Equation of state for a highly porous material

An equation of state for describing a highly porous material is proposed. The porous medium is considered as a simple thermodynamically equilibrium mixture for which the hypothesis of additivity of volumes of its components holds true. The equilibrium state is determined by conditions of equality of pressures, temperatures, and velocities of the mixture components. A model of interpenetrating and interacting continua is used for the mixture description. The gas available in pores is taken into account in the model. The equations of state of both solid and gaseous components are presented equally (in the form of the Mie–Grüneisen equation with the density-dependent Grüneisen factor). By means of presenting functions as Taylor series, relations are deduced that allow the parameters of the equation of state for a porous material to be expressed through the appropriate parameters and mass fractions of the components. Numerical calculations of shock-wave loading of porous copper, nickel, iron, and tungsten–nickel–copper mixtures are performed. The derived equation of state is shown to describe quite exactly the behavior of highly porous materials when shock waves propagate in them.