Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session Y45: Focus Session: Granular Materials and Continuum Descriptions of Discrete Media III |
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Sponsoring Units: GSNP GSOFT Chair: Ken Kamrin, Massachusetts Institute of Techology Room: 216AB |
Friday, March 6, 2015 8:00AM - 8:12AM |
Y45.00001: Shear jamming for highly strained granular materials Jonathan Bares, Robert Berhinger Bi et al. (Nature 2011) have shown that, if sheared, a granular material can jam even if its packing fraction ($\phi$) is lower than the critical isotropic jamming point $\phi_J$. They have introduced a new critical packing fraction value $\phi_S$ such that for $\phi_S<\phi<\phi_J$ the system jams if sheared. Nevertheless, the value of $\phi_S$ as a function of the shear profile or the strain necessary to observe jamming remain poorly understood because of the experimental complexity to access high strain without shear band. We present a novel 2D periodic shear apparatus made of 21 independent, aligned and mirrored glass rings. Each of ring can be moved independently which permits us to impose any desired shear profile. The circular geometry allows access to any strain value. The forces between grains are measured using reflective photoelasticity. This talk will present this novel apparatus and discuss inital results. [Preview Abstract] |
Friday, March 6, 2015 8:12AM - 8:24AM |
Y45.00002: Ergodicity in a model for earthquake fault systems undergoing hydraulic fracturing James Silva, Wiliam Klein, Harvey Gould, Nick Lubbers The frequency of large seismic events in regions with a large amount of hydraulic fracturing activity has been of great interest in recent media reports of earthquake events in Oklahoma. In this talk a model for earthquake fault systems undergoing hydraulic fracturing will be introduced. The question of how seismic failure events occur and how unique the individual systems are will be addressed. This will be done by presenting work on the statistics of events and ergodicity within this model. [Preview Abstract] |
Friday, March 6, 2015 8:24AM - 8:36AM |
Y45.00003: Continuum modeling of secondary rheology in slow granular flows David Henann, Daren Liu, Ken Kamrin Recent dense granular flow experiments have shown that shear deformation in one region of a granular medium fluidizes its entirety, including regions far from the sheared zone, effectively erasing the yield condition everywhere. This enables slow creep deformation to occur when an external force is applied to a probe in the nominally static regions of the material. The apparent change in rheology induced by far-away primary motion is termed the ``secondary rheology'' - a curious phenomenon that arises due to the cooperativity of slow granular flows. Recently, the new nonlocal granular fluidity (NGF) model was successfully used to predict a wide variety of steady granular flow fields. In this talk, we show that the NGF model is also capable of capturing secondary rheology. Specifically, we will demonstrate (i) the vanishing of the yield condition in the presence of primary flow, (ii) the rate-independent nature of secondary rheology for sufficiently slow primary flow rates, (iii) an exponential-type relationship between the force applied to the intruder and the consequent creep rate, and (iv) the anisotropy of secondary rheology, in which the observed phenomenology changes depending on whether the intruder is forced along with or counter to the primary flow. [Preview Abstract] |
Friday, March 6, 2015 8:36AM - 9:12AM |
Y45.00004: Fragmentation, Acoustic Effects, and Flash Heating in Sheared Granular Materials: Implications of Geophysical Processes and Physical Constraints for Dynamic Friction Invited Speaker: Jean Carlson Incomplete understanding of friction, deformation, and failure is a primary limiting factor in forecasting seismic hazards. We report recent progress on a physics-based framework for constitutive laws. Our methods are rooted in the underlying statistical thermodynamics of amorphous materials, and bridge the gap between microscopic dynamics, laboratory experiments, and dynamic rupture. We expand Shear-Transformation-Zone theory, describing frictional response of sheared gouge layers over a wide range of velocities and normal stresses, to account for geophysically relevant processes such as breakage and thermal heating, as well as grain shapes. We combine theoretical advances with quantitative fits to experimental data obtained within the fault and rock mechanics community. Fragmentation is described by a constitutive equation for grain size reduction involving the applied work rate and pressure, constrained by energy balance. We show that grain breakage is a potential weakening mechanism at high strain rates. It promotes strain localization and may explain long-term persistence of shear bands in natural faults. Shape effects are modeled by an orientational bias that describes grain interlocking and geometric frustration. We interpret inter-particle friction as an additional source of acoustic noise. We obtain quantitative agreement between experimental measurements and theoretical predictions for both internally generated acoustic noise and externally applied vibrations. Frictionally generated thermal heating is incorporated using a contact strength model that accounts for local increases in temperature at grain contacts during sliding. The magnitude of this effect depends on grain size and porosity of the granular layer. Our model predicts logarithmic rate dependence of steady state shear stress in the quasi-static regime. In the dense flow regime frictional strength decreases rapidly with increasing slip rate due to thermal softening at granular interfaces. The transient response following a step in strain rate includes a direct effect and subsequent evolution effect, both depending on the magnitude and direction of the velocity step. The resulting friction models are appropriate for dynamic rupture simulations that extrapolate results to geophysically relevant regimes that are beyond reach of laboratory experiments. Our work offers experimentalists and field workers insights for interpreting data, identifying features to target in future work, and estimating seismic hazards. [Preview Abstract] |
