Uncovering the secrets to relieving stress: discrete element analysis of force chains in particulate media

Abstract

The traditional analyses for structures that are either built upon (for example, foundations), or are used for storage and handling of particulate solids (for example, bins, silos, hoppers, and bunkers) cannot account for important processes originating in the evolution of microscale particle kinematics and kinetics. Until recently, the complexity of these processes could only be perceived through macroscale experiments, but information derived from these experiments lacks the necessary level of detail that is needed for sound theoretical development. Limited information on the evolution of microstructural properties in deforming particulate solids emerged through ingenious experiments using photoelastic techniques. These techniques revealed the complex microstructural fabric and force propagation, the evolution of which governs what is observed as the constitutive response of the material. More recently, numerical simulations using the discrete element method have also proven to be powerful tools --- effectively providing a virtual laboratory for studying microstructural evolution. We use the discrete element technique to examine the propagation of forces within a particulate solid that is subject to an indenting rigid flat punch on its surface. Particular attention is given to the formation, evolution and collapse of ``force chains'' (that is, quasi-linear chains of load-bearing particles). These force chains are surrounded by a weak network of particles that, despite carrying only a small amount of the load, provides the necessary stability for such chains to persist. A mathematical framework for the characterisation of these chains is used to investigate the evolution of the force chain network with indentation, with a focus on microstructure, force chain lengths, and length distributions. Finally, the first steps toward establishing correlations across multiple length scales are made by linking the macroscopic load-penetration response to the underlying evolution of contact forces and force chains.