Constitutive Model for Granular-Fluid Flows Based on Stress Decomposition
In Bagnold’s description of rheological properties of a solid-fluid suspension, the shear and normal stresses demonstrate linear dependence on the shear rate in the ‘macro-viscous’ regime and quadratic dependence in the ‘grain-inertia’ regime. Based on this pioneering work, a framework for the modeling of solid-fluid flows is proposed in this paper. In the framework, the total stress of the solid phase is decomposed into a frictional term contributed from prolonged contact of solid particles, a viscous term due to the viscosity of interstitial fluid and a inertia term results from particle collisions. A constitutive model for simple-shearing granular-fluid flows is developed based on this framework and verified in the element tests of granular-fluid materials under rapid shear.