Creep and fluidity of a real granular packing near jamming

Confinement controls the creep rate in soft granular packings

Flow in soft materials encompasses a wide range of viscous, plastic and elastic phenomena which provide challenges to modelling at the microscopic level. To create a controlled flow, we perform falling ball viscometry tests on packings of soft, frictionless hydrogel spheres. Systematic creep flow is found when a controlled driving stress is applied to a sinking sphere embedded in a packing. Here, we take the novel approach of applying an additional global confinement stress to the packing using an external load. This has enabled us to identify two distinct creep regimes. When confinement stress is small, the creep rate is independent of the load imposed. For larger confinement stresses, we find that the creep rate is set by the mechanical load acting on the packing. In the latter regime, the creep rate depends exponentially on the imposed stress. We can combine the two regimes via a rescaling onto a master curve, capturing the creep rate over five orders of magnitude. Our results indicate that bulk creep phenomena in these soft materials can be subtly controlled using an external mechanical force.

Quantitative Understanding of the Onset of Dense Granular Flows

The question of when and how dense granular materials start to flow under stress, despite many industrial and geophysical applications, remains largely unresolved. We develop and test a simple equation for the onset of quasistatic flows of granular materials which is based on the frictional aging of the granular packing. The result is a nonmonotonic stress-strain relation which-akin to classical friction-is independent of the shear rate. This relation suffices to understand the quasistatic deformations of aging granular media, and its solid-to-liquid transition. Our results also elucidate the (flow) history dependence of the mechanical properties, and the sensitivity to the initial preparation of granular media.

Creep Control in Soft Particle Packings

Granular packings display a wealth of mechanical features that are of widespread significance. One of these features is creep: the slow deformation under applied stress. Creep is common for many other amorphous materials such as many metals and polymers. The slow motion of creep is challenging to understand, probe, and control. We probe the creep properties of packings of soft spheres with a sinking ball viscometer. We find that in our granular packings, creep persists up to large strains and has a power law form, with diffusive dynamics. The creep amplitude is exponentially dependent on both applied stress and the concentration of hydrogel, suggesting that a competition between driving and confinement determines the dynamics. Our results provide insights into the mechanical properties of soft solids and the scaling laws provide a clear benchmark for new theory that explains creep, and provide the tantalizing prospect that creep can be controlled by a boundary stress.

Yielding and resolidification of colloidal gels under constant stress

We examine the macroscopic deformation of a colloidal depletion gel subjected to a step shear stress. Three regimes are identified depending on the magnitude of the applied stress: (i) for stresses below yield stress, the gel undergoes a weak creep in which the bulk deformation grows sublinearly with time similar to crystalline and amorphous solids. For stresses above yield stress, when the bulk deformation exceeds approximately the attraction range, the sublinear increase of deformation turns into a superlinear growth which signals the onset of non-linear rearrangements and yielding of the gel. However, the long-time creep after such superlinear growth shows two distinct behaviors: (ii) under strong stresses, a viscous flow is reached in which the strain increases linearly with time. This indicates a complete yielding and flow of the gel. In stark contrast, (iii) for weak stresses, the gel after yielding starts to resolidify. More homogenous gels that are produced through enhancement of either interparticle attraction strength or strain amplitude of the oscillatory preshear, resolidify gradually. In contrast, in gels that are more heterogeneous resolidification occurs abruptly. We also find that heterogenous gels produced by oscillatory preshear at intermediate strain amplitude yield in a two-step process. Finally, the characteristic time for the onset of delayed yielding is found to follow a two-step decrease with increasing stress. This is comprised of an exponential decrease at low stresses, during which bond reformation is decisive and resolidification is detected, and a power law decrease at higher stresses where bond breaking and particle rearrangements dominate.

Brownian Granular Flows Down Heaps

We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle θ_{c}, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple one-dimensional model based on Kramers' escape rate to describe these Brownian granular avalanches, which reproduces the main observations.

Flow-Arrest Transitions in Frictional Granular Matter

The transition between shear-flowing and shear-arrested states of frictional granular matter is studied using constant-stress discrete element simulations. By subjecting a dilute system of frictional grains to a constant external shear stress and pressure, friction-dependent critical shear stress and density are clearly identified with both exhibiting a crossover between low and high friction. The critical shear stress bifurcates two nonequilibrium steady states: (i) steady state shear flow characterized by a constant deformation rate, and (ii) shear arrest characterized by temporally decaying creep to a statically stable state. The onset of arrest below critical shear stress occurs at a time t_{c} that exhibits a heavy-tailed distribution, whose mean and variance diverge as a power law at the critical shear stress with a friction-dependent exponent that also exhibits a crossover between low and high friction. These observations indicate that granular arrest near critical shear stress is highly unpredictable and is strongly influenced by interparticle friction.

