Granular structure and the nonequilibrium thermodynamics

Granular materials posses disorder structures which are the origin of dynamical heterogeneity. On the basis of non-equilibrium thermodynamics, the structure characteristics, complex deformations, and energy dissipations are analysed. Based on the photoelastic tests, the granular elasticity is discussed. The strain increments are classified into three categories. By means of the non-equilibrium thermodynamics, two granular temperatures, Tk, Tc, are introduced as the state variables, which denote the fluctuations of the kinetic energy and the elastic energy, respectively. Further, a two-granular-temperature thermodynamics (i.e. TGT theory) are developed for granular materials. The thermodynamic forces and fluxes are particularly analyzed. TGT theory is also compared with the previous internal variable thermodynamics for sands (IVT theory) developed a few decades ago. It is found that from TGT the Gibbs free energy in the IVT theory can be deduced, and the energy dissipation function can be apparently expressed from TGT theory.