Model of the Grüneisen coefficient for a wide range of densities on the example of copper

A method for describing the Grüneisen coefficient, which makes it possible to describe in a unified way both continuous materials, for which the shock adiabats behave in a normal way, and highly porous materials, which shock adiabats have an anomalous course, is proposed. A porous material is considered as a simple thermodynamically equilibrium mixture, for which the hypothesis of additivity of the volumes of its components is fulfilled. The equilibrium state is determined by the conditions of equality of pressures, temperatures, and velocities of the components of the mixture. When describing a mixture, the model of interpenetrating and interacting continuums is used. The model takes into account the presence of gas in the pores. Numerical calculations of shock-wave loading and isentropic expansion of copper samples of different porosity are performed. By comparing the calculated and experimental shock adiabats and rarefaction isentropes, it is shown that the proposed model of the Grüneisen coefficient quite accurately describes the behavior of solid materials and materials with low and high porosity.