Biomedical Engineering Reference
In-Depth Information
In this case it is assumed that the dimensions of
and
at the same time much smaller than
L
. Provided, that it is possible to specify
such a subvolume
V
are much larger than
λ
x
), from which
the microscopic deviations have disappeared, however, which is still containing
macroscopic variations: the real density field, according to Eq. (
7.4
), is
homoge-
nized
. Continuum theory deals with physical properties that, in a way as described
above, are made continuous. The results cannot be used on a microscopic level
with a length scale
V
this results in a continuous density field
ρ
(
, but on a much more global level.
In the above reasoning we talk about two scales: a macroscopic and a micro-
scopic scale. However, in many applications a number of intermediate steps from
large to small can be of interest. This is often seen in technical applications, but is
especially of importance in biological materials. In such a case the characteristic
measure
λ
of the components could suddenly become the relevant macroscopic
length scale!
λ
Example 7.1
Figure
7.6
illustrates some of the scales that can be distinguished in biomechanical
modelling. Figure
7.6
(a) could be a model to study a high-jumper. Typically, this
kind of model would be used to study the coordination of muscles, describing the
human body as a whole and examining how it moves. The macroscopic length
(a)
(b)
(c)
(d)
Figure 7.6
Examples of models at different length scales (a) model of a leg (b) model of a skeletal muscle
(c) representative volume element of a cross section of a muscle (d) model of the cytoskeleton
of a single cell.
