We report recent results of molecular dynamics simulations of frictional athermal particles at constant volume fraction and constant applied shear stress, focusing on a range of control parameters where the system first flows, but then jams after a time tjam. On decreasing the volume fraction, the mean jamming time diverges, while its sample fluctuations become so large that the jamming time probability distribution P(tjam) becomes a power-law. We obtain an insight on the origin of this phenomenology focusing on the flowing regime, which is characterized by the presence of a clear correlation between the shear velocity and the mean number of contacts per particles Z, whereby small velocities occur when Z acquires higher values.
Critical properties of frictionless spherical particles below jamming are studied using extensive numerical simulations, paying particular attention to the non-affine part of the displacements during the athermal quasi-static compression. It is shown that the squared norm of the non-affine displacement exhibits a power-law divergence toward the jamming transition point. A possible connection between this critical exponent and that of the shear viscosity is discussed. The participation ratio of the displacements vanishes in the thermodynamic limit at the transition point, meaning that the non-a…
We simulate numerically the compression driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios $α$. We find the critical packing fraction $ϕ_J(α)$ for the jamming transition, and the average number of contacts per particle $z_J(α)$ at jamming. We find that both are nonmonotonic, with a peak at $α\approx 1$. We find that configurations at the compression driven jamming point are always hypostatic for all $α$, with $z_J<z_\mathrm{iso}=2d_f=6$ the isostatic value. We show that, for moderately elongated spherocylinders, there is…
We study athermal jamming as well as the thermal glassy dynamics in systems composed of spheres that interact according to repulsive interactions that exponentially decay as a function of distance. As usual, a cutoff is employed in the simulations. While the athermal jamming transition that is determined by trying to remove overlaps is found to depend on the arbitrary and therefore unphysical choice of the cutoff, we do not find any athermal jamming transition or crossover that only relies on the physical decay length. In contrast, the glassy dynamics mainly depends on the decay length. Our fi…
Dynamics of jammed packings of soft athermal disks under finite-rate shear are studied by means of molecular dynamics simulations. Particularly, we investigate the spatial structures of stress drop events, which are expected to provide information about plasticity. Investigating the displacement fields during stress drop events, we show that there are qualitatively different two types of events in the low rate limit: localized ones and extended ones. We further investigate the time evolution of events and clarify that both types of events are due to oscillatory motion of the stress, which is u…
We carry our numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, $ξ$ and $\ell$, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function, and argue that the more divergent length $\ell$ is a consequence of a dangerous irrelevant scaling variable, and that it is $ξ$ which is the correlation length that determines the divergence of the system viscosity as jamming is app…
We simulate a densely jammed, athermal assembly of repulsive soft particles immersed in a solvent. Starting from an initial condition corresponding to a quench from a high temperature, we find non-trivial slow dynamics driven by a gradual release of stored elastic energy, with the root mean squared particle speed decaying as a power law in time with a fractional exponent. This decay is accompanied by the presence within the assembly of spatially localised and temporally intermittent `hot-spots' of non-affine deformation, connected by long-ranged swirls in the velocity field, reminiscent of the…
Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress leve…
We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven in uniform steady state shear. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a model for a non-Brownian suspension with a Newtonian rheology. We study pressure $p$ and deviatoric shear stress $σ$ as a function of packing fraction $ϕ$, strain rate $\dotγ$, and a parameter $α$ that measures the asphericity of the particles. We consider the anisotropy of the stress tensor, the macroscopic friction $μ=σ/…
The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses, colloidal and polymer gels, foams and granular matter) on the basis of whether these materials are in the jammed or unjammed state. Whilst such simple classification is appealing, it fails to capture that the criterion of rigidity of such amorphous solids may be defined with respect to a particular deformation orientation or mode (i.e. shear, extrusion, consolidat…
We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additio…
We investigate criticality near the jamming transition in both quiescent systems and those under shear by considering the effect of mechanical training on the jamming transition and nonlinear rheology. We simulate frictionless soft particles undergoing athermal quasi-static shear using initial configurations trained with athermal quasi-static cyclic volume deformations. The jamming transition density of the initial configuration $φ_{\rm J0}$ is systematically altered by tuning the ``depth'' of mechanical training. We exert a steady shear on these configurations and observe either shear jamming…
