Browsing by Author "Behringer, Robert P"

In 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.

Flow in a hopper is both a fertile testing ground for understanding fundamental granular flow rheology and industrially highly relevant. Despite increasing research efforts in this area, a comprehensive physical theory is still lacking for both jamming and flow of granular materials in a hopper. In this work, I have designed a two dimensional (2D) hopper experiment using photoelastic particles ( particles' shape: disk or ellipse ), with the goal to build a bridge between macroscopic phenomenon of hopper flow and microscopic particle-scale dynamics. Through synchronized data of particle tracking and stress distributions in particles, I have shown differences between my data of the time-averaged velocity/stress profile of 2D hopper flow with previous theoretical predictions. I have also demonstrated the importance of a mechanical stable arch near the opening on controlling hopper flow rheology and suggested a heuristic phase diagram for the hopper flow/jamming transition. Another part of this thesis work is focused on studying the impact of particle shape of particles on hopper flow. By comparing particle-tracking and photoelastic data for ellipses and disks at the appropriate length scale, I have demonstrated an important role for the rotational freedom of elliptical particles in controlling flow rheology through particle tracking and stress analysis. This work has been supported by International Fine Particle Research Institute (IFPRI) .

Granular impact, where a foreign object strikes a granular material like sand, is common in nature and industry. Due to experimental difficulties in obtaining sufficiently fast data at the scale of a single grain, a description of this process which connects to physics at the grain-scale is lacking. In this thesis, I will present data from a series of two-dimensional granular impact experiments. By cutting each grain out of a photoelastic material and using a very fast camera, we obtain data on the intruder trajectory, as well as the particle flow and force response of the granular material. Past experiments have shown that the decelerating force on an intruder moving through a granular medium is often well captured by a force law which is dominated by a velocity-squared drag force. Using the intruder trajectories, as well as the flow and force response of the granular material, I will demonstrate that, while these force laws describe the intruder trajectories on slow time scales, the instantaneous force on the intruder is highly fluctuating in space and time. I will particularly focus on the velocity-squared drag force, showing that it arises from random, locally normal collisions with chain-like clusters of particles which send energy and momentum away into the granular material. In this regime, the particles and intruder reach a kind of adiabatic steady state, where the particle motion scales linearly with the intruder speed. However, for impact velocities which are fast compared to the rate of momentum transfer within the granular material, the system response qualitatively changes, behaving like an elastic solid with a shock-like response at impact.

Granular materials are hard to understand due to their discrete and a-thermal nature. The mechanical response of a granular packing under external deformations, although highly relevant in industrial processes, is still poorly understood, partly due to the difficulty to generate a homogeneous granular packing. In this thesis, I present a novel shear apparatus that avoids the formation of inhomogeneities known as shear bands. This apparatus provides quasi-static, quasi-uniform simple shear deformation to a 2D model granular system under fixed packing fraction &phi. The position, orientation and forces for each particle are obtained at each shear step, using the photo-elastic technique. This model granular system exhibits coupling between the shear strain, &gamma, and the pressure, P, which we characterize by the `Reynolds pressure', and a `Reynolds coefficient', R(&phi) = (&partial^2 P/ &partial &gamma^2)/2. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle n: &Delta P &simeq - &beta ln(n/n_0). &beta depends only on the shear cycle amplitude, suggesting an activated process where &beta plays a temperature-like role. In addition, particles in the sheared system are diffusive. The translational and rotational diffusion, observed under stroboscopic view during cyclic shear, are observed to depend on the packing fraction but not on the stress states of the system. Finally, the structure of the force network, and how that connects to the mechanical behavior, is also briefly discussed.

Granular materials under shear are common in nature and industry. Previous results show changes of system behaviors when friction is added and particle shapes are varied, e.g. shear jamming for frictional grains. Understanding these changes depends on characterization of deformation induced by shear. However, previous studies mainly focus on yielding processes and are locally symmetric, e.g. shear transformation zones (STZ's). Besides, the grain scale explanation is lacking. In this thesis, I study the shear response of granular materials with various particle properties in two dimension, utilizing a novel setup that suppresses shear banding. Particles made of photoelastic materials can reveal inter-particle contact forces and be customized to have different friction and shapes. I propose novel minimum structures, trimers and branches, that account for shear jamming. These structures are locally asymmetric, which is contrary to STZ's. Systems with three different friction coefficients $\mu$ are studied: $0.15, 0.7$ and one higher than $1.7$. Shear jamming is still observed for the lowest $\mu$ studied, with the lowest value of packing fraction $\phi$ for shear jamming, $\phi_S$, increasing as $\mu$ decreases. Furthermore, these systems for all $\mu$ show abnormal diffusion under cyclic shear. The diffusion exponents show transitions as $\phi$ increases, with a $\mu$-dependent onset $\phi$. This behavior is consistent with the non-affine displacements under linear shear. In addition, systems composed of ellipses exhibit novel structural and mechanical responses different from disks, e.g., nematic ordering and local density variability under shear.

