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Unformatted text preview: 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 = , which would imply that s 22 = s 33 = . 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 more straightforward....
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