Averaging method of granular materials

This paper presents an averaging method to link discrete to continuum variables of granular materials. Compared to the other methods proposed in the literature, it has advantages of being applicable to all flow regimes, and to granular flows with or without the effect of physical boundaries. Its application is demonstrated in the determination of the macroscopic properties such as mass density, velocity, stress, and couple stress distributions of a hopper flow, where the discrete results are generated by means of discrete particle simulation. While highlighting the need for considering properly the effect of physical boundaries, the results indicate that the proposed method is an effective way to determine the flow properties of granular materials.