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This paper presents a breakage model of particulate solids under impact loading based on a mechanical approach. Existing breakage models are assessed using the experimental data from single particle impact tests, indicating a more general breakage model is required. Indentation fracture mechanics is used to account for surface damage under dynamic loading. The effect of impact angle is considered in the model, which rationalizes the contributions of both the normal and tangential impact velocity. A unified curve of breakage propensity is constructed using the equivalent velocity under oblique impact based on the experimental data from this study and the literature. This model provides a basis to evaluate breakage propensity of brittle/semi-brittle particles subject to oblique impact and the proposed equivalent velocity has a potential to improve the description of impact energy spectra for milling processes where oblique impact of particle is common and typically ignored.

Breakage occurs in several particulate systems that are simulated using the discrete element method (DEM), namely crushing and grinding as well as inadvertently in several others that include transportation, handling, mixing, separation and geotechnical applications. Different approaches may be used to describe particle breakage using DEM, but in cases in which particle breakage influences significantly the flow behaviour of the material, imbedding the breakage description in DEM provides the only valid alternative. This study describes the implementation of a detailed breakage model based on particle replacement with spheres in the commercial software EDEM. It accounts for variability and size-dependency in particle fracture energies, weakening of particles by unsuccessful stressing events, as well as addressing several reported shortcomings in sphere replacement schemes. The model is verified in great detail on the basis of single-particle breakage information and validated using measurements in unconfined particle beds of mineral ores.

Regardless of its origin, in the near future the challenge will not be how to generate data, but rather how to manage big and highly distributed data to make it more easily handled and more accessible by users on their personal devices. VELaSSCo (Visualization for Extremely Large-Scale Scientific Computing) is a platform developed to provide new visual analysis methods for large-scale simulations serving the petabyte era. The platform adopts Big Data tools/architectures to enable in-situ processing for analytics of engineering and scientific data and hardware-accelerated interactive visualization. In large-scale simulations, the domain is partitioned across several thousand nodes, and the data (mesh and results) are stored on those nodes in a distributed manner. The VELaSSCo platform accesses this distributed information, processes the raw data, and returns the results to the users for local visualization by their specific visualization clients and tools. The global goal of VELaSSCo is to provide Big Data tools for the engineering and scientific community, in order to better manipulate simulations with billions of distributed records. The ability to easily handle large amounts of data will also enable larger, higher resolution simulations, which will allow the scientific and engineering communities to garner new knowledge from simulations previously considered too large to handle. This paper shows, by means of selected Discrete Element Method (DEM) simulation use cases, that the VELaSSCo platform facilitates distributed post-processing and visualization of large engineering datasets.

Despite many attempts to establish material grindability in a milling process, it remains very difficult to predict the milling performance. In this study, impact milling tests were carried out under varying operational conditions in a UPZ100 impact pin mill. The product size distribution and fineness of milled alumina particle are reported and analyzed. A multiscale framework coupling discrete element method (DEM) and population balance model (PBM) is proposed to predict the milling performance of the mill. The impact velocity and impact frequency information from DEM is utilized to inform the mill operation parameters of the PBM model at the process scale, whilst the material grindability parameters are evaluated using constrained optimization to match a milling test. The predictions of the product size distribution show very good agreement with the experimental results. This indicates that the multiscale model is promising for optimizing the design and operation of mills.

Bonded contact models have been increasingly used in the discrete element method (DEM) to study cemented and sintered particulate materials in recent years. Several popular DEM bond models have been proposed in the literature; thus it is beneficial to assess the similarities and differences between the different bond models before they are used in simulations. This paper identifies and discusses two fundamental types of bond models: the Spring Bond Model where two bonded particles are joined by a set of uniform elastic springs on the bond’s cross-section, and the Beam Bond Model in which a beam is used to connect the centres of two particles. A series of cantilever beam bending simulation cases were carried out to verify the findings and assess the strength and weakness of the bond models. Despite the numerous bond models described in the literature, they can all be considered as a variation of these two fundamental model types. The comparative evaluation in this paper also shows that all the bond models investigated can be unified to a general form given at a predefined contact point location.

Realistic yet efficient representation of particle shape is a major challenge for the Discrete Element Method. This paper uses angle-of-repose and direct-shear test simulations to describe the influence of several shape representation methods, and their parameters, on the bulk response of granular assemblies. Three rolling resistance models, with varying coefficient of rolling friction, are considered for spherical particles. For non-spherical particles, superquadrics with varying blockiness and multi-spheres with varying bumpiness are used to model cuboids and cylinders of several aspect ratios. We present extensive quantitative results showing how the various ways used to represent shape affect the bulk response, allowing comparisons between different approaches. Simulations of angle-of-repose tests show that all three rolling friction models can model the avalanching characteristics of cube/cuboid and cylindrical particles. Simulations of direct-shear tests suggest that both the shear strength and the dilative response of the considered non-spherical particles (but not their porosity) can only be predicted by the elasto-plastic rolling resistance model. The quantitative nature of the results allows identifying values of the shape-description parameters that can be used to obtain similar results when using alternative shape representation methods.Graphical abstract

