Solidlike behavior and anisotropy in rigid frictionless bead assemblies

Abstract

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension and simple shear. Generalizing recent result, we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface in principal stress space differs somewhat from the Mohr-Coulomb prediction, and is more adequately described by the Lade-Duncan or Matsuoka-Nakai criteria. We study geometric characteristics and force networks under varying stress levels within the supported range. Although the scalar state variables stay equal to the values observed in systems under isotropic pressure, the material, once subjected to a deviator stress, possesses some fabric and force distribution anisotropies. Each kind of anisotropy can be described, in good approximation, by a single parameter. Within the supported stress range, along each one of the three investigated stress paths, among those three quantities: deviator stress to mean stress ratio, fabric anisotropy parameter, force anisotropy parameter, any one determines the values of the two others. The pair correlation function also exhibits short range anisotropy, up to a distance between bead surfaces of the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed.

Universal jamming phase diagram in the hard-sphere limit

“…Thus, at low values of pσ 3 / for soft spheres, the athermal dynamic yield stress y0 must scale with pressure: y0 ∼ p at T /pσ 3 = 0. This is consistent with granular experiments and simulations that find a macroscopic dynamic friction coefficient in the limit of low strain rate [10][11][12]18,19].…”

“…(2) isolates the interaction energy scale in only one of the three control parameters, the dimensionless pressure pσ 3 / . The combinations /p andγ √ m/pσ are familiar to the granular materials community [10][11][12]. The dimensionless shear stress /p is a macroscopic dynamic friction coefficient, while the dimensionless strain rateγ m/pσ 3 is typically called the inertial number and is understood physically as follows.…”

Effect of particle collisions in dense suspension flows

“…[18] hold true when particles are frictional. This is not obvious at all, because in the inertial case friction affects the scaling exponents near jamming [32,33]. However, in the presence of inertia, the change of scaling behavior stems from a change in the dominant dissipation mechanism, which becomes dominated by friction instead of collisions close to jamming [34].…”

Unifying Suspension and Granular flows near Jamming

“…(15,19) lead to a prediction for the exponent γ μ entering in the constitutive relation μ(J). Together with previous results showing that c ∼ 1/ √ δz [8,48], we obtain expressions for γ and α , corresponding to: c ∼ δμ −(1+θ e )/(3+θ e ) ∼ δμ −0.41 (20) both for inertial and viscous flows.…”

“…(1)(2)(3)(4)(5)(6)(7). Observations support that as jamming is approached, particles form an extended network of contacts, and that the stress is dominated by contact forces [2,5,15,31]. In this work we review a framework to de- scribe flow in such situations.…”