Weighting function in the averaging method of granular materials and its application to hopper flow

The weighting function plays a very important role in the averaging theory of granular material to link discrete to continuum variables. Criteria for its suitable selection are proposed in this paper based on some physical arguments. A weighting function based on the so-called Johnson's S_B distribution function is recommended. Its application is demonstrated in the calculation of the stress field of hopper flow, where the discrete results are generated by means of the Distinct Element Method (DEM). The continuum variables are computed, based on the new averaging equations which are developed by modifying those recently proposed by Babic and applicable to the entire domain including interior and physical boundaries of granular material.