Stress deviator tensor

Summary

The stress deviator tensor is what remains of the Cauchy stress tensor after its mean, hydrostatic part is removed: $s = \sigma - \tfrac13 (\operatorname{tr} \sigma) I$. The hydrostatic part tends to change volume, while the deviator tends to change shape. Because metals yield by changes of shape, plasticity theory, for example the von Mises criterion, is written in terms of the deviator.