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We describe the shear flow of a disordered granular material in the presenceof grain fracture using the shear-transformation-zone (STZ) theory of amorphousplasticity adapted to systems with a hard-core inter-particle interaction. Tothis end, we develop the equations of motion for this system within astatistical-thermodynamic framework analogous to that used in the analysis ofmolecular glasses. For hard-core systems, the amount of internal,configurational disorder is characterized by the compactivity $X = \partial V /\partial S_C$, where $V$ and $S_C$ are respectively the volume andconfigurational entropy. Grain breakage is described by a constitutive equationfor the temporal evolution of a characteristic grain size $a$, based onfracture mechanics. We show that grain breakage is a weakening mechanism,significantly lowering the flow stress at large strain rates, if the materialis rate-strengthening in character. We show in addition that if the granularmaterial is sufficiently aged, spatial inhomogeneity in configurationaldisorder results in strain localization. We also show that grain splittingcontributes significantly to comminution at small shear strains, while grainabrasion becomes dominant at large shear displacements.

Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization