  We describe the shear flow of a disordered granular material in the presence
of grain fracture using the shear-transformation-zone (STZ) theory of amorphous
plasticity adapted to systems with a hard-core inter-particle interaction. To
this end, we develop the equations of motion for this system within a
statistical-thermodynamic framework analogous to that used in the analysis of
molecular 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 and
configurational entropy. Grain breakage is described by a constitutive equation
for the temporal evolution of a characteristic grain size $a$, based on
fracture mechanics. We show that grain breakage is a weakening mechanism,
significantly lowering the flow stress at large strain rates, if the material
is rate-strengthening in character. We show in addition that if the granular
material is sufficiently aged, spatial inhomogeneity in configurational
disorder results in strain localization. We also show that grain splitting
contributes significantly to comminution at small shear strains, while grain
abrasion becomes dominant at large shear displacements.
