Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A16: Focus Session: Continuum Description of Discrete Materials 
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Sponsoring Units: GSNP Chair: Kenneth Kamrin, Massachusetts Institute of Technology Room: 401 
Monday, March 3, 2014 8:00AM  8:12AM 
A16.00001: Bipotential continuum models for granular mechanics Joe Goddard Most currently popular continuum models for granular media are special cases of a generalized Maxwell fluid model, which describes the evolution of stress and internal variables such as granular particle fraction and fabric,in terms of imposed strain rate. It is shown how such models can be obtained from two scalar potentials, a standard elastic free energy and a ``dissipation potential" given rigorously by the mathematical theory of Edelen. This allows for a relatively easy derivation of properly invariant continuum models for granular media and fluidparticle suspensions within a thermodynamically consistent framework. The resulting continuum models encompass all the prominent regimes of granular flow, ranging from the quasistatic to rapidly sheared, and are readily extended to include highergradient or Cosserat effects. Models involving stress diffusion, such as that proposed recently by Kamrin and Koval ({\it PRL} {\bf 108} 178301), provide an alternative approach that is mentioned in passing. This paper provides a brief overview of a forthcoming review articles by the speaker ({\it The Princeton Companion to Applied Mathematics}, and {\it Appl. Mech. Rev.},in the press, 2013). [Preview Abstract] 
Monday, March 3, 2014 8:12AM  8:24AM 
A16.00002: Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization Charles K.C. Lieou, Ahmed E. Elbanna, Jean M. Carlson We describe the shear flow of a disordered granular material subject to grain fracture using the sheartransformationzone (STZ) theory of amorphous plasticity adapted to systems with a hardcore interparticle interaction. To this end, we develop the equations of motion for this system within a statisticalthermodynamic framework analogous to that used in the analysis of molecular glasses. For hardcore systems, the amount of internal, configurational disorder is characterized by the compactivity $X = \partial V / \partial S_C$, where $V$ and $S_C$ are respectively the volume and configurational entropy. Grain breakage is described by a constitutive equation for the temporal evolution of a characteristic grain size $a$, based on fracture mechanics. We show that grain breakage is a weakening mechanism, significantly lowering the flow stress at large strain rates, if the material is ratestrengthening in character. We show in addition that if the granular material is sufficiently aged, spatial inhomogeneity in configurational disorder results in strain localization. We also show that grain splitting contributes significantly to comminution at small shear strains, while grain abrasion becomes dominant at large shear displacements. [Preview Abstract] 
Monday, March 3, 2014 8:24AM  8:36AM 
A16.00003: A granularcontinuum model of channelization in sedimentary layers by subsurface flow Vikrant Yadav, Arshad Kudrolli We discuss experiments where channels form in a quasitwo dimensional bed of consolidated granular particles by fluid flow. A continuum three phase model was developed recently [A. Mahadevan, A.V. Orpe, A. Kudrolli, and L. Mahadevan, EPL, 2012] which shows that channels can develop from small differences in packing in an otherwise homogeneous medium which leads to increased porosity and nonlinear feedback. To build on this model, an erodible porous medium composed of millimeter scale grains and Bentonite clay was prepared in a HeleShaw cell. The cohesive strength between the grains is directly proportional to the amount of clay binder. When water is pumped through this porous medium, the binder dissolves and loose beads are advected out of the erodible medium, and an initially uniform flow of water through the porous medium gets localized into channels over time. We will discuss the measured integrated rates of erosion as well as the statistical development of heterogeneity and comparison with the threephase model as a function of binding strength and consolidation of the medium. [Preview Abstract] 
Monday, March 3, 2014 8:36AM  8:48AM 
A16.00004: Rate and agedependence of shear yield stress in loose sphere packings Greg Farrell, Narayanan Menon Frictional packings of hard spheres can be stable in loose volume fractions well below random close packing. We study the stability of these solids to shear perturbations in the littlestudied regime close to the random loose packing limit [1]. We present experimental data on the shear yield stress as a function of rate and age in sedimented loose packings of frictional, noncohesive, PMMA spheres. The yield stress is found to depend on both the rate of strain and age of the packing since last breakage, both to approximately the positive onethird power. The regime of elastic response at finite strainrate is insensitive to the viscosity of the interstitial fluid. With this common choice of materials and preparation conditions, no rateindependent elastic regime was seen, even at the smallest strains experimentally achieved. [1] Farrell GR, Martini KM, and Menon N, \emph{Soft Matter}, \textbf{6}, 2925 (2010). [Preview Abstract] 
