Continuum theory of granular media

The mechanics of granular materials are analyzed using the balance laws associated with microscopic and macroscopic continua. The notion of microscopic rotation and dilation was introduced into the continuum structure as a means for describing the local arrangement of granules at a material point. The differential equations and boundary conditions governing the microscopic behavior of granular media undergoing small deformations in equilibrium field and describing very small velocity effects in nonequilibrium field were derived by means of a systematic and consistent application of the laws of continuum physics to a defined macroscopic model. The application of the equation of the conservation of energy, the second law of thermodynamics, and the principle of material objectivity enable the determination of the constitutive equations of the nonlinear theory for both the equilibrium and the nonequilibrium fields.