The effect of evolving micro-structural length scale on the macroscopic constitutive behaviour of granular media

Abstract

Granular media are ubiquitous throughout the world and developing a comprehensive understanding of their behaviour is a pressing challenge. Of particular importance is accounting for the localisation of deformation into thin bands that feature intense grain crushing. This thesis develops a framework that predicts the formation of these bands and the grain size evolution, using experimental, theoretical and numerical approaches. Our experimental approach uses spatio-temporal plotting and Fourier analysis to extract information from photographs, allowing a sub-grain resolution of the velocity field. We investigate the effect of grain size polydispersity on the width of shear bands. Our theoretical approach develops a novel constitutive model that combines two existing formulations. We enrich Breakage Mechanics with the Cosserat continuum by an elastic upscaling that includes Cosserat state variables. This regularises Breakage Mechanics, allowing it to predict strain localisation phenomena such as shear bands, and adds physical fidelity to Cosserat models. Our numerical approach uses linear stability analysis and the finite element method to determine the conditions that result in strain localisation. The linear stability analysis gives the expected initial thickness and the initial post-localisation tendencies of the system. This information informs the finite element analysis, which is used to perform a rigorous post-localisation analysis. This thesis provides a framework which can be used to explore and further model the evolution of systems that experience strain localisation accompanied by intense grain crushing, ranging from standard laboratory tests to seismogenic faults.