Multiscale Analysis of the Effects of Changing Gravity on Stress Propagation in a Material Subject to an Indenting Rigid Flat Punch

The effects of changing gravity on force transmission within a particulate material that is subject to indentation on its surface by a frictionless rigid flat punch is examined. Particular attention is given to the development of the force chain network as indentation proceeds. As gravity decreased, or, as packing fraction increased, the spatial distribution of the force chain network changed from a dense, tangled network to one consisting of less tangled, longer chains. The distribution of chain lengths was found to be exponential. The magnitude of the resistance force experienced by the punch as it indents scaled with gravity, as did the magnitude of the fluctuations in the load-deflection relation. Using the force chain network, the origin of these fluctuations was examined. Consistent with experiments, the fluctuations in the load-deflection graphs were found to be due to the formation and collapse of force chains. The collapse of force chains was found to be correlated with the transition from solid-like behaviour to liquid-like behaviour of the material, that is, the transition regime at which dilatation and large particle rotations occur in the material surrounding the punch corners.