This paper presents a generic framework of Model Driven Design (MDD) with its application for a twin screw granulation process using a mechanistic-based population balance model (PBM). The process kernels including nucleation, breakage, layering and consolidation are defined in the PBM. A recently developed breakage kernel is used with key physics incorporated in the model formulation. Prior to granulation experiments, sensitivity analysis of PBM parameters is performed to investigate the variation of model outputs given the input parameter variance. The significance of liquid to solid ratio (L/S ratio), nucleation and breakage parameters is identified by sensitivity analysis. The sensitivity analysis dramatically reduces the number of fitting parameters in PBM and only nine granulation experiments are required for model calibration and validation. A model validation flowchart is proposed to elucidate the evolution of kinetic rate parameters associated with L/S ratio and screw element geometry. The presented MDD framework for sensitivity analysis, parameter estimation, model verification and validation can be generalized and applied for any particulate process.

Multi-spheres and Superquadrics are popular approaches for addressing particle shape effect in the Discrete Element Method (DEM). This study focuses on the mechanical characteristics of cubical particles, modeled by the two methods (using EDEM and LIGGGHTS), through conducting a series of numerical case studies at both single particle and bulk levels. In the first part of the study, several testing scenarios, which clarify the impact, interlocking, sliding and tilting characteristics of the particle, are discussed and the respective simulations are carried out. The results emphasize the importance of surface bumpiness and edge sharpness in the single-particle behaviour and are used for informing the bulk response. Further, role of the two shape descriptors on bulk response is evaluated in angle of repose, Jenike shear and silo flow simulations. The results of these tests are assessed both at the micro, directly through DEM outputs, and at the meso- and macro-scales, using a coarse graining technique. It is seen that the properties of edge and surface in superquadric and multi-sphere particles considerably influence the heap profile in the angle of repose test. However, in a Jenike direct shear, the shape complexity only significantly affects the shear strength, porosity and mode of motion when the packing is dense. Additionally, in silo discharge, the effect of shape features is even less on the flow pattern and mass flow rate but is found to have a significant influence on the stress distribution.

The bulk properties of powders depend on material characteristics and size of the primary particles. During storage and transportation processes in the powder processing industry, the material undergoes various modes of deformation and stress conditions, e.g., due to compression or shear. In many applications, it is important to know when powders are yielding, i.e. when they start to flow under shear; in other cases it is necessary to know how much stress is needed to keep them flowing. The measurement of powder yield and flow properties is still a challenge and will be addressed in this study. In the framework of the collaborative project T-MAPPP, a large set of shear experiments using different shear devices, namely the Jenike shear tester, the ELE direct shear tester, the Schulze ring shear tester and the FT4 powder rheometer, have been carried out on eight chemically-identical limestone powders of different particle sizes in a wide range of confining stresses. These experiments serve two goals: i) to test the reproducibility/consistency among different shear devices and testing protocols; ii) to relate the bulk behaviour to microscopic particle properties, focusing on the effect of particle size and thus inter-particle cohesion. The experiments show high repeatability for all shear devices, though some of them show more fluctuations than others. All devices provide consistent results, where the FT4 powder rheometer gives lower yield/steady state stress values, due to a different pre-shearing protocol. As expected, the bulk cohesion decreases with increasing particle size (up to 150 μm), due to the decrease of inter-particle cohesion. The bulk friction, characterized in different ways, is following a similar decreasing trend, whereas the bulk density increases with particle size in this range. Interestingly, for samples with particle sizes larger than 150 μm, the bulk cohesion increases slightly, while the bulk friction increases considerably—presumably due to particle interlocking effects—up to magnitudes comparable to those of the finest powders. Furthermore, removing the fines from the coarse powder samples reduces the bulk cohesion and bulk density, but has a negligible effect on the bulk friction. In addition to providing useful insights into the role of microscopically attractive, van der Waals, gravitational and/or compressive forces for the macroscopic bulk powder flow behaviour, the experimental data provide a robust database of cohesive and frictional fine powders for industrially relevant designs such as silos, as well as for calibration and validation of models and computer simulations.

This paper investigates the mechanical behavior and strain localization of methane hydrate bearing sediments (MHBS) at different temperatures and water pressures via the distinct element method (DEM). A thermo-hydro-mechanical contact model of MHBS has been employed in the DEM to simulate biaxial tests and mechanical behavior of MHBS is studied with different temperatures and water pressures. Three MHBS specimens are simulated at different temperature-pressure conditions to provide an insight on the evolution of macro and micro variables during strain localization of MHBS, as well as the geometric characteristics of shear band. The results show that MHBS appears to be strain-softening with dilatancy and the existence of MH will increase the cohesion but decrease the friction angle of MHBS. As temperature increases or water pressure decreases, the cohesion and friction angle of MHBS decrease with increasing dilatancy. The strain localization is closely related to bond breakage as well as localization of other micro and macro variables such as contact force chains, principal stress fields, particle velocity fields and average pure rotation rate distributions. As temperature and water pressure change, three different types of shear band can form. The thickness and inclination angle of these shear bands increase as the temperature increases or water pressure decreases.

