how to find maximum shear/normal strain

Hi,

This is a general mechanics question. Suppose the 3D strain state at a point is known, so is the coordinate system, XYZ. The strain state can be decomposed into a local coordinate system (i.e., xyz) in such a way that the Z axis always remains the same (i.e., you can rotate about the Z axis to get a local coordinate system, Z always the same as z). My question is, under such a condition, how best to find the maximum shear strain along e_xz, e_yz, or e_xy? Also, how to find the maximum normal strain e_xx, e_yy, and e_zz? It seems a Morh's circle method does not work because of the decomposing constraint.

Thanks very much!