Discrete Element Method Simulations Research Articles

Sustainable dye extraction: Annatto powder production in a fountain confined spouted bed

AbstractThis study proposes an efficient and sustainable process for annatto powder production using a fountain confined spouted bed. With widespread applications in industries such as food, pharmaceuticals, and cosmetics, conventional extraction methods face environmental and economic challenges. Our study explores a solvent‐free and eco‐friendly approach using mechanical attrition within a fountain confined spouted bed, offering a cost‐effective solution for annatto cultivation. We systematically investigated the impact of four parameters—fountain confiner position and length, draft tube diameter, and airflow velocity—employing experimental design, multiple regression analysis, particle swarm optimization, and computational fluid dynamics–discrete element method (CFD‐DEM) simulations. The proposed optimization condition shows significantly higher collision intensity, improving annatto powder production compared to other central composite design tests. This study contributes to developing of a sustainable and economically viable method for dye production, with potential implications for annatto‐producing regions globally.

An improved model for discrete element method simulation of spatial gradient distributions of freeze-thaw-induced damage to sandstone

The investigation into the freeze-thaw (F-T) damage holds paramount theoretical significance in comprehending the mechanisms underlying F-T disasters, predicting catastrophes, and devising engineering protection systems. F-T damage in rock evolves progressively from the surface towards the interior, however, current models exhibit conspicuous deficiencies in simulating such progressive damage. Drawing upon experimental findings concerning the evolution of F-T damage in water-saturated rock, an improved discrete element model (DEM) for rock F-T damage is developed. In this model, thermal conduction model and volume expansion theory are integrated to describe the volumetric expansion characteristics during the freezing of internal pore water, thus effectively simulating the initiation and progression characteristics of frost heave cracks. We validated this model through comparisons with theoretical analyses and experiments, exploring the effects of model parameters. Employing moment tensor, the spatial gradient distribution patterns of F-T damage in water-saturated rock from the vantage point of fracture energy was analyzed. The results reveal that at −20 °C, 20 F-T cycles are requisite for the propagation of damage from the outer layer to the center of the Sichuan sandstone samples. The extent of damage in the outer layer exceeds that of the center, with the maximum fracture energy density of the outer layer being approximately 38.7 times that of the center. This model aptly delineates the progressive development of F-T damage characteristics and holds promise for further applications in identifying and delineating F-T damage zones in cold region rock engineering.

Correlation of fabric parameters and characteristic features of granular material behaviour in DEM in constitutive modelling

AbstractThe anisotropic microstructure of granular materials has a profound effect on their macroscopic behaviour and can be characterised using a fabric tensor. To include of fabric in the critical state theory (CST), anisotropic critical state theory (ACST) was proposed by modifying the state parameter $$(\psi )$$ ( ψ ) of CST to a fabric-dependent dilatancy state parameter $$(\upzeta )$$ ( ζ ) . Noteworthy that $$\uppsi$$ ψ showed a very strong correlation with characteristic features (e.g. instability, phase transformation and characteristic state) of macroscopic behaviour and, as a result, it has been adopted in many constitutive models. While $$\upzeta$$ ζ aided the inclusion of fabric in ACST models, the correlation between $$\upzeta$$ ζ and characteristic features has not been evaluated in detail yet, although a large number of works are found on micromechanics and fabric only. In this study, a large number of discrete element method simulations for drained and undrained triaxial were conducted to evaluate the correlation between $$\upzeta$$ ζ and characteristic features. To this purpose, the correlation between stress ratio and both classic and dilatancy state parameter ($$\psi$$ ψ and $$\upzeta$$ ζ ) were studied in important characteristic features (e.g. instability, phase transformation and characteristic state). It was found that this correlation was improved using $$\upzeta$$ ζ which might be due to the inclusion of fabric in our model. This observation is new and significant for inclusion of fabric evolution in constitutive modelling.

