Biomedical Engineering Reference
In-Depth Information
¥
22
1
2
µ
KTT
(
1
cos
) (
)
2
2
¦
¦
¦
¦
¶
¶
¶
¶
¥
§
¦
Re
µ
·
¶
2
(
TT
KT T T T
)
(4.2)
23
cD
2
2
sin
(
)(
3
)
§
·
1
2
2
where
is the angle between the light beam and
T
1
(Fig. 4.2). If
the radial stress component
T
3
is considered zero, equation (4.4) is
reduced to
K
Re
2
2
( in
TKTK
1
s)
(4.3)
2
cD
Light Source
Model of
Vasculature
σ
2
σ
1
σ
Light
Beam
2
Light Source
σ
3
σ
1
Stress Analysis
Point
Light
Beam
ϕ
Principal Stress
Plane
Principal
Stress Plane
a)
b)
Figure 4.2
(a) Stress components in photoelastic stress analysis. (b)
Angle
K
between principal stress component
T
2
and light beam
(right).
The difference between the principal stresses on each side of a
biaxial stress ield
is obtained when the light beam is parallel
to
T
3
,
v
1
=
v
2
=
0 and
v
3
=
1 [3, 4]:
T
1
,
T
2
2
Re
cD
TT
(4.4)
1
For stress analysis in model borders we consider that the model of
vasculature has a cylindrical shape, and we set its axis perpendicular
to the light source beam. Therefore in this case equation (4.1) can be
reduced to
T
2
Re
cD
(4.5)
Measurement of stress relying on photoelastic effect (equations
4.1-4.5) depends on the photoelastic coeficient of the material and
the optical path length (amount of photoelastic material between the
light source and the observation point). The method for measuring
those parameters is explained in the following sections.
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