Self-assembly of granular spheres under one-dimensional vibration

The self-assembly of uniform granular spheres is related to the fundamentals of granular matter such as the transitions of phases, order/disorder and jamming states. This paper presents a DEM (discrete element method) study of the continuous self-assembly of uniform granular spheres from random close packing (RCP) to partially and nearly fully ordered packings under one-dimensional (1D) sinusoidal vibration without other interventions. The effects of the vibration amplitude and frequency are investigated in a wide range. The structures of the packings are characterized in terms of packing fraction and other microscopic structural parameters, including the coordination number, bond-orientational orders, and, in particular, ordered clusters, by adaptive common neighbor analysis (a-CNA). It is shown that 1D vibrations can also lead to the self-assembly of uniform granular spheres with packing fractions exceeding the RCP limit, and FCC (face centered cubic) and HCP (hexagonal close packed) structures coexist in the self-assembled packings while their total fraction can reach nearly 100%. The structures of these packings can be better correlated with the vibration velocity amplitude rather than the commonly used vibration intensity. The dynamics of such self-assembly is also preliminarily analyzed. Our study not only presents the conditions for the self-assembly of uniform granular spheres under 1D vibration, but also characterizes the order-disorder transitions during the process, which can improve our understanding of the fundamentals of granular materials and jamming states.

Glassy dynamics of landscape evolution

Soil is apparently solid as it moves downhill at glacial speeds, but can also liquefy from rain or earthquakes. This behavior is actually similar to that of glass, which creeps very slowly at low temperatures but becomes a liquid at higher temperatures. We develop a discrete granular-physics hillslope model, which shows that the similarities between soil and glass are more than skin deep. Despite the geologic and climatic complexity of natural environments, the shapes and erosion rates of hillsides over geologic timescales appear to be governed by generic dynamics characteristic of disordered and amorphous materials.

Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales.

Foam rheology at large deformation

Large deformations are prone to cause irreversible changes in materials structure, generally leading to either material hardening or softening. Aqueous foam is a metastable disordered structure of densely packed gas bubbles. We report on the mechanical response of a foam layer subjected to quasistatic periodic shear at large amplitude. We observe that, upon increasing shear, the shear stress follows a universal curve that is nearly exponential and tends to an asymptotic stress value interpreted as the critical yield stress at which the foam structure is completely remodeled. Relevant trends of the foam mechanical response to cycling are mathematically reproduced through a simple law accounting for the amount of plastic deformation upon increasing stress. This view provides a natural interpretation to stress hardening in foams, demonstrating that plastic effects are present in this material even for minute deformation.

Avalanche precursors in a frictional model

We present a one-dimensional numerical model based on elastically coupled sliders on a frictional incline of variable tilt. This very simple approach makes it possible to study the precursors to the avalanche and to provide a rationalization of different features that have been observed in experiments. We provide a statistical description of the model leading to master equations describing the state of the system as a function of the angle of inclination. Our central results are the reproduction of large-scale regular events preceding the avalanche, on the one hand, and an analytical approach providing an internal threshold for the outbreak of rearrangements before the avalanche in the system, on the other hand.

Why granular media are thermal, and quite normal, after all

Two approaches exist to account for granular dynamics: The athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. Discrete element method (DEM), granular kinetic theory and athermal statistical mechanics (ASM) belong to the first, granular solid hydrodynamics (GSH) to the second one. A discussion of the conceptual differences between both is given here, leading, among others, to the following insights: 1) While DEM and granular kinetic theory are well justified to take grains as athermal, any entropic consideration is far less likely to succeed. 2) In addition to modeling grains as a gas of dissipative, rigid mass points, it is very helpful take grains as a thermal solid that has been sliced and diced. 3) General principles that appear invalid in granular media are repaired and restored once the true entropy is included. These abnormalities (such as invalidity of the fluctuation-dissipation theorem, granular temperatures failing to equilibrate, and grains at rest unable to explore the phase space) are consequences of the athermal approximation, not properties of granular media.