The macroscopic response of a geomaterial is entirely determined by changes at the particle scale. It has been established that particle crushing is affected by particle size, shape and mineral composition and initial density; and the initiation of breakage has often been related to the onset of yielding. Encouraged by the success of X-ray tomography in revealing particle-scale mechanisms of deformation, we present our findings regarding the onset of particle breakage, deriving from our study of 3D images of a dry granular assembly undergoing crushing. We propose two bespoke image analysis algorithms, which allow us to track breakage and identify contacts prior to breakage. The combination of the two algorithms, along with the high resolution of the 3D images enables us for the first time to track breakage of individual particles, identify different breakage modes for each particle and simultaneously study the effect of particle morphology and coordination number on breakage. Three different breakage types are identified: chipping, splitting and fragmentation. We have found that particle heterogeneity and sphericity mainly contribute to fragmentation, whereas the coordination number also affects chipping. The confining stress state within the particles with high coordination number made them more resistive to fragmentation, whereas particles with low coordination number mainly undergo fragmentation. The shearing of the particles at their contact points, leads to local stress concentrations resulting into surface chipping. Finally, we discuss the relation between the initiation of breakage and yielding, showing that some breakage occurs before the point where yielding is traditionally defined.

Many industrial processes involve granular heat transfer. Within these processes are a sub-set of applications where the particles are densely packed and the surrounding gas is predominantly stagnant. For materials with low thermal conductivity much of the heat transfer will occur through the interstitial gases so capturing this effect is critical to represent these systems numerically. Resolving the gas phase explicitly using a fluid solver and coupling to a particle method is possible but computationally expensive. Higher fidelity models often make simulation of applications at the industrial scale intractable. With this in mind we seek a numerical method that captures the important heat transfer phenomena in dense granular systems with minimal additional computational effort. In this work we first characterize one common particle based approach proposed by Rong and Horio that calculates the contribution through a stagnant gas film surrounding each particle. We compare this approach to fluid simulations of a particle-wall and a particle-particle collision to evaluate the validity of the underlying assumptions of the Rong and Horio model. We then use a multi-scale approach to examine the relationship between the local packing structure and the contribution of the interstitial gas. From this we propose a new dimensionless parameter that permits the inclusion of the gas effect in a particle based simulation method with minimal additional computational effort and without explicitly having to include the gas phase. The model is then validated against a static experiment and compared with the Rong and Horio model.

We simulate a small-scale dense gas–solid fluidized bed using an approach coupling the averaged Navier–Stokes equation with a discrete description of particle dynamics. The simulation results are compared to the voidage, solid velocity and granular temperature measured using magnetic resonance (MR), and other experimental measurements for the same fluidized bed. It is found that the simulation is able to predict the minimum fluidization velocity and pressure drop with reasonable agreement and qualitatively capture the solid circulation pattern to a similar degree achieved by previous such simulations. The discrepancies for the solid velocities near the walls and in the central region at upper and lower bed heights were investigated by examining various models of the physical system and the sensitivity of the simulation results to these models. We demonstrate that the particle–wall interaction dominates the particle dynamics in a boundary layer of about 5 particle diameters to the wall and that modeling the wall using fixed particle of comparable size to the fluidized particles provides enhanced resistance reducing solid wall-slip velocity and granular temperature at the boundary layer. Modeling of particle size is shown to be important for capturing the variation of bed dynamics along the bed height direction.

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.

We present a numerical study on the DEM modeling of cohesive solids using a visco-elasto-plastic frictional adhesive contact model [1]. The capabilities of the contact model to capture the mechanical macroscopic behavior of cohesive materials were investigated by means of cone penetration and unconfined compression simulations. The results show that the simulations are able to reproduce qualitatively the typical trend of the penetration resistance profile in cohesive solid characterized by a steady-state at large penetration depths. The contact model is also capable of capturing the dependence of the penetration resistance on the consolidation stress history. Furthermore, the simulations reproduce the relationship between the unconfined strength and the penetration resistance that has been reported in real cohesive materials. Finally, we investigated the scaling laws of the contact model parameters to produce the same load–deformation behavior invariant of the particle size used in the simulations. The results demonstrate the suitability of the proposed model to simulate complex processes involving cohesive solid at large engineering scale scenarios.

