Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session E34: Continuum Descriptions of Discrete Materials IFocus

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Sponsoring Units: GSNP GSOFT Chair: Ken Kamrin, Massachusetts Institute of Technology Room: 337 
Tuesday, March 15, 2016 8:00AM  8:36AM 
E34.00001: Fabric variables in dense sheared suspensions Invited Speaker: Farhang Radjai The rheology of granular flows and dense suspensions can be described in terms of their effective shear and bulk viscosities as a function of packing fraction. Using stress partition and equivalence between frictional and viscous descriptions in the dense state, we show that the effective viscosities can be expressed in terms of the forcenetwork anisotropy. This is supported by our extensive DEMLBM simulations for a broad range of inertial and viscous parameters. [Preview Abstract] 
Tuesday, March 15, 2016 8:36AM  8:48AM 
E34.00002: Jammed granular cones affect frictional resistive forces at the onset of intrusion Jeffrey Aguilar, Daniel Goldman Characterizing the functional form of granular resistive forces has allowed for analysis of the locomotion of animals and robots on and within dry granular media. Resistive force theory (RFT) has been an effective tool in predicting these forces for various locomotive gaits within the ``frictional fluid'' regime, where intrusions are sufficiently slow such that granular inertial effects are negligible. These forces have been typically described by a linear dependence to submersion depth. However, recent experiments on robotic jumping [Aguilar {\&} Goldman, Nature Physics, 2015] have revealed the importance of considering the nonlinear effects at the onset of intrusion to accurately predict robot kinematics. Particle image velocimetry (PIV) analysis of sidewall grain flow during foot intrusion reveals a jammed granular cone that develops beneath the foot at the onset of intrusion. A geometric model of cone development combined with empirical RFT forces on angled conical surfaces was able to predict the nonlinear force trajectory vs. depth for experimental intrusions of various foot sizes, suggesting that intruders experience nonlinear frictional forces according to the shape of the granular jamming fronts that form at the onset of movement. [Preview Abstract] 
Tuesday, March 15, 2016 8:48AM  9:00AM 
E34.00003: Jammed Clusters and Nonlocality in Dense Granular Flows Prashidha Kharel, Pierre Rognon We investigate the micromechanisms underpinning dense granular flow behaviour from a series of DEM simulations of pure shear flows of dry grains. We observe the development of transient clusters of jammed particles within the flow. Typical size of such clusters is found to scale with the inertial number with a power law that is similar to the scaling of shearrate profile relaxation lengths observed previously\footnote{K. Kamrin and G. Koval, Physical Review Letters 108, (2012); M. Bouzid, et al., Physical Review Letters 111, (2013); P. G. Rognon, et al., Journal of Fluid Mechanics 764, 171 (2015)}. Based on the simple argument that transient clusters of size $\ell$ exist in the dense flow regime, the formulation of steady state condition for nonhomogeneous shear flow results in a general nonlocal relation, which is similar in form to the nonlocal relation conjectured for soft glassy flows\footnote{Goyon, et al., Nature 454, 84 (2008)}. These findings suggest the formation of jammed clusters to be the key micromechanism underpinning nonlocal behaviour in dense granular flows. [Preview Abstract] 
Tuesday, March 15, 2016 9:00AM  9:12AM 
E34.00004: Velocity profiles and rheology of a granular bed sheared by a fluid flow Benjamin Allen, Arshad Kudrolli We discuss an experimental investigation of motion of a granular bed driven by a laminar fluid flow as a function of applied shear rate. This is a model system to investigate a variety of examples where such a situation arises including wind blowing over sand, sediment transport in rivers, slurries, and turbidity currents. We have developed an experimental apparatus which allows examination of the fluid as well as the grain dynamics both at the surface as well as deep into the bed under steady state conditions with refractive index matching technique. This allows us to obtain both the applied local shear stress by the fluid as well as the local strain rate inside the bed. We find that that the granular flux as a function of depth decays exponentially into the bed. Further, the velocity profile is observed to exhibit a crossover from a regime where particles are fully suspended to where there is bed load transport. We will discuss the observed velocity and density profiles in light of various models of granular suspensions. [Preview Abstract] 
Tuesday, March 15, 2016 9:12AM  9:24AM 
