Muddy Card Responses Lecture M24 12/8
*You mentioned that
E
1111
≠
Young's modulus. Why is that?.
This is correct
E
1111
≠
Young's modulus. If you consider the strain that arises due to a uniaxial stress applied (say

ns
11
in the x
1
direction  so
s
11
)
, there should be a strain of
e
11
=
s
11
and
e
22
=
e
33
=
in the
E
E
transverse directions.
But the tensor stiffness form of the stressstrain relationship for an
isotropic material gives:
s
11
s
11
s
11
=
E
1111
e
11
+
E
1122
e
22
+
E
1133
e
33
=
E
1111
s
11

n
E
1122
E

n
E
1133
E
E
i.e. the axial stress picks up contributions from the offaxis stress. Another way to look at this
is to consider what would happen if
e
22
=
e
33
=
0
, which would imply that
s
22
=
s
33
=
≠
0
.
This is an important point, so it is worth convincing yourself of the reasoning.
*The different forms of notation are confusing. Why are they useful?
I agree that it is a bit
confusing, and in some ways it would make life easier if there was a consistent set of
notation. The reason for the two types of notation is that tensor notation is mathematically
more straightforward. However, the engineering notation and the engineering elastic
constants correspond more directly to what can be experimentally measured.
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 Winter '12
 CharlesColeman
 Aeronautics, Astronautics, stiffness matrix ceases, tensor stiffness form

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