A simple constitutive framework for thinning-thickening transitions in dense granular-fluid mixtures

A unified constitutive framework is developed for dense fine-granular mixtures exhibiting apparent shear thinning and continuous or discontinuous shear thickening in the macro-viscous flow regime. The effective granular stress is decomposed into viscoplastic structural and suspension-stress contributions. The former is obtained from a hypoplastic model combined with a Herschel-Bulkley rheology, whereas the latter encompasses the $\mu \left(I_m\right)$ rheology and the Wyart-Cates frictional-contact transition, and shows stress-dependent jamming state. Benchmark calculations show that the proposed formulation captures the transition between shear-thinning and shear-thickening behaviour. A depth-averaged long-wave analysis further shows that non-monotonicity induced by discontinuous shear thickening may persist to promote instability in the macro-viscous flow regime.