Transition In Granular Media Research Articles

Critical scaling near the yielding transition in granular media.

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low-inertial-number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress Σ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied Σ, isotropically prepared states with size L must undergo a total strain γ_{ms}(Σ,L). The number density of MS packings (∝γ_{ms}^{-1}) vanishes for Σ>Σ_{c}≈0.11 according to a critical scaling form with a length scale ξ∝|Σ-Σ_{c}|^{-ν}, where ν≈1.7-1.8. Above the yield stress (Σ>Σ_{c}), no MS packings that can support Σ exist in the large-system limit L/ξ≫1. MS packings generated via shear possess anisotropic force and contact networks, suggesting that Σ_{c} is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.

Mobility and stability of glasses

Recently, the mobility and stability of glasses have received a great deal of attention. In particular, there has been a resurgence in trying to understand the mechanism by which mechanical stress or deformation imparts excess mobility (faster dynamics) to glassy and jammed systems. Because there is still no recognized structural signature that identifies the glassy or jammed state, appearing as a frozen amorphous ‘‘liquid,’’ it is not completely clear what structural changes occur with increased mobility via deformation or temperature. It is also not clear if the transition to a more mobile (or more fluid-like) state via increasing mechanical load is the same as that occurring via increasing temperature. There are reports that observe some surprisingly common features between these very different systems. One of the big questions that remain is: How is the molecular glass transition obtained on decreasing temperature related to the colloidal glass transition or jamming transition in granular media obtained on increasing volume fraction? Understanding the common elements that these disparate systems display should provide insight into the underlying dynamics and packing frustration. Current efforts analyze these systems in a variety of different ways: potential energy barriers and landscapes, distribution of relaxation times, density fluctuations, distribution of force chains, shear transformation zones, and a random first order transition theory. Many of these approaches have in common the idea of local regions comprised of clusters of units (e.g., molecules, polymer segments or colloidal particles), which may be dynamically faster or slower than the average structural relaxation time, where changes in stress or strain can concentrate.

Jamming transition in granular media: A mean-field approximation and numerical simulations

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean-field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity, we have applied the theory to a lattice model, and a transition with exactly the same nature of the glass transition in mean-field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics, and a jamming transition with glassy features is observed. In particular, two-step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature.

Vibration-induced jamming transition in granular media

The quasistatic frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency f(p) in the range 10(-4) Hz to 5 Hz, while weak vibrations at high-frequency f(s), in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration Gamma is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of Gamma or f(p). In a plot of ln f(p) against 1/Gamma, the position of the peak follows an Arrhenius-like behavior over four orders of magnitude in f(p). The data can be described as a stochastic hopping process involving a probability factor exp(-Gamma(j)/Gamma) with Gamma(j) a f(s)-dependent characteristic vibration intensity. An f(s)-independent description is given by exp(-tau(j)/tau), with tau(j) an intrinsic characteristic time, and tau=Gamma(n)/2pif(s), n=0.5-0.6, an empirical control parameter with unit of time. tau is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behavior of the vibrated granular system, which, at the time scale 1/f(p), is solid-like at low Gamma, and the oscillator is jammed into the granular material, and is fluid-like at high Gamma, where the oscillator can slide viscously.