Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to $1$. Inspired by the contact mechanics in the Hertz's limit, we show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.
It has been conjectured by Bagnold [1] that an assembly of hard non-deformable spheres could behave as a compressible medium when slowly sheared, as the average density of such a system effectively depends on the confining pressure. Here we use discrete element simulations to show the existence of transverse and sagittal waves associated to this dynamical compressibility. For this purpose, we study the resonance of these waves in a linear Couette cell and compare the results with those predicted from a continuum local constitutive relation.
The $μ(I)$-rheology has been recently proposed as a potential candidate to model the flow of frictional grains in a dense inertial regime. However, this rheology was shown to be ill-posed in the mathematical sense for a large range of parameters, notably in the slow and fast flow limits \citep{Barker2015}. In this rapid communication, we extend the stability analysis to compressible flows. We show that compressibility regularizes mostly the equations, making them well-posed for all parameters, at the condition that sufficient dissipation is associated with volume changes. In addition to the us…
We experimentally probe nonlinear wave propagation in weakly compressed granular media, and observe a crossover from quasi-linear sound waves at low impact, to shock waves at high impact. We show that this crossover grows with the confining pressure $P_0$, whereas the shock wave speed is independent of $P_0$ --- two hallmarks of granular shocks predicted recently. The shocks exhibit powerlaw attenuation, which we model with a logarithmic law implying that local dissipation is weak. We show that elastic and potential energy balance in the leading part of the shocks.
Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $μ(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with $I$-dependent rheology. When the $I$-dependence comes from a specific friction coefficient $μ(I)…
We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure $π$ of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension $ϕ$, we can determine $ϕ$ from $π$, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using $ϕ$, is larger than its hard-sphere value for the stiffer microgels that we study and progr…
We numerically study the effect of inter-particle friction coefficient on the response to cyclical pure shear of spherical particles in three dimensions. We focus on the rotations and translations of grains and look at the spatial distribution of these displacements as well as their probability distribution functions. We find that with increasing friction, the shear band becomes thinner and more pronounced. At low friction, the amplitude of particle rotations is homogeneously distributed in the system and is therefore mostly independent from both the affine and non-affine particle translations…
We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critic…
A mechanism of negative compressibility occurring in compressed layered compounds in the presence of a pressure transmitting fluid medium is discussed within a simple model. It takes into account the excluded volume effects and soft fluid-matrix repulsion. It is demonstrated that a non-monotonic behavior of the interlayer spacing with the applied pressure results from a competition between the applied pressure and the internal one induced by the adsorbed fluid. Recent experimental data on the graphite oxide "structure breathing" under compression in the presence of water are analyzed in the li…
Creep mechanisms in uniaxially compressed 3D granular solids comprised of faceted frictionless grains are studied numerically using a constant pressure and constant stress simulation method. Rapid uniaxial compression followed by slow dilation is predicted on the basis of a logarithmic creep phenomenon. Micromechanical analysis indicates the existence of a correlation between granular creep and grain-scale deformations. Localized regions of large strain appear during creep and grow in magnitude and size with time. Furthermore, the accumulation of non-affine granular displacements increases lin…
We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $α$, have found that the ensemble-averaged shear modulus $\langle G \rangle$ increases with pressure $P$ as $\sim P^{(α-3/2)/(α-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles…
We propose a cruiser able to move in a granular medium made of nearly 50-50 bidisperse dissipative particles under gravity. The cruiser has a circular shape with a square indentation on its edge. By shifting and then ejecting granular particles entering its indent-region facing a given direction, the cruiser gains thrust to push itself forward in the same direction, which can be either perpendicular or parallel to gravity. Using molecular dynamics (MD) simulations, we identify three universal phases during one particle-ejection process: 1) acceleration by the ejection thrust, 2) deceleration b…
We report three-dimensional particle mechanics static calculations that predict the microstructure evolution during die-compaction of elastic spherical particles up to relative densities close to one. We employ a nonlocal contact formulation that remains predictive at high levels of confinement by removing the classical assumption that contacts between particles are formulated locally as independent pair-interactions. The approach demonstrates that the coordination number depends on the level of compressibility, i.e., on the Poisson's ratio, of the particles. Results also reveal that distribut…
We investigate the mechanical response of a compressed monolayer of large and dense particles at a liquid-fluid interface: a granular raft. Upon compression, rafts first wrinkle; then, as the confinement increases, the deformation localizes in a unique fold. This characteristic buckling pattern is usually associated to floating elastic sheets and as a result, particle laden interfaces are often modeled as such. Here, we push this analogy to its limits by comparing the first quantitative measurements of the raft morphology to a theoretical continuous elastic model of the interface. We show that…
We experimentally study nonlinear force propagation into granular material during impact from an intruder, and we explain our observations in terms of the nonlinear grain-scale force relation. Using high-speed video and photoelastic particles, we determine the speed and spatial structure of the force response just after impact. We show that these quantities depend on a dimensionless parameter, $M'=t_c v_0/d$, where $v_0$ is the intruder speed at impact, $d$ is the particle diameter, and $t_c$ is the collision time for a pair of grains impacting at relative speed $v_0$. The experiments access a…
