A new method is introduced to simulate jamming of polyhedral grains under controlled stress that incorporates global degrees of freedom through the metric tensor of a periodic cell containing grains. Jamming under hydrostatic/isotropic stress and athermal conditions leads to a precise definition of the ideal jamming point at zero shear stress. The structures of tetrahedra jammed hydrostatically exhibit less translational order and lower jamming-point density than previously described `maximally random jammed' hard tetrahedra. Under the same conditions, cubes jam with negligible nematic order. Grains with octahedral symmetry jam in the large-system limit with an abundance of face-face contacts in the absence of nematic order. For sufficiently large face-face contact number, percolating clusters form that span the entire simulation box. The response of hydrostatically jammed tetrahedra and cubes to shear-stress perturbation is also demonstrated with the variable-cell method.
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 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…
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 study numerically the critical behavior and marginal stability of the shear jamming transition for frictionless soft spheres, observed to occur over a finite range of densities, associated with isotropic jamming for densities above the minimum jamming (J-point) density. Several quantities are shown to scale near the shear jamming point in the same way as the isotropic jamming point. We compute the exponents associated with the small force distribution and the interparticle gap distribution,and show that the corresponding exponents are consistent with the marginal stability condition observe…
The jamming transition is accompanied by a rich phenomenology, such as hysteresis or non-local effects, which is still not well understood. Here we experimentally investigate a model frictionless granular layer flowing down an inclined plane, as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis, yet the layer stability is increased as it gets thinner. Rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting that non-loca…
We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $α\to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is non-monotonic in the packing fraction $ϕ$, and that as $α\to 0$ $S_{2}$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts p…
We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate $\dotε$, we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction $ϕ$ and compressi…
By exploring the properties of the energy landscape of a bidisperse system of soft harmonic disks in two dimensions we determine the thermal jamming transition. To be specific, we study whether the ground state of the system where the particle do not overlap can be reached within a reasonable time. Starting with random initial configurations, the energy landscape is probed by energy minimization steps as in case of athermal jamming and in addition steps where an energy barrier can be crossed with a small but non-zero probability. For random initial conditions we find that as a function of pack…
We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $…
We use numerical simulations to study the flow of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. We study the resulting spatial structure of the sheared system, and compute correlation functions of the velocity, the particle density, the nematic order parameter, and the particle angular velocit…
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…
Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically-stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly four million particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying p…
We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition is under quasistatic shear is discontinuous, with an instantaneous emergence of a system spanning rigid cluster at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transi…
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 numerically study a three dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure $p$, shear stress $σ$, and macroscopic friction $μ=σ/p$, as functions of particle packing fraction $ϕ$ and compression rate $\dotε$, we find good agreement for all critic…
We study how solidification of model freely rotating polymers under athermal quasistatic compression varies with their bond angle $θ_0$. All systems undergo two discrete, first-order-like transitions: entanglement at $ϕ= ϕ_E(θ_0)$ followed by jamming at $ϕ= ϕ_J(θ_0) \simeq (4/3 \pm 1/10)ϕ_E(θ_0)$. For $ϕ< ϕ_E(θ_0)$, systems are in a "gas" phase wherein all chains remain free to translate and reorient. For $ϕ_E(θ_0) \leq ϕ\leq ϕ_J(θ_0)$, systems are in a liquid-like phase wherein chains are entangled. In this phase, chains' rigid-body-like motion is blocked, yet they can still locally relax via…
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/…
We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states (vDOS), which is a key ingredient of linear viscoelastic theory. The vDOS e…
