Biomedical Engineering Reference
In-Depth Information
∑
()
−
()
−
Π
=
RT
C
t
C
t
Π
,
j
=
M P
,
,
(6.44)
1
Gj
,
Aj
,
hw
j
∑
()
−
()
+
Π
=
RT
C
t
C
t
Π
,
j
=
M P
,
,
(6.45)
2
Gj
,
Cj
,
hw
j
As discussed before, these stresses will be related to the induced stretches
λ
+
λ
-
on the anode and the cathode sides, respectively, by equations (6.28) and
(6.29). The resulting cubic equations are then solved for
and
λ
+
and
λ
-
to calculate the
induced curvature
κ
E
such that:
(
)
(6.46)
κ
=
λ
−
λ
/
t
,
E
+
−
g
where
t
g
is the thickness of the gel strip. The resulting cubic equations are
(
)
(
)
3
2
λ
+
3
Π
/
Y
λ
−=
1
0
,
(6.47)
+
+
+
1
(
)
(
)
λ
3
+
3
Π
/
Y
λ
2
−=
1
0
.
(6.48)
−
2
−
−
Let us convert the cubic equations (6.47) and (6.48) to a reduced form by
substituting
λ
+
=
x
+
- (
Π
1
/
Y
+
) and
λ
-
=
x
-
- (
Π
2
/
Y
-
), respectively, in equation (6.47)
and (6.48) to obtain:
3
x
+
3
p x
+
2
q
=
0,
(6.49)
+
+
+
+
x
3
+
3
p x
+
2
q
=
0,
(6.50)
−
−
−
−
where
()
()
(
)
2
3
−
2
−
3
p
=
Π
Y
,
q
=
Π
Y
−
12
/
,
(6.51)
+
1
+
+
1
+
()
()
(
)
2
3
−
2
−
3
p
=
Π
Y
,
q
=
Π
Y
−
12
/
,
(6.52)
−
2
−
−
2
−
The discriminants for equations (6.49) and (6.50) are, respectively,
3
()
(
)
(
)
6
3
3
3
−
6
Dp
=−
−
q
=−
Π
Y
−
Π
/
Y
−
12
/
,
(6.53)
+
+
+
1
+
1
+
