Biomedical Engineering Reference
In-Depth Information
σ= ε+ ε+ε− −α
c
c
c
e
E
HT
−λ
,
rr
11
rr
12
θθ
13
zz
31
z
31
z
1
σ=ε+ ε+ε− −α
c
c
c
e
E
HT
−λ
,
θθ
12
rr
11
θθ
13
zz
31
z
31
z
1
σ=ε+ ε+ε− −α
c
c
c
e
E
HT
−λ
,
zz
13
rr
13
θθ
33
zz
33
z
33
z
3
σ= ε− −α
c
e
E
H
,
zr
44
zr
15
r
15
r
De
=ε+κ +
EdH
,
(3.71)
r
15
zr
1
r
1
r
De
=ε+ε +ε+κ +
(
)
e
E
dH
− χ
T
,
z
31
rr
θθ
33
zz
3
z
3
z
3
B
=α ε+ +µ
d EH
,
r
15
zr
1
r
1
r
B
=α ε+ε+αε+
(
)
d EHmT
+µ−
,
z
31
rr
θθ
33
zz
3
z
3
z
3
hkq
=
,
h
=
kq
r
r
r
z
zz
eAeAeE
=
()
+
E
()
+
AeEAeH
E
()
+
M
()
+
AeH
M
()
r
r
z
z
r
r
z
z
(3.72)
ε
ε
ε
+
Ae
()(
εε ε
+
)
+
Ae
()
+
Ae
()
ε
rr
rr
θθ
zz
zz
rz
rz
where
B
i
and
H
i
are components of magnetic induction and magnetic field,
respectively
α
ij
are piezomagnetic constants
d
i
are magnetoelectric constants
μ
i
are magnetic permeabilities
m
3
is the pyromagnetic constant
The associated magnetic field is related to magnetic potential ψ by
H
r
= ψ
, r
H
z
= ψ
, z
(3.73)
If we consider again a hollow circular cylinder of bone as shown in
Figure 3.1, subjected to an external temperature change
T
0
, a quasistatic axial
load
P,
an external pressure
p,
an electric potential load φ
a
(o r/a n d φ
b
), and a
magnetic potential load ψ
a
(a n d/o r ψ
b
), the governing equations (3.8) and (3.9)
and boundary condition (3.5) are, in this case, replaced by
2
∂
∂
1
∂
∂
(3.74)
+
(
cu
+ϕ+α ψ=
e
)
0
44
z
15
15
2
r
r
r
2
∂
∂
1
∂
∂
+
(
eu
−κϕ− ψ=
d
)
0
(3.75)
15
z
1
1
2
r
r
r
2
α−ϕ−µψ=
∂
∂
1
∂
∂
(3.76)
+
(
ud
)
0
15
z
1
1
2
r
r
r
