c
1
ð Þ
¼ 1=s
E
33 ,
e
1
ð Þ
¼ d 33 =s
E
33 ,
ε
1
ð Þ
¼ ε
T
33 À d
2
33 =s
E
33 :
ð6:43Þ
Similarly, for the semiconductor,
T
2
ð Þ
¼ c
2
ð Þ S,
D
2
ð Þ
¼ ε
2
ð Þ E,
ð6:44Þ
where
c
2
ð Þ
¼ 1=s 33 ,
ε
2
ð Þ
¼ ε 33 :
ð6:45Þ
For the currents in the semiconductor, we use the linearized constitutive relations
with uniform doping:
J
p
ffi qp 0 μ
p E À qD
p ∂ Δp
ð Þ
∂z
,
J
n
ffi qn 0 μ
n E þ qD
n ∂ Δn
ð Þ
∂z
,
ð6:46Þ
where
μ
p
¼ μ
p
33 , D
p
¼ D
p
33 ,
μ
n
¼ μ
n
33 , D
n
¼ D
n
33 :
ð6:47Þ
For the composite rod, the total axial force can be calculated from
b
T ¼ T
1
ð Þ A
1
ð Þ
þ T
2
ð Þ A
2
ð Þ
¼ c
1
ð Þ S À e
1
ð Þ E
A
1
ð Þ
þ c
2
ð Þ S
A
2
ð Þ
¼ c
1
ð Þ A
1
ð Þ
þ c
2
ð Þ A
2
ð Þ
S À e
1
ð Þ A
1
ð Þ E
¼ b cS À b eE,
ð6:48Þ
where
b c ¼ c
1
ð Þ A
1
ð Þ
þ c
2
ð Þ A
2
ð Þ ,
b e ¼ e
1
ð Þ A
1
ð Þ
:
ð6:49Þ
6.2 Extension of Rods
149