Granular flow down an inclined plane with highly nonconvex particles: Macroscopic behavior, microstructure, and nonlocal rheology

We investigate the flow behavior of highly nonconvex particles on an inclined plane using three-dimensional Contact Dynamics simulations. These particles, termed Platonic polypods, are generated by extruding arms from the faces of Platonic solids, with the number of arms n_{b} taking values in {4,6,8,12,20}. Assemblies of these polypods adhere to established flow initiation laws. Interestingly, the onset angle initially decreases with increasing n_{b} before slightly rising for larger values. Conversely, the maximum angle marking the transition from dense to collisional flow exhibits the opposite trend. As a result, the angular range supporting dense flow widens with increasing n_{b}. In the steady dense flow regime, we analyze the stress, packing fraction, velocity, and connectivity profiles of the assemblies. Away from the boundaries, the granular material exhibits uniform packing fraction, inertial number, and coordination number within the bulk. In this region, the flow follows the classical μ(I) rheology. However, near the walls, a "dead zone" emerges, characterized by a localized increase in packing fraction and a sharp reduction in grain velocity. This results in a concave velocity profile over several grain diameters, leading to a breakdown of the μ(I) law. A detailed microstructural analysis reveals enhanced interlocking between particles near the walls compared to the bulk. To reconcile the differences between the flowing region and the dead zone, we adapt a recently proposed nonlocal approach, originally developed for rotating drum flows [Wang et al., Phys. Rev. Res. 6, 043310 (2024)2643-156410.1103/PhysRevResearch.6.043310], to the inclined plane geometry. This approach relies on a fluidity-based description governed by the local packing fraction. The resulting model, consistent with Bagnold scaling, successfully reproduces the full velocity profiles without requiring any fitting parameters.