Biomedical Engineering Reference
In-Depth Information
4
The mechanical behaviour of fibres
4.1
Introduction
Fibres and fibre-like structures play an important role in the mechanical proper-
ties of biological tissues. Fibre-like structures may be found in almost all human
tissues. A typical example is the fibre reinforcement in a heart valve, Fig.
4.1
(a).
Another illustration is found in the intervertebral disc as shown in Fig.
4.1
(b).
Fibre reinforcement, largely inspired by nature, is frequently used in prosthesis
design to optimize mechanical performance. An example is found in the aortic
valve prosthesis, see Fig.
4.2
.
Fibres are long slender bodies and, essentially, have a tensile load bearing
capacity along the fibre direction only. The most simple approximation of the,
often complicated, mechanical behaviour of fibres is to assume that they behave
elastically. In that case fibres have much in common with springs. The objective of
this chapter is to formulate a relation between the force in the fibre and the change
in length of a fibre. Such a relation is called a
constitutive model
.
4.2
Elastic fibres in one dimension
Assume, for the time being, that the fibre is represented by a simple spring as
sketched in Fig.
4.3
. At the left end the spring is attached to the wall while the right
end is loaded with a certain force
F
. If no load is applied to the spring (fibre) the
length of the spring equals
0
, called the reference or initial length. After loading
of the spring the length changes to
, called the current length. It is assumed that
there exists a linear relationship between the change in length of the fibre
−
0
and the applied force:
F
=
a
(
−
0
) .
(4.1)
The constant
a
reflects the stiffness properties of the spring and can be identified
by, for instance, attaching a known weight, i.e. a known force, to the spring in
