I see your problem now, one I am quite familiar with!

Back to your problem, I am not so sure I understand your plan. If you compare principal stretches you are automatically comparing quantities defined in different coordinate systems. I mean, however complex the deformation, the computation of principal stretches implies locally rotating the coordinate system to an orientation such that the strain tensor is diagonal. The key aspect in uniaxial deformation is that such rotation is nihil everywhere, i.e. if you select your global orientation as the one for which the strain tensor of an arbitrary point is diagonal, then the strain tensor is diagonal in this system for all material points.

Let me clarify with an example. Imagine a bar of material undergoing uniaxial strain, apart from a small region undergoing localized shear (shear band, for example). Then you can choose the shear strain in such a way the principal strain is in magnitude constant! which if I understood you correctly, would invalidate your approach (your metric would suggest the deformation being uniaxial)

That us why i proposed to quantify the rotation needed to bring the strain tensor in an arbitrary point in the diagonal form. If your manager prefers colour plots, you can still:

1) choose a region of the product where the strain field in mainly uniaxial

2) Compute the principal strain orientation and consider this your reference orientation

3) For all other integration points, you compute the prinical stretches: the difference between their orientation and the orientation chosen at step 2) is then a scalar field you can use to obtain a colour plot.

As a variation of the procedure, you can also assign different weights to different material points, based on the principal stretch magnitude: in this way your metric will assign more importance to areas characterized by high strains.

Hope this is of some help, let us know how it goes!

PS: On second thought, why not try something simpler for our manager? Show him a plot (after performing a good selection of the global reference system, i.e. aligned as much as possible with the prevailing uniaxial strain field)) of the diagonal terms in the strain tensor (linked to normal strains), and the off-diagonal terms (linked to shear). In an uniaxial deformation the second plot should be zero everywhere!