Geometrical properties of rigid frictionless granular packings as a function of particle size and shape
AbstractThree-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedra) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analog of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E 84, 041309 (2011)PLEEE81539-375510.1103/PhysRevE.84.041309]. This seeming discrepancy between experimental and numerical results is believed to result from difficulties in overcoming inter particle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches 30%. Contrarily, substituting up to 50% of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role in packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond 30% to 50% of flat or flat-elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat-elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.