The work presented in this paper was carried out as part of the PARDEM project. The overall aim was to quantify the predictive capability of a coupled CFD-DEM approach to simulating the horizontal pneumatic conveying of spherical and low-aspect-ratio non-spherical particles. Carefully controlled experiments were carried out in a 6.5 m long, 0.075 m diameter horizontal conveying line with the aid of the laser Doppler anemometry (LDA). Three different sizes of spherical glass beads, ranging from 0.8 mm to 2 mm and low-aspect-ratio cylindrical shaped particle of size 1×1.5 mm were employed. Simulations of the experiments were performed using a two-way coupled computational fluid dynamics and discrete element method (CFD-DEM) implemented in the commercial software FLUENT-EDEM in an Eulerian-Lagrangian framework. Experimental and simulation results of gas and particle velocities for particle laden flow with spherical particles were compared, showing that the CFD-DEM method could capture the experimental trends. However, quantitative discrepancies between simulation and experimental results were observed. Further modelling of low-aspect-ratio cylindrical particles was conducted using a multi-sphere model to represent cylindrical particles in the DEM code. Drag equations were modified in the code to take the effect of particle shape into account. The simulation results of mean axial particle velocity agreed reasonably well with maximum 25% discrepancy when compared to experimental measurements using the LDA technique. The discrepancies between simulation and experimental results were attributed to the selected drag model, mesh size and lack of an appropriate mesh interpolation scheme in the selected code.

Current theories and design codes pertaining to storage structures for bulk solids have been developed in the context of rigid-walled silos and may not be applicable for smaller and highly flexible containers that are often used for industrial packaging and intermediate storage. The focus of this study is to investigate the effect of wall flexibility on the bulk stresses and wall pressures during storage using finite element analysis. The results show that when the wall stiffness is low, the computed bulk stresses in the vertical bin section are dominated by plasticity, while the stresses in the hopper section remain in the elastic state. In this situation, the wall pressure in the bin section is heavily influenced by the strength of the stored solid, which controls the extent of plastic flow. Overall, the normal wall pressure in the bin section is found to decrease with wall flexibility leading to a corresponding increase in vertical stress in the stored solid. As a consequence, the stresses in the hopper also increase leading to increasing loads on the hopper walls and potential exacerbation of handling issues for cohesive materials in highly flexible containers.

Discrete and continuum modelling of granular flow in a conical hopper discharge is presented. The Discrete Element Method (DEM) is used for discrete modelling and Finite Element Method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation for continuum modelling. The ALE model has shown its capability to model granular flow and macroscopic behaviour in silos in the authors’ previous work (Wang et al., 2013). The use of ALE overcomes mesh distortion problem due to material large deformation which is often encountered in standard finite element modelling of silo discharge. However, there is still limitation when a continuum method is used to model silo discharge, in particular, to pursue particle-scale features in such granular flow. In this study, wall pressure, flow pattern and flow rate during silo discharge are investigated using both ALE and DEM simulation. Classical theories are used as a comparison, to verify the two numerical models. By comparison, it is indicated that both FE model using ALE formulation and DEM model have the capacity to model the granular behaviour and wall pressure for granular process in silos. The conclusion that ALE has advantages over DEM in wall pressure prediction giving stable pressure profile with smooth trend; while DEM has the ability to evaluate the role of particle-scale parameters on macro-scale response in such granular flow after carefully smoothing out the results has been drawn in the present study.

The volume ratio in the total solid particle mixtureis an important parameter indicating the characteristics ofpartculate mixtures. Therefore, a simple measurement method isdesirable. In this paper, the normalized permittivity of two groupsof particle mixtures are tested using Electrical CapacitanceTomography (ECT) with the series and parallel models. Theexperimental results show that normalized permittivity changesobtained from the series ECT model have a very strong linearrelationship with the volume ratio of higher permittivity materialsin the mixture. The Maxwell Garnett Formula (MGF) can predictthe normalized permittivity only after the permittivity of each typeof particle is known. The comparison between two methodssuggests that ECT with series model is a better way for monitoringthe volume ratio in the mixtures with two types of solid particles.

An investigation on the predictive capabilities of Discrete Element Method simulations of a powder mixing process in a laboratory scale paddle blade mixer is presented. The visco-elasto-plastic frictional adhesive DEM contactmodel of Thakur et al. (2014) was used to represent the cohesive behaviour of an aluminosilicate powder in which the model parameters were determined using experimental flow energy measurements from the FT4powder rheometer. DEM simulations of the mixing process using the contact model parameters were evaluated against the experimental measurements of the mixing rate. The results demonstrated thatwhilst the DEM modelis capable of reproducing the FT4 flow energy of the powder to an excellent agreement, the simulations of the mixing process produced a qualitative agreement on the trend of the mixing rate in the experiments for bothdry andwet powders. The mixingwas under-predicted in the simulations, suggesting that flowenergy measurements alone may not be sufficient for the optimization of a DEM model of powder mixing.