DEM investigation on flow instability of particulate assemblies under coupling between volumetric and axial strains

AbstractThe discrete element method (DEM) is employed to investigate the impact of coupling between volumetric and axial strains on the flow liquefaction vulnerability of 3D cubic particulate specimens. The virtual testing program conducted here encompasses a wide range of initial states and varying degrees of coupling between volumetric and axial strains. Utilizing data obtained from DEM simulations, the evolution of micro- and macroscale variables, including coordination number, contact fabric anisotropy, redundancy index, strong force networks, invariants of the effective stress tensor, and excess pore-water pressure, is examined. Results from DEM tests indicate that coupling expansive volumetric strain with axial strain leads to a gradual loosening of the load bearing microstructure, a decrease in coordination number, and a faster change in contact anisotropy. DEM simulations demonstrate that the triggering of flow liquefaction instability is followed by a sudden increase in contact fabric anisotropy and abrupt drops in coordination number and redundancy index. Moreover, a detailed analysis of the findings suggests that the stress ratio at the onset of post-peak softening decreases with increasing expansive volumetric strains.

Improvement of a pharmaceutical powder mixing process in a tote blender via DEM simulations

An industrial-scale pharmaceutical powder blending process was studied via discrete element method (DEM) simulations. A DEM model of two active pharmaceutical ingredient (API) components and a combined excipient component was calibrated by matching the simulated response in a dynamic angle of repose tester to the experimentally observed response. A simulation of the 25-minute bin blending process predicted inhomogeneous API distributions along the rotation axis of the blending container. These concentration differences were confirmed experimentally in a production-scale mixing trial using high-performance liquid chromatography analysis of samples from various locations in the bin. Several strategies to improve the blend homogeneity were then studied using DEM simulations. Reversing the direction of rotation of the blender every minute was found to negligibly improve the blending performance. Introducing a baffle into the lid at a 45° angle to the rotation axis sped up the axial mixing and resulted in a better final blend uniformity. Alternatively, rotating the blending container 90° around the vertical axis five minutes prior to the process end was predicted to reduce axial segregation tendencies.

Impact of several coarse-graining models on a pilot-scale fluidized bed behavior using discrete element method–computational fluid dynamics

Impact of several coarse-graining models on a pilot-scale fluidized bed behavior using discrete element method–computational fluid dynamics

Impact of particle arrangement and model dimensions on DEM modeling of high-speed railway ballasted tracks in 2D and 3D

Modelling railway projects has a main challenge in the discrete element method (DEM). The granular material of the embankment consists of millions of fine angular particles which are difficult to model due to the long computational time. The long computational time also prevents the modeling of the higher number of loading cycles. As a result, researchers prefer to simulate the project in 2D to accelerate the simulation. While 2D simulations present a seemingly simple option for modeling railways, they tend to oversimplify the intricacies of particle interactions and the distribution of stress. Nonetheless, the extent to which these simplifications affect the authenticity of the simulations has remained ambiguous. In this study, the periodic cell replication method is used to build extensive long railway tracks significantly faster than conventional methods. Then, this DEM model is calibrated against the measurement results of a physical full-scale ballasted track. The model is then used to simulate several railway projects with different initial particle arrangements and model dimensions in both 2D and 3D. The results show that the 2D models are more dependant on the initial particle arrangement which shows different behavior for the same model. In addition, 2D simulations are incapable of reproducing the principal stress rotation in granular layers due to the moving load of the train wheel. As a result, 3D DEM simulations using the periodic cell replication method is suggested for studying the railway tracks.

