Role of convexity in the morphology of granular packings of rod-like polylobed particles

The morphology of granular packings (GPs) is strongly influenced by particle shape, yet the role of non-convexity remains poorly understood. In this work, we use the Discrete Element Method (DEM) to investigate gravity-driven GPs of rod-like non-convex particles, including cylinders, trilobes, and quadrilobes, over a prescribed shape parameter space. A two-stage deposition protocol is employed to generate monodisperse packings while reducing sensitivity to insertion conditions and improving reproducibility. We show that porosity is governed primarily by particle sphericity, exhibiting a negative linear correlation within the parameter space considered here, whereas convexity alone is not a comparably effective descriptor. In contrast, the mean coordination number shows no simple correlation with the reduced shape descriptors, indicating that particle connectivity depends on detailed geometric features and on the modified stability conditions associated with non-convex contacts. At the microstructural level, particle orientation distributions vary systematically with both aspect ratio and convexity, and the mean orientation angle is strongly correlated with the ratio of convexity to aspect ratio. Motivated by this observation, we develop a granular orientation model based on a mean-field argument, which provides an analytic framework for predicting both the mean orientation and the corresponding orientation distribution. In addition, the anisotropies of the orientation fabric tensor and the branch-vector fabric tensor both exhibit systematic shape dependence, although the branch-vector anisotropy remains more sensitive to local geometric details. Overall, these results clarify the distinct roles of sphericity and convexity in non-convex granular packings: porosity is controlled mainly by sphericity, whereas convexity has a stronger influence on orientation, fabric anisotropy, and contact-network organization, while also introducing stability constraints that distinguish non-convex packings from their convex counterparts.