An analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure

The objective of this paper is to develop an analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure. This expression for the temperature is obtained for both constant and variable specific heat models and can be used in common models for the material yield strength that include thermal softening due to increase in temperature. Also, the material parameters in the model can easily be calibrated to match known experimental data and the model has been used to determine the value of the shock pressure at the onset of melting during shock loading.