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In an isotropic elastic solid, Young's modulus, Poisson's ratio and the shear modulus are not independent of one another. You can see this by

 

In an isotropic elastic solid, Young's modulus, Poisson's ratio and the shear modulus are not independent of one another. You can see this by applying a shear stress (see diagram below) then rotating the coordinates by 45 (by performing the tensor transformation) about the z-axis to get the corresponding normal components of stress, evaluating the corresponding normal components of strain and then returning back to the original coordinate system. E Derive G = using this tensor transformation procedure described 2(1+v) above. Upload Choose a File X

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