# Browsing by Subject "Granular materials"

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Item Open Access Flow and Jamming of Granular Materials in a Two-dimensional Hopper(2012) Tang, JunyaoFlow 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) .

Item Open Access Mesoscale Forces and Grain Motion in Granular Media Exhibiting Stick-Slip Dynamics: Effects of Friction and Grain Shape(2021) Kozlowski, Ryan HenryAn important challenge in the physics of granular materials is understanding how the properties of single grains, such as grain shape and friction, influence the mechanical strength and dynamical response of the bulk granular material. While spherical grains are often used to study granular materials in experiments and simulations, the interactions among grains, and in many cases the flow and stability of granular packings, change when grain shape is modified. In this dissertation, we explore the influence of friction and grain shape on grain-scale dynamics, properties of mesoscale force chains, and macroscopic stick-slip dynamics of granular materials through novel experiments. In one set of experiments, an intruder is pushed by a spring through an annular cell filled with a quasi-2D monolayer of photoelastic grains that either contact a glass substrate or float on water. We characterize the effects of basal friction between the substrate and grains, intergrain friction, intruder size, and grain shape on the dynamics of the intruder, the flow of grains during slip events, and spatial distribution of stresses within the granular material in stable sticking periods. In another set of experiments, a slider is pulled by a spring across a quasi-2D monolayer of gravity-packed grains set between two glass plates. We observe the influence of grain angularity on statistical properties characterizing the stick-slip dynamics of the slider as well as grain-scale dynamics and stresses.

We first compare the dynamics of the intruder driven through packings of disks that either contact the glass base -- having basal friction -- or float on water -- having no basal friction. At high packing fractions, we find that the intruder exhibits stick-slip dynamics when basal friction acts on the grains, but the intruder instead flows freely through the granular material, with only occasional sticking periods (called intermittent flow or clogging-like dynamics, quantified by the average time between sticking periods), when basal friction is removed. We also observe when basal friction is present that the intruder's dynamics transition from stick-slip to intermittent flow with decreasing packing fraction; this transition occurs at a higher packing fraction with lower intergrain friction. Lastly, in simulations that model this experimental system, we vary static and dynamic basal friction coefficients and show that dynamic basal friction, rather than static basal friction, determines whether the intruder exhibits stick-slip or intermittent flow at high packing fractions.

We next vary the size of the intruder and, at several different packing fractions for each intruder size, compute statistics of the waiting time between sticking periods, duration of sticking periods, energy released in slip events, and force of grains acting on the intruder. We show that each statistical measure for all intruder sizes collapses to a single curve when packing fraction is rescaled by the packing fraction below which the intruder carves out a completely open channel in the granular material. With a geometrical model, we relate the packing fraction of open channel formation to a characteristic packing fraction of the material and the ratio of the intruder's diameter and the width of the annular cell, and we confirm the prediction of this model.

We thirdly compare the dynamics of the intruder and grains with packings of disks and pentagons. We observe that the packing of pentagons exerts comparable forces on the intruder as the packing of disks, though at significantly lower packing fractions. We also find from the average flow fields of grains during slip events that disks circulate around the intruder and rotate about their centers of mass significantly more than pentagons, which tend to flow forward from the intruder. Lastly, using photoelasticimetry, for the packing of disks we measure a significantly larger spatial extent of stresses around the annular cell, and a significantly larger fraction of events that feature back-bending force chains, compared with the packing of pentagons.

In the last set of experiments, we vary grain angularity of a vertical (gravity-packed) granular material sheared by a slider. We observe that the average shearing force required to initiate slip events increases with angularity. As a result, sticking periods last longer and slip events release more energy in packings with more angular grains. We also observe differences in the flow fields of disks and angular grains in slip events; disks tend to form a pile in front of the slider, while other grains do not. Moreover angular grains are able to form local column-like structures at the surface of the bed that prop up the slider during sticking periods, while disks do not. We lastly show that the depth of the shear band and the depth of stress fluctuations between sticking periods are unaffected by grain angularity.

Overall, these novel observations from each experiment demonstrate that friction and grain shape are important factors determining properties of macroscopic stick-slip dynamics of granular materials, stress transmission in stable granular materials, and grain-scale dynamics during slip events. Our observations also serve as motivation for more robust modeling and theoretical descriptions of granular stability and flow more generally by considering the influences of basal friction and changes in grain shape.

Item Open Access Nonlinear Dynamics and Network Properties in Granular Materials under Shear(2013) Ren, JieGranular 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.

Item Open Access Response of Granular Materials to Shear: Origins of Shear Jamming, Particle Dynamics, and Effects of Particle Properties(2018) Wang, DongGranular 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.

Item Open Access Shape Effects on Jamming of Granular Materials(2012) Farhadi, SomayehIn 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.