The principal stresses are unique for a given stress tensor.

Therefore, the principal stresses of the brittle material need to be compression.

The principal stresses of a stress tensor are its eigenvalues.

Mean stress is the time average of the principal stress.

Isochromatics are the locus of the points along which the difference in the first and second principal stress remains the same.

If the material is incompressible then and the principal stresses can be arbitrary.

This theory does not take into account the effect of the other two principal stresses.

And finally the wellbore pressure must be greater than one of the three principal stresses in the formation.

Functions of the principal stresses, such as the yield function, can be represented by surfaces in stress space.

However, when one of principal stresses becomes smaller (or larger) than the others the material is subject to shearing.