M. Massoudi et G. Ahmadi, RAPID FLOW OF GRANULAR-MATERIALS WITH DENSITY AND FLUCTUATION ENERGY GRADIENTS, International journal of non-linear mechanics, 29(4), 1994, pp. 487-492
A constitutive relationship for the stress tensor of granular material
s during the rapid flow regime that includes the effects of density gr
adient and fluctuating velocity is proposed. Explicit expressions for
various stress components are obtained and simple examples are present
ed. It is shown that this continuum-based model is capable of predicti
ng normal stress differences. The model also contains many earlier mod
els as its special cases. The results also show that the model may be
suitable for analyzing rapid, as well as slow, motions of granular mat
erials.