Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session B57: Physics of Granular MediaFocus

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Sponsoring Units: GSOFT DMP DFD GSNP Chair: David Henann, Brown Univ Room: LACC 518 
Monday, March 5, 2018 11:15AM  11:51AM 
B57.00001: A Van der WaalsCahnHilliard regularization of granular instability via dissipation potentials Invited Speaker: Joe Goddard This talk deals with the viscoplastic Hadamard (shortwavelength) instability of the socalled μ(I) model of dense rapidlysheared granular flow, as reported recently by Barker et al. (2015, J. Fluid Mech, 779, 794818). As explained in a subsequent paper by Goddard & Lee (2017, J. Fluid Mech., in press), one achieves stabilizing effects from higher velocity gradients by means of an enhancedcontinuum model based on the dissipative analog of the Van der WaalsCahnHilliard equation of equilibrium thermodynamics. This model involves a dissipative hyperstress, with surface viscosity arising as counterpart of elastic surface tension. This allows for a description of diffuse shear bands as the rough analog of the diffuse interfaces of equilibrium thermodynamics. The later paper also presents a more comprehensive linear stability analysis, including convective (Kelvin) wavevector stretching by the base flow that leads to asymptotic stabilization of the nonconvective instability found by Barker et al. This suggests a theoretical connection between their nonconvective instability and the loss of generalized ellipticity in the quasistatic field equations. Apart from the theoretical interest, the present work may suggest stratagems for the otherwise difficult numerical simulation of continuum field equations involving Hadamardunstable viscoplasticity. 
Monday, March 5, 2018 11:51AM  12:03PM 
B57.00002: Nonlinear softening of unconsolidated granular materials Charles Lieou, Eric Daub, Robert Guyer, Paul Johnson

Monday, March 5, 2018 12:03PM  12:15PM 
B57.00003: Granular flow in confined geometries: jamming, clogging, and instability Ko Okumura In this talk, we will discuss three smallscale granular experiments, all prepared in two dimension: (1) drag friction in a granular medium [13], (2) granular statics and dynamics in a certain hopper [4], and (3) meandering airflow in a granular medium (Fig. 1) [5]. For the drag friction, we highlight the divergence of the friction force towards the jamming transition and a simple physical explanation for it. For the hopper problem, we discuss the statics of an unstable state and the dynamics of bubbles and its connection to clogging, again in simple physical frameworks. For the meandering problem, we discuss the mechanism of its destabilization and stabilization, together with a quasistatic nature. In all cases, we derive scaling laws for the phenomena on physical grounds, which agree well with experiments. 
Monday, March 5, 2018 12:15PM  12:27PM 
B57.00004: Elements of mesoscale continuum theory of granular matter Sinisa Mesarovic Owing to its disordered multiphase microstructure, dense granular matter exhibits characateristic behavior, including: (1) Transition between solid and fluid state, (2) Dilatancy: volume increase when sheared under constant pressure, (3) Localization in shear bands with characteristic width, and, (4) Vortex flow within shear bands, and in the bulk. 
Monday, March 5, 2018 12:27PM  12:39PM 
B57.00005: Hard Xray nanotomography of jammed sphere packings Yeseul Kim, Jun Lim, Byung Mook Weon Packing structures of spheres in three dimensions is important in understanding arrangement and geometry of pours media, metallic glasses, colloidal particles, and granular matter. Most theory and analysis are focused on random packing structures at large scale, while Xray tomographic observations of colloidal particles on micro and nanoscales are rare. Here we demonstrate jammed packings of colloidal microparticles with Xray nanotomography. Projected images of jammed microparticles prepared by centrifuging colloidal suspensions are recorded and reconstructed to threedimensional structures. Analysis of individual particle positions and pare correlation functions would help the nature of packing structures of colloidal particles. We believe that hard Xray nanotomography would be a powerful tool to visualize and identify the packing systems that consist of colloidal particles. 
Monday, March 5, 2018 12:39PM  12:51PM 
B57.00006: Linear stability of the nonlocal granular fluidity model for steady, dense granular flow Shihong Li, David Henann Dense granular flows are ubiquitous in nature and industrial applications, and significant effort has gone into developing continuumlevel constitutive equations for the steadystate rheology of dense granular materials. The most widely used rheology for dense granular flow is the local inertial rheology of MiDi (2004), which has had success in describing steady, dense, rapid flows down chutes or in silos. Recent work (Barker et al., 2015) has shown that the inertial rheology displays a linear instability against short wavelength perturbations – i.e., Hadamard instability – in particular, in the slow, quasistatic flow regime. It is expected that the inclusion of higherorder gradients into the rheology can restore linear stability, and indeed, Goddard and Lee (2017) have shown that higherorder velocity gradients can have a stabilizing effect. In our recent work, we have proposed a nonlocal rheology – called the nonlocal granular fluidity (NGF) model – which has been shown to quantitatively describe a wide variety of steady, dense flows. In this talk, we consider the linear stability of the NGF model in its steadystate form under planar shear flow. Our results show that the NGF model is linearly stable against short wavelength perturbations. 
Monday, March 5, 2018 12:51PM  1:03PM 
B57.00007: A Hybrid Material Point and Discrete Element Method for Granular Media Modeling Maytee Chantharayukhonthorn, Breannan Smith, Yonghao Yue, Peter Chen, Kenneth Kamrin, Eitan Grinspun Capturing the propagation of microscale physics to macroscale phenomena for many systems is intractable. Granular media simulation is especially susceptible to this issue, wherein two extremes are often taken. In one, grains are modeled as continuum elements, lowering the degrees of freedom but ignoring inherent length scales. In discrete element methods (DEM), every grain and the interactions between them are simulated. DEM is accurate but solve time scales poorly with large grain numbers. A hybrid scheme which bridges these two approaches is presented. 
