For the purpose of answering/explaining this, it does not need to be restricted to strains (i.e., it can be stresses too). I am mainly trying to understand when to use which one (i.e., if I am designing something, when would each be important to consider)? Also, for a 2D case, where all strains are restricted to the plane, are they equal?
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2 Answers
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Nature doesn't care how we assign our coordinate system, so we have to look for a special reason to be concerned with a certain elasticity parameter in a certain plane that we've defined.
Perhaps we need to constrain the deformation in that particular plane.
Perhaps we're working with a certain anisotropic material system that's weak in that particular plane.
In any case, if there's no out-of-plane stress (strain), then the maximum in-plane stress (strain) equals the overall maximum principal stress (strain).
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If my memory serves me correctly, the "max principal strain" is the maximum strain caused by the out-of-plane stresses, for which shear stress is zero. The maximum in-plane strain, on the other hand, is the strain caused by pure shear, for which the normal stresses are zero.
