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When a mechanical wave travels through a medium, its intensity diminishes with distance. The research focuses on the energy transfer with distance as well as across different wavenumbers, as the mechanical wave propagates. The diffusive characteristic of energy propagation has been discussed for one-dimensional chains composed of random, pre-stressed soft and stiff particles interacting through Hertzian repulsive forces, which can be solved analytically after linearization. The effect of soft-stiff ratio (disorder in property) on energy transfer across wavenumbers is examined using a standing sinusoidal wave initial condition (with a specific wavenumber). From the total energy signals in wavenumber space, as a function of time, it is observed that stronger disorder leads to a more rapid loss of energy of the signal and faster transfer of energy to other wavenumbers.

Powders &amp; Grains 2021

Energy propagation in 1D granular soft-stiff chain

[EPJ Web of Conferences, Volume 249 (2021)](https://www.epj-conferences.org/articles/epjconf/abs/2021/03/contents/contents.html)

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Powders & Grains 2021

Powders & Grains 2021 will be held in Buenos Aires (Argentina, VIRTUAL) July 5, 13, 21, 29 and Aug 6, 2021. The aim of the conference is to give an up-to-date picture of the broad research field of granular media, powders and grains. Contributions from experts around the world will focus on research topics that cover a wide range of open problems in the field.

poster

Knowledge transfer from micromechanics of granular media failure to geohazard forecasting and mitigation has been slow. But in the face of a rapidly expanding data infrastructure on the motion of individual grains for laboratory samples – and ground motion data at the field scale – opportunities to accelerate this knowledge transfer are emerging. In particular, such data assets coupled with data-driven approaches enable a re-examination of granular failure with ‘new eyes’. To this end, effective strategies that can jump scales from bench to field are urgently needed. Here we demonstrate one strategy that focusses on the study of deformation patterns in the precursory failure regime using kinematic data. Unlike previous studies which focus on regions of high strains, here we probe the development and evolution of near- undeforming regions through the lens of explosive percolation. We find a common dynamical signature in which undeforming regions, which are initially transient in the precursory failure regime, become persistent from the time of imminent failure. We demonstrate the robustness of these findings for data on individual grain motions in a classical laboratory test and ground motion in two real landslides at vastly different scales.

Dynamics of undeforming regions in the lead up to failure: jumping scales from lab to field

In this paper, an assembly of disordered packings is considered as a suitable set of packing cells of ordered spheres. In consequence, any of its parameters can be obtained by averaging the values of the set. Namely, the density of a packing of ordered spheres is described by two variables: the angle of the base, and the angle of the inclined edge of the associated parallelepiped. Then, the density of a packing of disordered spheres is obtained by averaging the angle of the base, and the subsequent averaging of the other angle, according to the kind of strain induced by the experiment. The average packing yields the density limits of loose sphere assemblies achieved by a process of fluidization and sedimentation in air, in water, and in viscous liquid at zero gravitational force. It also models the close sphere assemblies shaped by gentle tapping, vertical shaking, horizontal and multidirectional vibrations. The theory allows to elucidate the mechanism of each of the limits, as, for example, the metastable columns of spheres in the loosest packing, as well as the random close packing, and crystallization. The limits obtained coincide very well with the published experimental, numerical and theoretical data.

An average model for disordered sphere packings

The question of how soft granular matter, or dense amorphous systems, re-arrange their micro-structure under isotropic compression and decompression, at different strain rates, will be answered by particle simulations of frictionless model systems in a periodic three-dimensional cuboid. Starting compression below jamming, the systems experience the well-known jamming transition, with characteristic evolutions of the state variables elastic energy, elastic stress, coordination number, and elastic moduli. For large strain rates, kinetic energy comes into play and the evolution is more dynamic. In contrast, at extremely slow deformation, the system relaxes to hyper-elastic states, with well-defined elastic moduli, in static equilibrium between irreversible (plastic) re-arrangement events, discrete in time. Small, finite strains explore those reversible (elastic) states, before larger strains push the system into new states, by irreversible, sudden re-arrangements of the microstructure.

How does static granular matter re-arrange for different isotropic strain rate?

