Biomedical Engineering Reference
In-Depth Information
C
B
130
120
A
110
100
90
80
70
60
50
40
30
20
10
0
15000
5000
10000
Strain [
μ
]
FIGURE 4.15
Bone shows hysteresis and shifting of stress-strain curves with repeated loading and unloading.
Adapted from [2].
Figure 4.15 shows that the elastic properties of bone also vary depending on whether the
load is being applied or removed, displaying hysteresis. From a thermodynamic view,
the energy stored in the bone during loading is not equal to the energy released during
unloading. This energy difference becomes greater as the maximum load increases (curves
A to B to C). The “missing” energy is dissipated as heat due to internal friction and damage
to the material at high loads.
The anisotropic nature of bone is sufficient in that its ultimate stress in compression is
200 MPa, while in tension it is only 140 MPa and in torsion 75 MPa. For torsional loading,
the
, relates the shear stress to the shear strain.
The modulus of rigidity is related to the elastic modulus via
shear modulus
or
modulus of rigidity
, denoted
G
Poisson's ratio
, n, where
e
transverse
e
longitudinal
n
¼
ð
4
:
51
Þ
3, meaning that longitudinal deformation is three times greater than
transverse deformation. For linearly elastic materials,
Typically, n
0
:
E
,
G
, and n are related by
E
G
¼
ð
4
:
52
Þ
2
ð
1
þ
n
Þ
One additional complexity of predicting biomaterial failure is the complexity of physi-
ological loading. For example, consider “boot-top” fractures in skiing. If the forward
motion of a skier is abruptly slowed or stopped, such as by suddenly running into wet
or soft snow, his forward momentum causes a moment over the ski boot top, producing
three-point bending of the tibia. In this bending mode the anterior tibia undergoes com-
pression, while the posterior is in tension and potentially in failure, since bone is much
stronger in compression than in tension. Contraction of the triceps surae muscle produces
high compressive stress at the posterior side, reducing the amount of bone tension and
helping to prevent injury. Example Problem 4.9 shows how topics from statics and
mechanics of materials may be applied to biomechanical problems.