E34.00005: Modeling Shear Banding in Amorphous Solids, from Atomistic to Continuum Darius AlixWilliams, Michael Falk Molecular dynamics simulations of strain localization are carried out using different materials systems and interatomic potentials including CuZr modeled via the embeddedatom method (EAM), amorphous Si modeled using StillingerWeber (SW) and a binary LennardJones (LJ) system. Quench schedules and strain rates are varied. Different systems exhibit marked similarities in plastic behavior. Systematic differences between systems are analyzed in the context of Shear Transformation Zone (STZ) theory in the effort to develop a generalized constitutive framework for plasticity in glasses. Effective temperature inferred from the potential energy is explored as a local coarsegrained measure of the degree of disorder. [Preview Abstract] 
Tuesday, March 15, 2016 9:24AM  9:36AM 
E34.00006: Identifying shear transformation zones in amorphous solids via a virtual strain method Michael Falk, Sylvain Patinet One outstanding problem in the mechanical response of amorphous solids is the identification of flow defect sites, so called shear transformation zones (STZs), a priori in the structure. Many methods have been utilized in order to predict local STZ sites including shortrange order, softmode analysis and machine learning. Here we directly probe local regions of the material via shear in order to detect nearby saddle points that can result in transformations. This nonperturbative method gives excellent correlation with global shear of the system. It also provides a means to crosscorrelate the existence of such local transition pathways with other proposed diagnostics such as the softspot method of Manning and Liu. We use the information gained by this method to consider the coarsegraining necessary to connect atomistic methods to continuum theories. [Preview Abstract] 
Tuesday, March 15, 2016 9:36AM  9:48AM 
E34.00007: Stickslip instabilities in sheared granular flow: The role of friction and acoustic vibrations Charles K. C. Lieou, Ahmed E. Elbanna, James S. Langer, Jean M. Carlson We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stickslip behavior at intermediate shear rates, even if the material is rate strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stickslip amplitude, or suppress stickslip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stickslip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics and thus produce useful information about a variety of granular phenomena, including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing. [Preview Abstract] 
Tuesday, March 15, 2016 9:48AM  10:00AM 
E34.00008: A microstructural description of shear thickening in dense suspensions. Abhinendra Singh, Romain Mari, Ryohei Seto, Jeff Morris, Morton Denn The mechanism of shear thickening in dense suspensions has been recently linked to a transition from a lubricated ``frictionless'' to an unlubricated ``frictional'' rheology. Recent particle simulations have been successful to quantitatively reproduce both the continuous and discontinuous shear thickening as observed experimentally. However, a microstructural description of these suspensions is still lacking, which would aid in understanding and predicting the flow behavior of shear thickening suspensions. To tackle this challenging issue, we explore various microscopic properties, like the interparticle force distribution, the particle motion correlations, and the anisotropy (in both contact and force network). Further, we also attempt to link the observed rheological behavior observed at the macro scale to mean displacement and fluctuations at the particle scale. [Preview Abstract] 
Tuesday, March 15, 2016 10:00AM  10:12AM 
E34.00009: Deformation in Metallic Glass: Connecting Atoms to Continua Adam R. Hinkle, Michael L. Falk, Chris H. Rycroft, Michael D. Shields Metallic glasses like other amorphous solids experience strain localization as the primary mode of failure. However, the development of continuum constitutive laws which provide a quantitative description of disorder and mechanical deformation remains an open challenge. Recent progress has shown the necessity of accurately capturing fluctuations in material structure, in particular the statistical changes in potential energy of the atomic constituents during the nonequilibrium process of applied shear. Here we directly crosscompare molecular dynamics shear simulations of a ZrCu glass with continuum shear transformation zone (STZ) theory representations. We present preliminary results for a methodology to coarsegrain detailed molecular dynamics data with the goal of initializing a continuum representation in the STZ theory. [Preview Abstract] 
Tuesday, March 15, 2016 10:12AM  10:24AM 
E34.00010: Size effects and internal length scales in the elasticity of random fiber networks. Catalin Picu, Kamel Berkache, Ali Shahsavari, JeanFrancois Ganghoffer Random fiber networks are the structural element of many biological and manmade materials, including connective tissue, various consumer products and packaging materials. In all cases of practical interest the scale at which the material is used and the scale of the fiber diameter or the mean segment length of the network are separated by several orders of magnitude. This precludes solving boundary value problems defined on the scale of the application while resolving every fiber in the system, and mandates the development of continuum equivalent models. To this end, we study the intrinsic geometric and mechanical length scales of the network and the size effect associated with them. We consider both Cauchy and micropolar continuum models and calibrate them based on the discrete network behavior. We develop a method to predict the characteristic length scales of the problem and the minimum size of a representative element of the network based on network structural parameters and on fiber properties. [Preview Abstract] 
