Elastic fields of 2D and 3D misfit particles in an infinite medium

In micromechanics, accurate quantification of the elastic field (stress, strain, and displacement) caused by the presence of an inclusion in an infinite body is desired for both the particle and matrix materials. Ideally, the solution should be applicable to any particle geometry or shape and for any distribution of misfit along the interface (i.e. misfit profile). This work presents a dislocation-based numerical method, that is an extension to earlier work in this journal [Lerma, J.D., Khraishi, T., Shen, Y.L., Wirth, B.D., 2003. The elastic fields of misfit cylindrical particles: a dislocation-based numerical approach. Mech. Res. Commun. 30, 325–334], for determining the elastic fields of volume misfit particles with arbitrary misfit distribution or particle shape.     

Averaging a granular medium with spherical packing

The problem of averaging three-component media consisting of rigid grains, a viscous or elastic deformable meterial occupying the intergranular gaps and an inviscid pore liquid (or gas) is examined. When the deformable material completely fills the gaps, the medium is reduced to two-component form. The volume of the interlayers is comparable with the volume of the grains (the grains are spherical and the distance between the nearest points on neighboring spheres is small as compared with the diameter).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–81, May–June, 1990.     

Density-induced granular segregation in a slurry rotating drum

We experimentally investigated the effects of interstitial fluid density and viscosity on density-induced granular segregation in a rotating drum. Image processing and a particle-tracking method were used for determining the segregation index and dynamic properties of granular materials. The results indicate that the interstitial fluid density has a crucial role in density-induced granular segregation. A dimensionless factor was defined for quantifying the effect of interstitial fluid density on density-induced granular segregation. The segregation intensity increased as the interstitial fluid viscosity increased. In addition, the Stokes number associated with density-induced granular segregation was discussed in this study.     

Two-dimensional model of a granular medium

A two-dimensional model of a granular medium is represented as a square lattice composed of elastically interacting round particles with translational and rotational degrees of freedom. In the long-wave approximation, we derive linear partial differential equations describing the propagation and interaction of waves of various types in such a medium. If microrotations of particles in the lattice and the related moment interactions are taken into account, then a microrotation wave (a spin wave) appears in the medium. We establish the one-to-one correspondence between the parameters of the microstructure and the elastic constants of second order. We analyze the dependence of the medium elasticity constants on the grain dimensions. In the continuum approximation, we compare the model proposed here with the model of two-dimensional Cosserat continuum.     

Micro-macro scale instability in 2D regular granular assemblies

Instability and stress–strain behavior were investigated for 2D regular assemblies of cylindrical particles. Biaxial shear experiments were performed on three sets of assemblies with regular, albeit increasingly defective structures. These experiments revealed unique instability behavior of these assemblies. Continuum models for the assemblies were then constructed using the granular micromechanics approach. In this approach, the constitutive equations governing the behavior of inter-particle contacts are written in local or microscopic level. The behavior of the RVE is then retrieved by using either kinematic constraint or least squares (static constraint) along with the principle of virtual work to equate the work done by microscopic force–displacement conjugates to that of the macroscopic stress and strain tensor conjugates. The ability of the two continuum approaches to describe the measured stress–strain behavior was evaluated. The continuum models and the local constitutive laws were used to perform instability analyses. The onset of instability and orientation of shear band was found to be well predicted by the instability analyses with the continuum models. Further, macro-scale instability was found to correlate with the instability of inter-particle contacts, although with some variations for the two modeling approaches.     

Scaling granular material with polygonal particles in discrete element modeling

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.     

Averaging of processes in a granular medium with non-Newtonian interlayers

The problem of averaging of the processes in three-component media consisting of rigid grains, a non-Newtonian viscous material occupying the gaps between the grains, and an inviscid liquid or gas in the pores. When the latter component is missing and the viscous material completely fills the gaps, the medium in question is a two-component system. The distance between neighboring grains (between their nearest points) is assumed to be small as compared with the grain dimensions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 84–97, July–August, 1992.     

A new physical model on the capillary phenomenon of granular particles

Similar to the capillary phenomenon of liquid, granular particles can move up to a certain height along a vertically vibrating tube. The certain height, which is called the equilibrium height, is related to some parameters, e.g., the inner diameter of the tube, the amplitude, and the vibration frequency. In this paper, a theoretical model is proposed to explain the physical origin of the capillary phenomenon and the effects of the inner diameter of the tube, the amplitude, and the vibration frequency on the equilibrium height. In this model, the volumes of the inflowing and outflowing particles in a vibration period are calculated, which can significantly broaden our understanding in the flow of particles in the bottom of the tube. In order to prove the assumption of this physical model that the particles in the bottom of the tube move in the form of sine, several experiments are conducted. The granular climbing heights at different granular positions and different time stages are measured. The results show that granules move in the form of sine, which almost coincides with the motion of the tube. Moreover, motivated by the sampling on the asteroid regolith based on this mechanism, the sampling efficiencies for various vibration amplitudes and frequencies are discussed based on the new proposed model. It is found that there is an optimum frequency at which sampling is the most effective.     

2D DEM simulation of particle mixing in rotating drum:A parametric study

Mixing behaviors of equal-sized glass beads in a rotating drum were investigated by both DEM simulations and experiments. The experiments indicated that higher rotation speed can significantly enhance mixing. The particle profiles predicted by 2D DEM simulation were compared with the experimental results from a quasi-2D drum, showing inconsistency due to reduction of contacts in the single-layer 2D simulation which makes the driving friction weaker than that in the quasi-2D test, better results could be rea...     

Elastic properties of a fluid-saturated granular medium

We present a theoretical constructive model describing the elastic properties of a liquid-saturated granular medium with the external pressure taken into account. This model permits calculating the bulk and shear moduli, the speed of sound, the natural frequencies, and the mode shapes of acoustic pressure and vibrational velocity. The desired fundamental characteristics are determined in terms of the medium structure parameters, which is important in geophysical and technical applications. We show that the speed of sound polynomially depends on the pressure in loose media. This dependence was confirmed by numerical laboratory experiments in a wide range of pressure measurements and of the working space geometry. We separately study the case of pressure caused by the weight of the upper layers of the medium (ground). We establish some qualitative mechanical effects concerning the dependence of the elastic properties on various parameters of the medium.     

Dynamic compaction model for a granular medium

A model for dynamic compaction of granular medium is proposed for the case in which the external action far exceeds the yield strength of the material. A radial axisymmetric compaction problem is solved for a granular medium with nanosize structure in the presence of a rigid rod at the symmetry axis. Simulated data are compared with experimental data on magnetic pulsed compaction of oxide nanopowders. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 211–215, March–April, 2008.     

Low-frequency model of a granular medium saturated with a viscous fluid

A mathematical model of a granular medium saturated with a viscous homogeneous fluid is constructed. The steady-state one-dimensional oscillations of cylindrical granules and an incompressible fluid under the action of a plane sonic wave whose length is significantly greater than the cell dimensions are investigated. The steady-state flow of the medium across the cell cross-section and the mean fluid velocity (Darcy’s law) are determined by means of passages to the limits with respect to the frequency and granule mass. The expressions obtained for the soil permeability coefficient under the action of a gravitational hydraulic head are compared with the representations of other authors.     

Crushing of particles in idealised granular assemblies

Four idealised assemblies of equally sized spherical particles are subjected to a range of macroscopic compressive principal stresses and the contact forces on individual particles are determined. For each set of contact forces the stress fields within individual particles are studied. A failure criterion for brittle materials is imposed and indicates that crushing (or rupture) occurs when the maximum contact force reaches a threshold particle strength value, irrespective of the presence and magnitude of other lesser contact forces acting on the particle and the material properties of the particle. Combining the crushing mechanism with an assembly instability mechanism enables failure surfaces to be drawn in the three-dimensional stress space. A simple spatial averaging technique has been applied to the failure surfaces to remove the effects of assembly anisotropies. Sections of the failure surfaces on π planes have similarities to those commonly used in sand modelling.     

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.