Shear modulus of frictionless granular materials near the jamming transition under oscillatory shear is numerically investigated. It is found that the shear modulus $G$ satisfies a scaling law to interpolate between $G \sim (ϕ- ϕ_J)^{1/2}$ and $G \sim γ_0^{-1/2}(ϕ-ϕ_J)$ for a linear spring model of the elastic interaction between contacting grains, where $ϕ$, $ϕ_J$, and $γ_0$ are, respectively, the volume fraction of grains, the fraction at the jamming point, and the amplitude of the oscillatory shear. The linear relation between the shear modulus and $ϕ- ϕ_J$ can be understood by slip avalanches.
We present the experimental and numerical studies of a 2D sheared amorphous material constituted of bidisperse photo-elastic disks. We analyze the statistics of avalanches during shear including the local and global fluctuations in energy and changes in particle positions and orientations. We find scale free distributions for these global and local avalanches denoted by power-laws whose cut-offs vary with inter-particle friction and packing fraction. Different exponents are found for these power-laws depending on the quantity from which variations are extracted. An asymmetry in time of the ava…
We study the avalanche dynamics of a pile of micron-sized silica grains in miniaturized rotating drums filled with water. Contrary to what is expected for classical granular materials, the avalanches do not stop at a finite angle of repose. Below an angle $θ$\_c, we observe a creep regime where the piles slowly flow until they become flat. In this regime, the relaxation is logarithmic in time and is slower when the ratio between the weight of the grains and the thermal agitation is increased. We propose a simple 1D model based on Kramer's escape rate to describe this flow.
An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a…
We investigate the sliding of objects on an inclined granular surface close to the avalanche threshold. Our experiments show that the stability is driven by the surface deformations. Heavy objects generate footprint-like deformations which stabilize the objects on the slopes. Light objects do not disturb the sandy surfaces and are also stable. For intermediate weights, the deformations of the surface destabilize the objects and generate sliding. A characteristic pressure for which the solid friction is minimal is evidenced. Applications to the locomotion of devices and animals on sandy slopes …
The behavior of granular media under quasi-static loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regim…
Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances int…
In this study, we have investigated the fluctuations of particle motion, i.e. the non-affine motion, during the avalanche process, discovering a rich dynamics from the microscopic to the macroscopic scales. We find that there is strong correlation between the magnitude of the velocity fluctuation and the velocity magnitude in the spatial and temporal domains. The possible connection between this finding and STZ is discussed based on the direct measurement of the T1 events. In addition, the velocity magnitude of the system and the stress fluctuations of the system are strongly correlated tempor…
We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a toy-model system -- a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector $δu(t)$ and velocity $v(t)$ of particles are directly measured for the first time to yield insights into their spatial correlation $C_{δu,v}$, which is stronger near the unjamming but is weaker near the jamming transition, consistent with the recent work of Banigan et al., Nature Phys. $\bf{9}$, 288, (2013). $v(t)$ shows rich dynamics: it grows exponentiall…
We study the avalanche dynamics of a pile of micrometer-sized silica grains in water-filled microfluidic drums. Contrary to what is expected for classical granular materials, avalanches do not stop at a finite angle of repose. After a first rapid phase during which the angle of the pile relaxes to an angle $θ\_c$, a creep regime is observed where the pile slowly flows until the free surface reaches the horizontal. This relaxation is logarithmic in time and strongly depends on the ratio between the weight of the grains and the thermal agitation (gravitational Péclet number). We propose a simple…
Universality in materials deformation is of intense interest: universal scaling relations if exist would bridge the gap from microscopic deformation to macroscopic response in a single material-independent fashion. While recent agreement of the force statistics of deformed nanopillars, bulk metallic glasses, and granular materials with mean-field predictions supports the idea of universal scaling relations, here for the first time we demonstrate that the universality extends beyond the statistics, and applies to the slip dynamics as well. By rigorous comparison of two very different systems, b…
In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divi…
The shear modulus of jammed frictional granular materials with the harmonic repulsive interaction under an oscillatory shear is numerically investigated. It is confirmed that the storage modulus, the real part of the shear modulus, for frictional grains with sufficiently small strain amplitude $γ_0$ discontinuously emerges at the jamming transition point. The storage modulus for small $γ_0$ differs from that of frictionless grains even in the zero friction limit, while they are almost identical with each other for sufficiently large $γ_0$, where the transition becomes continuous. The stress-st…
We investigate experimentally the mechanical response of a monolayer of bi-disperse frictional grains to an inhomogeneous shear perturbation across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 0.001 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilat…
We study the bulk properties of isotropic bidisperse granular mixtures using discrete element simulations. The focus is on the influence of the size (radius) ratio of the two constituents and volume fraction on the mixture properties. We show that the effective bulk modulus of a dense granular (base) assembly can be enhanced by up to 20% by substituting as little as 5% of its volume with smaller sized particles. Particles of similar sizes barely affect the macroscopic properties of the mixture. On the other extreme, when a huge number of fine particles are included, most of them lie in the voi…
Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that e…
We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus $G'$ and the loss modulus $G''$ in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying $G'>0$) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed $G'$ after the reduction of the strain …
Building materials such as concretes and mortar are formed by solidifying granular slabs. Such materials are often fractured by giant forces such as during earthquakes, leading to the collapse of structures and potentially casualties. One avenue of enquiry to prevent cracking would be to realize a material that can maintain a stable shape without being solidified. Here, we focus on sand grains coated with silicone oil, experimentally investigating the Young's modulus of a granular slab where ordinary grains and the coated grains are mixed in a mixing ratio $α$. It is found that the Young's mod…
If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size $X_c$, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an "uphill front" that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments controlling the distance between the apex of the sandpile and the container feeding it from above, we show that $X_c$ grows linearly with the input flux,…
We numerically investigate the mechanical and geometrical properties of dense wet granular particles with irreversible attractive interaction. The shear modulus exhibits two inflection points as the packing fraction increases, and the bulk modulus shows a non-monotonic behavior. The coordination number also exhibits two inflection points. The peak position in the pair correlation function shifts to a lower value due to attractive interaction. The Voronoi tessellation of the particle configuration reveals that the probability density function for the volume of the Voronoi cell broadens as the p…
Cohesion-induced hysteresis and breakdown of marginal stability in jammed granular materials
Institute of Science and Engineering, Shimane University（岛根大学理工学研究科）；Department of Applied Physics, Tokyo University of Science（东京理科大学应用物理系）；Graduate School of Arts and Sciences, The University of Tokyo（东京大学大学院人文社会系研究科）
Foams made of complex fluids such as particle suspensions have a great potential for the development of advanced aerated materials. In this paper we study the rheological behavior of liquid foams loaded with granular suspensions. We focus on the effect of small particles, i.e. particle-to-bubble size ratio smaller than 0.1, and we measure the complex modulus as a function of particle size and particle volume fraction. With respect to previous work, the results highlight a new elastic regime characterized by unequaled modulus values as well as independence of size ratio. A careful investigation…
Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing thr…
DEM simulations were used to study the sensitivity of a granular system to the change of the mechanical properties of the grains, applied to the penetration of a cylindrical intruder near a vertical wall. The simulations reproduce a real experimental setup, changing the friction, the Young modulus and the restitution coefficient of the particles.
