Jamming at zero temperature, zero friction, and finite applied shear stress

Fabric-based jamming phase diagram for frictional granular materials

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

Interplay between jamming and motility-induced phase separation in persistent self-propelling particles

In living and engineered systems of active particles, self-propulsion induces an unjamming transition from a solid to a fluid phase and phase separation between a gas and a liquidlike phase. We demonstrate an interplay between these two nonequilibrium transitions in systems of persistent active particles. The coexistence and jamming lines in the activity-density plane meet at the jamming transition point in the limit of hard particles or zero activity. This interplay induces an anomalous dynamic in the liquid phase and hysteresis at the active jamming transition.

A jamming plane of sphere packings

The concept of jamming has attracted great research interest due to its broad relevance in soft-matter, such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to sphere packing and optimization problems. Here, we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with initial equilibrium configurations prepared by an efficient swap algorithm. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the metastable glass basin to which the initial configuration belongs to or the absence of such basins. All jammed states, either compression- or shear-jammed, are isostatic and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks nontrivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For crystalline packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close-packing problem and provides a more complete framework to understand jamming.

Correlating the force network evolution and dynamics in slider experiments

The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.

Criticality of the zero-temperature jamming transition probed by self-propelled particles

We perform simulations of athermal systems of self-propelled particles (SPPs) interacting via harmonic repulsion in the vicinity of the zero-temperature jamming transition at point J. Every particle is propelled by a constant force f pointing to a randomly assigned and fixed direction. When f is smaller than the yield force f_y, the system is statically jammed. We find that f_y increases with packing fraction and exhibits finite size scaling, implying the criticality of point J. When f > f_y, SPPs flow forever and their velocities satisfy the k-Gamma distribution. Velocity distributions at various packing fractions and f collapse when the particle velocity is scaled by the average velocity v[combining macron], suggesting that v[combining macron] is a reasonable quantity to characterize the response to f. We thus define a response function R(ϕ,f) = v[combining macron](ϕ,f)/f. The function exhibits critical scaling nicely, implying again the criticality of point J. Our analysis and results indicate that systems of SPPs behave analogically to sheared systems, although their driving mechanisms are apparently distinct.

Rattler-induced aging dynamics in jammed granular systems

Granular materials jam when developing a network of contact forces able to resist the applied stresses. Through numerical simulations of the dynamics of the jamming process, we show that the jamming transition does not occur when the kinetic energy vanishes. Rather, as the system jams, the kinetic energy becomes dominated by rattler particles, which scatter within their cages. The relaxation of the kinetic energy in the jammed configuration exhibits a double power-law decay, which we interpret in terms of the interplay between backbone and rattler particles.

Jamming of Semiflexible Polymers

We study jamming in model freely rotating polymers as a function of chain length N and bond angle θ_{0}. The volume fraction at jamming ϕ_{J}(θ_{0}) is minimal for rigid-rodlike chains (θ_{0}=0), and increases monotonically with increasing θ_{0}≤π/2. In contrast to flexible polymers, marginally jammed states of freely rotating polymers are highly hypostatic, even when bond and angle constraints are accounted for. Large-aspect-ratio (small θ_{0}) chains behave comparably to stiff fibers: resistance to large-scale bending plays a major role in their jamming phenomenology. Low-aspect-ratio (large θ_{0}) chains behave more like flexible polymers, but still jam at much lower densities due to the presence of frozen-in three-body correlations corresponding to the fixed bond angles. Long-chain systems jam at lower ϕ and are more hypostatic at jamming than short-chain systems. Implications of these findings for polymer solidification are discussed.

Change of criticality in a prototypical thermoacoustic system

In this paper, we report on the existence of the phenomenon of change of criticality in a horizontal Rijke tube, a prototypical thermoacoustic system. In the experiments, the phenomenon is shown to occur as the criticality of the Hopf bifurcation changes with varying air flow rates in the system. The dynamics of a nonlinear system exhibiting Hopf bifurcation can be described using a Stuart-Landau equation (SLE) in the vicinity of the bifurcation point. The criticality of Hopf bifurcations can be determined by the Landau constant of the Stuart-Landau equation, which represents the effect of nonlinearities in the system. We propose an SLE to model the bifurcations seen in the horizontal Rijke tube. We identify a rescaled version of Strouhal number as the Landau constant, which determines the criticality of the bifurcation in the present study.

Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach

A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.

Poiseuille flow of soft glasses in narrow channels: from quiescence to steady state

Using numerical simulations, the onset of Poiseuille flow in a confined soft glass is investigated. Starting from the quiescent state, steady flow sets in at a time scale which increases with a decrease in applied forcing. At this onset time scale, a rapid transition occurs via the simultaneous fluidization of regions having different local stresses. In the absence of steady flow at long times, creep is observed even in regions where the local stress is larger than the bulk yielding threshold. Finally, we show that the time scale to attain steady flow depends strongly on the history of the initial state.

