Meso-scale signatures of inertial transitions in granular materials

Granular materials have a complex collective behavior based on simple interactions between grains. The global behavior stems from dynamic rearrangements in the micro-structure. The local increase (resp. decrease) of the density generates jamming (resp. unjamming). In this paper, instabilities in the form of localized bursts of kinetic energy are studied at both the micro-scale (i.e. grain scale) and meso-scale (i.e. cluster scale). The bursts are defined from the variation of kinetic energy. The meso-domains (grain loops in 2D) are built from the tessellation of the medium. We analyze the gain and loss of meso-structures during a localized burst. Surprisingly, micro-structural reorganizations are able to keep the overall statistical equilibrium constant. The introduction of strain-like and stress-like quantities at the mesoscopic scale makes it possible to propose an expression that can be assimilated to mesoscopic second-order work. At this intermediate scale, the negative values of the second-order work are correlated to the appearance of bursts of kinetic energy, which stands for a meso-scale counterpart of Hill’s macroscopic criterion of mechanical instability.