Rheology of nonconvex granular flows based on particle rotational characteristics

Particle shape has a profound impact on the flow behaviors of granular materials, yet effectively incorporating the role of particle shape into granular rheology remains challenging. In this study, we employ three representative types of nonconvex particles generated through the multisphere approach and identify a consistent one-to-one relationship between the rescaled friction coefficient and the inertial number I across both inertial and quasistatic flow regimes. However, variations in particle shape cause notable deviations in rheological data compared to their spherical counterparts. Based on the observed dependence of rheological data on I for various nonconvex particles and their convergence at high I, we propose an inertial number I_{s} to effectively capture the impact of particle shape on flow states. The model parameters defining I_{s} are shown to be nearly independent of flow states and configurations, with physical interpretations related to particle rotational characteristics during shear. For practical application, we propose an empirical formula to capture the dependence of model parameters on particle geometrical shapes. The robustness of the proposed model is validated by predicting flow in an inclined flow configuration and applying it to additional nonconvex particles with more irregular and asymmetric features. This establishes a crucial foundation for extending the application of this generalized rheological model to other complex granular flows.