On effects of internal friction in the revised Goodman–Cowin theory with an independent kinematic internal length

Abstract

In the present study, the revised Goodman–Cowin theory with an independent kinematic internal length proposed by Fang et al. for rapid dry granular flows is extended to account for the effects of internal friction. A thermodynamic analysis, based on the Muller–Liu entropy principle, is performed to deduce the ultimate equilibrium expressions of the constitutive equations. Results show that while internal friction contributes significantly to the equilibrium expressions of the constitutive variables, the dependence on internal friction of the Helmholtz free energy becomes a critical point for the present formulation in practical applications. In comparison with other constitutive formulations based on the revised Goodman–Cowin theory, the present formulation is the most general one and shows an ability to take into account the microstructural effects of volume fraction variation, internal friction and evolution of internal length of dry granular flows simultaneously.