Simulation Of Granular Materials Research Articles

Application of micro computed tomography for adjustment of model parameters for discrete element method

Nowadays the Discrete Element Method (DEM) is widely applied for the numerical simulation of granular materials. However, for the effective application of DEM detailed information about material properties is needed. Some material parameters of individual particles can be directly measured using various experimental set-ups like shear cell, compression tester, electron microscopy, etc. Nevertheless, in the majority of cases such measurements do not suffice to get overall information about the material. Therefore, various macroscopic experiments like determination of static or dynamic angle of repose are often used to validate DEM simulations and to adjust model parameters. In this contribution, an alternative non-intrusive technique for the estimation of unknown parameters, which is based on particle tracking in sets of the micro computed tomography images, is proposed. In comparison to other methods this technique allows to obtain detailed information about particle motion inside the granular material and does not only rely on the surface properties.In the presented contribution experiments and simulation studies were performed using a cylindrical mixer apparatus filled with polyethylene microspheres. Based on the analysis of obtained images, the exact 3D-positions of all particles in the mixing volume were determined and extracted. For numerical calculations the DEM implemented into component-based simulation framework MUSEN was used.

Dynamic Random Arching in the Flow Field of Top-Coal Caving Mining

The large mining height fully mechanized top-coal caving mining technique has developed rapidly and become the most extensively used mining method for ultra-thick coal seams. The arching of coal/gangue and the drawing out of gangue are peculiar phenomena in the process of fully mechanized top-coal caving mining, which not only affects the recovery of top-coal, but also affects the quality of the coal. This paper studies the arching phenomenon in top-coal caving mining process of ultra-thick coal seam. A series of laboratory granular material simulation experiments were performing and a top-coal arching model in the framework of mechanics was established to explore the formation characteristic of arches and their effects to top-coal loss. Then the countermeasures against the arches and technology path of intelligent mining based on improving top-coal recovery were put forward and performed in practice. The results show that the recovery ratio of top-coal has increased nearly 6%, and increased the production efficiency at the same time. The research on arching mechanism and removing strategies of dynamic random arches effectively improves the efficiency of fully mechanized top-coal caving mining in ultra-thick coal seams, and provides the foundation for the realization of intelligent top-coal caving mining technology.

A unified numerical framework for rigid and compliant granular materials

A numerical framework for the simulation of granular materials composed of mixed rigid and compliant grains is presented in this paper. This approach is based on a multibody meshfree technique, coupled in a very natural way with classic concepts from the discrete element method. The equations of motion (for the rigid grains) and of continuum mechanics (for the compliant ones) are solved using an adaptive explicit scheme, in fully dynamic conditions. The parallelization strategy is described and tested on an illustrative simulation involving both kinds of grains.

Experiments and 3D DEM of Triaxial Compression Tests under Special Consideration of Particle Stiffness

Discrete element modelling is commonly used for particle-scale modelling of granular or particulate materials. Developing a DEM model requires the determination of a number of micro-structural parameters, including the particle contact stiffness and the particle-particle friction. These parameters cannot easily be measured in the laboratory or directly related to measurable, physical material parameters. Therefore, a calibration process is typically used to determine the values for use in simulations of physical systems. This paper focuses on how to define the particle stiffness for the discrete element modelling in order to perform realistic simulations of granular materials in the case of linear contact model. For that, laboratory tests and numerical discrete element modelling of triaxial compression tests have been carried out on two different non-cohesive soils i.e. poorly graded fine sand and gap graded coarse sand. The results of experimental tests are used to calibrate the numerical model. It is found that the numerical results are qualitatively and quantitatively in good agreement with the laboratory tests results. Moreover, the results show that the stress dependent of soil behaviour can be reproduced well by assigning the particle stiffness as a function of the particle size particularly for gap graded soil.

A state boundary surface model for improving the dilatancy simulation of granular material in reinforced anchors

It is acknowledged that for extending the experimental results to real scale design, it is necessary to use an appropriate numerical analysis. The good analysis in geotechnical problems needs to adopt a suitable constitutive model for the materials. This paper presents a modeling approach to investigate the complex behavior of granular trench and reinforcement system. For this purpose, an experimental and numerical investigation has been carried out on the behavior of pullout resistance of an embedded anchor (circular plate) with and without geogrid reinforcement layers in stabilized loose and dense sand using a granular trench. Different parameters have been considered, such as number of geogrid layers, embedment ratios, relative density of soil, and height ratios of granular trench. Finite element analysis with Hardening Soil Model was utilized for sand and CANAsand constitutive model was used for granular trench to investigate failure mechanism and the associated rupture surfaces. Results showed that, when soil was improved with the granular-geogrid trench, the uplift force significantly increased, but in geogrid-reinforced granular trench condition, the ultimate pullout resistance at failure increased as the number of geogrid layers increased up to the third layer, the fifth layer had a negligible effect in comparison with the third layer of reinforcement. The ultimate uplift capacity of anchor plate and the variation of surface deformation for all the tests indicated a close agreement between the experimental and numerical models.

