Biomedical Engineering Reference
In-Depth Information
analysis involves an understanding of material properties and the “Theory of
Elasticity” [3]. Modern techniques for predicting the behavior of materials under
loading allow reasonable prediction of such behavior if used in light of knowledge of
material properties and elasticity theory. Without such knowledge, however, the
results can be very misleading. Thus, this chapter will include a discussion of some
classical methods which may be used to augment the computer intensive modern,
numerical methods.
An understanding of the risks of biological failure is also essential. Such failure
may occur in the absence of any damage to the implants by the release of toxic
material from an implant by leaching or corrosion [4]. Biological failure, however, is
often associated with mechanical problems such as loosening due to bone necrosis
resulting from wear, or mechanical subluxation due to component subsidence.
The science associated with failure prediction is very complex and not
completely understood. This chapter, therefore, presents a rather simplified view
of the concepts of failure analysis. A more complete understanding may be
obtained from the references cited.
2.2 Stress Analysis
Stress analysis involves the prediction of stress and strain in a body under loading
or thermal effects. Only the effects of loading will be discussed here.
2.2.1 Stress
The stresses discussed in Chapter 1 are referred to as “simple”, one dimensional
stresses. If one defines a finite plane in or on a body then if the force is perpendicular
to the plane the stress resulting from this force is called a “normal” stress. If the force
pulls on the body it is a “tensile” stress and if it pushes on a body it is a
“compressive” stress. If the force is parallel to the plane then it is called a “shear”
stress. The “average stress” is the force divided by area of the plane.
Average stress is, however, of very limited use. More usual is the situation in
which the stress varies from point to point within the body. Thus, often, at critical
points in the body one needs to estimate the stress on an infinitesimal element of
the body. Thus, we will define “stress” as
=∆÷∆
(1)
Where:
∆→0
∆ is the area loaded
∆ is the force on this area
and
is the stress
.
