Nonlinear finite elements/Deviatoric and volumetric stress

Deviatoric and volumetric stressEdit

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 stressEdit

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 stressEdit

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

 

where