Ahmed Elbanna

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.

A two‐scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity

We develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone (STZ) theory, a statistical thermodynamic theory, to describe irreversible macroscopic plastic deformations due to local rearrangements of the gouge particles. We track the temperature evolution at the grain contacts using a one dimensional heat diffusion equation. At low temperatures, the strength of the asperities is limited by the flow strength, as predicted by dislocation creep models. At high temperatures, some of the constituents of the grains may melt leading to the degradation of the asperity strength. Our model predicts a logarithmic rate dependence of the steady state shear stress in the quasi-static regime. In the dense flow regime the frictional strength decreases rapidly with increasing slip rate due to the effect of thermal softening at the granular interfaces. The transient response following a step in strain rate includes a direct effect and a following evolution effect, both of which depend on the magnitude and direction of the velocity step. In addition to frictional heat, the energy budget includes an additional energy sink representing the fraction of external work consumed in increasing local disorder. The model links low-speed and high-speed frictional response of gouge layers, and provides an essential ingredient for multiscale modeling of earthquake ruptures with enhanced coseismic weakening.

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.

Crack propagation in bone on the scale of mineralized collagen fibrils: role of polymers with sacrificial bonds and hidden length

Sacrificial bonds and hidden length (SBHL) in structural molecules provide a mechanism for energy dissipation at the nanoscale. It is hypothesized that their presence leads to greater fracture toughness than what is observed in materials without such features. Here, we investigate this hypothesis using a simplified model of a mineralized collagen fibril sliding on a polymeric interface with SBHL systems. A 1D coarse-grained nonlinear spring-mass system is used to model the fibril. Rate-and-displacement constitutive equations are used to describe the mechanical properties of the polymeric system. The model quantifies how the interface toughness increases as a function of polymer density and number of sacrificial bonds. Other characteristics of the SBHL system, such as the length of hidden loops and the strength of the bonds, are found to influence the results. The model also gives insight into the variations in the mechanical behavior in response to physiological changes, such as the degree of mineralization of the collagen fibril and polymer density in the interfibrillar matrix. The model results provide constraints relevant for bio-mimetic material design and multiscale modeling of fracture in human bone.

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.

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.

Dynamics of Polymer Molecules with Sacrificial Bond and Hidden Length Systems: Towards a Physically-Based Mesoscopic Constitutive Law

We investigate the entropic force-elongation behavior of a polymer chain in the presence of the sacrificial bond and hidden length (SBHL) system observed experimentally in many biomaterials. We show that in most cases the SBHL system leads to a significant increase in toughness. However, the presence of a large number of bonds or relatively strong bonds in the SBHL system can reduce the net gain in toughness. We also incorporate the polymer model into a network of polymers with random properties (e.g., contour length, number and strength of sacrificial bonds, length of hidden loops). This allows us to derive a physically-based mesoscopic force-displacement law that governs the collective behavior.

Modulating Elastic Band Gap Structure in Layered Soft Composites Using Sacrificial Interfaces

A wide range of engineered and natural composites exhibit a layered architecture whereby individual building blocks are assembled layer by layer using cohesive interfaces. We present a novel mechanism for evolving acoustic band gap structure in a model system of these composites through patterning the microstructure in a way that triggers nonplanar interfacial deformations between the layers as they are stretched. Through the controlled deformation and growth of interlayer channels under macroscopic tension, we observe the emergence of multiple wide band gaps due to Bragg diffraction and local resonance. We describe these phenomena in details for three example microstructures and discuss the implications of our approach for harnessing controlled deformation in modulating band gap properties of composite materials. [DOI: 10.1115/1.4034537]

Localization and instability in sheared granular materials: role of friction and vibration

Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies, and variability under different loading conditions have not been fully explored. Here we use a nonequilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as the presence and absence of acoustic vibrations. Our results suggest that at low and intermediate strain rates, persistent shear bands develop only in the absence of vibrations. Vibrations tend to fluidize the granular network and delocalize slip at these rates. Stick-slip is observed only for frictional grains, and it is confined to the shear band. At high strain rates, stick-slip disappears and the different systems exhibit similar stress-slip response. Changing the vibration intensity, duration or time of application alters the system response and may cause long-lasting rheological changes. We analyze these observations in terms of possible transitions between rate strengthening and rate weakening response facilitated by a competition between shear-induced dilation and vibration-induced compaction. We discuss the implications of our results on dynamic triggering, quiescence, and strength evolution in gouge-filled fault zones.