Discontinuous rigidity transition associated with shear jamming in granular simulations.

We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

Stress-stress correlations reveal force chains in gels.

We investigate the spatial correlations of microscopic stresses in soft particulate gels using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space. This leads to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis of the model particulate gels at low particle volume fractions demonstrates that stress-stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress-stress correlations can distinguish floppy from rigid gel networks and that the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.

Estimation of the equilibrium free energy for glasses using the Jarzynski equality.

The free energy of glasses cannot be estimated using thermodynamic integration as glasses are intrinsically not in equilibrium. We present numerical simulations showing that, in contrast, plausible free-energy estimates of a Kob-Andersen glass can be obtained using the Jarzynski relation. Using the Jarzynski relation, we also compute the chemical potential difference of the two components of this system and find that, in the glassy regime, the Jarzynski estimate matches well with the extrapolated value of the supercooled liquid. Our findings are of broader interest as they show that the Jarzynski method can be used under conditions where the thermodynamic integration approach, which is normally more accurate, breaks down completely. Systems where such an approach might be useful are gels and jammed glassy structures formed by compression.

Computation of the chemical potential and solubility of amorphous solids.

Using a recently developed technique to estimate the equilibrium free energy of glassy materials, we explore if equilibrium simulation methods can be used to estimate the solubility of amorphous solids. As an illustration, we compute the chemical potentials of the constituent particles of a two-component Kob-Andersen model glass former. To compute the chemical potential for different components, we combine the calculation of the overall free energy of the glass with a calculation of the chemical potential difference of the two components. We find that the standard method to compute chemical potential differences by thermodynamic integration yields not only a wide scatter in the chemical potential values, but also, more seriously, the average of the thermodynamic integration results is well above the extrapolated value for the supercooled liquid. However, we find that if we compute the difference in the chemical potential of the components with the non-equilibrium free-energy expression proposed by Jarzynski, we obtain a good match with the extrapolated value of the supercooled liquid. The extension of the Jarzynski method that we propose opens a potentially powerful route to compute the free-energy related equilibrium properties of glasses. We find that the solubility estimate of amorphous materials obtained from direct-coexistence simulations is only in fair agreement with the solubility prediction based on the chemical potential calculations of a hypothetical "well-equilibrated glass." In direct-coexistence simulations, we find that, in qualitative agreement with experiments, the amorphous solubility decreases with time and attains a low solubility value.

Unified phase diagram of reversible-irreversible, jamming, and yielding transitions in cyclically sheared soft-sphere packings.

Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram.

Numerical method for computing the free energy of glasses.

We propose a numerical technique to compute the equilibrium free energy of glasses that cannot be prepared quasireversibly. For such systems, standard techniques for estimating the free energy by extrapolation cannot be used. Instead, we use a procedure that samples the equilibrium partition function of the basins of attraction of the different inherent structures (local potential energy minima) of the system. If all relevant inherent structures could be adequately sampled in the (supercooled) liquid phase, our approach would be rigorous. In any finite simulation, we will miss the lower-energy inherent structures that become dominant at very low temperatures. We find that our free energy estimates for a Kob-Andersen glass are lower than those obtained by very slow cooling, even at temperatures down to one-third of the glass transition temperature. The current approach could be applied to compute the chemical potential of ultrastable glassy materials and should enable the estimation of their solubility.

The jamming transition is a k-core percolation transition.

We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the emergence of the giant 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdös-Rényi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network.

Force networks and jamming in shear-deformed sphere packings.

The emergence of rigidity upon changes of temperature, density, or applied stresses in disordered assemblies of particles is of interest in a wide range of soft matter, from glass formers, gels, foams, and granular matter. Shear jamming of frictional grains presents an interesting special case wherein the application of shear stress leads to rigidity rather than its loss. The formation of self-organized structures that resist shear deformation offers an appealing geometric picture of shear jamming, which nevertheless is incompletely developed, and not well integrated with ideas concerning rigidity in frictionless systems. Exploiting the observation that athermally sheared sphere assemblies develop structural features necessary for shear jamming even in the absence of friction [H. A. Vinutha and S. Sastry, Nature Physics 12, 578 (2016)1745-247310.1038/nphys3658], we analyze conditions for jamming in such assemblies computationally. Solving force and torque balance conditions for their contact geometry, we show, and validate with frictional simulations, that the mean contact number Z equals D+1 (for spatial dimension D=2,3) at jamming for both finite and infinite friction, above the "random loose packing" limit density, at variance with previous analyses of frictional jamming. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems. Along lines explored in studying covalent glasses, we perform rigidity percolation analysis for D=2 and find that rigidity percolation precedes shear jamming, which, however, coincides with the percolation of over-constrained regions, leading to the identification of a regime analogous to the intermediate phase observed in covalent glasses. Together, these results provide a geometric description of shear jamming that relate closely with analyses of jamming, rigidity, and the glass transition in frictionless systems, and thus help develop a unified description of jamming phenomenology in diverse disordered matter.

Free volume under shear.

Using an athermal quasistatic simulation protocol, we study the distribution of free volumes in sheared hard-particle packings close to, but below, the random-close packing threshold. We show that under shear, and independent of volume fraction, the free volumes develop features similar to close-packed systems - particles self-organize in a manner as to mimick the isotropically jammed state. We compare athermally sheared packings with thermalized packings and show that thermalization leads to an erasure of these structural features. The temporal evolution in particular the opening-up and the closing of free-volume patches is associated with the single-particle dynamics, showing a crossover from ballistic to diffusive behavior.