Monday, March 5, 2018 1:03PM  1:15PM 
B57.00008: Constitutive Relations for Shear Fronts in Shearthickening Suspensions Endao Han, Matthieu Wyart, Heinrich Jaeger When a shearthickening suspension is submitted to a sudden driving force at a boundary, a front can be generated, which propagates into the bulk and turns the suspension into a solidlike material in its wake. To explain this phenomenon, we generalized the WyartCates model by introducing a characteristic strain scale that controls the crossover from startup response to steadystate behavior. With the generalized model, we derived a constitutive relation for dense suspensions in the dynamic jamming regime. We found that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a prefactor that can be much larger than the material density. The prediction of the model matches well with the experimental results obtained with a quasione dimensional system. This theoretical framework unifies both transient and steadystate properties of shearthickening materials. 
Monday, March 5, 2018 1:15PM  1:27PM 
B57.00009: Investigating Continuum Properties of Granular Materials Using Discrete Experiments and Simulations Ryan Hurley, Stephen Hall, Eric Herbold, Jonathan Wright Accurate measurements and simulations of discrete particle behavior are required to develop and validate continuum models of granular solids. In this work, we used experiments and simulations to investigate properties of granular solids relevant to continuum modeling. In particular, we used xray measurements during uniaxial and triaxial compaction of sapphire and barium titanate spheres to study energy dissipation due to grain fracture, homogenization length scales for various mechanical properties, and the development and size of shear bands. To supplement these measurements, we employed discrete element simulations of granular materials undergoing uniaxial and triaxial compaction to assess the homogenization behavior of larger particle ensembles. We will discuss ongoing efforts to use the data to develop and validate models of granular materials. 
Monday, March 5, 2018 1:27PM  1:39PM 
B57.00010: Modeling silo jamming with a nonlocal continuum model Kenneth Kamrin, Sachith Dunatunga The fact that a silo or hopper jams when the opening size is reduced below a critical value defies most, if not all, local continuum models of granular media. Nonlocal models, which account for the affect of a finite grain size within the rheology, have the unique ability among continuum apporaches to address this issue. Previously, the Nonlocal Granular Fluidity (NGF) model has shown the ability to capture an analogous situation, the apparent strengthening due to thinness that causes thin layers of grains to require more tilt to flow down a rough incline than thicker layers; i.e. the Hstop effect. In this talk, we will show the same model can also capture the apparent strengthening due to thinness that causes silos and hoppers to jam when the nozzle size is smaller than a critical value. To show this, the model is implemented in a set of silo geometries with a meshless solver. We show the model predicts a jamming criterion that is in the proper range for simple grains, and explore the form of the flow/noflow phase diagram it predicts. 
Monday, March 5, 2018 1:39PM  1:51PM 
B57.00011: StressInduced FlowArrest Transitions in Frictional Granular Materials Ishan Srivastava, Jeremy Lechman, Gary Grest, Leo Silbert Using discrete element simulations, we study the mechanical response of frictional granular materials that are subjected to homogeneous normal and shear stresses. Depending on the applied stress state, such materials either flow toward a steady or socalled critical state, or creep toward a statically stable arrested state. The transition from creep to flow for increasing stresses is characterized by increased fluctuations in the bulk strain rate, and increased dilation, indicating mechanical instability in the vicinity of this transition. Extensive simulations are performed to characterize the static yield stress of such frictional granular materials. A phase diagram mapping the boundary between flowing and arrested states is developed for a wide range of applied stresses, and is found to be strongly dependent on the intergranular Coulombic friction. Microstructural analyses of the granular fabric highlight direct connections between continuum $\mu(I)$ rheology and mechanics of the socalled shearjammed state. Such bulk measurements provide essential input towards the development of continuum models for granular mechanics and flow. 
Monday, March 5, 2018 1:51PM  2:03PM 
B57.00012: A coupled, twophase fluidsediment material model and mixture theory implemented using the material point method Aaron Baumgarten, Kenneth Kamrin Dynamic fluidsediment interactions present a challenge to traditional numerical modelling techniques. These flows can involve bulk motion of millions of sediment particles (e.g. riverbed and shoreline erosion) and therefore require intensive computational resources for modeling using discrete element methods (DEM). Other flows of interest have highly turbulent regions (e.g. the head of submerged slope avalanches) and are therefore difficult to capture in finite element methods (FEM). Recent work on modeling granular materials as continuum using the material point method (MPM) has shown promise for capturing such complex material dynamics. 
Monday, March 5, 2018 2:03PM  2:15PM 
B57.00013: A highergradient nonlocal model for slow granular flows, and its predictions for selected complex flows Prabhu Nott A variety of nonlocal plasticity models have been proposed for dense, slow granular flows, motivated by several experimental observations, such as the occurrence of thin shear layers adjacent to moving boundaries, and the apparent creep in regions far from the shear layers. While some models have a clear mechanical basis, others are based on analologies to other physical systems whos relevance to granular flows is unconvincing. A rational basis for arriving at a simple nonlocal plasticity model that accurately captures the observed experiemntal features is therefore of interest. Here we present a nonlocal model that is based on the simple idea of volume averaging over rapidlyvarying quantities. We show that it overcomes many of the shortcomings of the previously proposed models. In addition to capturing regions of sharp velocity gradients, the model also incorporates the accompanying reduction in density within such regions. The predictions of the model for some selected flow geometries that yield complex two or three dimensional flows will be presented, and comparisons will be made with experiments. 
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