Deformation - Orthopaedic Biomaterials in Research and Practice - page 23

CHaPTer TWO

Deformation

Statics and dynamics describe the motion of objects, such as body seg-
ments, surgical instruments, or implants, in response to forces. In solv-
ing such problems, one usually assumes that the object is rigid, that is,
nondeformable. If that assumption were correct, then static and dynamic
analysis would yield a full description of the interaction between forces
and materials.
However, the assumption is incorrect. In fact, the opposite assump-
tion is correct: all material objects deform under the action of forces and
moments. The resulting deformations may be temporary or permanent
and may lead to changes in physical properties and cumulative or sudden
loss of integrity. In some cases, either by chance or design, their defor-
mations and cumulative effects are so small that they can be neglected in
biomechanical analysis. In the general case, force-induced deformation
must be included and the mechanical analysis must be extended from
the extrinsic, structural (or biomechanical) level down to the intrinsic,
material (or mechanics of materials) level. In this chapter, we shall deal
with the principles of deformation of materials.

elongation

Tensile
deformation

Suppose two equal and opposed forces, F /2 and F ′/2 (= − F /2), act on a bar
of material with initial length L 0 , as shown on the far left in Figure 2.1.
We know from experience that if the rod is made of a “soft” material,
such as a soft plastic, it will stretch visibly—that is, deform longitudi-
nally under the action of the two forces. Since it is getting longer, we call
this type of deformation elongation.
In Figure 2.1, we can see this happen as the load increases from a
to c. The bar is also becoming narrower; this is because materials tend to
conserve their volume when undergoing deformation. If we continue to
increase the force, a strange thing begins to happen. A region of the bar
begins to narrow, at the expense of the rest, as at d . This is called “neck-
ing.” At the same time, we find that the bar begins to stretch more easily
with a sense of “giving way”; that is, it elongates more rapidly even when