A Nonhydrostatic equation of state for a solid

[Useful nucleus]

I could find many equation of states for solids under hydrostatic compression such as Birch-Murnaghan and Vinet but I could not find any derived equation of state for non-hydrostatic case. Are there any texts or papers that discuss such equations of states in some detail ?

 

[Frabjous]

Typically one splits the stress tensor into a hydrostatic and deviatoric component. The magnitude of the deviatoric component is generally limited by the flow stress of the material which is generally small compared to high pressures. Typically the deviatoric component is handled via elasticity/plasticity. If you are below yield, things are generally expressed in the language of linear/nonlinear elasticity and the concept of pressure is not used.