By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density $ϕ_J$ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, $μ_s$-dependent jamming density $ϕ_J^{\mathrm{mono}}(μ_s)$ is the only input required in the model, where $μ_s$ is the coefficient of friction. The predictions of the model are validated by robust estimates of $ϕ_J$ obtained from computer simulations of up to $10^7$ particles for a wide range of $μ_s$, and size ratios up to 40:1. Although $ϕ_J$ varies nonmonotonically with the volume fraction of sma…
In stark contrast to the jamming of frictionless hard-sphere (hard-disk if in two dimensions) packings, the critical jamming of frictional packings is much more elusive and still under intense debate. Here we show that frictional hard-disk packings self-organize near a critical jamming state when subjected to quasi-static steady-state cyclic shear, displaying scale-free fluctuations in particle velocity fields as characterized by the power spectra $E(k)\propto k^{-α}$ for both longitudinal and transverse modes in wavevector space, with $α\approx2.0\pm0.15$, and the nearly flat spectra $E(ω)\pr…
We compare the structural and mechanical properties of mechanically stable (MS) packings of frictional disks in two spatial dimensions (2D) generated with isotropic compression and simple shear protocols from discrete element modeling (DEM) simulations. We find that the average contact number and packing fraction at jamming onset are similar (with relative deviations $< 0.5\%$) for MS packings generated via compression and shear. In contrast, the average stress anisotropy $\langle {\hat Σ}_{xy} \rangle = 0$ for MS packings generated via isotropic compression, whereas $\langle {\hat Σ}_{xy} \ra…
We use numerical simulations to study the shear-driven steady-state flow of athermal, frictionless, overdamped, two dimensional cross-shaped particles of varying aspect ratios, and make comparison with the behavior of rod-shaped and staple-shaped particles. We find that the extent of non-convexity of the particle shape plays an important role in determining both the value of the jamming packing fraction as well as the rotational motion and orientational ordering of the particles.
We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by…
Pressure-imposed rheometry is used to examine the influence of surface roughness on the rheology of immersed and dry frictional spheres in the dense regime. The quasi-static value of the effective friction coefficient is not significantly affected by particle roughness while the critical volume fraction at jamming decreases with increasing roughness. These values are found to be similar in immersed and dry conditions. Rescaling the volume fraction by the maximum volume fraction leads to collapses of rheological data on master curves. The asymptotic behaviors are examined close to the jamming t…
Dense suspension of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening and shear jamming. Shear thickening is known to be enhanced by increasing the particles' frictional interactions and also by making their shape more anisotropic. For shear jamming, however, only the role of interparticle friction has been investigated, while the effect of changing particle shape has so far not been studied systematically. To address this we here synthesize smooth silica particles and design the particle surface chemistry to generate strong frictional interactions such that …
We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $ϕ$ and mean-square velocity fluctuations $\langle v^2\rangle$ the mean-square displacement of the disks $\langle d^2\rangle$ spans 4-5 orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behabvior at long times. The statistics of $\langle d^n\rangle$ at all times are multiscaling, since the probability distribution function (pdf) of displacements has very broad wings. Even where a diffusion consta…
Athermal systems across a large range of length scales, ranging from foams and granular bead packings to crumpled metallic sheets, exhibit slow stress relaxation when compressed. Experimentally they show a non-monotonic stress response when decompressed somewhat after an initial compression, i.e. under a two-step, Kovacs-like protocol. It turns out that from this response one can tell for how long the system was in a compressed state, suggesting an interpretation as a memory effect. In this work we use a model of an athermal jammed solid, specifically a binary mixture of soft harmonic particle…
We numerically investigate non-local 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 non…
We numerically study the impact-induced hardening in dense suspensions. We employ the lattice Boltzmann method and perform simulations of dense suspensions under impacts, which incorporate the contact between suspended particles with the free surface of the suspension. Our simulation for a free-falling impactor on a dense suspension reproduces experimental results, where rebound takes place for frictional particles at high-speed impact and high volume fraction shortly after the impact before subsequently sinking. We found that the shear stress of the suspension is not affected by the impact, w…
Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations…
