Biomedical Engineering Reference
In-Depth Information
Table 6.1
The elasticity
and compliance in different
notations
1
2
3
1
2
3
C
1111
c
11
c
11
^
S
1111
s
11
S
11
S
22
C
2222
c
22
c
22
S
2222
s
22
C
3333
c
33
c
33
^
S
3333
s
33
S
33
c
12
S
12
C
1122
c
12
S
1122
s
12
S
13
C
1133
c
13
c
13
^
S
1133
s
13
C
2233
c
23
c
23
S
2233
s
23
S
23
2
S
44
C
2323
c
44
1
2
c
44
S
2323
1
4
s
44
1
2
S
55
C
1313
c
55
1
2
c
55
S
1313
1
4
s
55
1
C
1212
c
66
1
2
c
66
S
1212
1
4
s
66
2
S
66
1
C
1323
c
54
1
2
S
1323
1
4
s
54
2
S
54
^
c
54
1
2
S
56
C
1312
c
56
1
2
^
c
56
S
1312
1
4
s
56
1
2
S
64
C
1223
c
64
1
2
c
64
S
1223
1
4
s
64
1
p
S
41
C
2311
c
41
1
c
41
S
2311
1
2
s
41
1
p
p
S
51
C
1311
c
51
1
c
51
S
1311
1
2
s
51
1
p
p
S
61
C
1211
c
61
1
^
c
61
S
1211
1
2
s
61
1
p
p
S
42
C
2322
c
42
1
^
c
42
S
2322
1
2
s
42
1
p
C
1322
c
52
1
S
1322
1
2
s
52
S
52
^
c
52
1
p
p
C
1222
c
62
1
S
1222
1
2
s
62
p
S
62
^
c
62
1
p
C
2333
c
43
1
S
2333
1
2
s
43
p
S
43
c
43
1
p
p
S
53
C
1333
c
53
1
S
1333
1
2
s
53
c
53
1
p
p
S
63
Column 1 illustrates the Voigt notation of these quantities as
fourth order tensor components in a three-dimensional Car-
tesian space. Column 2 represents the Voigt matrix or double
index notation. Column 3 illustrates the Kelvin-inspired
notation for
C
1233
c
63
1
c
63
S
1233
1
2
s
63
1
p
these quantities as
second order
tensor
components in a six-dimensional Cartesian space
2
3
2
3
2
3
T
11
T
22
T
33
T
23
T
13
T
12
c
11
c
12
c
13
c
14
c
15
c
16
E
11
E
22
E
33
2
E
23
2
E
13
2
E
12
4
5
4
5
4
5
c
12
c
22
c
23
c
24
c
25
c
26
c
13
c
23
c
33
c
34
c
35
c
36
ΒΌ
:
(6.21)
c
14
c
24
c
34
c
44
c
45
c
46
c
15
c
25
c
35
c
45
c
55
c
56
c
16
c
26
c
36
c
46
c
56
c
66
This matrix represents the classical notation of Voigt (1910) for the anisotropic
stress-strain relations. Unfortunately the matrix
c
appearing in (
6.21
) does not
represent the components of a tensor, while symmetric matrices
C
and
S
do
represent the components of a second-order tensor in a 6-dimensional space.
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