arXiv subjects

R. P. Behringer

Publications and source records attributed to R. P. Behringer.

At least 19 recordsLinked to original sources

arXiv2017

Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern, which results from either minimizing the energy cost or maximizing the entropy or both. In this work, we focus on a class of systems, where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled solely by the constraints of mechanical equilibrium. We argue that these constraints lead to a broken translational symmetry in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this broken symmetry. We extend our earlier work, by comparing and contrasting real space measures of rheology with those obtained from the dual space. We investigate the structure and behavior of the dual space as the system evolves through the rigidity transition in two different shear protocols. We analyze the robustness of the shear-jamming scenario with respect to protocol and packing fraction, and demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which signals the onset of rigidity.

cond-mat.soft↗

arXiv2017

Refractive Index Matched Scanning and Detection of Soft Particle

We describe here how to apply the three dimensional imaging technique of refrecative index matched scanning to hydrogel spheres. Hydrogels are water based materials with a low refractive index, which allows for index matching with water-based solvent mixtures. We discuss here various experimental techniques required to handle specifically hydrogel spheres as opposed to other transparent materials. The deformability of hydrogel spheres makes their identification in three dimensional images non-trivial. We will also discuss numerical techniques that can be used in general to detect contacting, non-spherical particles in a three dimensional image. The experimental and numerical techniques presented here give experimental access to the stress tensor of a packing of deformed particles.

cond-mat.soft↗

arXiv2016

Protocol dependence of the jamming transition

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via purely repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to induce jamming in initially unjammed packings from the measured probability to jam at packing fraction $ϕ$ from isotropic compression. We compare our predictions to results from numerical simulations of jamming and find quantitative agreement. We also show that the packing fraction range, over which strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.

cond-mat.soft↗

arXiv2015

Nonlinear Force Propagation during Granular Impact

We experimentally study nonlinear force propagation into granular material during impact from an intruder, and we explain our observations in terms of the nonlinear grain-scale force relation. Using high-speed video and photoelastic particles, we determine the speed and spatial structure of the force response just after impact. We show that these quantities depend on a dimensionless parameter, $M'=t_c v_0/d$, where $v_0$ is the intruder speed at impact, $d$ is the particle diameter, and $t_c$ is the collision time for a pair of grains impacting at relative speed $v_0$. The experiments access a large range of $M'$ by using particles of three different materials. When $M' \ll 1$, force propagation is chain-like with a speed, $v_f$, satisfying $v_f \propto d/t_c$. For larger $M'$, the force response becomes spatially dense and the force propagation speed departs from $v_f\propto d/t_c$, corresponding to collective stiffening of a strongly compressed packing of grains.

cond-mat.soft↗

arXiv2013

Origin of Rigidity in Dry Granular Solids

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern. In this work, we focus on the emergence of shear-rigidity in a class of solids where this paradigm is challenged. Dry granular materials have no energetically or entropically preferred density modulations. We show that, in contrast to traditional solids, the emergence of shear rigidity in these granular solids is a collective process, which is controlled solely by boundary forces, the constraints of force and torque balance, and the positivity of the contact forces. We develop a theoretical framework based on these constraints, which connects rigidity to broken translational symmetry in the space of forces, not positions of grains. We apply our theory to experimentally generated shear-jammed (SJ) states and show that these states are indeed characterized by a persistent, non-uniform density modulation in force space, which emerges at the shear-jamming transition.

cond-mat.soft↗

arXiv2013

Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full utility of this statistical framework in shear jammed (SJ) experimental states [1,2], a special class of granular solids created by pure shear, which is a strictly non-equilbrium protocol for creating solids. We demonstrate that the stress ensemble provides an excellent quantitative description of fluctuations in experimental SJ states. We show that the stress fluctuations are controlled by a single tensorial quantity: the angoricity of the system, which is a direct analog of the thermodynamic temperature. SJ states exhibit significant correlations in local stresses and are thus inherently different from density-driven, isotropically jammed (IJ) states.

cond-mat.soft↗

arXiv2012

Contacts Dynamics Reveals Widom Lines for Jamming

We experimentally study the vicinity of the Jamming transition by investigating the statics and the dynamics of the contact network of an horizontally shaken bi-disperse packing of photo-elastic discs. Compressing the packing very slowly, while maintaining a mechanical excitation, yields a granular glass, namely a frozen structure of vibrating grains. In this glass phase, we observe a remarkable dynamics of the contact network, which exhibits strong dynamical heterogeneities. Such heterogeneities are maximum at a packing fraction $ϕ^*$, \emph{distinct} and smaller than the jamming packing fraction $ϕ_J$, which is indicated by the abrupt variation of the average number of contact per particle. We demonstrate that the two cross-overs, one for the maximum dynamical heterogeneity, and the other for static jamming, converge at point J in the zero mechanical excitation limit, a behavior reminiscent of the Widom lines in the supercritical phase of a second order critical point. Our findings are discussed in the light of recent numerical and theoretical studies of thermal soft spheres.

cond-mat.soft↗

arXiv2012

Granular Impact Dynamics: Acoustics and Fluctuations

In the corresponding fluid dynamics video, created for the APS DFD 2012 Gallery of Fluid Motion, we show high-speed videos of 2D granular impact experiments, where an intruder strikes a collection of bidisperse photoelastic disks from above. We discuss the force beneath the intruder, which is strongly fluctuating in space and time. These fluctuations correspond to acoustic pulses which propagate into the medium. Analysis shows that this process, in our experiments, is dominated by collisions with grain clusters. The energy from these collisions is carried into the granular medium along networks of grains, where is it dissipated.

