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

ELASKAR, SERGIO; GODOY, LUIS

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES

Pergamon

Año: 1998 vol. 40 p. 1001 - 1018

0020-7403

This paper is about constitutive relations which can model the flow with granular materials whot cohesion, friction, and collision between particles. The cosntitutive model represents compressible viscoplastic fluid with second order effects in which the Cauchy stress tensor depends on the velocity components, presurre and the rate of volume distribution. An alternative model employs the maximun volume distribution to take second order effects in account. It is shown that the simplification of the model in which compressibility and second order effects are neglected ledas to the constitutive model of Diez and Godoy. The formulation is employed to solve the flow through an inclined channel, for wich the probles reduces to a one-dimensional situation. Explicit solutions are obtained for this case, and are presented in some details for differents 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 function of the volume distribution is the most general of the constitutive relations presented.