Particle breakage can significantly change the fabric (size and shape of particles and contact network) of a granular material, affecting highly the material's macroscopic response. In this paper, oedometric compression tests are performed on zeolite specimens and x-ray computed micro-tomography is employed, to acquire high resolution 3D images of the specimens throughout the test. The images are processed, to describe breakage spatially and quantify it throughout the test and gain information about the mechanisms leading to particle breakage. In addition to the image processing, the discrete element method (DEM) is used to study the initiation and likelihood of particle breakage, by simulating the experimental test during the early stages of loading and using quantitative results from the images to inform and validate the DEM model. A discrete digital image correlation is used, in order to incrementally identify intact grains and simultaneously get results about the strain field within the specimen, as well as the kinematics of individual grains and fragments. In the initial stages of breakage, there is a clear boundary effect on the spatial distribution of breakage, as it is concentrated at the moving boundary (more than 90% of total breakage) and circumferentially (more than 70% of total breakage) close to the apparatus cell. The DEM model can reproduce the bulk response of the material until the point where substantial breakage governs the macroscopic response and it starts to soften. Additionally, there is an initial indication that the spatial distribution of the force network matches the localisation of breakage radially, but it does not seem to localise close to the loading platen. This analysis will enrich our understanding of the mechanisms and evolution of particle breakage.

Silos, especially the ones consisting of cylindrical section with conical hopper, are commonly used for bulk material handling in many industries. Whilst the pressure acting on silo walls during filling is reasonably well understood, a reliable prediction of pressure during discharge remains an important open problem for silo design. This paper describes a finite element analysis of the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The computations were performed using an Arbitrary Lagrangian-Eulerian formulation with an explicit time integration approach to permit large deformations and overcome mesh distortion problems. The finite element results of silo pressure were temporally averaged and compared with the experimental observations in a model silo, which shows a satisfactory agreement in the wall pressure distribution. Two critical modelling issues have been addressed in some detail: one is the numerical treatment of the abrupt transition between the cylindrical section and the conical hopper, and the other is the interaction between the granular solid and the silo walls that is modelled using a dynamic friction model in this study. The simulation results show significant pressure fluctuations during silo discharge, which are comparable to the fluctuating pressure patterns reported in previous experiments. Two dominant frequencies are identified from the dynamic pressure, and a scrutinization of the simulation results suggests that the causes may be attributable to the propagation of the longitudinal waves within the stored granular solid and the intermittent macro-slip of the granular solid against the silo wall. These dynamic events could be a source of silo quaking and honking phenomena. (C) 2014 Elsevier B.V. All rights reserved.

There is an increasing use of the discrete element method (DEM) to study cemented (e.g. concrete and rocks) and sintered particulate materials. The chief advantage of the DEM over continuum based techniques is that it does not make assumptions about how cracking and fragmentation initiate and propagate, since the DEM system is naturally discontinuous. The ability for the DEM to produce a realistic representation of a cemented granular material depends largely on the implementation of an inter-particle bonded contact model. This paper presents a new bonded contact model based on the Timoshenko beam theory which considers axial, shear and bending behaviour of the bond. The bond model was first verified by simulating both the bending and dynamic response of a simply supported beam. The loading response of a concrete cylinder was then investigated and compared with the Eurocode equation prediction. The results show significant potential for the new model to produce satisfactory predictions for cementitious materials. A unique feature of this model is that it can also be used to accurately represent many deformable structures such as frames and shells, so that both particles and structures or deformable boundaries can be described in the same DEM framework.

This paper presents an experimental and numerical study of the packing, compression, and caking behaviour of spray dried detergent (SDD) powders with a two-fold aim: an experimental process of observation and evaluation of the packing, compression and caking behaviour of SDD powders, and a numerical approach based on discrete element modelling (DEM). The mechanical properties, including the stress–strain response and the corresponding porosity change as a function of consolidation stress in a confined cylinder, the stress–strain response during unconfined shearing and the cake strength as a function of consolidation stress, were evaluated and compared for different SDD powders using an extended uniaxial tester (Edinburgh Powder Tester – EPT). The experiments using EPT showed excellent reproducibility in the measurement of packing, compression and caking behaviour and were therefore very useful for describing the handling characteristics of these powdered products including screening new products and different formulations. It was found that the sample with higher moisture had lower bulk porosity but higher compressibility and cake strength. The porosity, compressibility and cake strength were found to vary across different size fractions of the same sample. The larger sieve-cut samples had higher initial bulk porosity, compressibility and cake strength. It is revealed that moisture plays a significant role in packing, compression, and shearing behaviour of the powder. Three-dimensional DEM modelling using a recently developed elasto-plastic adhesive-frictional contact model showed that the contact model is able to capture the detergent behaviour reasonably well and can be used to model complex processes involving these powders.

