October 5, 2022 at 9:15 pm

peteroznewman

Subscriber

The Stress Tensor is a 3×3 matrix with six independent components.

Several scalar values called Invariants can be extracted from the Stress Tensor. One example is VonMises equivalent stress. Another one is called Stress Intensity, which when divided by 3 is called Hydrostatic Stress.

The formula you show has tr( ) indicating a trace matrix operator, but the stuff in the brackets is not a matrix.

Pressure is generally defined as negative one-third the trace of the stress tensor.

If the P in the formula is intended to represent pressure, then the equation is missing the divide by 3 factor.