Continuum mechanics/Deviatoric and volumetric stress

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Deviatoric and volumetric stress[edit | edit source]

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 | edit source]

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 | edit source]

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