Arches and contact forces in a granular pile

Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch-grains whereas the anisotropic component is marginally distinguishable between the two types of particles. The contact force distributions demonstrate that an exponential tail (compatible with the maximization of entropy under no extra constraints) is followed only by the out-of-arch contacts. In-arch contacts seem to be compatible with a Gaussian distribution consistent with a recently introduced approach that takes into account constraints imposed by the local force balance on grains.Comment: 7 pages, 7 figures, major revisio

Dynamic Critical Response in Damped Random Spring Networks

he isostatic state plays a central role in organizing the response of many amorphous materials. We construct a diverging length scale in nearly isostatic spring networks that is defined both above and below isostaticity and at finite frequencies and relate the length scale to viscoelastic response. Numerical measurements verify that proximity to isostaticity controls the viscosity, shear modulus, and creep of random networks.Process and EnergyMechanical, Maritime and Materials Engineerin

On the apparent yield stress in non-Brownian magnetorheological fluids

We use simulations to probe the flow properties of dense two-dimensional magnetorheological fluids. Prior results from both experiments and simulations report that the shear stress σ scales with strain rate as σ ∼ 1-Δ, with values of the exponent ranging between 2/3 &lt; Δ ≤ 1. However it remains unclear what properties of the system select the value of Δ, and in particular under what conditions the system displays a yield stress (Δ = 1). To address these questions, we perform simulations of a minimalistic model system in which particles interact via long ranged magnetic dipole forces, finite ranged elastic repulsion, and viscous damping. We find a surprising dependence of the apparent exponent Δ on the form of the viscous force law. For experimentally relevant values of the volume fraction φ and the dimensionless Mason number Mn (which quantifies the competition between viscous and magnetic stresses), models using a Stokes-like drag force show Δ ≈ 0.75 and no apparent yield stress. When dissipation occurs at the contact, however, a clear yield stress plateau is evident in the steady state flow curves. In either case, increasing φ towards the jamming transition suffices to induce a yield stress. We relate these qualitatively distinct flow curves to clustering mechanisms at the particle scale. For Stokes-like drag, the system builds up anisotropic, chain-like clusters as Mn tends to zero (vanishing strain rate and/or high field strength). For contact damping, by contrast, there is a second clustering mechanism due to inelastic collisions.</p

Normal stresses, contraction, and stiffening in sheared elastic networks

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.Engineering Thermodynamic

Nonlocal effects in inhomogeneous flows of soft athermal disks

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.Engineering Thermodynamic

Viscous forces and bulk viscoelasticity near jamming

When weakly jammed packings of soft, viscous, non-Brownian spheres are probed mechanically, they respond with a complex admixture of elastic and viscous effects. While many of these effects are understood for specific, approximate models of the particles' interactions, there are a number of proposed force laws in the literature, especially for viscous interactions. We numerically measure the complex shear modulus G* of jammed packings for various viscous force laws that damp relative velocities between pairs of contacting particles or between a particle and the continuous fluid phase. We find a surprising sensitive dependence of G* on the viscous force law: the system may or may not display dynamic critical scaling, and the exponents describing how G* scales with frequency can change. We show that this sensitivity is closely linked to manner in which viscous damping couples to floppy-like, non-affine motion, which is prominent near jamming.Engineering Thermodynamic

Moduli and modes in the Mikado model

We determine how low frequency vibrational modes control the elastic shear modulus of Mikado networks, a minimal mechanical model for semi-flexible fiber networks. From prior work it is known that when the fiber bending modulus is sufficiently small, (i) the shear modulus of 2D Mikado networks scales as a power law in the fiber line density, G ∼ ρα+1, and (ii) the networks also possess an anomalous abundance of soft (low-frequency) vibrational modes with a characteristic frequency ωκ ∼ ρβ/2. While it has been suggested that α and β are identical, the preponderance of evidence indicates that α is larger than theoretical predictions for β. We resolve this inconsistency by measuring the vibrational density of states in Mikado networks for the first time. Supported by these results, we then demonstrate analytically that α = β + 1. In so doing, we uncover new insights into the coupling between soft modes and shear, as well as the origin of the crossover from bending- to stretching-dominated response. This journal is Engineering ThermodynamicsMulti Phase System