Static Granular Packings Research Articles

Elastic waves in particulate glass-rubber mixtures.

We investigate the propagation of waves in dense static granular packings made of soft and stiff particles subjected to hydrostatic stress. Physical experiments in a triaxial cell equipped with broadband piezoelectric wave transducers have been performed at ultrasound frequencies. The time of flight is measured in order to study the combined effect of applied stress and rubber content on the elastic properties of the mixtures. The bulk stiffness deduced from the wave speed is nonlinear and non-monotonic with the increasing percentage of rubber with a more prominent effect at higher pressures. Moreover, in the frequency domain, a spectral analysis gives insights on the transition from a glass- to a rubber-dominated regime and the influence of rubber particles on the energy dissipation. Mixtures with rubber content below 30% show enhanced damping properties, associated with slightly higher stiffness and lighter weight.

Granular packing as model glass formers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175121, 11675110, and U1432111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110073120073).

Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.

Wang-Landau algorithm for entropic sampling of arch-based microstates in the volume ensemble of static granular packings

We implement the Wang-Landau algorithm to sample with equal probabilities the static configurations of a model granular system. The "non-interacting rigid arch model" used is based on the description of static configurations by means of splitting the assembly of grains into sets of stable arches. This technique allows us to build the entropy as a function of the volume of the packing for large systems. We make a special note of the details that have to be considered when defining the microstates and proposing the moves for the correct sampling in these unusual models. We compare our results with previous exact calculations of the model made at moderate system sizes. The technique opens a new opportunity to calculate the entropy of more complex granular models.Received: 19 January 2015, Accepted: 25 February 2015; Reviewed by: M. Pica Ciamarra, Nanyang Technological University, Singapore; Edited by: C. S. O'Hern; DOI: http://dx.doi.org/10.4279/PIP.070001Cite as: D Slobinsky, L A Pugnaloni, Papers in Physics 7, 070001 (2015) This paper, by Demian Slobinsky, Luis Ariel Pugnaloni , is licensed under the Creative Commons Attribution License 3.0.

Impact of the timestep in some molecular dynamics simulations on compression of granular systems

We conduct two-dimensional molecular dynamics simulations to study the statistical distribution of the force-moment (defined as stress multiplied by volume) of static granular packings under external isotropic compression. To that end, we generate packings by compressing initially ordered lattices using irregular, randomly generated, walls. Velocity-Verlet algorithm and linear spring-dashpot interactions are employed. With this specific method, the obtained statistical distributions of the force-moment are similar for different initial packings. However they depend on the timestep selection within a range of values. This shows that inadequate molecular dynamic simulations may provide different classes of solutions for the same physical process, and this could cause problems to validate theoretical approaches based on statistical mechanics.

Vibrations of jammed disk packings with Hertzian interactions

Contact breaking and Hertzian interactions between grains can both give rise to nonlinear vibrational response of static granular packings. We perform molecular dynamics simulations at constant energy in 2D of frictionless bidisperse disks that interact via Hertzian spring potentials as a function of energy and measure directly the vibrational response from the Fourier transform of the velocity autocorrelation function. We compare the measured vibrational response of static packings near jamming onset to that obtained from the eigenvalues of the dynamical matrix to determine the temperature above which the harmonic approximation breaks down. We compare packings that interact via single-sided (purely repulsive) and double-sided Hertzian spring interactions to disentangle the effects of the shape of the potential from contact breaking. Our studies show that while Hertzian interactions lead to weak nonlinearities in the vibrational behavior (e.g. the generation of harmonics of the eigenfrequencies of the dynamical matrix), the vibrational response of static packings with Hertzian contact interactions is dominated near jamming by contact breaking as found for systems with repulsive linear spring interactions.

Towards a relevant set of state variables to describe static granular packings

We analyze, experimentally and numerically, the steady states, obtained by tapping, of a two-dimensional granular layer. Contrary to the usual assumption, we show that the reversible (steady state branch) of the density-acceleration curve is nonmonotonous. Accordingly, steady states with the same mean volume can be reached by tapping the system with very different intensities. Simulations of dissipative frictional disks show that equal volume steady states have different values of the force moment tensor. Additionally, we find that steady states of equal stress can be obtained by changing the duration of the taps; however, these states present distinct mean volumes. These results confirm previous speculations that the volume and the force moment tensor are both needed to describe univocally equilibrium states in static granular assemblies.

Force balance in canonical ensembles of static granular packings

We investigate the role of local force balance in the transition from a microcanonicalensemble of static granular packings, characterized by an invariant stress, to a canonicalensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect offorce balance is that the area of this tiling is also invariant in a microcanonical ensemble.We present analytical relations between stress, tiling area and tiling area fluctuations, andshow that a canonical ensemble can be characterized by an intensive thermodynamicparameter conjugate to one or the other. We test the equivalence of different ensemblesthrough the first canonical simulations of the force network ensemble, a model system.

Elegance of Disordered Granular Packings: A Validation of Edward’s Hypothesis

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming a constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly related to the coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states.

Ensemble theory for force networks in hyperstatic granular matter

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P(f). For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P(f) 's differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.

Reply to “Comment on mechanical analog of temperature for the description of force distribution in static granular packings”

Metzger [preceding paper, Phys. Rev. E 69, 053301 (2004)] put forward a number of arguments against the Gaussian force distribution concluded in the investigations by Ngan [Phys. Rev. E 68, 011301 (2003)] and by some previous workers. It is shown here that, with a more proper choice for the constraint in the free energy minimization, the Shannon entropy approach can predict three-dimensional force distributions that are in much better agreement with simulated distributions. In two-dimensional packings, if one accepts a Gaussian distribution at some finite strain in a Hookean force-law situation, then the superposition principle of linear elasticity predicts that the same Gaussian distribution will be maintained at vanishing strains. This argument forms an interesting dilemma with Metzger's argument about the noninvolvement of the force law in statically determinate packings.

Force network ensemble: a new approach to static granular matter.

An ensemble approach for force distributions in static granular packings is developed. This framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. We show how the formalism yields realistic results, both for disordered and regular triangular "snooker ball" configurations, and obtain a shear-induced unjamming transition of the type proposed recently for athermal media.

Erratum: Mechanical analog of temperature for the description of force distribution in static granular packings [Phys. Rev. E68, 011301 (2003)

Received 13 October 2003DOI:https://doi.org/10.1103/PhysRevE.68.069902©2003 American Physical Society

Mechanical analog of temperature for the description of force distribution in static granular packings.

It is shown that in a stressed granular packing, the effect of the applied pressure and structural randomness on the contact force distribution can be described accurately by a variational principle of minimizing energy subject to the constraint of keeping entropy at a fixed value. The constraint on entropy may be regarded as a measure of the degree of retained disorderness in the system. This procedure leads to the introduction of a parameter known as the "mechanical temperature." Similar to the role of the conventional thermal temperature in a thermal system, the mechanical temperature can be viewed as a parameter controlling the mixity between energy minimization and entropy maximization in the equilibrium condition.

Granular materials: Towards the statistical mechanics of jammed configurations

The properties of granular materials can be well defined, that is be a branch of physics, but conventional statistical mechanics is inadequate to handle what amounts to the physics of disordered packings of hard-core particles, either static or driven by external forces. A new approach that employs statistical-mechanical concepts is offered for the description of such systems. An analysis of the stress field in static granular packings is given within the framework of this approach. There are more conventional systems such as polymer glasses which have a rather similar statistical physics to granular media, and some speculative ideas are offered which are a real departure from conventional glass theories.

Force Distributions near Jamming and Glass Transitions.

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.