physics.flu-dyn↗

arXiv2009

Landing on the Moon Cratering from a Jet

This paper describes work done in investigating cratering processes by impinging jets. It accompanies a video made for the fluid dynamics video presentations at the Division of Fluid Dynamics meeting, November 22-24, 2009.

physics.flu-dyn↗

arXiv2009

Statistical Properties of a 2D Granular Material Subjected to Cyclic Shear

This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, $P$, and the mean contact number, $Z$. This relationship applies to the shear stress $τ$, except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as $P$, $τ$ and $Z$ are strongly hysteretic functions of the strain, $ε$. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks.

cond-mat.soft↗

arXiv2008

Signal propagation through dense granular systems

The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to learn more about this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the spatial and temporal scales introduced by the perturbation. The features of the response provide a test-bed for any continuum theory attempting to predict signal properties. We illustrate this connection between micro-scale physics and macro-scale behavior by comparing the system response to a simple elastic model with damping.

cond-mat.soft↗

arXiv2007

Experimental Measures of Affine and Non-affine Deformation in Granular Shear

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces smooth affine deformations in such a solid and also irresversible so-called non-affine particle displacements. We examine both processes. We show that the non-affine part is associated with diffusion, and also can be used to define a granular temperature. Distributions for single particle non-affine displacements, $\dri$, satisfy $P_1(\dri) \propto \exp [-|\dri/Δr|^α]$ ($α\stackrel{<}{\sim} 2$). We suggest that the shear band forms due to a radially outward diffusive flux/non-affine motion which is balanced in the steady state by inward diffusion due to density gradients.

cond-mat.other↗

arXiv2006

The Jamming Transition in Granular Systems

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number, Z, at a critical volume fraction, phi_c. Above phi_c, Z and the pressure, P are predicted to increase as power laws in phi-phi_c. In experiments using photoelastic disks we corroborate a rapid increase in Z at phi_c and power-law behavior above phi_c for Z and P. Specifically we find power-law increase as a function of phi-phi_c for Z-Z_c with an exponent beta around 0.5, and for P with an exponent psi around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.

cond-mat.soft↗

arXiv2005

Sensitivity of the stress response function to packing preparation

A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression, shearing etc. We show using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected and in most cases significant departures from isotropy should be observed. This suggests a new path toward a non-intrusive test of granular material constitutive properties.

cond-mat.soft↗

arXiv2005

From the stress response function (back) to the sandpile `dip'

We relate the pressure `dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -- albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.

cond-mat.soft↗

arXiv2004

Slow Drag in 2D Granular Media

We study the drag force experienced by an object slowly moving at constant velocity through a 2D granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three important control parameters for the system: the packing fraction, the drag velocity and the size of the tracer particle. We find that the mean drag force increases as a power-law (exponent of 1.5) in the reduced packing fraction, $(γ- γ_c)/γ_c$, as $γ$ passes through a critical packing fraction, $γ_c$. By comparison, the mean drag grows slowly (basically logarithmic) with the drag velocity, showing a weak rate-dependence. However, the system nevertheless exhibits strong statistical invariance in the sense that many physical quantities collapse onto a single curve under appropriate scaling. We also show that the system can be understood using simple failure models, which reproduce many experimental observations. These experimental data and simulations indicate that fluctuations in the drag force seem to be associated with the force chain formation and breaking in the system. Moreover, our simulations suggest that the logarithmic increase of the mean drag force with rate can be accounted for if slow relaxation of the force chain networks is included.

cond-mat.soft↗

arXiv2004

Transients in sheared granular matter

As dense granular materials are sheared, a shear band and an anisotropic force network form. The approach to steady state behavior depends on the history of the packing and the existing force and contact network. We present experiments on shearing of dense granular matter in a 2D Couette geometry in which we probe the history and evolution of shear bands by measuring particle trajectories and stresses during transients. We find that when shearing is stopped and restarted in the same direction, steady state behavior is immediately reached, in agreement with the typical assumption that the system is quasistatic. Although some relaxation of the force network is observed when shearing is stopped, quasistatic behavior is maintained because the contact network remains essentially unchanged. When the direction of shear is reversed, a transient occurs in which stresses initially decrease, changes in the force network reach further into the bulk, and particles far from the wheel become more mobile. This occurs because the force network is fragile to changes transverse to the force network established under previous shear; particles must rearrange before becoming jammed again, thereby providing resistance to shear in the reversed direction. The strong force network is reestablished after displacing the shearing surface $\approx 3d$, where $d$ is the mean grain diameter. Steady state velocity profiles are reached after a shear of $\leq 30d$. Particles immediately outside of the shear band move on average less than 1 diameter before becoming jammed again. We also examine particle rotation during this transient and find that mean particle spin decreases during the transient, which is related to the fact that grains are not interlocked as strongly.

cond-mat.soft↗

arXiv2004

Self-diffusion in dense granular shear flows

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear in a 2D Couette geometry. We find that self-diffusivities are proportional to the local shear rate with diffusivities along the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D \approx \dotγa^2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and drag at the moving boundary lead to particle displacements that can appear sub- or super-diffusive. In particular, diffusion appears superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems with no obvious analog in rapid flows. Specifically, the diffusivity is supressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean flow, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Levy flights are also observed. Although correlated motion creates velocity fields qualitatively different from Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.

cond-mat.soft↗