We experimentally investigate the effect of the grain shape on the flow of granular material. The grain shape is modified to highlight the effect of grain circularity on granular flow in a 2D rotating drum. Using a laser cutter, we create particles with decreasing circularity. We observe that the effect of grain shape depends on the rotation speed of the drum. For high rotation speed, granular flow is influenced by the packing’s dilatancy whereas, at low rotation speed, packing fraction seems to influence flowing dynamics. We link these two measurements to grain shape in order to explain its effect on granular flow.

Effect of grain shape on the dynamics of granular materials in 2D rotating drum

The rhombic sphere packing can be used to model granular soils in a very simple way. According to the angle of assemblage, the packing is dilatant or contractive. Correspondingly, the overall stresses are transmitted as chains of forces or oblique forces of contact. The connection of the soil stress-strain behaviour and the packing void ratio is achieved by mapping both of the plots. The mapping shows that dense soils are dilatant and loose soils are contractive, separated by the critical state. It also shows that the bifurcation point and the peak strength are features of dense soils. The line of strain localization is analysed in the elastic regime, and its inclination is found maximizing the intensity of the mobilized stress ratio. The stresses within the shear band are obtained by assuming a partially coaxial packing rotated for reaching the full plastic state. The equilibrium of the overall stress at the line of discontinuity leads to the relationship between the peak friction angle and the coefficient of lateral pressure at rest. As long as these parameters are independently obtained from each other, they allow the validation of the theory.

A sphere packing model for shear bands in dense soils

The present study is on segregation of granular mixtures during heap formation in a quasi two-dimensional rectangular bin where binary mixture of a specified composition is poured intermittently into the auxiliary hopper and then allowed to pass through the gap (k = 10 mm) between the divider and the plate and finally settle on to the heap. The profiles of number fraction of big particles are plotted along the flow directions to study the segregation phenomena for surface profile. It shows that larger particles travel more distance and smaller particles settle near the pouring point for all cases studied.

Experimental investigation of segregation of granular mixtures during heap formation

A nonlinear programming problem was developed for the separation and classification of
Portland cement particles into different fractions through the optimal design of two cyclones classifier in
series. The equations and restrictions considered included the global mass balances, the equations for the
geometric design of the cyclones, the equations for the efficiency calculation, the operating limitations of
the process and the pressure drops of the equipment. The results show that an increase on the particles cut
size led to a greater dimensions cyclone, as expected. Moreover, fractional efficiencies obtained increase
with the reduction of the cut size. The solids load effect is also evaluated, reductions of the solids feed by
50% of its maximum value does not result in a remarkably decrease of efficiencies values. The proposed
model has provided useful information and constitutes a starting point for a better understanding of the
overall separation process of multi-component Portland cement mixtures. It is a valuable tool for the correct
design of this type of separators, given its versatility to optimize under different operating conditions and
with different materials.


Optimal design of cyclones in series for the separation of multi-component mixtures of Portland cement

Simple geometry and multiple applications such as drying, mixing, segregation, drying, granulation and heat conduction have inspired many researchers from the mechanical, chemical, pharmaceutical and mining engineering fields to study the dynamics of the particle flow inside rotating drums. Therefore, knowledge of the dynamics of particles in a drum is of high interest in engineering such as velocity profiles. Various experimental and numerical studies have been carried out to study the velocity profiles of the particles inside horizontal rotating drums. Little emphasis has been laid on inclined rotating drums, though these drums are extensively used in granular process industries. In this study Discrete Element Method (DEM) is used to analyse the effect of angle of inclination of the drum on the particles velocity profile.

Particle velocity profile in an inclined rotating drum

DEM-simulated model cohesive assemblies of spherical grains of diameter d, with contact tensile strength F_0, once prepared in loose states, are quasistatically subjected to growing isotropic pressure P, and then to triaxial compression, maintaining lateral stresses sigma_2 = sigma_ 3 = P_0 while increasing axial stress 1 = P + q and strain epsilon_1. Reduced pressure P*= d^2 P/F_0 varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Phi = 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (e.g. epsilon_1 = 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as both q (deviator) and Phi steadily increase, gets slower for smaller P*. Critical ratio q/p strongly increases for decreasing P* as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.

Energy propagation in 1D granular soft-stiff chain

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Dynamics of undeforming regions in the lead up to failure: jumping scales from lab to field

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