Constitutive relations for compressible granular materials using non-Newtonian fluid mechanics

This paper is about constitutive relations which can model the flow of granular materials with cohesion, friction, and collisions between particles. The constitutive model represents compressible viscoplastic fluids with second-order effects, in which the Cauchy stress tensor depends on the velocity components and on the rate of volume distribution. An alternative model employs the maximum volume distribution to take second-order effects into account. It is shown that the simplification of the model in which compressibility and second-order effects are neglected leads to the constitutive model of Diez and Godoy. The formulation is employed to solve the flow through an inclined channel, for which the problem reducesto a one-dimensional situation. Explicit solutions are obtained for this case, and are presented in some detail for different degrees of approximation. The results are compared with theoretical values by other authors and with experimental data available in the literature, by Drake and Walton and by Savage, with excellent agreement. The constitutive equation in which second-order terms are a function of the volume distribution is the most general of the constitutive relations presented.