Tresca yield criterion ($f=\frac{1}{2}{\max }_{i,j}|{\sigma }_i-{\sigma }_j|\le {\tau }_Y$)

The Tresca yield criterion bounds the largest resolved shear stress, expressed through the principal stresses. In spherical symmetry, the two tangential principal stresses coincide, so $f=|{\tau }_{rr}-{\tau }_{\theta \theta }|/2$. Here ${\tau }_Y$ is a shear yield stress; the corresponding uniaxial yield strength is $2{\tau }_Y$.