Shock Compaction of Brittle Granular Media: Comminution Particle Size Statistics and the Localization of Thermal and Mechanical Dissipation

A material response model is proposed that addresses the compaction of brittle granular media in the shock-wave environment. The model bridges deficiencies inherent to continuum compaction models on one hand and computational meso models on the other. Central to the model is assessment of the evolving particle size distribution as compaction comminution ensues. This aspect of the model relies on an extended history of crush and comminution of brittle solids and the bounded scale invariant fracture and resulting fractal character of the emerging particulate. Statistical features of the compaction process are inherent to the model and through this formulation the dynamics of energy localization emerge naturally. The model intentionally spans length scales from the mesoscopic to the continuum. Application results in transient local temperature intensities and persistence concurrent with and subsequent to the Hugoniot state shock compaction of the granular solids. Calculations address experimental shock compaction data for granular quartz sand and for nonreacting granular HMX.