水稻穴播器取种装置设计与试验

The core equipment of rice dry direct-seeding with film mulching devices shows poor adaptability to rice varieties, struggling to accommodate diverse seeding quantity for both hybrid and conventional rice varieties. A seed-filling component with unilateral and bilateral seed-filling function was designed to solve this challenge. Through theoretical analysis the key structural parameters of the seed-filling component were determined. Then Discrete Element Method (DEM) simulations were conducted to analyze the seeding performance, leading to the identification of optimal parameters for orifice width and orifice deflection angle of the seed-filling component, which are 7.7 to 8.5 mm and 1.71 to 2.41 degrees, respectively. Bench experiments using the central composite design indicates that the optimal parameters for the seed-filling component's orifice width and orifice deflection angle are 8.1 mm and 1.99 degrees, respectively. In the optimal combination of orifice parameters, for unilateral seed-filling in hybrid rice, the miss-seeding rate is 4%, the qualified rate is 84.8%, and the reseeding rate is 11.2%. For bilateral seed-filling in conventional rice, the miss-seeding rate is 4.2%, the qualified rate is 85.2%, and the reseeding rate is 10.6%. The result of field hole-seeding with film mulching is consistent with the result of indoor bench experiments, demonstrating that the seed-filling component of the hole seeder can meet the seeding requirements for rice precision direct-seeding with film mulching. This paper provides theoretical reference for the design and optimization of the seed-filling component for rice hole-seeding equipment.

Design and Parameter Optimization of a Dual-Disc Trenching Device for Ecological Tea Plantations

This paper addresses challenges in the application of existing colters in Chinese ecological tea plantations due to abundant straw roots and insufficient tillage depth. Aligned with the agronomic requirements of hilly eco-tea plantations, our study optimizes the structural advantages of the joint use of rotary tillage blades and double-disc colters to design an efficient trenching device. Our investigation explores the motion characteristics of a double-disc colter during deep trenching operations, in conjunction with rotary tillage blades. Employing discrete element method (DEM) simulations, this paper aims to minimize the working resistance and enhance the tillage depth stability. Single-factor experiments are conducted to determine the impact of key structural parameters on the tillage depth stability and working resistance. The optimal parameters are determined as a relative height of 80 mm to 120 mm, a 280 mm to 320 mm diameter for the double-disc colter, and a 10° to 14° angle between the two discs. The central composite design method is used to optimize the structural parameters of the double-disc colter. The results indicate that when the relative height is 82 mm, the diameter of the double-disc colter is 297 mm, and the angle between the two discs is 14°, the tillage depth stability performance reaches 91.64%. With a working resistance of merely 93.93 N, the trenching device achieves optimal operational performance under these conditions. Field validation testing shows a tillage depth stability coefficient of 92.37% and a working resistance of 104.2 N. These values deviate by 0.73% and 10.93%, respectively, from the simulation results, confirming the reliability of the simulation model. A field validation test further confirms that the operational performance of the colter aligns with the agronomic requirements of ecological tea plantations, offering valuable insights for research on trenching devices in such environments.

A mixing index for uniformly and gap-graded cohesionless particles influenced by mixing rate and diameter of stirring rods

Soil mechanics, sometimes, deals with the mixing of soil such as in deep mixing of soil and mixing of soil in tunnel boring machines, i.e., earth pressure balance (EPB-TBM) shields. The geometry of mixing apparatus such as size of stirring rods plays an important role to achieve higher degree of mixing. Moreover, the effect of gap-graded particles being mixed on degree of mixture should also be evaluated. It is important to estimate the extent of mixing of the soil to confirm the required performance of such phenomenon.This study aims to propose a simple method to quantify the degree of mixture of solid particles stirred by rotation of rods with varying diameters at different mixing rates. Discrete element method (DEM) is used to simulate the stirring process and evaluate the degree of mixture at each rotation based on the spatial distribution of different types of particles. To reduce complexity in the mixing process of particles, this study focuses on monodispersed (i.e., uniformly graded) and bidispersed (i.e., narrowly gap-graded) spherical particles where inter-particle cohesion is not considered. The DEM results reveal spatial variation of the degree of mixture (dm) in the given volume; however, its mean (dm¯) increases with the rotation number of stirring rods. Besides, dm¯ depends on the size of stirring rods whereas the mixing rate is less sensitive to dm¯ for the non-cohesive sandy particles. The dm¯ of narrowly gap-graded particles cases is slightly on the lower side as compared to that of uniformly graded particles. The results of the DEM simulations are validated through the model test.

