Biomedical Engineering Reference
In-Depth Information
(
)
µ+ λ
µλ+µ
42
(3
a
b
2
0
2
2)
0
H
=
(4.70)
5
2
2
c
Fc
1
−
µ+λ
µλ+µ
−
2
(3
a
b
33
0
2
+
2)
1
∗
2
−
c
3
11
12
0
1
H
=
(4.71)
6
2
µ+λ
µλ+µ
+
2
(3
c
Fc
1
−
µ+λ
µλ+µ
2
(3
b
a
33
0
2
+
∗
2
2)
−
c
2)
3
11
12
0
2
c
Fc
1
−
µ+λ
µλ+µ
2
(3
b
a
33
0
22
+
∗
2
−
c
2)
3
11
12
0
H
=
(4.72)
7
2
2
µ+λ
µλ+µ
+
2
(3
c
Fc
1
−
µ+λ
µλ+µ
2
(3
b
a
33
0
2
+
∗
2
2)
−
c
2)
3
11
12
0
Equation (4.61) is similar to Equation (4.33) and can thus be solved by fol-
lowing the solution procedure described in Section 4.2.4.
4.5 Numerical Examples for Thermopiezoelectric Bones
Consider again the femur used in Section 3.7. The geometrical and material
coefficients of the femur are the same as those used in Section 3.6, except that
the volume fraction change
e
is now taken to be zero here. In addition, the
surface remodeling rate coefficients are assumed to be
e
e
e
C
=−
9.6 m/sec,
C
=−
7.2 m/sec,
C
=−
5.4 m/sec,
rr
θθ
zz
p
p
C
e
=−
8.4 m/sec,
C
=−
12.6 m/sec,
C
=−
10.8 m/sec,
zr
rr
θθ
p
p
−
9
−
1
2
C
=−
9.6 m/sec,
C
=−
12 m/sec,
C
=
10
Vm/sec
zz
zr
r
and
e
p
C
=
0.0008373 m/sec,
C
=
0.00015843 m/sec
0
0
and ε
0
= 0, η
0
= 0 are assumed.
In the following, numerical results are provided to show the effect of
temperature and external electric load on the surface bone remodeling
