Shear Stress Fluctuations in the Granular Liquid and Solid Phases

Abstract

We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distribution's skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.

A random neighbour model for yielding

“…It seems remarkable that it is also well fitted by a log-normal distribution (or similar) [16]. Such a distribution seems to be a generic signature of the strong correlations introduced into the system by the force chains [17], and some authors have resorted to universality as some underlying feature for such observations [25].…”

Friction memory in the stick-slip of a sheared granular bed

“…In the experiments considered [4,15], the granular medium is composed of glass beads 2 mm ± 10% in diameter confined to a circular PVC Couette cell of height 7 cm and inner and outer diameters 25 and 40 cm. The shear force (energy injection) is provided by an overhead plate of weight 0.75 kg rotating in the channel on the granular surface, driven via a torsion spring so as to generate a stickslip motion (a simple sketch of the apparatus is shown in fig.…”

“…For velocities in the range of steady sliding (θ N ∼ 10 −1 rad/s), the state variable approaches ϕ = ϕ ss = θ 0 =˙θ. Therefore, up to a logarithmic term the friction torque for the rate-andstate model has a quadratic dependence on velocity [13][14][15] with the prefactor given by χ.…”

“…Although fundamentally different in nature, granular matter has been shown to share many similarities with solid surfaces as far as shear stress is concerned [3], with the addition of possible hardening when the top plate velocity becomes large enough [13][14][15][16]. It has been found in particular that the ageing of static friction with time and the weakening of dynamic friction with velocity in granular gouges can be described by the same phenomenological laws as solids [3,8,9], generally known as rate-and-state friction laws (RS).…”

“…[4]) in the stochastic motion equation for the plate. To this end classic rate-andstate equations are suitably modified to allow for the Bagnold [13] and weakening-hardening [14][15][16][17] regimes characteristic of granular systems. However some discrepancies do remain and we shall discuss their possible origin.…”