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mudzm19

# mudzm19 - Muddy Card Responses Lecture M24 12/8*You...

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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 stress-strain 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 off-axis 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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