# Browsing by Subject "Granular matter"

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Item Open Access An experimental study of the jamming phase diagram for two-dimensional granular materials.(2020) Zhao, YiqiuWhat affects the transition of a collection of grains from flowing to a rigid packing? Previous efforts towards answering this important question have led to various versions of ``jamming’’ phase diagrams, which specify conditions under which a granular material behaves like solid, i.e., in a jammed phase. In this dissertation, we report two sets of experiments to study the influence of particle shape and of the form of the applied shear strain on the jamming phase diagram of slowly deformed frictional granular materials. We use 2d photoelastic particles to measure the overall pressure of the system and various physical quantities that characterize the contact network such as the averaged number of contacts per particle.

In the first set of experiments, we systematically compare the mechanical and geometrical properties of uniaxially compressed granular materials consisting of particles with shapes of either regular pentagon or disk. The compression is applied quasi-statically and induces a density-driven jamming transition. We find that pentagons and disks jam at similar packing fraction. At the onset of jamming, disks have contact numbers consistent with predictions from an ideal constraint counting argument. However, this argument fails to predict the right contact number for pentagons. We also find that both jammed pentagons and disks show the Gamma distribution of the Voronoi cell area with the same parameters. Moreover, jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. Finally, we report observations that for jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.

In the second set of experiments, we use a novel multi-ring Couette shear apparatus that we developed to eliminate shear banding which unavoidably appears in conventional Couette shear experiments. A shear band is a narrow region where a lot of rearrangements of particles occur. The shear band usually has a much smaller packing fraction than the rest of the system. We map out a jamming phase diagram experimentally, and for the first time perform a systematic direct test of the mechanical responses of the jammed states created by shearing under reverse shear. We find a clear distinction between fragile states and shear-jammed states: the latter do not collapse under reverse shear. The yield stress curve is also mapped out, which marks the stress needed for the shear-jammed states to enter a steady regime where many plastic rearrangements of particles happen and the overall stress fluctuates around a constant. Interestingly, for large packing fraction, a shear band still develops when the system remains strongly jammed in the steady regime. We find that the cooperative motion of particles in this regime is highly heterogeneous and can be quantified by a dynamical susceptibility, which keeps growing as the packing fraction increases.

Our observations not only serve as important data to construct theories to explain the origin of rigidity in density-driven jamming and shear-induced jamming but also are relevant to many other key problems in the physics of granular matter from the stability of a jammed packing to the complex dynamics of dense granular flows.

Item Open Access Crackling Noise in a Granular Stick-Slip Experiment(2019) Abed Zadeh, AghilIn a variety of physical systems, slow driving produces self-similar intermittent dynamics known as crackling noise. Barkhausen noise in ferromagnets, acoustic emission in fracture, seismic activities and failure in sheared granular media are few examples of crackling dynamics with substantial differences at the microscopic scale but similar universal laws. In many of the crackling systems, the origin of this universality and the connection between microscopic and macroscopic scales are subjects of current investigations.

We perform experiments to study the microscopic and macroscopic dynamics of a sheared granular medium. In our experiments, a constant speed stage pulls a slider with a loading spring across a 2D granular medium. We measure the pulling force on the spring, and image the medium to extract the local stress and particle displacement. Using novel signal and image analysis methods, we identify fast energy dissipating events, i.e.\ avalanches, and investigate their statistics and dynamics.

The pulling force exhibits crackling dynamics for low driving rates with intermittent slip avalanches. The energy loss in the spring has a power-law distribution with an exponent that strongly depends on the driving rate and is different from $-1.5$ predicted by several models. In our experiments for low driving rate, we find a slip rate power-spectrum of form $\mathcal{P}_v(\omega) \sim \frac{\omega^2}{1+\omega^{2.4}}$, a power-law distribution of the slip rate $P(v) \sim v^{-2.9}$, and average temporal profile of the slider motion (avalanche shape) of form $\mathcal{P}_D(u)=[u(1-u)]^{1.09}$. These findings are different from several theoretical and numerical studies \citep{dahmen2011simple, colaiori2008exactly, Laurson13_natcom}.

Avalanche temporal correlation is also investigated using certain conditional probabilities. At low driving rates, we observe uncorrelated order of the avalanches in terms of Omori-Utsu and B\r{a}th laws and temporal correlation in terms of the waiting time law. At higher driving rates, where the sequence of slip avalanches shows strong periodicity, we observe scaling laws and asymmetrical avalanche shapes that are clearly distinguishable from those in the crackling regime. We provide a novel dynamic phase diagram of granular matter as a function of driving rate and stiffness and characterize the crackling to periodic transition. We also find intermittent fluctuations in internal stress both in the crackling and the periodic regime.

Finally, we observe a narrow shear band with most of particle displacements, but stress fluctuations all over the medium. We identify the spatio-temporal connected components of local stress drops, which we call local avalanches. We find power-law distributions of the local avalanches with an exponent of $-1.7 \pm 0.1$, different from spring energy avalanche distribution with an exponent of $-0.41 \pm 0.05$ for the same experiments.

Our study constrains theoretical frameworks for granular dynamics and crackling noise in sheared granular media. Moreover, it may be relevant for characterizing the role of granular matter in fault gouges during seismic events.