We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume V replaces the internal energy U as a function of entropy S in conventional statistical mechanics. In place of the effective temperature, the compactivity X=∂V/∂S characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg, and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.

Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features by providing a molecular-scale mechanism for energy dissipation. One example is in the polymeric glue connection between collagen fibrils in animal bone. In this paper we propose a simple kinetic model that describes the breakage of sacrificial bonds and the release of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation. This enables us to predict the mechanical behavior of a quasi-one-dimensional ensemble of polymers at different stretching rates. We find that both the rupture peak heights and maximum stretching distance increase with the stretching rate. In addition, our theory naturally permits the possibility of self-healing in such biological structures.

We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.

Naturally occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of autoacoustic compaction-nonmonotonic variation of shear band volume with shear rate in angular particles-recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions and propose additional experiments that provide stringent tests on the new theoretical elements.

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 = ∂V /∂SC, where V and SC 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.