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# When to use equation of state models for modeling hydrodynamic response in metals?

Equation of state models (Mie-Gruneisen equation of state etc) have been widely used to study hydrodynamic response of material during explosive deformation, ballistic impacts for a long time. As far as I understand, a hydrodynamic response is required to be incorporated in a model if the pressure of impact leads to an increase volumetric strength. That is the stress wave speed in the material exceeds the speed of sound in the material (v = sqrt(elastic modulus/density)). Ballistic impacts occur at strain rates close to 10^9 to 10^12/s. These strain rates are in the shock regime which does warrant a hydrodynamic response to be considered. However, what about situations when the strain rates are less than the overdriven shock range? Should one consider hydrodynamic response even then?

My question is, when should one used an EOS to model the volumetric response of a material? Most commercial FE packages have these EOS models inbuilt. So, it is pretty convinient to use them. But, I would like to know when one should use these models?

An example: The sound wave speed within the body (E =22GPa, rho=8.1gm/cc) comes to around 4969 m/s. So, suppose I hit a spherical body of size 30 microns at 4969 m/s, the strain rate it will endure is 10^8 /s. The shock induced strengthening should thus be considered above this strain rate. Thus, for strain rates less than this the EOS should not be used. Am I right in thinking this?

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