Yield criterion ($f(\tau ,q)\le 0$)

A yield criterion specifies the admissible elastic stress region, possibly depending on internal hardening variables $q$. Plastic loading occurs on its boundary. The Tresca yield criterion uses maximum principal-stress difference, while the Von Mises yield criterion uses a quadratic deviatoric-stress invariant. Thus a numerical stress difference must be compared to a yield stress using the convention of the selected criterion.