Friday, March 6, 2015 9:12AM - 9:24AM |
Y45.00005: Interaction of intruding objects within granular media using continuum modeling. Hesam Askari, Ken Kamrin The interaction of objects with granular media is very common in various aspects of our lives. Interestingly, such a broad problem is not easy to solve due to the complexity of the response of the granular materials to deformation and lack of understanding of the mechanics and physics of their deformation. Exclusively on the topic of the interaction with intruding objects, attempts have been made - mostly driven by experimental observation and validation - to describe this interaction using Resistive Force Theory (RFT), which works based on superposition rules. Understanding the origin of these empirical rules and delving deeper into the requirements on the validity of such hypotheses are crucial to understanding this theory. In an attempt to explain this theory, we hypothesize that the RFT is arising from the laws of continuum frictional plasticity. To demonstrate this we use the Finite Element Method to study the interaction of an intruder with a continuum granular media. We use a custom user-material definition in ABAQUS using a friction-based law for the flow rule as well as adjustments required to represent a discrete granular system in a continuum model. The findings of our model are in agreement with the experiments and numerical discrete element method results in the literature. These results are suggesting that the superposition rule can be obtained by the plasticity approach and the effects of the shape, size and depth of the object can be represented by a universal scaling law. [Preview Abstract] |
Friday, March 6, 2015 9:24AM - 9:36AM |
Y45.00006: Model-free test for nonlocal effects in jammed matter Brian Tighe, Karsten Baumgarten There is growing evidence that the mechanical response of materials close to the jamming transition is nonlocal, i.e. the deformation (rate) at one position is influenced by stresses at a distance. Nonlocal models successfully describe flow in a number of geometries where conventional local models fail not just quantitatively but qualitatively. Research to date has advanced by proposing a nonlocal model, which generally contains free parameters, and fitting its predictions to experimental or numerical data. This makes it difficult to distinguish the general effects of nonlocality from the details of a particular model. We take a different approach by introducing a model-free test for nonlocality. The test is easily implemented in computer simulations and provides a quantitative measure of the amplitude of nonlocal effects, without assuming a model for the nonlocal mechanics of the material. We demonstrate this method in several model systems, including soft spheres near jamming. [Preview Abstract] |
Friday, March 6, 2015 9:36AM - 9:48AM |
Y45.00007: ABSTRACT WITHDRAWN |
Friday, March 6, 2015 9:48AM - 10:00AM |
Y45.00008: Shear flow of angular grains: Acoustic effects and stick-slip instabilities Charles K. C. Lieou, Ahmed E. Elbanna, James S. Langer, Jean M. Carlson We propose a model for stick-slip instabilities in a sheared granular medium composed of frictional grains. We show that friction between particles is essential in producing stick-slip failure at inter-mediate shear rates, even if the material is rate-strengthening in character in the limit of large shear rates. In addition, externally generated acoustic vibrations promote stick-slip instabilities at low shear rates, but suppresses it at low confining pressure. We construct separate phase diagrams that indicate the parameter regimes for which stick-slip occurs, in the presence and absence of acoustic vibrations. These results connect the microscopic physics to macroscopic stress dynamics, elucidate the role of interparticle frictional interactions and acoustic vibrations on frictional dynamics, and provide important insight on the physical origin of earthquake rupture and seismic slip. Our findings show good agreement with laboratory experiments on simulated fault gouge. [Preview Abstract] |
Friday, March 6, 2015 10:00AM - 10:12AM |
Y45.00009: Spatio-temporal dynamics of brittle fracture in particle rafts Aryesh Mukherjee, Mahesh Bandi Brittle solids fracture at tremendous speeds, making it difficult to experimentally analyse their spatial and temporal dynamics. Both these challenges can be circumvented with macroscopic analog models, such as heterogeneous, irregular glass spheres floating at the air-water interface (particle rafts). Different structural constants can be set up by varying the initial packing fraction. Fracture is initiated by a surfactant drop introduced at the center of the petri dish; the spreading drop applies compressive and tensile stresses on the rafts, causing it to fracture. High speed imaging shows that the crack area and length do not proceed as previously predicted, and is sensitive to the initial packing fraction. Tracking individual raft particles as the cracking proceeds reveals three distinct stages. First, a fast compressive wave passes through the solid followed by a slower compaction wave that causes global anisotropic rearrangements. At this stage, the radial component of the instantaneous strain field proceeds circularly and symmetrically whereas the azimuthal component shows spiral patterns. Finally, the compaction recedes and thin cracks appear that travel intermittently and show long range correlated movement through the solid. [Preview Abstract] |