Monday, March 3, 2014 8:48AM  9:00AM 
A16.00005: Continuum modeling of diffusion and dispersion in dense granular flows Ivan C. Christov, Howard A. Stone Continuum modeling of granular flows remains a challenge of modern statistical physics. Granular materials do not perform Brownian motion, yet diffusion and shear dispersion can be observed in such systems when agitation causes inelastic collisions between particles. In a number of canonical flow regimes (e.g., in a rotating container or down an incline), granular materials can behave like fluids. We formulate and solve the granular counterparts to two basic fluid mechanics problems: diffusion of a pulse and shear dispersion of a pulse for dense granular materials in rapid flow. We provide a theory to account for the concentrationdependent diffusivity of bidisperse granular mixtures, and we give an asymptotic argument for the selfsimilar behavior of such a diffusion process for which an exact selfsimilar analytical solution does not exist. For shear dispersion, we show that the effective dispersivity of the depthaveraged concentration of the dispersing powder varies as the P\'eclet number squared, as in classical TaylorAris dispersion of molecular solutes. The calculation is extended to generic shear profiles, showing a significant enhancement for convex profiles due to the shearrate dependence of the diffusivity of granular materials. [Preview Abstract] 
Monday, March 3, 2014 9:00AM  9:12AM 
A16.00006: Connecting the behavior of granular layers on inclined planes to the nonlocal fluidity model Ken Kamrin, David Henann Recently, a grainsizesensitive rheology for granular flow has been proposed based on the nonlocal fluidity concept. While primarily intended to describe the effect that grain size has on developed flow fields, this talk will show how the same framework also explains the Hstop phenomenon commonly observed in thin granular layers on inclined planes, in which thinner layers appear to be stronger than thicker ones. Moreover, the experimental phase diagram for flow vs noflow of a layer of glass beads in this geometry is wellpredicted using the same modeling parameters that describe the steady flow of those beads in splitbottom cells and other geometries. [Preview Abstract] 
Monday, March 3, 2014 9:12AM  9:24AM 
A16.00007: Collisional Diffusion of Granular Materials: From Creep to Rapid Flow Paul Umbanhowar, Yi Fan, Julio Ottino, Richard Lueptow The diffusion of granular material is driven by random collisions between particles and quantified by the diffusion coefficient, $D$. We computationally study the dependence of $D$ on local shear rate, $\dot{\gamma}$, from the dense flow regime to the creep flow regime in open and closed heap flows. Measurements of $D$ obtained for both geometries, monodisperse and bidisperse systems, various flow rates, and at different streamwise positions collapse onto a single curve when plotted vs.\ $\dot{\gamma}\bar{d}^2,$ where $\bar{d}$ is the local mean particle diameter. In the dense flow regime, where $\dot{\gamma}$ is larger, $D$ is proportional to $\dot{\gamma}\bar{d}^2$, similar to previous studies. However, in the creep flow regime, where $\dot{\gamma}$ is smaller, $D$ is independent of $\dot{\gamma}.$ The solids fraction and velocity fluctuations are also constant in this regime. Further study of the effect of gravity on $D$ shows that it determines the transition between ratedependent and rateindependent regimes and controls the value of $D$ in the creep regime. These results demonstrate that the shear rate is not the relevant time scale in the creeping flow regime. [Preview Abstract] 
Monday, March 3, 2014 9:24AM  9:36AM 
A16.00008: Microscopic Order Parameter for Shear Anisotropy for Systems near Shear Jamming Robert Behringer, Dong Wang, Jie Ren, Joshua Dijksman Sheared granular systems at packing fractions between $\phi_S \le \phi \leq \phi_J$ can exist in states with zero and nonzero stress. When a system, prepared in a stressfree states in this density range, is sheared, it exhibits first fragile, then shear jammed states, both having high stress and fabric anisotropy. The onset of shear jammed states resembles an orderdisorder transition. In recent work, we showed that the order appears in a force space (Bi et al. PRL 2013). Here, we identify an order parameter associated with individual particles, making it possible to construct spatial correlations. We identify local (particlescale) order with $\Gamma$, the deviatoric part of the forcemoment tensor. This is a real symmetric, traceless matrix characterized by two coefficients, a and b, such that $\Gamma = aU_1+bU_2$, and where $U_1$ is diagonal with elements $\pm1$, and $U_2$ has 0's on the diagonal, and 1 for the offdiagonal elements. The $U_i$'s are orthogonal under an appropriate scalar product. Then, $(a,b)$ provides a vector particlescale order parameter. $\Gamma$ is additive over all particles, and is analogous to the magnetization in a spin system. Also, particles with orthogonal shear stresses now correspond to antiparallel vectors. We use this representation to investi [Preview Abstract] 
Monday, March 3, 2014 9:36AM  9:48AM 
