Relationship between stress tensor eigenvalues and principal stresses

[fpdlskf]

First of all, thanks for all the helpful comments to my previous posts.


I'm trying to get a grasp of stress tensors and have been doing some studying.
In the literature I've been looking at, it says something about the eigenvalues of
stress tensors and the principle stresses. This is where I'm stuck.

Is there a relationship btwn the eigenvalues of the stress tensors and the principle stresses?
If so how would I derive that relationship?

 

[meldraft]

When your three axes are oriented in the principal stress directions, all the non-diagonal elements of the stress tensor are 0, and the diagonals are the principal stresses (that is actually how you define them).

As to how they relate to the eigenvalues, there is a pretty rigorous description here:

http://en.wikipedia.org/wiki/Stress_(mechanics)#Principal_stresses_and_stress_invariants