Biomedical Engineering Reference
In-Depth Information
Fig. 3.16 On the definition of stress: a loaded body in the CCFG, b body with section cut in the
CCFG and reaction stress vectors in the cut area A and c related area elements in the ICFG and
CCFG
The stress vectors t
0
and t, may in addition be, a function of position X, the
direction of the corresponding area element n
0
and n, respectively, and the time
t such that
t
0
¼
t
0
ð
X
;
t; n
0
Þ;
t
¼
t
ð
X
;
t; n
Þ:
ð
3
:
86
Þ
The normal vectors n
0
and n, are defined such that they are perpendicular to the
corresponding area element dA
0
and dA, respectively, and point outwards,
cf. Fig.
3.16
. Cutting a volume element dV with edge length dx
1
, dx
2
, dx
3
from a
body in the CCFG, cf. Fig.
3.16
, leads to six orthogonal (infinitesimal) cutting
planes with normal vectors n
1
, n
2
and n
3
, as well as a (C
AUCHY
) stress vector t
1
, t
2
and t
3
respectively, assigned to each plane, cf. Fig.
3.17
a. Here, for clarity, only
the planes with positive normal vectors are depicted.
The stress vectors t
i
(i = 1, 2, 3) can be divided into three components with the
coordinates r
i1
, r
i2
and r
i3
(i = 1, 2, 3) with respect to the OBS e
1
, e
2
, e
3
(illustrated in Fig.
3.17
b using the example of t
1
)to