Dilute horizontal pneumatic conveying has been the subject of this experimental and numerical study. Experiments were performed utilising a 6.5 m long, 0.075 m diameter horizontal pipe in conjunction with a laser-Doppler anemometry (LDA) system. Spherical glass beads with three different sizes 0.8–1 mm, 1.5 mm, and 2 mm were used. Simulations were carried out using the commercial discrete element method (DEM) software, EDEM, coupled with the computational fluid dynamics (CFD) package, FLUENT. Experimental results illustrated that, for mass solid loading ratios (SLRs) ranging from 2.3 to 3.5, the higher the particle diameter and solid loading ratio, the lower the particle velocity. From the simulation investigations it was concluded that the inclusion of the Magnus lift force had a crucial influence, with observed particle distributions in the upper part of the conveying line reproducible in the simulation only by implementing the Magnus lift force terms in the model equations.

Many industrial bulk solids are commonly stored in open stockpiles that are progressively formed by depositing from above. A classic phenomenon concerning such simple piles is the observation of a significant pressure dip in the vertical pressure on the base underneath the apex which is counter-intuitive as this is the location where a maximum pressure might be expected. Numerous experimental, analytical and numerical studies have been conducted to investigate this problem over the last few decades, but a comprehensive understanding of the problem remains elusive. Mechanical anisotropy developed during pile formation process has recently been suggested to be the main cause of the pressure dip. However, more recent finite element method (FEM) studies have predicted a pressure dip beneath the apex using isotropic material models. The review of the literature shows a lack of understanding of the underlying mechanism and the roles of various factors on the prediction of the pressure dip, such as the progressive mesh activation, stress dependency of modulus and plastic failure parameters. The aim of this paper is to investigate the effects of these factors by modelling a set of conical sandpile experiments formed on a rigid base by concentrated deposition. The results show that significant pressure dip can be predicted without considering material anisotropy. However, within the realm of elasto-plastic models investigated, it appears that the prediction of pressure dip requires a model considering the construction process and the associated plastic deformation. Incorporating stress-hardening elasticity enhances significantly the extent of the dip. The results demonstrate that a greater mobilisation of the base shear traction is an important mechanism in enhancing the arching effect that leads to a significant central pressure dip.

Author's version of an article in the journal: Chemical Engineering Science. Also available from the publisher at: http://dx.doi.org/10.1016/j.ces.2012.11.028 A silo with a shallow hopper is designed to achieve the required silo capacity when the headroom available is limited, provided that the issue of segregation of stored particulate solids is not a problem. Several analytical models have been proposed to try to predict the design loads for such shallow silo hoppers to guarantee their structural integrity. In this study, a novel finite element analysis has been conducted to explore the development of pressures and tractions on the wall of a full scale shallow hopper when it is filled with sand. Simple meshes were used to represent the sand and the hopper wall. Coulomb friction modelled the interaction between the sand and the wall. The process of progressive filling was simulated by temporarily suspending and then re-activating appropriate parts of the mesh. The two computational models of "switched-on filling" and "progressive-filling" were used to determine whether this simple treatment of the deposition process makes a significant difference to the predicted forces on the hopper wall: it is evident that progressive filling produces some significant changes that lead to more realism. Experiments were also conducted that measured local pressures on the shallow hopper wall under axisymmetric filling with sand. Comparisons between the numerical predictions, the measurements and existing algebraic models are presented. The results show clearly that wall friction is not fully developed in a shallow hopper, and that one algebraic model captures the behaviour well. However, the results also show that this problem is quite complicated and worthy of further study.

The solid volume fraction and volume composition ratio of different solid particles in a silo are important parameters indicating the character of granular mixtures. In this paper, measurement of the two parameters is studied by utilizing Electrical Capacitance Tomography (ECT). This preliminary work focuses on comparing normalized permittivity changes from ECT with those predicted by the Maxwell Garnett formula (MGF) relating to solid volume fraction and volume composition ratio. Experimental results show that normalized permittivity changes from the two methods have a strong linear correlation in gas-solid two- and three-phase systems. This work demonstrates that ECT is a promising technique for monitoring solid volume fraction of single solid particles and the volume composition ratio of mixtures of two different solid particles in a silo.

The study of stress waves in granular materials is of some importance in several industrial bulk materials handling systems. In particular, the growth in the magnitude of rarefaction waves due to friction has been thought to play an important role in the silo quaking phenomenon. To this end, this paper examines the propagation of rarefaction waves in granular columns subject to Coulomb wall friction, focusing on the effect of geometry by examining converging and diverging tapered columns. A one-dimensional dynamic model of these systems is developed and analytical solutions of this model are compared to a numerical model based on the Arbitrary Lagrangian–Eulerian formulation in a finite element analysis. This numerical model was first validated using the known behaviour of cylindrical columns. In all cases, the rarefaction waves examined in this work grew with the distance travelled up the column; however, the rate was shown to depend on the half-angle of the taper. Over a range of small angles, the analytical model was found to accurately predict this behaviour.