Friday, March 6, 2015 10:12AM - 10:24AM |
Y45.00010: Jamming and unjamming of foam flow in a straight channel Karthik Menon, Rama Govindarajan, Shubha Tewari Rheological studies on foams in the flowing state have focused primarily on shear driven foams. Some recent studies have begun addressing the steady flow of foams in channels where there is a strong influence of the geometry on the flow. There remain many unanswered questions about jamming characteristics of foams in simple settings where the geometry of the channel has a minimal role to play. This work aims to understand the flowing behaviour and the behaviour close to jamming in a foam flowing through a straight channel. We undertake a numerical study using the Bubble Model of D.J. Durian, due to its relevance to foams with a non-zero liquid fraction. Our study of the stress distributions and energy fluctuations during the flow, and at the onset of jamming provide some insight into the dynamics and time-scales involved in these rearrangement events. Our results indicate a shift of the flow regime from a steady to an intermittent flow close to jamming, in which rearrangements and energy relaxation become more periodic. Further, our investigations into the behaviour of contact forces and stress states of the flow add to our understanding of the jamming and unjamming characteristics of flowing foams, and aid in developing a continuum model of foam flow. [Preview Abstract] |
Friday, March 6, 2015 10:24AM - 10:36AM |
Y45.00011: Rheological {\&} electrical characterization of carbon black suspensions under shear Ahmed Helal, Xin Wei Chen, Frank Fan, Yet-Ming Chiang, Gareth McKinley Carbon black suspensions are complex fluids that are of interest for applications such as flow batteries, inks, paints {\&} in the oil/gas industry. As the loading concentration of carbon increases, the carbon black forms an electronically-conductive fractal network that gives rise to a gel-like behavior of the suspension beyond percolation. The macroscopic rheological and electrical properties of the suspension depend on the mechanical deformation applied as the microstructure becomes increasingly anisotropic under shear. Using a torsional rheometer with a parallel plate geometry, we characterize the viscoelastic properties of this attractive colloidal dispersion using small amplitude oscillatory shear measurements with increasing concentrations of carbon black. In addition, using a custom-made fixture, we perform measurements of DC {\&} AC conductivity under oscillatory strain sweeps as well as under steady shearing flow and experimentally characterize the decay of conductivity with increasing shear. This characterization of the macroscopic rheological {\&} electrical macroscopic properties will enable experimental verification of continuum models for such materials under shear using concepts such as internal fabric tensors {\&} the evolution of the contact network. [Preview Abstract] |
Friday, March 6, 2015 10:36AM - 10:48AM |
Y45.00012: Continuum model for suspension conductivity under flow Tyler Olsen, Ken Kamrin An electrically insulating fluid may be made conductive by suspending conductive particles in it. In these suspensions, the conductivity is imparted by a percolating contact network between the particles. It has been shown experimentally that shearing flow strongly affects the conductivity of a suspension, presumably via altering the structure of the contact network. This contact structure can be described by a statistical tensor quantity known as the fabric tensor, which reflects the average number and orientation of contacts on a particle. We derived a model that relates the electrical conductivity tensor to the fabric tensor. Additionally, we propose an evolution for the fabric under flow. Using these two models, we have been able to fit conductivity measurements of carbon-black suspensions under steady-state shear and transient shear flows. [Preview Abstract] |
Friday, March 6, 2015 10:48AM - 11:00AM |
Y45.00013: Dynamics of suspension of interacting yolk-shell particles Luis E. Sanchez Diaz, Ernesto Cortes Morales, Xin Li, Wei-Ren Chen, Magdaleno Medina Noyola In this work we study the self-diffusion properties of a liquid of hollow spherical particles (shells) bearing a smaller solid sphere in their interior (yolks). We model this system using purely repulsive hard-body interactions between all (shell and yolk) particles, but assume the presence of a background ideal solvent such that all the particles execute free Brownian motion between collisions, characterized by short-time self-diffusion coefficients $D^0_s$ for the shells and $D^0_y$ for the yolks. Using a softened version of these interparticle potentials we perform Brownian dynamics simulations to determine the mean squared displacement and intermediate scattering function of the yolk-shell complex. These results can be understood in terms of a set of effective Langevin equations for the $N$ interacting shell particles, pre-averaged over the yolks' degrees of freedom, from which an approximate self-consistent description of the simulated self-diffusion properties can be derived. Here we compare the theoretical and simulated results between them, and with the results for the same system in the absence of yolks. We find that the yolks, which have no effect on the shell-shell static structure, influence the dynamic properties in a predictable manner, fully captured by the theory [Preview Abstract] |
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