Effects of central symmetry and elongation on the dense disordered packings of entangled particles

Abstract

Geometric shape is an important factor that affects the packing and mechanical properties of granular material. In this paper, we use four families of assembled rods to model an entangled material in simulations. The particles are all non-convex and have the ability to interpenetrate. Together with elongation, central symmetry, which is attributed to the intersection location of the elementary rods, is also a main factor that produces varieties of particle shapes. With a certain total elongation, the dense disordered packing density is verified to be independent of the elongation distribution of the elementary rods. The specific shape hardly affects the packing densities. Therefore, the empirical formula to predict the packing density is extended to apply to all assembled rods with any elongation distribution. Different from the packing density, the shape disparity caused by central symmetry is found to significantly influence the contacts between neighboring particles. Due to more multipoint contacts contributing more constraints around the central particle, the centrally symmetric 3DX-shaped particles can more easily interpenetrate in the granular system. Moreover, the higher number of constraints contributed by neighboring contacts reflects the hyperstaticity of packings, which suggests mechanical stability for disordered packings of non-convex assembled rods.