Deviatoric stress (${\mathbf{\sigma }}_{\mathrm{dev}}$)

The deviatoric part of a three-dimensional stress tensor is ${\mathbf{\sigma }}_{\mathrm{dev}}=\mathbf{\sigma }-\mathrm{tr}(\mathbf{\sigma })\mathbf{I}/3$. It is traceless. Adding an isotropic pressure does not change a normal-stress difference.