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

Abstract

The morphology of many naturally occurring and man-made materials at different length scales can be modelled using the packing of correspondingly shaped and sized particles. The mechanical behaviour of this vast category of materials -which includes granular media, particle reinforced materials and foams -depends strongly upon the shape and size distribution of the particles. This paper presents a method for the generation and packing of arbitrarily shaped polyhedral particles. The algorithm for the generation of the particles is based on the Voronoi tessellation technique, whilst the packing is performed using a geometrical approach, which guarantees the non-overlapping of the bodies without relying upon any, otherwise typically computationally expensive, contact detection and interaction algorithm. The introduction of three geometrical parameters allows to control the shape, size and spacial density of the polyhedral particles, which are used to build numerical models representative of densely packed granular assemblies, granular reinforced materials and closed-cell foams. 339properties of the structure. The same can be said about the modelling of pores in closed-cell foams, as demonstrated by [8].Several investigations [9][10][11] focused on the definition of numerical parameters to describe the shape (i.e. the external morphology) of single grains. Wadell [9] identified three independent properties of the shape to describe the morphology of the particles: form, roundness and surface texture. Each of those properties can be expressed by several parameters, as reported in the comprehensive review by Barrett [10]. 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. X-ray and neutron imaging), combined with surface mesh reconstruction software, can be used to generate accurate models of loose grains [14,15], whilst destructive techniques (e.g. serial sectioning) are usually adopted for particle reinforced materials and foams [16]. These methods require fairly complex post-processing that might lead to non-unique topologies, and are generally computationally expensive, which limits their application to quite small domains.The introduction of numerical approaches for the generation of representative geometries allows to overcome the limitations offered by the experimental methods described.Most of the approaches developed during the pas...

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