Biomedical Engineering Reference
In-Depth Information
Trabecular bone
Marrow cavity
b
Cortical bone
c
a
Figure 7.1
Structure of bone at different length scales (Images courtesy of Mr Bert van Rietbergen).
critically evaluate whether or not the chosen homogenization is allowed and to be
aware of the limitations of the model at hand. In Section
7.3
we will discuss when
a continuum approach is allowed.
To model a continuum, physical variables are formulated as continuous func-
tions of the position in space. Related to this, some attention will be given in
this chapter to the visualization of physical fields. In addition, derivatives of vari-
ables will be discussed. The gradient operator, important in all kinds of theoretical
derivations, constitutes a central part of this. The chapter ends with a section on the
properties of second-order tensors, which form indispensable tools in continuum
mechanics.
7.2
Orientation in space
For an orientation in three-dimensional space a Cartesian
xyz
-coordinate system
is defined with origin O, see Fig.
7.2
. The orientation of the coordinate system is
laid down by means of the Cartesian vector basis
{
e
x
,
e
y
,
e
z
}
, containing mutually
