Biomedical Engineering Reference
In-Depth Information
Figure
7.4
shows a cylinder subjected to a torsion stress. The angle
α
is called the
shear deformation angle and can be calculated from
α ¼
r
ϕ
/
h
and
ϕ
is the
angle of torsion.
It is very common to break the tibia by twisting the leg after a misstep caused by
an unnoticed irregularity. The fracture is not transversal, but in the form of a spiral,
in the same direction the leg was twisted.
7.5 Elastic Properties of Bones
As already mentioned, heterogeneous solids composed of materials with different
elastic characteristics present different values of Young's modulus for tensile and
compressive stresses. This is the case of the bone, for which the tensile strength is
due to collagen and the compressive strength, to the mineral bone.
Tables
7.2
and
7.3
give the elastic characteristics of bones under tension and
compression, respectively. The bone shear modulus is not given in the table, but
measurements showed that its value is about 1.0
10
10
Pa, hence similar to
Young's modulus for the femur subjected to compressive stress. Research done
during more than 25 years by H. Yamada with “fresh” bones of adult Japanese
cadavers with ages between 40 and 59 years provided data published in the topic
Strength of Biological Materials, edited by F.G. Evans, Williams and Williams
Co. Baltimore, 1970. It is important to point out that the data have been obtained
through tests similar to those carried out in an engineering laboratory with inorganic
materials. The behavior of these bones inside the body can be very different, since
they are connected to muscles through ligaments and tendons and the tests are made
only with bones. It is also not known whether or not the values obtained by Yamada
depend on race.
Table 7.2
Tensile properties of bones
Young's modulus
(10
10
Pa)
Tensile strength
(fracture point) (10
7
Pa)
Bone
Maximum strain
Human femur
1.6
12.1
0.014
Horse femur
2.3
11.8
0.0075
Human vertebra
0.017
0.12
0.0058
Table 7.3
Compressive properties of bones and of intervertebral discs
Young's modulus
(10
10
Pa)
Compressive strength
(fracture point) (10
7
Pa)
Bone
Maximum strain
Human femur
0.94
16.7
0.0185
Horse femur
0.83
14.2
0.024
Human vertebra
0.0088
0.19
0.025
Intervertebral disc
0.0011
1.10
0.30
