  A bonded particle model is used to explore how variations in the material
properties of brittle, isotropic solids affect critical behavior in
fragmentation. To control material properties, a new model is proposed which
includes breakable two- and three-body particle interactions to calibrate
elastic moduli and mode I and II fracture toughnesses. In the quasistatic
limit, fragmentation leads to a power-law distribution of grain sizes which is
truncated at a maximum grain mass that grows as a non-trivial power of system
size. In the high-rate limit, truncation occurs at a mass that decreases as a
power of increasing rate. A scaling description is used to characterize this
behavior by collapsing the mean squared grain mass across rates and system
sizes. Consistent scaling persists across all material properties studied
although there are differences in the evolution of grain size distributions
with strain as the initial number of grains at fracture and their subsequent
rate of production depend on Poisson's ratio. This evolving granular structure
is found to induce a unique rheology where the ratio of the shear stress to
pressure, an internal friction coefficient, decays approximately as the
logarithm of increasing strain rate. The stress ratio also decreases at all
rates with increasing strain as fragmentation progresses.
