Granular Matter

Interparticle friction is an intrinsic property of particles, which plays an important role in the macroscopic and microscopic shear mechanical properties of granular materials. In this research, we investigate the shear behavior of granular materials with different friction coefficients using ring shear tests. The particle image velocimetry (PIV) technique was also used to analyze the shear flow characteristics. The results indicate that the peak shear strength of granular materials increases with the increase in shear rates, especially for granular materials with high friction coefficients. The shear stress fluctuation difference is smaller under low normal stress. Under high normal stress, the shear stress fluctuation of granular materials with high friction coefficient is higher than that of granular materials with low friction coefficient. In addition, the shear stress fluctuation shows a trend of increasing with the increase of shear rates. The range of the liquid phase flow region of granular materials decreases with the increase of friction coefficient and normal stress. This work reveals the shear flow characteristics of granular materials under different conditions, which can provide reference for the flow processes of geological disasters such as landslides and debris flows.

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.

We perform discrete element simulations of freely cooling, dense granular materials, previously sheared at a constant rate. Particles are identical, frictional spheres interacting via linear springs and dashpots and the solid volume fraction is constant and equal to 60% during both shearing and cooling. We measure the average and the distributions of contacts per particle and the anisotropy of the contact network. We observe that the granular material, at the beginning of cooling, can be shear-jammed, fragile or unjammed. The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively. While anisotropic solids and isotropic fluids rapidly reach an apparent final steady configuration, the microstructure continues to evolve for anisotropic fluids. We explain this with the presence of vortices in the flow field that counteract the randomizing and structure-annihilating effect of collisions. We notice, in accordance with previous findings, that the initial fraction of mechanically stable particles permits to distinguish between shear-jammed, fragile or unjammed states and, therefore, determine beforehand the fate of the freely evolving granular materials. We also find that the fraction of mechanically stable particles is in a one-to-one relation with the average number of contacts per particle. The latter is, therefore, a variable that must be incorporated in continuum models of granular materials, even in the case of unjammed states, where it was widely accepted that the solid volume fraction was sufficient to describe the geometry of the system.

Solitary wave propagation in a monodisperse granular chain was simulated using the finite element method. The model was built to address a discrepancy between numerical and experimental results from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408 1985). In their work, solitary waves were generated in a chain of particles through impact of a piston, and results were quantified by comparing the chains’ reactions to a rigid wall. Their numerical calculations resulted in a solitary wave with a force amplitude of 83 N, while it was measured experimentally to be 71 N. In the present work, the configuration of the granular chain and piston was duplicated from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408, 1985). Qualitatively similar solitary waves were produced, and von Mises stress values indicated that localized plastic deformation is possible, even at low piston impact velocities. These results show that localized plastic deformation was a likely source of dissipation in experiments performed by Lazaridi and Nesterenko.

We present a new method capable of inferring, for the first time, inter-particle contact forces in irregularly-shaped natural granular materials (e.g., sands), using basic Newtonian mechanics and balance of linear momentum at the particle level. The method furnishes a relationship between inter-particle forces and corresponding average particle stresses, which can be inferred, for instance, from measurements of average particle strains emanating from advanced experimental techniques (e.g., 3D X-ray diffraction). Inter-particle forces are the missing link in understanding how forces are transmitted in complex granular structures and the key to developing physics-based constitutive models. We present two numerical examples to verify the method and showcase its promise.

When a granular material is freely discharged from a silo through an orifice at its base, the flow rate remains constant throughout the discharge. However, it has been recently shown that, if the discharge is forced by an overweight, the flow rate increases at the final stages of the discharge, in striking contrast to viscous fluids (Madrid et al. in Europhys Lett 123:14004, 2018). Although the general mechanism that drives this increase in the flow rate has been discussed, there exist yet a number of open questions regarding this phenomenon. One such questions is to what extent is the internal velocity profile affected, beyond the trivial overall increase consistent with the increasing flow rate. We study via discrete element method simulations the internal velocity profiles during forced silo discharges and compare them with those of free discharges. The changes in velocity profiles are somewhat subtle. Interestingly, during free discharges, while the velocity profiles are steady at the silo base and above a height equivalent to one silo diameter, there exists a transition region where the profile evolves in time, despite the constant flow rate. In contrast, forced discharges present steady profiles at all heights of the granular column during the initial constant flow phase, followed by an overall increase of the velocities when the acceleration phase develops.

This paper investigates the induced anisotropy and multi-scale shear characteristics of granular materials by quantifying force chain distribution in two-dimensional specimens of rigid particles under quasi-static loading. A new criterion is proposed and implemented into the existing algorithm which can effectively solve the identification instability of force chains at branching and merging points. Force chain is then classified into three categories according to the variation of force chain quantity and average stress with segment length: stable segments, meta-stable segments and unstable force chain segments. The stable force chain segments dominate the load-bearing behavior of the granular materials. The directional distribution of force chain segments is more anisotropic and more sensitive to the applied stress than contact normal vectors, which show obvious local peaks in both vertical and horizontal directions at high deviatoric stress. Therefore, the probability density of directional distribution of force chains needs to be described by the first two deviatoric components of Fourier expansion with deviators A1 and A2, which are indicators reflecting the intensity of the induced-anisotropy of the granular materials. As the absolute values of A1 and A2 increase, the induced anisotropy is more significant. The final shear failure types are determined by the quantities of force chains orienting in two potential shear failure directions: if there is an obvious difference between the quantities of the two directions, single shear band occurs within the direction with less force chains; otherwise, conjugated double shear bands occur and lie in the two potential shear failure directions.