Bridging percolation and particle dynamics models of the granular rigidity transition (original) (raw)

Force percolation transition of jammed granular systems

Physical review. E, 2017

The mechanical and transport properties of jammed materials originate from an underlying percolating network of contact forces between the grains. Using extensive simulations we investigate the force-percolation transition of this network, where two particles are considered as linked if their interparticle force overcomes a threshold. We show that this transition belongs to the random percolation universality class, thus ruling out the existence of long-range correlations between the forces. Through a combined size and pressure scaling for the percolative quantities, we show that the continuous force percolation transition evolves into the discontinuous jamming transition in the zero pressure limit, as the size of the critical region scales with the pressure.

Structural evolution of granular systems: Theory

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems-the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of examples: dense systems undergoing progressive compaction; initial dilation of very dense systems; and the approach to steady state of general systems. It is shown that the convergence to steady state is exponential, except when contacts are only broken and no new contacts are made, in which case the approach is algebraic in time. Where no closed form solutions are possible, numerical solutions of the evolution dynamics are shown, which agree with results in the literature. The formalism can be extended to other structural characteristics, making it possible to understand the structural organisation of granular systems in general.

Percolation process in a model granular system in two dimensions

Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1996

The role of grain shape on aggregation is studied on the basis of a percolation theory. It is demonstrated that the coverage at the percolation point depends strongly on projections of grains.

Evolution of Percolating Force Chains in Compressed Granular Media

Physical Review Letters, 2002

The evolution of effective force chains percolating through a compressed granular system is investigated. We performed experiments by compressing an ensemble of spherical particles in a cylindrical container monitoring the macroscopic constitutive behavior and the acoustic signals emitted by microscopic rearrangements of particles. As a novel approach, we applied the continuous damage model of fiber bundles to describe the evolution of the array of force chains during the loading process. The model provides a nonlinear constitutive behavior in good quantitative agreement with the experimental results. For a system of hard particles the model predicts a universal power law divergence of stress when approaching a critical deformation. The amplitude distribution of acoustic signals was found experimentally to follow a power law with exponent δ = 1.15 ± 0.05 which is in a good agreement with the analytic solution of the model.

Percolation of a fine particle in static granular beds

Physical Review E

We study the percolation of a fine spherical particle under gravity in static randomly packed large-particle beds with different packing densities φ and large to fine particle size ratios R ranging from 4 to 7.5 using discrete element method simulations. The particle size ratio at the geometrical trapping threshold, defined by three touching large particles, R t = √ 3/(2 − √ 3) = 6.464, divides percolation behavior into passing and trapping regimes. However, the mean percolation velocity and diffusion of untrapped fine particles, which depend on both R and φ, are similar in both regimes and can be collapsed over a range of R and φ with the appropriate scaling. An empirical relationship for the local percolation velocity based on the local pore throat to fine particle size ratio and packing density is obtained, which is valid for the full range of size ratio and packing density we study. Similarly, in the trapping regime, the probability for a fine particle to reach a given depth is well described by a simple statistical model. Finally, the percolation velocity and fine particle diffusion are found to decrease with increasing restitution coefficient.

Modelling phase transition in granular materials: From discontinuum to continuum

International Journal of Solids and Structures, 2020

This work focuses on the behaviour of granular materials under unsteady, simple shear conditions and, in particular, on from solid-to fluid-like phase transition. The authors introduce a theoretical model, based on continuum mechanics, able of predicting the mechanical behaviour of granular media under both quasi-static and dynamic conditions. The model assumes a parallel scheme where confining and shear stresses are computed as the sum of two contributions: the quasi-static and the collisional one. The quasi-static contribution is obtained by employing an elastic-plastic model including the critical state concept, while the collisional one is derived from the kinetic theory of granular gases. In order to test the model under unsteady conditions, DEM numerical simulations of time evolving homogeneous shear flows have been performed by considering an assembly of frictional, deformable spheres, under constant volume conditions. Simulations have been performed by systematically changing both void ratio and shear rate. The comparison between theoretical model predictions and DEM results is done in terms of time evolution of stresses and granular temperature. Suitable initial conditions are imposed to reproduce both solid to fluid (liquefaction) and fluid to solid (solidification) phase transitions.

A microscopic 2D lattice model of dimer granular compaction with friction

Physical Review E, 2002

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the

Microscopic two-dimensional lattice model of dimer granular compaction with friction

2002

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time τ during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if τ is not very large, while a power law tail develops for larger values of τ . Moreover, in the absence of friction, a critical value τ * exists which signals the crossover between two different regimes: for τ < τ * the asymptotic density scales with a power law of τ , while for τ > τ * it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.

Shearing of loose granular materials: a statistical mesoscopic model

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the "density" of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a nontrivial patterning of the system, with high-density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band, which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is, ...