A16.00009: Shearinduced rigidity in athermal materials Bulbul Chakraborty, Sumantra Sarkar In this talk, we present a minimal model of rigidity and plastic failure in solids whose rigidity emerges directly as a result of applied stresses. Examples include shearjamming (SJ) in dry grains and discontinuous shear thickening (DST) of dense nonBrownian suspensions. Both SJ and DST states are examples of nonequilibrium, selfassembled structures that have evolved to support the load that created them. These are stronglyinteracting systems where the interactions arise primarily from the strict constraints of force and torque balance at the local and global scales. Our model is based on a reciprocalspace picture that strictly enforces the local and global constraints, and is, therefore, best suited to capturing the strong correlations in these nonequilibrium systems. The reciprocal space is a tiling whose edges represent contact forces, and whose faces represent grains. A separation of scale between force fluctuations and displacements of grains\footnote{ Sumantra Sarkar et al, Phys. Rev. Lett. 111, 068301 (2013)} is used to represent the positional disorder as quenched randomness on variables in the reciprocal space. Comparing theoretical results to experiments, we will argue that the packing fraction controls the strength of the quenched disorder. [Preview Abstract] 
Monday, March 3, 2014 9:48AM  10:24AM 
A16.00010: Granular Materials by Design Invited Speaker: Heinrich Jaeger Granular materials are large amorphous aggregates of discrete, individually solid particles. One of the key issues has long been how to link particlelevel properties in a predictive manner to the behavior of the aggregate as a whole. In particular, the shape of particles has been recognized as important factor, with smooth spherical shapes known to behave quite differently from angular or faceted ones. However, except for a small set of simple convex shapes, very little detailed knowledge exists that allows one to predict aggregate mechanical response from individual particle properties. Furthermore, for actually designing a granular material, the inverse problem needs to be solved: for a given desired overall mechanical response, the task becomes finding the appropriate particlelevel properties. This talk discusses recent experiments on a wide range of convex and nonconvex particle shapes in an effort to provide a baseline for modeling the effect of nonsphericity on parameters such as the effective Young`s modulus or yield stress of a granular material. It also discusses a new approach to tackle the inverse problem by bringing concepts from artificial evolution to granular materials design, making it possible to find with high efficiency the shapes best adapted to a given goal. These results have general applicability and open up wideranging opportunities for materials optimization and discovery. [Preview Abstract] 
Monday, March 3, 2014 10:24AM  10:36AM 
A16.00011: Random Organization of Suspensions: Geometry versus Hydrodynamics Emmanouela Filippidi, Alexandre Franceschini, Paul Chaikin, David Pine Suspensions of athermal spheres at moderate volume fractions (0.20.4) under slow periodic strain undergo a phase transition from an absorbing to an active state despite the low Reynolds number regime of the flow imposed. In the absorbing state, the particles return to their original positions after every cycle, while in the active steady state, they appear diffusive. To explain the scaling near the transition and explore its universality class, we propose to replace the spherical particle with an effective particle whose shape depends on strain. We experimentally measure the particle pair correlation and the time evolution of the rheology and the stressstrain curves. The pair correlation is compared to the one expected for our effective particle and the time evolution curves are compared to theoretical existing models. While the geometrical approach of the effective particle captures the main physics of the system, it overestimates the effects. The consideration of hydrodynamics seems essential in understanding the finer details and the stresses in the suspension. Together, reductionist geometrical approach and detailed hydrodynamics provide a more complete picture in understanding the observed critical phase transition. [Preview Abstract] 

A16.00012: ABSTRACT WITHDRAWN 
Monday, March 3, 2014 10:48AM  11:00AM 
A16.00013: Continuum modeling of mechanicallyinduced creep using the nonlocal fluidity model David Henann, Ken Kamrin Recently, the nonlocal fluidity model applied to granular materials has successfully been used to predict the size of flow features in a wide variety of flow configurations, including all variations of the splitbottom cell as well as other geometries. A related problem in granular flow is that of mechanicallyinduced creep, in which shear deformation in one region of a granular medium fluidizes quiescent regions far from the sheared zone. This enables creep deformation when a force is applied in the quiescent region through an intruder such as a cylindrical or spherical probe. In this talk, we show that the nonlocal fluidity model is capable of describing this phenomenology. Specifically, we explore the creep of a rod in an annular Couette cell and show that the model captures all salient features observed in experiments. [Preview Abstract] 
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