Continuum mechanics/Deviatoric and volumetric stress

Deviatoric and volumetric stress edit

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.

Decomposition of the Cauchy stress edit

The Cauchy stress can be additively decomposed as


where   is the deviatoric stress and   is the pressure and


In index notation,


Decomposition of the 2nd P-K stress edit

The second Piola-Kirchhoff stress can be decomposed into volumetric and distortional parts as