Wave propagation in a dynamic system of soft granular materials

The wave propagation in a dynamic system of soft elastic granules is investigated theoretically and numerically. The perturbation theory for simple fluids is applied to the elastic granular system in order to relate the elastic properties of individual particles with the "thermodynamic" quantities of the system. The properties of a piston-driven shock are derived from the obtained thermodynamic relations and the Rankine-Hugoniot relations. The discrete particle simulation of a piston-driven shock wave in a granular system is performed by the discrete element method. From theoretical and numerical results, the effect of the elastic properties of a particle on shock properties is shown quantitatively. Owing to the finite duration of the interparticle contact, the compressibility factor of the elastic granular system decreases in comparison with that of the hard-sphere system. In addition, the relation between the internal energy and the granular temperature changes due to the energy preserved with the elastic deformation of the particle. Consequently, the shock properties in soft particles are considerably different from those in the hard-sphere system. We also show the theoretical prediction of the speed of sound in soft particles and discuss the effect of the elasticity on an acoustic wave.