Charles K. C. Lieou

Stick-slip instabilities in sheared granular flow: The role of friction and acoustic vibrations

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.

Shear flow of angular grains: Acoustic effects and nonmonotonic rate dependence of volume

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.

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

We describe the shear flow of a disordered granular material in the presence of grain fracture using the shear-transformation-zone theory of amorphous plasticity adapted to systems with a hard-core interparticle 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 / ∂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.

Sacrificial bonds and hidden length in biomaterials: a kinetic constitutive description of strength and toughness in bone.

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 Bells 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.

Simulating stick‐slip failure in a sheared granular layer using a physics‐based constitutive model

We model laboratory earthquakes in a biaxial shear apparatus using the Shear-Transformation-Zone (STZ) theory of dense granular flow. The theory is based on the observation that slip events in a granular layer are attributed to grain rearrangement at soft spots called STZs, which can be characterized according to principles of statistical physics. We model lab data on granular shear using STZ theory and document direct connections between the STZ approach and rate-and-state friction. We discuss the stability transition from stable shear to stick-slip failure and show that stick-slip is predicted by STZ when the applied shear load exceeds a threshold value that is modulated by elastic stiffness and frictional rheology. We also show that STZ theory mimics fault zone dilation during the stick phase, consistent with lab observations.

Dynamic friction in sheared fault gouge: Implications of acoustic vibration on triggering and slow slip

Friction and deformation in granular fault gouge are among various dynamic interactions associated with seismic phenomena that have important implications for slip mechanisms on earthquake faults. To this end, we propose a mechanistic model of granular fault gouge subject to acoustic vibrations and shear deformation. The grain-scale dynamics is described by the Shear-Transformation-Zone theory of granular flow, which accounts for irreversible plastic deformation in terms of flow defects whose density is governed by an effective temperature. Our model accounts for stick-slip instabilities observed at seismic slip rates. In addition, as the vibration intensity increases, we observe an increase in the temporal advancement of large slip events, followed by a plateau and gradual decrease. Furthermore, slip becomes progressively slower upon increasing the vibration intensity. The results shed important light on the physical mechanisms of earthquake triggering and slow slip and provide essential elements for the multiscale modeling of earthquake ruptures. In particular, the results suggest that slow slip may be triggered by tremors.

Slow Dynamics and Strength Recovery in Unconsolidated Granular Earth Materials: A Mechanistic Theory

Rock materials often display long-time relaxation, commonly termed aging or “slow dynamics”, after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the Shear-Transformation-Zone (STZ) theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains, and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log-linear recovery of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady-state behavior at long times. We demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones.

Dynamic recrystallization in adiabatic shear banding: Effective-temperature model and comparison to experiments in ultrafine-grained titanium

Abstract Dynamic recrystallization (DRX) is often observed in conjunction with adiabatic shear banding (ASB) in polycrystalline materials. The recrystallized nanograins in the shear band have few dislocations compared to the material outside of the shear band. In this paper, we reformulate the recently-developed Langer-Bouchbinder-Lookman (LBL) continuum theory of polycrystalline plasticity and include the creation of grain boundaries. While the shear-banding instability emerges because thermal heating is faster than heat dissipation, recrystallization is interpreted as an entropic effect arising from the competition between dislocation creation and grain boundary formation. We show that our theory closely matches recent results in sheared ultrafine-grained titanium. The theory thus provides a thermodynamically consistent way to systematically describe the formation of shear bands and recrystallized grains therein.

Nonlinear softening of unconsolidated granular earth materials

Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones (STZs)—clusters of grains that are loose and susceptible to contact changes and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads, and demonstrate that the theory predicts nonlinear resonance shifts and reduction of the P-wave modulus, in agreement with experiments. The theory thus offers insights on the nature of the critical state prior to failure on earthquake faults.