In this work, we have focused on the jamming properties of systems composed of semi-2D elliptical shaped particles. In order to study these systems, we have performed three types of experiments: Couette shear, biaxial isotropic compression, and biaxial pure shear. In each experimental scheme, we take data for both systems of ellipses an bi-disperse disks, in order to probe the effect of broken spherical symmetry at the particle scale, on the global behavior. We use two synchronized cameras to capture the flow of particles and the local stress at the same time.

In Couette experiments, we study the rheological properties, as well as the stress fluctuations for very large strains (up to 20 revolutions of the inner wheel). The system is sheared for densities below the isotropic jamming point (point J). From these studies we learn that over a small range of packing fractions, ($0.85 \leq \phi \leq 0.86$),

systems of ellipses demonstrate exceptionally slow dynamical evolution when they are sheared. For

fixed density, and starting from an essentially unstressed state, the application of shear strain leads to

first a growth of average particle displacements in the system through a Reynolds dilatancy effect,

and then for very large strains, a steady decrease in particle displacements. In an intermediate

range of shear strains, the system exists in effectively meta-stable states for a very long time

before relaxing to an unjammed state, in which the flow of particles stops completely, and the

stress fluctuations drop to zero. The strain scale for this relaxation depends on the global packing

fraction. We characterize this slow dynamics by measuring the evolution of mean velocity, density,

and orientational order throughout the experiments. In a similar set of experiments performed on

disks, slow relaxation was observed as well. However, the increasing average displacement build-up

before relaxation, which was observed in ellipses, did not occur for disks. This suggests that the

slow relaxation towards an unjammed state in ellipses is associated with the possibility of small and

slow changes in their orientations, which then allow a more efficient packing.

In order to study the stress fluctuations, we implement photoelastic properties of the particles. We are able to track the $g^{2}$ (a measure of local stress) of each particle throughout the entire experiment.

Unlike disks, the power spectra of $g^2$, $P(\omega)$, is not rate invariant for ellipses. In other words, all curves of $R P(\omega)$ vs. $\omega / R$ (where $R$ is the shear rate) with different values of $R$, collapse to a single curve for disks, but not for ellipses.

The rate invariance of spectra was previously studied for sheared spherical glass beads and semi-2D pentagonal particles. This is the first experimental work in which the fluctuations of granular systems composed of elongated particles is addressed.

We have also studied the formation and destruction of stress avalanches during Couette shear in both systems of disks and ellipses. In particular, we introduce measures which characterize the size and shape of stress avalanches. Analysis of these measures shows that the build-up and release of stress in both systems of disks and ellipses have similar distributions which indicates that the deformation of particles in a Couette cell does not resemble stick-slip behavior. We also find that the build-up and release of stress is faster is larger avalanches.

Cyclic isotropic compression is performed on semi-2D systems of bi-disperse disks and identical ellipses with aspect ratio 2, which are composed of photoelastic particles. In each compression cycle, the system is compressed with a total strain of $1.6\%$ and then expanded to the initial state. After completion of each half cycle, the system is allowed to relax, then imaged by two synchronized cameras. The packing fraction, $\phi$, of compressed states are chosen above the isotopic jamming point (point J). In both systems of disks and ellipses, we observed relaxation of global stress over long compression cycles. We find that the global stress drops with a power law over time ($\sigma \sim C t^{-A}$). The exponent of decay, $A$, drops linearly with increasing $\phi$, and hits zero at $\phi \simeq 0.89$ for disks, and $\phi \simeq 0.93$ for ellipses. Above these packing fractions, the system is stable with respect to its global stress.

In order to understand the origin of this slow stress dilation, we have studied the structural changes of the system, including Falk-Langer measures of affine and non-affine deformations, as well as average contact per particle.