Shear flow of angular grains: acoustic effects and non-monotonic 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 auto-acoustic compaction -- non-monotonic 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 (STZ) 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.Comment: 12 pages, 3 figure

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.Comment: 12 pages, 8 figure

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g. the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods

A new paradigm for simulating pulse-like ruptures: the pulse energy equation

We investigate the chaotic behaviour of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of events. We observe that, although the spatiotemporal evolution of the amplitude of a slip pulse in a single event is surprisingly complex, the geometric description of the pulses is simple and self-similar with respect to the size of the pulse. This observation allows us to write an energy balance equation that describes the evolution of the pulse as it propagates through the known pre-stress. The equation predicts the evolution of individual ruptures and reduces the computational time dramatically. The long-time solution of the equation reveals its multiscale nature and its potential to match many of the long-time statistics of the original system, but with a much shorter computational time

Experimental Evidence of Amplitude-Dependent Surface Wave Dispersion via Nonlinear Contact Resonances

In this letter, we provide an experimental demonstration of amplitude-dependent dispersion tuning of surface acoustic waves interacting with nonlinear resonators. Leveraging the similarity between the dispersion properties of plate edge waves and surface waves propagating in a semi-infinite medium, we use a setup consisting of a plate with a periodic arrangement of bead-magnet resonators along one of its edges. Nonlinear contact between the ferromagnetic beads and magnets is exploited to realize nonlinear local resonance effects. First, we experimentally demonstrate the nonlinear softening nature and amplitude-dependent dynamics of a single bead-magnet resonator on both rigid and compliant substrates. Next, the dispersion properties of the system in the linear regime are investigated. Finally, we demonstrate how the interplay of nonlinear local resonances with plate edge waves gives rise to amplitude-dependent dispersion properties. The findings will inform the design of more versatile surface acoustic wave devices that can passively adapt to loading conditions.Comment: 6 pages, 5 figures, 2 table