Often it is convenient to decompose the stress tensor into volumetric and deviatoric (distortional) parts. Applications of such decompositions can be found in metal plasticity, soil mechanics, and biomechanics.
The Cauchy stress can be additively decomposed as
where is the deviatoric stress and p is the pressure and
In index notation,
The second PiolaKirchhoff stress can be decomposed into volumetric and distortional parts as
where
