Mechanical characterisation and modelling of statistically representative granular materials subjected to impact loading

Granular materials are used in several industrial processes involving natural and man-made materials at a vast range of length scales, such as mining, extraction, and handling of rocks and sand, as well as in agricultural and pharmaceutical industry. They are also widely adopted in civil and military applications (e.g. earthquakes, penetration of projectiles, stress waves attenuation) because of their ability to dissipate energy and attenuate shock loading. However, despite the wide-spread use, the comprehension of their mechanical behaviour at high strain rates is still limited. The main aim of this research is to provide a better understanding of the mechanics of granular materials and to develop a combined experimental/numerical capability to characterise and simulate the effects of high velocity excitations on the boundaries of granular domains and the consequent motion and deformation at high rates of strain. The achievement of this goal requires the knowledge of both meso-structural properties (i.e. initial density, wetness and confinement conditions) and the effects of micro-scale parameters (i.e. grain sizes and shapes, grains microstructure) upon the behaviour of granular assemblies. For this reason, attention is initially focused on the development of novel algorithms capable of correctly representing real mesostructures of granular materials, and on the estimation of their Representative Volume Elements. Subsequently, high strain rate experiments are conducted for a comprehensive mechanical characterisation of different types of sand and to evaluate the effect of micro-scale phenomena and rate dependency on the mechanical response of granular materials subjected to impact loading. In particular, after having assessed the geometric characteristics of given granular media, modelling tools for the generation of numerical samples that are statistically representative of real granular materials are developed. Two new efficient algorithms for the geometrical packing of spheres, able to concurrently assign total number of particles and radii distributions, are proposed. Then, a novel Voronoi-based method is presented to model a wide range of particles shapes. The obtained polyhedral grains are proved to successfully reproduce the relevant microscopic features of many naturally occurring granular media. The statistically representative packings thus generated are then used in Discrete Element simulations, which are executed to help designing experiments for the characterisation of granular materials at the meso-scale and to establish the dimensions of the Representative Volume Element of the investigated sands to be used in large-scale laboratory tests and multiscale simulations. A comprehensive experimental campaign on both single grains and granular assemblies at meso-scale is executed to gain insight into the complex behaviour of granular materials subjected to high strain rates and to produce valuable data for future calibration and validation of rate dependent constitutive models. The adoption of ad-hoc sample sizes allowed for the achievement of an improved dynamic equilibrium condition and enhanced reproducibility of the results with respect to what existing in literature. Additionally, a deeper understanding of the role of particles fracture on the behaviour of granular materials is gained by exploiting a number of conventional (microscopy) and novel (sound measurements) experimental techniques for in-situ and post-mortem analysis of samples subjected to a wide spectrum of rates of deformation. Finally, once identified - through experiments - the central role of micro-scale phenomena (grains failure) on the mechanical response of sand, a new mass-conserving modelling methodology capable of capturing the grains comminution happening during dynamic loading of granular materials is introduced, thus extending the range of applicability of DEM to dynamic phenomena.