. Such materials described under 7-9 are referred to as
viscoelastic and are said to exhibit a fading memory.
10. Pseudo-Elastic Materials. Nickel-Titanium alloys (Ni-Ti) show similar
behavior to linear-elastic ideal-plastic materials under loading, except that
at curve point D,asecond elastic path is followed. At unloading, from point
E to point F, backward creep takes place. Further unloading leads to the
initial undeformed state, similar to an elastic material. The underlying
processes rely on martensite-austenite transitions which are initiated due to
temperature differences. Materials that exhibit such behaviour are referred
to as Shape-Memory-Alloys and are said to have a memory of the shape at a
specific temperature.
Any combination of the above listed material classes, such as viscoplastic or
viscoelastic behaviour, are possible. Any material may exhibit any of the listed