This paper proposes a methodology to link the discrete element method (DEM) with the finite element analysis (FEA) to evaluate the loading of particulate solid on a contacting structure or machine. The mathematical formulation to convert the DEM boundary contact forces to the nodal forces and moments in triangular finite elements was derived based on the concept of shape function. To prove the feasibility of this proposed methodology, two numerical examples, confined compression and confined expansion of steel beads filled in a cylindrical container, were analysed. The DEM calculations for discrete steel beads were performed using the PFC3D code. The outputs from the DEM simulations were extracted and processed into ABAQUS FEA input decks by the proposed method. A finite element analysis was executed to calculate the stress distribution in the continuum steel cylinder for the two examples using a linear shell analysis. The DEM and FEA results were presented and discussed in this paper. The results show that the proposed methodology can provide an effective way to determine the stress distribution in contacting structures subjected to loading from particulate assemblies and can be applied to solve solid–structure interaction problems. The proposed methodology is not applicable to the cases where wall friction is significant.

The influence of particle shape and interparticle friction on mechanical response of a granular assembly in a uniaxial compression was determined in laboratory experiment and in DEM simulations. The test chamber of rectangular cross-section was used. In laboratory testing seeds of pea and bean were used, while in numerical simulations spherical and non-spherical particles of aspect ratios, which are ratios of the longest to the smallest particle dimensions, in the range from 1 to 2.8 were tested. After the seeds were filled in the chamber the load was applied to the assembly through a top platen driven by a testing machine. The vertical and horizontal forces were measured with load cells supporting the apparatus wall and bottom platen. Numerical results showed that an increase in particle aspect ratio strongly affected the mechanical response of specimen under uniaxial compression. The lateral-to-vertical pressure ratio was predicted to decrease as particle aspect ratio increased from unity to 1.6 and thereafter remained relatively stable with further increase in aspect ratio. Comparison of numerical and experimental results has shown that DEM predicted fairly close the effective modulus of elasticity of the system composed of perfect uniform spheres when compared to the physical tests on peas while a weaker quantitative agreement with experimental results was obtained in the case of oblong particles.

NOTICE: this is the author's version of a work that was accepted for publication in Thin-Walled Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in THIN-WALLED STRUCTURES, [VOL 49 (2011)] DOI http://dx.doi.org/10.1016/j.tws.2011.05.010

In this study, the discrete element method (DEM) was used to investigate the influence of particle shape and interparticle friction on the bulk friction in a Jenike direct shear test. Spherical particle and non-spherical particles using two overlapping sphere giving particle aspect ratio of up to 2 and a full range of interparticle contact friction coefficient were studied numerically. These were compared with physical Jenike shear tests conducted on single glass beads and paired glass beads. To separate the influence of sample packing density from interparticle contact friction on the bulk shearing response, the same initial packing was used for each particle shape in the simulations. The interplay between contact friction and particle interlocking arising from geometric interaction between particles to produce the bulk granular friction in a direct shear test is explored and several key observations are reported. The results also show that particle interlocking has a greater effect than packing density on the bulk friction and for each particle shape; DEM can produce a good quantitative match of the limiting bulk friction as long as similar initial packing density is achieved.

Over the past 30 years, the Discrete Element Method (DEM) has rapidly gained popularity as a tool for modelling the behaviour of granular assemblies and is being used extensively in both scientific and industrial applications. However, it is far from clear from reviewing the literature whether the large number of DEM codes have been verified and checked against fundamental benchmark problems. DEM simulates the dynamics of each particle in an assembly by calculating the acceleration resulting from all the contact forces and body forces. It is clearly necessary that such a model be validated or verified by comparing with experimental results, analytical solutions or other numerical results (e.g. Finite Element Analysis (FEA) results) at particle impact level. There appears to be no standard benchmark tests against which DEM codes can be verified. It is thus essential and useful to establish a set of standard benchmark tests to confirm that these DEM codes are modelling the particle dynamics as intended. This paper proposes a set of benchmark tests to verify DEM codes at particle impact level for spherical particles. The analytical solutions derived from elasticity theory for elastic normal collision of two spheres or a sphere with a rigid plane are first reviewed. These analytical solutions apply only to the elastic regime for normal impact. Secondly, the analytical solutions of frictional oblique impact between two spheres or a sphere with a rigid plane are scrutinized and derived. These analytical solutions originate from the dynamics principles and should be satisfied for any DEM contact force model with prescribed friction and restitution coefficients. A set of eight benchmark tests are designed and performed using commercial DEM codes. Test 1 and Test 2 consider the elastic normal impact of two spheres or a sphere with a rigid plane, whereas the other tests (Test 3–Test 8) investigate the energy dissipation due to the collision. These benchmark tests also involve different types of material. The DEM results were compared with the analytical solutions, experimental or FEA results found in the literature. All benchmark tests showed good to excellent match, providing a quantitative verification for the codes used in this study. These benchmark tests not only verify DEM codes but also enhance the understanding of fundamental impact phenomena for modelling a large number of particles.