Finite size analysis of zero-temperature jamming transition under applied shear stress by minimizing a thermodynamic-like potential

By finding local minima of a thermodynamic-like potential, we generate jammed packings of frictionless spheres under constant shear stress σ and obtain the yield stress σy by sampling the potential energy landscape. For three-dimensional systems with harmonic repulsion, σy satisfies the finite size scaling with the limiting scaling relation σy∼ϕ-ϕc,∞, where ϕc,∞ is the critical volume fraction of the jamming transition at σ=0 in the thermodynamic limit. The finite size scaling implies a length ξ∼(ϕ-ϕc,∞)-ν with ν=0.81±0.05, which turns out to be a robust and universal length scale exhibited as well in the finite size scaling of multiple quantities measured without shear and independent of particle interaction. Moreover, comparison between our new approach and quasistatic shear reveals that quasistatic shear tends to explore low-energy states.

Regime transitions of granular flow in a shear cell: a micromechanical study

The regime transitions of granular flow in a model shear cell are investigated numerically with a stress-controlled boundary condition. The correlations between the elastically and kinetically scaled stresses and the packing fraction are examined, and two packing fractions (0.58 and 0.50) are identified for the quasistatic to intermediate and intermediate to inertial regime transitions. The profiles and structures of contact networks and force chains among particles in different flow regimes are investigated. It is shown that the connectivity (coordination number) among particles and the homogeneity in the shear flow increase as the system goes through the inertial, intermediate, and then quasistatic regimes, and there is only little variation in the internal structure after the system has entered the quasistatic regime. Short-range force chains start to appear in the inertial regime, which also depend on the magnitude of the shear rate. The percolation of system-spanning force chains through the whole system is a characteristic of the onset of the quasistatic regime, which happens at a packing fraction that is close to the glass transition, i.e., about random loose packing (0.58) but far below the isotropic quasistatic (athermal) jamming packing fraction of random close packing (0.64). The tails of the probability density distribution P(f) of the scaled normal contact forces for the flows in different regimes are quantified by a stretched exponential P(f)=exp(-cf^{n}) with a remarkable finding that n ∼ 1.1 may be a potential demarcation point separating the quasistatic regime and the inertial or intermediate regimes.

Solid-on-solid single-block dynamics under mechanical vibration

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena are not well understood. Here we address these questions focusing on a simple spring-block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows us to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion, we identify the conditions under which friction is suppressed and/or recovered, and we evidence the critical role played by surface modulations and by the properties of the confining force.

Edwards thermodynamics of the jamming transition for frictionless packings: ergodicity test and role of angoricity and compactivity

This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables A and X describe the approach to jamming through a series of scaling relations as A → 0+ and X → 0-. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a "jamming temperature" T(J) composed of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O'Hern [Phys. Rev. E 74, 061304 (2006)], showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

Relaxations and rheology near jamming

We determine the form of the complex shear modulus G* in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of G* on the frequency and distance to the jamming transition, which is confirmed by numerics.

Jamming phase diagram for frictional particles

We investigate the jamming transition of frictional particulate systems via discrete element simulations, reporting the existence of new regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be "fragile" as speculated. In particular, we find a regime, characterized by extremely long processes, with a diverging time scale, whereby a suspension first flows but then suddenly jams. We link this sudden jamming transition to the presence of impeded dilatancy.

Critical scaling near jamming transition for frictional granular particles

The critical rheology of sheared frictional granular materials near jamming transition is numerically investigated. It is confirmed that there exists a true critical density which characterizes the onset of the yield stress and two fictitious critical densities which characterize the scaling laws of rheological properties. We find the existence of a hysteresis loop between two of the critical densities for each friction coefficient. It is noteworthy that the critical scaling law for frictionless jamming transition seems to be still valid even for frictional jamming despite using fictitious critical density values.

Fluidization of wet granulates under shear

Small amounts of a wetting liquid render sand a stiff and moldable material. The cohesive forces between the sand grains are caused by capillary bridges at the points of contact. Due to the finite strength of these bridges wet sand undergoes a transition from an arrested (i.e., solidified) to a fluidized state under an externally applied shear force. The transition between these two dynamic states is studied in a MD-type simulation of a two-dimensional assembly of bidisperse frictionless disks under the action of a cosine force profile. In addition to soft core repulsion the disks interact through a hysteretic and short ranged attractive force modeling the effect of the capillary bridges. In this model the transition between the fluidized and the arrested state is discontinuous and hysteretic. The parameter dependence of the critical force for solidification is modeled by combining theoretical arguments with a detailed numerical exploration of the transition. We address a range of densities from slightly below close packing until slightly above densities where the system approaches a shear-banded state. Differences and similarities of the transition in wet granulates to the jamming transition are also addressed.

From crystal to amorphous: A novel route to unjamming in soft disk packings

Numerical studies on the unjamming packing fraction of bi- and polydisperse disk packings, which are generated through compression of a monodisperse crystal, are presented. In bidisperse systems, a fraction f(+) = 0.400 up to 0.800 of the total number of particles has their radii increased by [Formula: see text] R , while the rest has their radii decreased by the same amount. Polydisperse packings are prepared by changing all particle radii according to a uniform distribution in the range [-ΔR, ΔR] . The results indicate that the critical packing fraction is never larger than the value for the initial monodisperse crystal, Φ(o) = π/√12, and that the lowest value achieved is approximately the one for random close packing. These results are seen as a consequence of the interplay between the increase in small-small particle contacts and the local crystalline order provided by the large-large particle contacts.

Model for the scaling of stresses and fluctuations in flows near jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and the values of the exponents depart from prior results. We validate predictions of the model with simulations.

Unjamming dynamics: the micromechanics of a seismic fault model

The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional molecular dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow us to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.