Editorial to special issue “Modeling and simulation of granular materials and granular flows”

Editorial to special issue “Modeling and simulation of granular materials and granular flows”

A multibody strategy for deformable grains

This article presents a numerical framework dedicated to the simulation of granular materials with highly deformable grains. This framework is based on a multibody meshfree strategy, which makes it possible to account for the constitutive model of the material composing each grain and for possibly complex contact laws (e.g. adhesion, friction, etc.). The main principles of the approach are first presented, and two illustrative cases are then detailed in order to emphasize its potential in several domains of the granular science.

Study on the meso-structure development in direct shear tests of a granular material

Stress induced anisotropy phenomenon has been the main interest of many researches, especially in granular materials. Discrete element method (DEM) is one of the important methods for the study of meso-mechanics of granular materials. Based on previous studies, a 3D meso-fabric statistical method have been established, which can be used for quantitative analysis of 3D meso-fabric development in DEM numerical simulation of granular materials under external loads. Taking the direct shear test of sand as an example, the stress induced anisotropy of sand in 3D under the shearing loads has been studied systematically. According to the analysis results: the magnitude of anisotropy significantly develops during shear tests and gradually become steady after the peak, and the principal directions of anisotropy rotates consistent with the principal stress direction; the connectivity between the particles decreases and a series of particle skeletons are formed in the sample which undertake the main external loads. Furthermore, the stress state does also influence the evolution of anisotropy and force chain networks.

Nonsmooth Contact Dynamics for the large-scale simulation of granular material

For the large-scale simulation of granular material, the Nonsmooth Contact Dynamics Method (NSCD) is examined. First, the equations of motion of nonsmooth mechanical systems are introduced and classified as a Differential Variational Inequality (DVI) that has a structure similar to Differential–Algebraic Equations (DAEs). Using a Galerkin projection in time, we derive nonsmooth extensions of the SHAKE and RATTLE schemes. A matrix-free Interior Point Method (IPM) is used for the complementarity problems that need to be solved in each time step. We demonstrate that in this way, the NSCD approach yields highly accurate results and is competitive compared to the Discrete Element Method (DEM).

A semi-implicit material point method for the continuum simulation of granular materials

We present a new continuum-based method for the realistic simulation of large-scale free-flowing granular materials. We derive a compact model for the rheology of the material, which accounts for the exact nonsmooth Drucker-Prager yield criterion combined with a varying volume fraction. Thanks to a semi-implicit time-stepping scheme and a careful spatial discretization of our rheology built upon the Material-Point Method, we are able to preserve at each time step the exact coupling between normal and tangential stresses, in a stable way. This contrasts with previous approaches which either regularize or linearize the yield criterion for implicit integration, leading to unrealistic behaviors or visible grid artifacts. Remarkably, our discrete problem turns out to be very similar to the discrete contact problem classically encountered in multibody dynamics, which allows us to leverage robust and efficient nonsmooth solvers from the literature. We validate our method by successfully capturing typical macroscopic features of some classical experiments, such as the discharge of a silo or the collapse of a granular column. Finally, we show that our method can be easily extended to accommodate more complex scenarios including two-way rigid body coupling as well as anisotropic materials.

Friction phenomena and their impact on the shear behaviour of granular material

In the discrete element simulation of granular materials, the modelling of contacts is crucial for the prediction of the macroscopic material behaviour. From the tribological point of view, friction at contacts needs to be modelled carefully, as it depends on several factors, e.g. contact normal load or temperature to name only two. In discrete element method (DEM) simulations the usage of Coulomb’s law of friction is state of the art in modelling particle–particle contacts. Usually in Coulomb’s law, for all contacts only one constant coefficient of friction is used, which needs to reflect all tribological effects. Thus, whenever one of the influence factors of friction varies over a wide range, it can be expected that the usage of only one constant coefficient of friction in Coulomb’s law is an oversimplification of reality. For certain materials, e.g. steel, it is known that a dependency of the coefficient of friction on the contact normal load exists. A more tribological tangential contact law is implemented in DEM, where the interparticle friction coefficient depends on the averaged normal stress in the contact. Simulations of direct shear tests are conducted, using steel spheres of different size distributions. The strong influence of interparticle friction on the bulk friction is shown via a variation of the constant interparticle friction coefficient. Simulations with constant and stress-dependent interparticle friction are compared. For the stress-dependent interparticle friction, a normal stress dependency of the bulk friction is seen. In the literature, measurements of different granular materials and small normal loads also show a stress dependency of the bulk friction coefficient. With increasing applied normal stress, the bulk friction coefficient reduces both in the experiments and in the simulations.