Tuesday, March 15, 2016 10:24AM  10:36AM 
E34.00011: Is the microscopic stress computed from molecular simulations in mechanical equilibrium? Alejandro TorresSánchez, Juan M. Vanegas, Marino Arroyo The microscopic stress field connects atomistic simulations with the mechanics of materials at the nanoscale through statistical mechanics. However, its definition remains ambiguous. In a recent work [1,2] we showed that this is not only a theoretical problem, but rather that it greatly affects local stress calculations from molecular simulations. We find that popular definitions of the local stress, which are continuously being employed to understand the mechanics of various systems at the nanoscale, violate the continuum statements of mechanical equilibrium. We exemplify these facts in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. Furthermore, we propose [1,3] a new physical and sound definition of the microscopic stress that satisfies the continuum equations of balance, irrespective of the manybody nature of the interatomic potential. Thus, our proposal provides an unambiguous link between discreteparticle models and continuum mechanics at the nanoscale. [1] TorresSanchez, A; Vanegas, J. M.; Arroyo, M.; Phys. Rev. Lett. 114, 258102 (2015). [2] Vanegas, J. M.; TorresSanchez, A; Arroyo, M.; J. Chem. Theor. Comput., 10 (2), 691–702 (2014). [3] TorresSanchez, A; Vanegas, J. M.; Arroyo, M.; Submitted to J. Mech. Phys. Solid [Preview Abstract] 
Tuesday, March 15, 2016 10:36AM  10:48AM 
E34.00012: Extending twophase theories of soft composite solids to the nondilute regime Francesco Mancarella, Robert Style, John Wettlaufer Composite materials are ubiquitous in the natural environment and in engineered materials and hence capture the interest of a wide audience. Eshelby's 1957 theory treats the interaction of macroscopic stress fields with isolated inclusions within an elastic solid, and it has been widely used to treat the mechanics of composite materials. However, due to its neglect of interface stress, which is a particularly key effect in soft materials, the theory breaks down whenever the typical inclusion size $R$ is of order or less than the elastocapillary lengthscale $L$. In this regime, under external stress, the effect of inclusion shape becomes strongly sizedependent. Here, we develop two new nondilute theories, estimate the elastic moduli of composites comprised of an isotropic, compressible, linearelastic compliant solid hosting a nondilute spatiallyrandom distribution of identical liquid droplets. The composite stiffness depends on a single dimensionless parameter $L/R$, and we find significant elastic moduli corrections for inclusions sizes $R$ as large as 100 $L$. By generalizing the exact theory recently developed for the corresponding dilute case, we find that when $R < 3L/2$ ($R=3L/2$) liquid inclusions stiffen (cloak the farfield signature of) of the host solid. [Preview Abstract] 
Tuesday, March 15, 2016 10:48AM  11:00AM 
E34.00013: Continuum modeling of dense granular flow down heaps David Henann, Daren Liu Dense, dry granular flows display many manifestations of grainsize dependence, or nonlocality, in which the finitesize of grains has an observable impact on flow phenomenology. Such behaviors make the formulation of an accurate continuum model for dense granular flow particularly difficult, since local continuum models are not equipped to describe sizeeffects. One example of grainsize dependence is seen when avalanches occur on a granular heap  a situation which is frequently encountered in industry, as in rotating drums, as well as in nature, such as in landslides. In this case, flow separates into a thin, quickly flowing surface layer and a slowly creeping bulk. While existing local granular flow models are capable of capturing aspects of the flowing surface layer, they fail to even predict the existence of creeping flow beneath, much less being able to quantitatively describe the flow fields. Recently, we have proposed a new, scaledependent continuum model  the nonlocal granular fluidity (NGF) model  that successfully predicted steady, slow granular flow fields, including grainsizedependent shearband widths in a variety of flow configurations. In this talk, we extend our model to the rapid flow regime and show that the model is capable of quantitatively predicting all aspects of gravitydriven heap flow. In particular, the model predicts the coexistence of a rapidly flowing, ratedependent top surface layer and a rateindependent, slowly creeping bulk  a feature which is beyond local continuum approaches. [Preview Abstract] 
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