We consider two (2D) and three (3D) dimensional granular systems exposed to compression, and ask what is the influence of the number of physical dimensions on the properties of the interaction networks that spontaneously form as these systems evolve. The study is carried out based on discrete element simulations of frictional disks in 2D and spheres in 3D. The main finding is that both the number of physical dimensions and the type of particle-particle interaction influence significantly the properties of interaction networks. These networks play an important role in bridging the microscale (p…
We used computer simulations to study spontaneous strain localization in granular materials, as a result of symmetry breaking non-homogeneous deformations. Axisymmetric triaxial shear tests were simulated by means of standard three-dimensional Distinct Element Method (DEM) with spherical grains. Carefully prepared dense specimens were compressed between two platens and, in order to mimic the experimental conditions, stress controlled, (initially) axisymmetric boundary conditions were constructed. Strain localization gave rise to visible shear bands, previously found experimentally under simila…
As a granular material is compressed, the particles and forces within the system arrange to form complex heterogeneous structures. Force chains are a prime example and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, characterizing the dynamic nature of mesoscale architectures in granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend current approaches by utilizing multilayer networks as a framework for directly qua…
When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are i…
We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intru…
Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations, that this is generically not the case since stress auto-correlation functions decay more slowly than the elastic Green's function. It was shown theoretically that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. Generic compressed frictional assemblies exhibit however abnormal …
We present findings from uniaxial (oedometric) compression tests on two cohesive industrially relevant granular materials (cocoa and limestone powder). Experimental results are presented for the compressibility, tested with two devices -- the FT4 Powder Rheometer and the custom made lambdameter. We focus on the stress response and the slow relaxation behavior of the cohesive samples tested. After compression ends, at constant volume, the ongoing stress relaxation is found to follow a power law consistently for both cohesive powders and for the different testing equipments. A simple (incrementa…
We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find …
For fundamentally characterizing the effect of hierarchical structure in granular matter, a set of compression-relaxation tests for dust particles and glass beads confined in a cylindrical cell was performed. Typical diameter of both grains is approximately 1~mm. However, dust particles are produced by binding tiny ($\sim 5$~{\textmu}m) glass beads. The granular columns were compressed with a piston until reaching a maximum load force of 20~N with a constant compression rate $v$ ($0.17 \leq v \leq 2000$~{\textmu}m~s$^{-1}$). After that, the piston was stopped and the relaxation process was qua…
We present an experiment in which a horizontal quasi-2D granular system with a fixed neighbor network is cyclically compressed and decompressed over 1000 cycles. We remove basal friction by floating the particles on a thin air cushion, so that particles only interact in-plane. As expected for a granular system, the applied load is not distributed uniformly, but is instead concentrated in force chains which form a network throughout the system. To visualize the structure of these networks, we use particles made from photoelastic material. The experimental setup and a new data-processing pipelin…
This work investigates phase separation of a monodisperse gas of inelastically colliding hard disks confined in a two-dimensional annulus, the inner circle of which represents a "thermal wall". When described by granular hydrodynamic equations, the basic steady state of this system is an azimuthally symmetric state of increased particle density at the exterior circle of the annulus. When the inelastic energy loss is sufficiently large, hydrodynamics predicts spontaneous symmetry breaking of the annular state, analogous to the van der Waals-like phase separation phenomenon previously found in a…
In glasses and other disordered materials, measurements of the vibrational density of states reveal that an excess number of long-wavelength (low-frequency) modes, as compared to the Debye scaling seen in crystalline materials, is associated with a loss of mechanical rigidity. In this paper, we present a novel technique for measuring the density of modes (DOM) in a real granular material, in which we mimic thermal excitations using white noise acoustic waves. The resulting vibrations are detected with piezoelectric sensors embedded inside a subset of the particles, from which we are able to co…
Dry granular materials such as sand, gravel, pills, or agricultural grains, can become rigid when compressed or sheared. At low density, one can distort the shape of a container of granular material without encountering any resistance. Under isotropic compression, the material will reach a certain {\it jamming} density and then resist further compression. {\em Shear jamming} occurs when resistance to shear emerges in a system at a density lower than the jamming density, and the elastic properties of such states have important implications for industrial and geophysical processes. We report on …
Being able to precisely characterize the mechanical properties of soft microparticles is essential for numerous situations from the understanding of the flow of biological fluids to the development of soft micro-robots. Here we present a simple measurement technique for the Poisson's ratio of soft micron-sized hydrogels in the presence of a surrounding liquid. This methods relies on the measurement of the deformation in two orthogonal directions of a rectangular hydrogel slab compressed uni-axially inside a microfluidic channel. Due to the in situ character of the method, the sample does not n…