Coupled Eulerian–Lagrangian simulation of granular medium sheet forming process and experimental ınvestigation at elevated temperature

The granular medium forming process is a newly proposed flexible die forming technique. It is mainly applied to fabricate thin-walled lightweight components such as titanium alloys and high-strength steel parts at relatively high temperatures (above 500 °C) with good forming quality. In order to investigate the flow behavior of the granular medium in the forming process, tri-axial compression test with different confinement pressures is performed. Test shows that the selected granular medium exhibits pressure-dependent properties with low-friction angle. Then, three classical geotechnical models, i.e., the Mohr–Coulomb, Drucker–Prager, and Duncan–Chang models are established for the numerical simulation process with the parameters obtained from the tri-axial compression test. To avoid the undesired mesh distortion during FEM simulation of forming process, Coupled Eulerian–Lagrangian (CEL) analysis method is developed. This enables the simulation of granular material involving large deformation. Finally, the granular medium forming experiment is implemented at 500 °C using commercially pure TA1 titanium sheet, and comparison study with the FEM simulation is carried out. Result indicates that the Mohr–Coulomb model exhibits the best performance regarding the calculation accuracy of shape dimension and thickness distribution.

A multibody meshfree strategy for the simulation of highly deformable granular materials

SUmmaryIn this paper, a multibody meshfree framework is proposed for the simulation of granular materials undergoing deformations at the grain scale. This framework is based on an implicit solving of the mechanical problem based on a weak form written on the domain defined by all the grains composing the granular sample. Several technical choices, related to the displacement field interpolation, to the contact modelling, and to the integration scheme used to solve the dynamic equations, are explained in details. A first implementation is proposed, under the acronym Multibody ELement‐free Open code for DYnamic simulation (MELODY), and is made available for free download. Two numerical examples are provided to show the convergence and the capability of the method. Copyright © 2016 John Wiley & Sons, Ltd.

An efficient layered simulation workflow for snow imprints

This paper introduces a novel workflow to generate snow imprints, and model the interaction of snow with dynamic objects. We decoupled snow simulation into three components: a base layer, snow particles, and snow mist. The base layer consists of snow that has not been in contact with a dynamic object yet, and is stored as a level set. Snow particles model the interaction between the snow and the dynamic objects. They are added when the dynamic objects collide with the base layer, and are animated using an adapted granular material simulation. The very thin and powdery snow released by airborne snow particles is modeled by the snow mist. This component is greatly influenced by the surrounding air medium; thus, it is animated using a fluid simulation. This decomposition allows to focus memory expensive and time-consuming computations only where dynamic objects interact with the snow, which is much more efficient than relying on a full-scale simulation.

Assessing the quasi-static conditions for shearing in granular media within the critical state soil mechanics framework

There has been a marked increase in the use of the discrete element method (DEM) in geomechanics in recent years. The way in which DEM simulations are set up can have a noticeable influence on the observed response. The conditions for quasi-static shearing in DEM simulations of granular materials were studied here within the critical-state framework of the soil behaviour. Thirty-two constant-p′ triaxial simulations were carried out from which the critical-state relationships were defined in the void ratio-mean effective stress and deviator fabric-mechanical coordination number planes. Clear trends were observed for the void ratio, the coordination number, and the deviatoric fabric at the critical state as the inertial number, I, was varied. The critical state relationships were aligned along distinct loci for each value of I. The critical state framework was used to show that there is an upper bound to the I values below which the simulation is quasi-static and that the observed behaviour is independent of the strain rate. The parameter I was shown to be a useful measure for assessing the quality of quasi-static DEM simulations.

Influence of coarse-graining parameters on the analysis of DEM simulations of silo flow

