Energy dissipation from particulate systems undergoing a single particle crushing event

The energy dissipation from particulate systems undergoing particle crushing is often assumed to scale solely with the increase in surface area, irrespective of the strain energy stored in the surrounding media. By analyzing idealized particulate systems undergoing a single particle crushing event, this assumption is questioned and proven invalid. Two analysis types are considered. One represents the particulate system as an idealized assembly and then represents particle contact forces as members belonging to a periodic lattice. The other treats the particulate system as an elastic continuum. Different sizes of two and three dimensional particulate systems are considered, as well as isotropic and anisotropic confining stress states. The overall dissipation is shown to depend strongly on the dimensionality of the system, the anisotropy of the confining stress state and the elastic properties of the system. The ratio between dissipation due to stored elastic energy redistribution from surrounding media and dissipation by fracture surface energy is calculated. The ratio is found to diminish with the increasing dimensionality of the system. It is also shown that this ratio is independent of the fracture surface energy of the material. The most relevant analysis of a three dimensional particulate system to accurately estimate this ratio seems to be a one dimensional analysis of the force chain containing the most heavily loaded particles.