Based on the von Mises yield criterion, a material begins to yield at a point when the state of stress at that point is such that the scalar known as the von Mises stress, exceeds the yield strength of the material as determined by a tension test. It is given by the equation:
where $\sigma_1$, $\sigma_2$, and $\sigma_3$ are the principal stresses. However, based on this yield criterion, if at a given point the 3 principal stresses are equal, the material at that point will not yield even if the 3 principal stresses take on a very large value, be it in compression or in tension. Intuitively, this should not be happening for the latter case. Is there anything that I have missed out?