The discrete element method (DEM) is used extensively for the simulation of granular materials and in powder technology. Averaging or coarse graining (CG) techniques, also referred to as the micro–macro transition, are applied to the particle data from DEM simulations to extract bulk continuum fields such as density, velocity and stress, which are important for the design of a great majority of engineering applications. Although numerous papers have been published on such CG techniques, there still remain considerable challenges, chiefly because both the spatial and the temporal scales vary between different engineering processes.The major aim of this paper is to answer the question of what temporal and spatial averaging scales should be adopted, and what is their influence on the micro–macro projected continuum fields. A model silo with a non-steady, inhomogeneous internal flow pattern is used as a test case, where three distinct flow regimes are present, i.e. : (i) a stagnant zone, (ii) a high shear localisation zone and (iii) a core zone with fast flow. The spatial and temporal scales are varied systematically and display interesting relationships with other model parameters such as the sampling frequency and simulation time; however, there is a range (plateau) of spatial and temporal scales which provide continuum fields independent on the coarse-graining width and time scales.Then we compare several ways to identify/locate the shear band centre and width. Based on the (simple-shear) strain rate (horizontal gradient of vertical velocity), the shear band is best defined, together with a fitting procedure that allows to smoothly find its centre and width. The other continuum fields are analysed, showing a strongly anisotropic stress tensor, with an arch of higher horizontal stresses observed in the central region, while the stress in the stagnant zone transfers the weight of the flow to the walls and the base plate. In the sheared and fast-flowing zones, the shear stress is predicted by the μ(I)−rheology, but this has to be based on the objective (complete tensorial) strain-rate, since the flow and shear geometry are not aligned along one direction. Further non-Newtonian mechanisms can be observed, but are not detailed in this study.

Grain‐scale‐based simulation of granular material

AbstractIn recent years, new developments in experimental mechanics, e. g., particle‐tracking methods using X‐ray micro‐tomography, have provided a new insight into the material behaviour of granular media. The possibility to capture the individual grain displacement and rotation of all particles within a sample provides a new fundament for a reliable numerical simulation of granulates. This is, in particular, the case for deformation localisation in shear zones as they are observed in bi‐ and triaxial compression tests, where the exact thickness of the localised zone as well as the amount of accompanying grain displacements and rotations are measurable in a precise and direct way. In this context, the Discrete‐Element (DE) Method has become a promising and frequently used modelling technique for granular materials. In contrast to macroscopically based continuum‐mechanical approaches, the DE approach treats each particle as a rigid and uncrushably body and is, therefore, defined on a microscopic level of description. This consequently allows a direct comparison with experimental data from grain‐scale tracking methods. In the present contribution, the DE method is applied in order to solve problems of localisation in granular media. Therefore, constitutive inter‐particle contact laws are formulated for forces and torques which are transferred between interacting particles. With a given solution of initial‐boundary‐value problems on the microscale, a computational homogenisation procedure leads to macroscopic quantities purely stemming from microscopic information. Herein, a particle‐centre‐based volume averaging technique leads to macroscopic quantities which correspond to quantities known from micropolar continuum theories. The contribution presents a framework for the homogenisation in all time steps in a fully 3‐dimensional context and discusses the activation of micropolar effects in the localised zone. Furthermore, the admissible size of the chosen Representative Elementary Volume (REV) is addressed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Towards a mechanistic contact model for elastoplastic particles at high relative densities

Triaxial compression of elastoplastic particles was studied with numerical and analytical methods in order to develop a mechanistic model for their interactions at high relative densities. The introduction of an equivalent particle radius that accounted for the elastic volumetric deformation enabled an almost perfect reduction of the results obtained for elastoplastic particles to those obtained for rigid, perfectly plastic ones. This, in turn, made possible a simplified yet mechanistic analytical analysis of the particle response in terms of the contact area, pressure and force. The developed model exhibited a good agreement with the numerical results, especially for intermediate and large strains, and hence laid the foundations for the development of mechanistic contact models suitable for simulations of granular materials at high relative densities with the Discrete Element Method (DEM).

IDEM: An impulse‐based discrete element method for fast granular dynamics

SummarySince the inception of discrete element method (DEM) over 30 years ago, significant algorithmic developments have been made to enhance the performance of DEM while emphasizing simulation fidelity. Nevertheless, DEM is still a computationally expensive numerical method for simulation of granular materials. In this study, a new impulse‐based DEM (iDEM) approach is introduced that uses collision impulse instead of contact force and directly handles velocity while bypassing integration of acceleration. Contact force required for engineering applications is retrieved with reasonable fidelity via an original proposed formulation. The method is robust, numerically stable and results in significant speed up of almost two orders of magnitude over conventional DEM. The proposed iDEM allows for the simulation of large number of particles within reasonable run times on readily accessible computer hardware. Copyright © 2015 John Wiley & Sons, Ltd.

Review of Finite Element Simulation of Granular Materials

The behaviour of granular materials especially under dynamic loading has been under investigation for years. In recent years, the advancing computer technology makes it possible to model complicate behaviour under different loadings. In this review paper, major advances and researches in the field of providing conceptual model for behaviour of granular materials have been reviewed. The reviewers have tried to categorise the researches in term of their approach to modelling the mechanical behaviour of granular materials and then identify the gaps to provide ground for the future researches.