Daniel Vågberg

Glassiness, Rigidity and Jamming of Frictionless Soft Core Disks

The jamming of bidisperse soft core disks is considered, using a variety of different protocols to produce the jammed state. In agreement with other works, we find that cooling and compression can lead to a broad range of jamming packing fractions ϕ{J}, depending on cooling rate and initial configuration; the larger the degree of big particle clustering in the initial configuration, the larger will be the value of ϕ{J}. In contrast, we find that shearing disrupts particle clustering, leading to a much narrower range of ϕ{J} as the shear strain rate varies. In the limit of vanishingly small shear strain rate, we find a unique nontrivial value for the jamming density that is independent of the initial system configuration. We conclude that shear driven jamming is a unique and well-defined critical point in the space of shear driven steady states. We clarify the relation between glassy behavior, rigidity, and jamming in such systems and relate our results to recent experiments.

Finite-size scaling at the jamming transition: Corrections to scaling and the correlation-length critical exponent

We carry out a finite-size scaling analysis of the jamming transition in frictionless bidisperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent ν ≈ 1 and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding ν < 1 are due to the improper neglect of these corrections.

Correlations of plasticity in sheared glasses

In a recent paper [Mandal et al., Phys. Rev. E 88, 022129 (2013)], the nature of spatial correlations of plasticity in hard-sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law, whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence-via simulations of a hard-sphere glass in two dimensions (2D)-that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature [Durian, Phys. Rev. Lett. 75, 4780 (1995)], the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field-type drag in the case of soft disks.

Nonlocal Elasticity near Jamming in Frictionless Soft Spheres

We use simulations of frictionless soft sphere packings to identify novel constitutive relations for linear elasticity near the jamming transition. By forcing packings at varying wavelengths, we directly access their transverse and longitudinal compliances. These are found to be wavelength dependent, in violation of conventional (local) linear elasticity. Crossovers in the compliances select characteristic length scales, which signify the appearance of nonlocal effects. Two of these length scales diverge as the pressure vanishes, indicating that critical effects near jamming control the breakdown of local elasticity. We expect these nonlocal constitutive relations to be applicable to a wide range of weakly jammed solids, including emulsions, foams, and granulates.

Dissipation and Rheology of Sheared Soft-Core Frictionless Disks Below Jamming

We use numerical simulations to investigate the effect that different models of energy dissipation have on the rheology of soft-core frictionless disks, below jamming in two dimensions. We find tha ...

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction ϕ, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate γ[over ̇]. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (ϕ,Q) plane for small γ[over ̇], we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing γ[over ̇], the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (ϕ,γ[over ̇]) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing γ[over ̇] at fixed ϕ, we find that discontinuous shear thickening can result if γ[over ̇] is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of γ[over ̇].

Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks.

We carry out constant volume simulations of steady-state shear-driven rheology in a simple model of bidisperse soft-core frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We discuss in detail the critical scaling ansatz for the shear-driven jamming transition and carry out a detailed scaling analysis of our resulting data for pressure p and shear stress σ. Our analysis determines the critical exponent β that describes the algebraic divergence of the Bagnold transport coefficients lim_{γ[over ̇]→0}p/γ[over ̇]^{2},σ/γ[over ̇]^{2}∼(ϕ_{J}-ϕ)^{-β} as the jamming transition ϕ_{J} is approached from below. For the low strain rates considered in this work, we show that it is still necessary to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data, in which the critical parameters become independent of the size of the window of data used in the analysis. We compare our resulting value β≈5.0±0.4 against previous numerical results and competing theoretical models. Our results confirm that the shear-driven jamming transition in Bagnoldian systems is well described by a critical scaling theory and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.

Effect of collisional elasticity on the Bagnold rheology of sheared frictionless two-dimensional disks

We carry out constant volume simulations of steady-state, shear-driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction ϕ and a parameter Q that measures the elasticity of binary particle collisions. We find a Q^{*}(ϕ) that marks the clear crossover from a region characteristic of strongly inelastic collisions, QQ^{*}, and give evidence that Q^{*}(ϕ) diverges as ϕ→ϕ_{J}, the shear-driven jamming transition. We thus conclude that the jamming transition at any value of Q behaves the same as the strongly inelastic case, provided one is sufficiently close to ϕ_{J}. We further characterize the differing nature of collisions in the strongly inelastic vs weakly inelastic regions, and recast our results into the constitutive equation form commonly used in discussions of hard granular matter.

Pressure distribution and critical exponent in statically jammed and shear-driven frictionless disks

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction ϕ in two dimensions. We use these distributions to address the question of how pressure increases as ϕ increases above the jamming point ϕ(J), p ∼ |ϕ-ϕ(J)(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations.