Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Discrete element modeling of first shear strain gradient effects on mechanical behaviors in granular materials

Granular Matter - We introduce an improved version of a computational algorithm that “clones”/generates an arbitrary number of new digital grains from a sample of real digitalized...     

An entropy model for shear deformation of granular materials

A statistical mechanical analogy for characterization of granular materials is discussed by using such notions as the state of the material, the density of states, entropy, canonical distribution and the partition function. The transition law of states during shear deformations of the material is microscopically investigated in the case of two-dimensional model granular materials. The assumption of entropy growth is shown to characterize the dilatancy of the material. A rough proof is given by assuming the measure preserving property of the transition and showing its ergodicity.     

Discrete element method for modelling solid and particulate materials

The collaborative structural analysis (CSA) system is capable of performing highly sophisticated structural analyses utilizing the beneficial features of existing individual structural analysis programmes. It requires a time consuming static condensation procedure if adopting an implicit integration scheme. The operator splitting (OS) method, which does not require the tangential stiffness, can be used to improve the system efficiency. Furthermore, the conventional OS method is not able to provide enough numerical stability, particularly for the analyses considering geometrical non‐linearity. Thus, improvement is needed. To this end, a modified OS method is proposed, which treats unbalanced forces in the current step as pseudo‐external forces in the immediate following step. In this paper, first, the conventional OS method is reformulated in an incremental form, and a CSA scheme based on it is proposed. Second, a modified OS method is developed to improve the numerical stability. Third, a fixed‐base steel column with a lumped mass assigned at its top is analysed using the CSA system as a numerical example. It is found that the OS methods are effective for CSA, and the modified OS method exhibits better numerical stability than the conventional one for the analysis considering geometrical non‐linearity. Copyright © 2007 John Wiley & Sons, Ltd.     

Instability of steady shear flow of granular materials

Summary We consider simple shearing flow of a granular material in which the stress is governed by the Coulomb-Mohr yield condition, and which deforms according to the double-shearing model of granular material behaviour for incompressible material. We also investigate deformations of a dilatant material in which this shearing deformation is accompanied by an expansion in the direction normal to the shear plane, in this case using the dilatant double-shearing model proposed by Mehrabadi and Cowin. In both cases it is found that in addition to the expected steady stress solution, the equations admit time-dependent stress solutions. For suitable initial conditions these solutions satisfy the positive energy dissipation requirements up to some finite shear. In the unsteady solutions the rotation of the principal stress axes is always away from the steady solution, and in no case is the steady solution approached as a limit of the unsteady solution; this indicates that the steady flow solutions are unstable.With 2 Figures     

Mechanistic modelling of tests of unbound granular materials

Various tests are used to characterise the strength and resilience of granular materials used in the subbase of a pavement system, but there is a limited understanding of how particle properties relate to the bulk material response under various test conditions. Here, we use discrete element method (DEM) simulations with a mechanistically based contact model to explore influences of the material properties of the particle on the results of two such tests: the dynamic cone penetrometer (DCP) and the resilient modulus tests. We find that the measured resilient modulus increases linearly with the particle elastic modulus, whereas the DCP test results are relatively insensitive to particle elastic modulus. The DCP test results are also relatively insensitive to inter-particle friction coefficient but strongly dependent on the particle shape. We discuss strengths and weaknesses of our modelling approach and include suggestions for future improvements.     

Compact shear test specimens for FRC materials

The shear strength and toughness index of polypropylene and steel fibre-reinforced concretes have been determined using two new compact test specimen geometries. The first geometry was a double-notched cube, the second a double-notched cylinder in the form of a disc. Two notch separation distances and two maximum sizes of coarse aggregates were used in the study to investigate the possibility of size effects with such compact specimens. The results were shown to be reproducible and independent of the test geometry. The shear- strength results were relatively independent of the fibre content and maximum size of the coarse aggregate used. The toughness index results were similar for the two test specimen geometries and toughness was shown to increase uniformly with increasing fibre content over the range of fibre concentrations used in the study.     

Discrete element modelling of under sleeper pads using a box test

It has recently been reported that under sleeper pads (USPs) could improve ballasted rail track by decreasing the sleeper settlement and reducing particle breakage. In order to find out what happens at the particle–pad interface, discrete element modelling (DEM) is used to provide micro mechanical insight. The same positive effects of USP are found in the DEM simulations. The evidence provided by DEM shows that application of a USP allows more particles to be in contact with the pad, and causes these particles to transfer a larger lateral load to the adjacent ballast but a smaller vertical load beneath the sleeper. This could be used to explain why the USP helps to reduce the track settlement. In terms of particle breakage, it is found that most breakage occurs at the particle–sleeper interface and along the main contact force chains between particles under the sleeper. The use of USPs could effectively reduce particle abrasion that occurs in both of these regions.     

Adaptive modelling of materials test results: Tear energy in filled rubber networks

We have elaborated a procedure for numerically modelling the behaviour of polymer-based materials as a function of two independent variables such as temperature and rate. The parameters of the model are chosen to have close physical significance, e.g. in terms of molecular theories or other measurements. The model may be adjusted to the data by a least-squares fit, yielding the optimal parameters provided the chi-squared test shows the fit to be acceptably good. Specimens may be compared by studying the dependence of individual fitted model parameters on preparation variables. Under certain conditions this procedure can be extended to result in the quantitative prediction of the ingredients and preparation needed to produce a material of desired properties. We describe the implementation of the procedure on a computergraphics facility, and apply it to the study of the tear energy in filled vulcanizates.     

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.     

DEM-aided direct shear testing of granular sands incorporating realistic particle shape

Discrete element method (DEM) of granular sands incorporating the effect of the realistic particle shape has been an important issue for many years. In this context, this study proposed a novel framework for the generation of realistic-shaped particles of natural sands in 3D DEM simulations. The generation framework mainly included micro-CT (μCT) scanning of sand particles, image processing of μCT images, spherical harmonic reconstruction of the particle surface, and clump generation by the overlapping multisphere clump method (OMCM) in DEM simulations. To validate the accuracy of OMCM, the volume and inertia moment of the clump were carefully investigated, and a set of optimized generation parameters was then determined to ensure the accuracy of the clump and the limit number of the filling spheres. Based on the generation framework, a clump sample with realistic particle shapes and a corresponding sphere sample were generated to conduct a series of direct shear testing. The simulation results demonstrated that the realistic particle shape highly increases the particle interlocking rather than the anisotropic intensity of strong contact force chains, and in turn enhances the shear resistance and the shear-induced dilation of the sands. It was also found that the inter-particle contacts of the clump sample have higher friction mobilization than that of the sphere sample, which identified the micromechanism of the shape effect on the particle interlocking.     

Using the annular shear cell as a rheometer for rapidly sheared granular materials: a DEM study

Discrete element simulations are performed to examine the kinematics of granular shear flows in an annular shear cell at high shearing rates. The interstitial fluid is absent and gravity is included. To investigate the feasibility of using annular shear cells as rheometers for rapidly sheared dense granular materials, this study focuses on the coupled effect of boundary conditions and the relative particle to shear cell size. Four different particle diameters and three different boundary types are used in the same annular shear cell. These cases correspond to physical experiments reported earlier by the authors. For many cases both shearing and non-shearing regions coexist. The transition from partially to fully shearing flow is shown to depend on the particle diameter, solids concentration, and the boundary conditions. The particles form layers at high solids concentration and with larger particles, as evidenced by the reduction of the flow diffusivity. The slip velocity at the bottom boundary is absent; at the top it varies. This variation is sensitive to the type of boundaries but insensitive to bulk solids concentration. This study shows the interconnectivity of the boundary, the particle to shear cell size, and the flow condition in an annular shear cell. Prior to using these cells as rheometers, a thorough understanding of this interconnectivity needs to be developed.     

Powerful FE approaches for Pochhammer's dispersion modelling

Simple and very effective finite element approaches for modelling of the dispersion of torsional, longitudinal and flexural waves propagated in infinite and elastic cylindrical bars (Pochhammer's problem) and hollow cylinders are presented. The approaches allow one to model given problems without using infinite elements and their usage is demonstrated by using dispersion curves, shapes of waves and tables of phase velocities. Comparison of finite element solutions (solved in one task from small‐sized models) with exact solutions shows an excellent agreement. The maximum relative differences among the 20 lowest FEM and analytical phase velocities was less than 0.000015%. The approaches and results hold also for cylinders with finite lengths, simply supported on both ends. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact results versus mean field solutions for binary granular gas mixtures

A novel method for obtaining the distribution functions from the Boltzmann equations for binary granular gas mixtures of smooth spheres has been developed. The method is capable of producing accurate results irrespective of the values of the parameters which define the system. Here we explain the method and present results obtained using it for the temperature ratio of the components, as well as for the flatness (and higher order measures of flatness) of the distribution functions, for the homogeneous cooling state. It turns out that the mean field approximation for the temperature ratio yields results which are within about 1% or better of the exact results for all checked values of the parameters (except when the mass ratio is very large (or small) and the system is very inelastic) even when the values of the flatness suggest that the distribution functions are not near-Maxwellian. The use of the method for obtaining constitutive relations is outlined but detailed results are deferred to another publication.     

Interface roughness effect on slow cyclic annular shear of granular materials

We experimentally investigate the mechanical behaviour in cyclic shear of a granular material near a solid wall in a pressure controlled annular shear cell. The use of a model system (glass beads and saw-tooth shaped solid surface) enables the study of the influence of the wall roughness. After an initial shakedown procedure ensuring reproducible results in subsequent tests, wall shear stress S, volumetric variation ΔV, and the displacement field of the sample bottom surface, are recorded as functions of wall displacement. A dimensionless roughness parameter R _n is shown to control the interface response. The local grain-level or mesoscale behaviour is directly correlated to the global one on the scale of the whole sample.     

Micro-mechanical analysis and modelling of granular materials loaded at constant volume

The present paper is devoted to the analysis and the modelling of the local phenomena, which are observed in a two-dimensional granular media loaded at constant volume. A micro-mechanical approach is followed here combined with a computer simulation method. Local phenomena observed during test are used to provide some necessary elements to build realistic models. The importance of the induced anisotropy during the test is especially shown, as well as its necessary link to the dilatancy. To illustrate the study a model based on a micro-mechanical approach is validated.