Hello Kiran,

Max. principal stress corresponds to the max. eigenvalue of the stress tensor (matrix).

Von-mises stress, on the other hand, is a metric of the stress tensor (built based on the invariant of the stress tensor) that describes stress in 3D that we can relate back to test data (i.e., usually in 1D). This is usually good as it boils complex state of stress down to a single number but it does not account for the hydrostatic pressure, only the deviatoric values.

For additional details on the formulation etc. Please refer to the following book section from the Applied Mechanics of Solids.

Von Mises is a theoretical measure of stress used to estimate yield failure criteria in ductile materials and is also popular in fatigue strength calculations (where it is signed positive or negative according to the dominant Principal stress), whilst Principal stress is a more "real" and directly measurable stress.

Also checkout this useful article for the differences.

Hope this helps.

Regards,

Sandeep