Biomedical Engineering Reference
In-Depth Information
Fig. 3.10 The concept of
body, continuum and material
point shown by the example
of a bone-muscle-fat tissue
composite in a human thigh
(based on MRI-slices with
3D-reconstruction)
infinitesimally small mass dm, which may contain any number of atoms, molecules
or cells. Essential for applying continuum mechanics to biological systems
is that for every point X of the body at time t the (always positive) density
q
ð
X
;
t
Þ¼
dm
=
dV [ 0 can be defined (Fung 1993).
3.2.3.3 Configuration and Motion
Kinematics, which deals with the geometric and analytical description of move-
ment by material bodies, is applied to assess and quantify deformation of a body,
whereby possible causes (force, stress) are disregarded. Practically, two different
positions or configurations of a body are observed: the reference or initial con-
figuration (ICFG) is the initial unchanged position of the body at time t
0
and the
current configuration (CCFG) which shows the body in its changed momentary
state at any time t (see Fig.
3.11
a). Every material point X (or volume element dV
0
or dV) of the body is then assigned in its ICFG location vector X and in the CCFG
location vector x. Displaying both
X
¼
X
i
e
i
and
x
¼
x
i
e
i
ð
3
:
46
Þ
in a cartesian orthogonal basis system e
i
(in the following shortened to OBS), X
i
represents the material and x
i
the spatial coordinate. The location vectors, x and X,
together surmount the vector function v according to
