New 3D geometrical deposition methods for efficient packing of spheres based on tangency

Abstract

SUMMARYThe morphology of many natural and man-made materials at different length scales can be simulated using particle-packing methods. This paper presents two novel 3D geometrical collective deposition algorithms for packed assemblies with prescribed distribution of radii: the 'planar deposition' and the '3D-clew' method. The 'planar deposition' method mimics an orderly granular flow through a funnel by stacking up spirally ordinated planar assemblies of spheres capable of achieving the theoretical maximum for monodisperse aggregates. The '3D-clew' method, instead, mimics the winding of a clew of yarn, thus yielding densely packed 3D polydispersed assemblies in terms of void ratio of the aggregate. The morphologies of such geometrically generated assemblies, achieved at several orders of magnitude reduced computational cost, are comparable with those consolidated uni-directionally by means of discrete element method. In addition, significantly faster simulations of mechanical consolidation of granular media have been performed when relying upon the proposed geometrically generated assemblies as starting configurations.

A method for the generation of 3D representative models of granular based materials

“…Therefore, the grains have to be repositioned disorderly to be representative of the desired structures. This paper presents the possibility of adopting geometric algorithms, in particular the 3D clew method [13], to produce an initial packing of particles with complex polyhedral shapes by enclosing them into the BSs. The radius of the BSs is controlled by defining a scaling factor ( ) to arbitrarily increase the radius of the MBSs, thus providing full control on the volume fraction of the granular particles (or voids), allowing for the generation of representative models of the structures analysed.…”

“…This approach does not impose any preferential growth direction and concentration of voids in the domain (uniform deposition). A detailed description of the method, its implementation and examples are presented in [13]. Figure 6 shows how the BSs are assembled using the 3D clew method -thus generating a polydisperse agglomerate of spheres -and how the final packing of polyhedral bodies is obtained by inserting each grain in its corresponding BS.…”

“…Similarly, the shape of the grains has been proven to largely influence the behaviour of particlereinforced materials, affecting -among others -the mechanical [2], thermal [6] and electrical [7] and artificial materials. The so-generated particles are enclosed in bounding spheres (BSs), which are assembled using the 3D geometrical deposition approach for the dense packing of spheres developed by the authors [13].…”

“…These three properties can be catalogued according to the different scales with respect to particle size. The form is the first-order property that defines the proportions of the grain; the roundness is the second-order property that indicates the angularity of the corners; finally, the surface texture (third-order property) describes the roughness of the surfaces.Although the challenge of defining representative particle size distributions has been successfully addressed by numerous authors [12,13], the correct representation of the shape of the particles still presents some challenges.The use of experimental techniques to reproduce the topology of the structure can provide realistic models. Specifically, 3D scanner techniques (e.g.…”

“…Although the challenge of defining representative particle size distributions has been successfully addressed by numerous authors [12,13], the correct representation of the shape of the particles still presents some challenges.…”