Granular solids in silos experience considerable principal stress rotations, which result in the non-coaxiality between principal stresses and plastic strain rates. This paper discusses the influences of the use of elastoplastic non-coaxial models for granular solids on predictions of wall pressure distributions in silos by using the finite element method. A well established non-coaxial model in geomechanics, the yield vertex model, is employed. Simulations are performed on a steep hopper characterized with a mass flow and a flat-bottomed silo with a semi-mass flow. The simulations indicate that the non-coaxiality does not influence predictions of wall pressures after filling. On the other hand, the predicted discharge wall pressures with non-coaxial considerations are larger than those without it. Its mechanism is discussed in this paper. The suppressed shear-dilatancy of granular solids in silos leads to a larger increase of normal stress with non-coaxial models.

Particulate systems are of interest in many disciplines. They are often investigated using the discrete element method because of its capability to investigate particulate systems at the individual particle scale. To model the interaction between two particles and between a particle and a boundary, conventional discrete element models use springs and dampers in both the normal and tangential directions. The significance of particle rotation has been highlighted in both numerical studies and physical experiments. Several researchers have attempted to incorporate a rotational torque to account for the rolling resistance or rolling friction by developing different models. This paper presents a review of the commonly used models for rolling resistance and proposes a more general model. These models are classified into four categories according to their key characteristics. The robustness of these models in reproducing rolling resistance effects arising from different physical situations was assessed by using several benchmarking test cases. The proposed model can be seen to be more general and suitable for modelling problems involving both dynamic and pseudo-static regimes. An example simulation of the formation of a 2D sandpile is also shown. For simplicity, all formulations and examples are presented in 2D form, though the general conclusions are also applicable to 3D systems.

There is extensive engineering literature concerning the prediction of pressure and flow in a silo. The great majority of them are based on continuum theories. The friction between the stored material and the silo wall as well as the inclination of the hopper at its base are considered to be the most influential parameters for the flow pattern within the silo. In this paper, the filling and discharge of a planar silo with a hopper at its base has been modelled using DEM. The aim is to investigate the influence of DEM model parameters on the predicted flow pattern in the silo. The parametric investigation particularly focused on the hopper angle of inclination and the contact friction between particles and walls. The shape of the particles was also considered by comparing spherical and non-spherical particles, thus providing an insight into how particle interlocking might influence solids flow behaviour in silos. The DEM computations were analysed to evaluate the velocity profiles at different levels as well as the wall pressure distribution at different stages during filling and discharge. A detailed comparison reveals several key observations including the importance of particle interlocking to predict a flow pattern that is similar to the ones observed in real silos.

In recent years, Particle Tracking Velocimetry (PTV) has been extensively used to measure the translational velocity field of granular assemblies in applications such as vibrated beds, rotating drums and Couette shear cells. However, this technique has not yet been shown to be able to determine the velocity field of non-spherical particles. The aim of this paper is to develop an improved PTV technique to determine translational and rotational velocities for non-spherical particles. To prove the feasibility of this new PTV technique, it was employed to investigate the convection behaviour of non-spherical particles in a vibrated bed. In the demonstration example, paired POM particles made by gluing two single POM beads were studied. The test example was a single layer quasi-2D model. The transport properties of the paired POM particles in a vibrated bed, such as local average velocities, local fluctuation velocities, granular temperatures, fluctuation velocity distributions, self-diffusion coefficients and dimensionless convection flow rates, were evaluated from the experimental results and discussed. The developed improved PTV technique is shown to have the ability to measure more accurately the velocity field of non-spherical particulate systems. The study has demonstrated the convection phenomenon of non-spherical particles in a vibrated bed and has shown that particle rotation is significant in the vibrated granular bed. In such a granular system with convection phenomenon, the average rotational kinetic energy constitutes approximately 5.4% of the average kinetic energy and in some local regions the rotational granular temperature amounts to over 17% of the total granular temperature.

The base pressure distribution underneath a granular pile is carefully investigated using the discrete element method. Simulations were performed using both spherical and non-spherical particles in several numerical models of granular piles. A pressure profile with a significant pressure dip under the apex was predicted for all three models under certain conditions. The spherical assembly appears to produce a more erratic pressure profile with a less significant pressure dip than the non-spherical particles. The history of the pile preparation is shown to be important whilst the base deflection is shown to be not a requirement for the dip to form. The results are in good agreement with some published experimental observations. The issue of lengthscale in terms of the dimension of the charging source relative to the dimension of the pile is explored. The granular fabric in terms of the magnitude of contact force, the contact orientation and the particle orientation within a granular pile have also been described.

This paper presents a computational modelling of the shot peening process, in which the finite element method was employed to study the elastic–plastic dynamic process of shots impacting on a metallic target, and the discrete element method was used to study the multiple particles dynamics. The results demonstrated the capability of the method to capture realistic behaviour including the interaction between incoming shots and rebounding shots. Statistical analyses of the shots impact data reveal the relationships between peening process parameters and peening quality, which are useful for identifying the parameters which need to be controlled and regulated in order to produce a more beneficial compressive residual stress distribution within the target.