Biomedical Engineering Reference
In-Depth Information
s
E
D T
9
5
3
3
e
D
1
1
Δ S
22
Figure 3.3 The number of independent variables for mm2 class. The darker circles show non-zero
components (By permission of Oxford University Press)
To avoid unnecessary complexity when dealing with temperature change and its effects,
experiments are normally conducted in an environment in which the temperature is con-
stant. In this case, the third terms of Equations 3.9-3.11 are 0. In many applications,
the changes in entropy are so negligible that they can be ignored. For instance, in the
majority of sensing and actuating problems, only Equations 3.12 and 3.13 are applicable:
= s E,T
ijkl σ kl + d kij E k
ε ij
(3.12)
D i = d ijk σ jk + k σ,T
E j
(3.13)
ij
For sensing applications in the absence of an electric field, these relationships can be
simplified even further:
= s E,T
ε ij
ijkl σ kl
(3.14)
D i = d ijk σ jk
(3.15)
For uniaxially drawn PVDF, the d ij , s ij ,and ε matrices have the following forms [2]:
s 11 s 12 s 13 000
s 12 s 22 s 23 000
s 13 s 23 s 33 000
000 s 44 00
0000 s 55 0
00000 s 66
[ s ] =
(3.16)
0000 d 15 0
000 d 24 00
d 31 d 32 d 33 000
[ d ]
=
(3.17)
ε 11 00
0 ε 22 0
00 ε 33
[ ε ] =
(3.18)
 
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