Biomedical Engineering Reference
In-Depth Information
upper body weight [Figure 5.7(a)]. When the stress strain curves are plotted for
various loads, they show identical characteristics (i.e., the tibia and fibula have sim-
ilar material strength per unit bone volume). However, the tibia has a larger cross
section relative to the fibula. Hence, for any given stress, the force experienced by
the tibia will be higher than the fibula. In addition, the failure of fibula will occur
at a much lower force than the tibia. Under such a circumstance the tibia is said to
have a higher structural strength than the fibula. Hence, while evaluating the mate-
rial characteristics, structural differences are important.
5.3.2 Axial Stress and Strain
If a material is pulled along a symmetric axis of the material with a small force
(called a tensile force), a temporary deformation occurs in the material due to the
elastic displacements of molecules [Figure 5.7(b)]. Removal of the force will gradu-
ally result in the recovery of this extension. British scientist Robert Hooke stated
that for small strains, stress is proportional to strain. This is called
Hooke's law
of
linear elasticity. In one dimension,
(5.14)
σ
=
E
*
ε
where
E
is called the Young's modulus with the units of force per unit area. Can-
cellous (or spongy)
bone has a modulus of 1 GPa, whereas a cortical (or compact)
bone has a modulus of 18 GPa (Table 5.4). The material returns to its original size
only to a certain applied force. This region is called the elastic region [Figure 5.8(a)]
and its stress-strain behavior proceeds in a linear fashion from point A to point B.
Hooke's law is also stated in terms of applied force (
F
) and observed displacement
(
x
) from its initial position as
(5.15)
F x
=
Figure 5.7
Tensile and compressive properties of materials: (a) the difference between the force-
elongation curve and the stress-strain curve, and (b) the effect of the axial tensile and compressive
loading on cylindrical materials.