Creep of sound paths in consolidated granular material detected through coda wave interferometry

The time evolution of the contact force structure of a consolidated granular material subjected to a constant stress is monitored using the coda wave interferometry method. In addition, the nature of the aging and rejuvenation processes are investigated. These processes are interpreted in terms of affine and nonaffine structural path deformations. During the later stages of creep, the rearrangements of subgrains are so small that they only produce affine deformations in the contact paths, without any significant changes in the structural configuration. As a result, the strain path distribution follows the macroscopic strain. Conversely, in the presence of ultrasonic perturbations, the nonaffine grain buckling mechanism dominates, producing relatively drastic changes in the structural configuration accompanied by path deformations of the order of the grain size. This plastic mechanism induces material rejuvenation that is observed macroscopically as an ultrasonically accelerated creep.

Creep and aging of hard-sphere glasses under constant stress

We investigate the aging behavior of glassy suspensions of nearly hard-sphere colloids submitted to a constant shear stress. For low stresses, below the yield stress, the system is subject to creep motion. As the sample ages, the shear rate exhibits a power-law decrease with time with exponents that depend on the sample age. We use a combination of rheological experiments with time-resolved photon correlation spectroscopy to investigate the time evolution of the sample dynamics under shear on various time and length scales. Long-time light-scattering experiments reveal the occurrence of microscopic rearrangement events that are linked with the macroscopic strain deformation of the sample. Dynamic time sweep experiments indicate that while the internal microscopic dynamics slow down continuously with waiting time, the storage and loss moduli are almost constant after a fast, weak decrease, resembling the behavior of quenched systems with partially frozen-in stresses.

Grains unchained: local fluidization of a granular packing by focused ultrasound

We report experimental results on the dynamics of a granular packing submitted to high-intensity focused ultrasound. Acoustic radiation pressure is shown to remotely induce local rearrangements within a pile as well as global motion around the focal spot in an initially jammed system. We demonstrate that this fluidization process is intermittent for a range of acoustic pressures and hysteretic when the pressure is cycled. Such a first-order-like unjamming transition is reproduced in numerical simulations in which the acoustic pressure field is modeled by a localized external force. Further analysis of the simulated packings suggests that in the intermittent regime unjamming is not associated with any noticeable prior structural signature. A simple two-state model based on effective temperatures is proposed to account for these findings.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology μ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Shear-Rate-Independent Diffusion in Granular Flows

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Mechanical fluctuations suppress the threshold of soft-glassy solids: The secular drift scenario

We propose a dynamical mechanism leading to the fluidization by external mechanical fluctuations of soft-glassy amorphous material driven below the yield stress. The model is based on the combination of memory effect and nonlinearity, leading to an accumulation of tiny effects over a long term. We test this scenario on a granular packing driven mechanically below the Coulomb threshold. We provide evidence for an effective viscous response directly related to small stress modulations in agreement with the theoretical prediction of a generic secular drift. We propose to extend this result more generally to a large class of glassy systems.

Applying GSH to a wide range of experiments in granular media

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, whose wide range of applicability is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: i) static stress distribution, clogging; ii) elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; iii) rapid dense flow: the μ-rheology, Bagnold scaling and the stress minimum; iv) elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and non-local fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

Emergence of cooperativity in plasticity of soft glassy materials

The elastic coupling between plastic events is generally invoked to interpret plastic properties and the failure of amorphous soft glassy materials. We report an experiment where the emergence of a self-organized plastic flow is observed well before the failure. For this we impose an homogeneous stress on a granular material, and measure local deformations for very small strain increments using a light scattering setup. We observe a nonhomogeneous strain that appears as transient bands of mesoscopic size and a well-defined orientation, which is different from the angle of the macroscopic frictional shear band that appears at the failure. The presence and the orientation of those microbands may be understood by considering how localized plastic reorganizations redistribute stresses in a surrounding continuous elastic medium. We characterize the length scale and persistence of the structure. The presence of plastic events and the mesostructure of the plastic flow are compared to numerical simulations.

