Biomedical Engineering Reference
In-Depth Information
Table 6.1
Mechanical properties of three biological materials: compact bone, trabecular bone, and
tendon-ligament. Adapted from Ref. [
9
]
Material
Ultimate strength (MPa)
Modulus (GPa)
Elongation (%)
Compact bone
100-150
10-15
1-3
Trabecular bone
8-50
-
2-4
Tendon, ligament
20-35
2-4
10-25
Young's modulus is representative for the stiffness of a material, the higher the
elastic slope, the stiffer the material. Point 3 represents the
elastic limit
, also known
as the yield strength or yield point. The segment between point 2 and 3 defines the
complete elastic behavior of the material, removing any load that falls within this
segment would allow the material to deform back to its original configuration. After
this point, the material behaves plastic and any further deformation is considered
permanent. In this example, the load that is applied on the object is removed at the
point on the curve between 3 and 4. The dotted line represents the linear regression
of the elastic deformation with the same Young's or rigidity modulus that eventu-
ally intersects the strain axis. The intersection point on this axis is called the
plastic
strain
that quantifies the amount of permanent strain, in this example 0.13%. Point
4 represents the
offset yield point
that can be derived using the offset method. The
offset method is used for cases where it is difficult to measure the exact point when
the material yields. Similarly to the previous derivation of plastic strain, the method
works by drawing a line, which starts generally with a strain offset of 0.1-0.2%, and
progresses in parallel with the linear-elastic segment of the curve. The intersecting
point 4 between this line and the original curve is considered the offset yield point.
Point 5 on the curve represents the ultimate tensile strength of the material followed
by point 6 that represents the rupture point of the material; when the object finally
fractures. An overview of mechanical properties for three biological materials is
shown in Table
6.1
.
6.2.2 The Musculoskeletal System
6.2.2.1 The Bones and Joints
The human body is a complex structure composed of a variety of interacting anatom-
ical entities. Among them, the skeletal system includes the bones, cartilages, liga-
ments, and tendons. The average adult skeleton has 206 bones although actual number
of bones slightly varies from person to person. The skeleton is usually divided into
the axial and appendicular skeletons. The axial skeleton forms the upright axis of
the body. It is divided into the skull, auditory ossicles, hyoid bone, vertebral column,
and thoracic cage, or rib cage. The axial skeleton protects the brain, the spinal cord,
and the vital organs housed within the thorax. The appendicular skeleton consists of
the bones of the upper and lower limbs and the girdles by which they are attached to