Force and flow at the onset of drag in plowed granular media

We study the transient drag force FD on a localized intruder in a granular medium composed of spherical glass particles. A flat plate is translated horizontally from rest through the granular medium to observe how FD varies as a function of the medium's initial volume fraction, ϕ. The force response of the granular material differs above and below the granular critical state, ϕc, the volume fraction which corresponds to the onset of grain dilatancy. For ϕ<ϕc FD increases monotonically with displacement and is independent of drag velocity for the range of velocities examined (<10 cm/s). For ϕ>ϕc, FD rapidly rises to a maximum and then decreases over further displacement. The maximum force for ϕ>ϕc increases with increasing drag velocity. In quasi-two-dimensional drag experiments, we use granular particle image velocimetry (PIV) to measure time resolved strain fields associated with the horizontal motion of a plate started from rest. PIV experiments show that the maxima in FD for ϕ>ϕc are associated with maxima in the spatially averaged shear strain field. For ϕ>ϕc the shear strain occurs in a narrow region in front of the plate, a shear band. For ϕ<ϕc the shear strain is not localized, the shear band fluctuates in space and time, and the average shear increases monotonically with displacement. Laser speckle measurements made at the granular surface ahead of the plate reveal that for ϕ<ϕc particles are in motion far from the intruder and shearing region. For ϕ>ϕc, surface particles move only during the formation of the shear band, coincident with the maxima in FD, after which the particles remain immobile until the sheared region reaches the measurement region.

Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material

At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no rearrangements. Yet between these limits, there may be a self-organized plastic regime with rearrangements, but with no net change upon reversing a deformation. We measure the oscillatory response of a jammed interfacial material, and directly observe rearrangements that couple to bulk stress and dissipate energy, but do not always give rise to global irreversibility.

Nonlocal rheology of granular flows across yield conditions

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A nonlocal constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

Onset of flow in a confined colloidal glass under an imposed shear stress

A confined colloidal glass, under the imposition of a uniform shear stress, is investigated using numerical simulations. Both at macro- and microscales, the consequent dynamics during the onset of flow is studied. When the imposed stress is gradually decreased, the time scale for the onset of steady flow diverges, associated with long-lived spatial heterogeneities. Near this yield-stress regime, persistent creep in the form of shear-banded structures is observed.

Experimental investigation of plastic deformations before a granular avalanche

We present an experimental study of the deformation inside a granular material that is progressively tilted. We investigate the deformation before the avalanche with a spatially resolved diffusive wave spectroscopy setup. At the beginning of the inclination process, we first observe localized and isolated events in the bulk, with a density which decreases with the depth. As the angle of inclination increases, series of microfailures occur periodically in the bulk, and finally a granular avalanche takes place. The microfailures are observed only when the tilt angles are larger than a threshold angle much smaller than the granular avalanche angle. We have characterized the density of reorganizations and the localization of microfailures. We have also explored the effect of the nature of the grains, the relative humidity conditions, and the packing fraction of the sample. We discuss those observations in the framework of the plasticity of granular matter. Microfailures may then be viewed as the result of the accumulation of numerous plastic events.

Ultrasound induces aging in granular materials

Aging and rejuvenation have been identified as the general mechanisms that rule the time evolution of granular materials subjected to some external confinement pressure. In creep experiments performed in a triaxial configuration, we obtained evidence that relatively high intensity ultrasound waves propagating through the material induce both weakening and significant plasticity. In the framework of glassy materials, it is shown that the effect of ultrasound can be simply accounted for by a general variable, the fluidity, whose dynamics are described by an effective aging parameter that strongly decreases with sound amplitude and vanishes at the yield stress limit. The response from step perturbations in ultrasound intensity provided a method to assess the effective-viscosity jumps which are direct evidence of acoustic fluidization.

Creep in colloidal glasses

We investigate the nonlinear response to shear stress of a colloidal hard-sphere glass, identifying several regimes depending on time, sample age, and the magnitude of applied stress. This emphasizes a connection between stress-imposed deformation of soft and hard matter, in particular, colloidal and metallic systems. A generalized Maxwell model rationalizes logarithmic creep for long times and low stresses. We identify diverging time scales approaching a critical yield stress. At intermediate times, strong aging effects are seen, which we link to a stress overshoot seen in stress-strain curves.

Hot spots in an athermal system

We study experimentally the dynamical heterogeneities occurring at slow shear, in a model amorphous glassy material, i.e., a 3D granular packing. The deformation field is resolved spatially by using a diffusive wave spectroscopy technique. The heterogeneities show up as localized regions of strong deformations spanning a mesoscopic size of about 10 grains and called the "hot spots." The spatial clustering of hot spots is linked to the subsequent emergence of shear bands. Quantitatively, their appearance is associated with the macroscopic plastic deformation, and their rate of occurrence gives a physical meaning to the concept of "fluidity," recently used to describe the local and nonlocal rheology of soft glassy materials.