Mechanism of cross-level settlements and void accumulation of wide and conventional sleepers in railway ballast

AbstractThe cross-level and twist irregularities are the most dangerous irregularity types that could cause wheel unloading with the risk of derailments and additional maintenance expenses. However, the mechanism of the irregularities initiation and development is unclear. The motivation of the present study was the previous experimental studies on the application of wide sleepers in the ballasted track. The long-term track geometry measurements with wide sleepers show an enormous reduction of the vertical longitudinal irregularities compared to the conventional track. However, wide sleepers had higher twist and cross-section level irregularities. The present paper aims to explain the phenomenon by discrete element method (DEM) modeling the development process of sleeper inhomogeneous support at cross-level depending on the sleeper form. The DEM simulations show that the maximal settlement intensity is up to 3.5 times lower for a wide sleeper in comparison with the conventional one. Nevertheless, the cross-level differential settlements are almost the same for both sleepers. The particle loading distribution after all loading cycles is concentrated on the smaller area, up to the half sleeper length, with fully unloaded zones under sleeper ends. Ballast flow limitation under the central part of the sleeper could improve the resilience of wide sleepers to the development of cross-level irregularities. The mechanism of initiation of the cross-level irregularity is proposed, which assumes the loss of sleeper support under sleeper ends. The further growth of inhomogeneous settlements along the sleeper is assumed as a result of the interaction of two processes: ballast flow due to dynamic impact during void closing and on the other side high pressure due to the concentration of the pressure under the middle part of the sleeper. The DEM simulation results support the assumption of the mechanism and agree with the experimental studies.

Experimental and numerical study on the dynamic mode III fracture behaviors of rock using an axially notched flattened Brazilian disc in SHPB tests

The dynamic mode I and mode II fracture of rock have been widely investigated over the past decades. However, the lack of dynamic mode III fracture testing method and the rare understanding of mode III fracture mechanism of rock remain a significant knowledge gap in the realm of rock mechanics. In this work, an innovative axially notched flattened Brazilian disc (ANFBD) sample is proposed for the mode III fracture tests of rocks using the split Hopkinson pressure bar (SHPB). Firstly, the optimal geometrical dimension of the ANFBD sample for achieving true mode III fracture of rocks is comprehensively discussed using finite element method (FEM) analysis. Then, the reliability of ANFBD-SHPB method is experimentally verified through dynamic mode III fracture experiments on the Fangshan marble (FM). Laboratory experimental results show that the mode III fracture toughness (KIIId) values of FM are approximately 2.8 times of the mode I fracture toughness (KId) values at similar dynamic loading rates. Post-mortem examinations on the fracture surfaces show that the famous facet coarsening mechanism in mode III fracture is suppressed under high loading rates. Furthermore, insightful assessments regarding the inner progressive fracturing behaviors of the ANFBD sample are given by virtue of three-dimensional discrete element method (DEM) simulation. Moment tensor (MT) analysis indicates that the shear fracture mechanism mainly dominates the whole failure process of the ANFBD sample, while the tensile fracture mechanism slightly increases during the facet coarsening process. These results are of significant importance for revealing the failure mechanism of rock under dynamic mode III loading and give some beneficial implications for natural strike-slip fault structures.

Fully Coupled CFD–DEM Simulation of Oil Well Hole Cleaning: Effect of Mud Hydrodynamics on Cuttings Transport

This paper presents a coupled computational fluid dynamics–discrete element method (CFD–DEM) simulation to predict cuttings transport by the drilling fluid (mud) in different oil well drilling conditions. The mud rheology is expressed by the Herschel–Bulkley behaviour and modelled in a Eulerian framework (CFD), while the cuttings are modelled using the Lagrangian approach (DEM). In this work, the effects of drill string rotation, inclination angle, cutting size, mud rheology, and annular velocity on cleaning efficiency are investigated. It is found that increasing the well deviation from vertical to horizontal leads to a higher cuttings concentration. However, at low annular velocity, the cuttings concentration for the inclined (45-degree) annulus is found to be higher than the horizontal one due to the sliding motion of cuttings on the lower section of the annulus. Overall, the drill pipe rotation has little effect on decreasing the cuttings concentration, but the effect is more pronounced at low annular velocity.

Correction of the spring-dashpot-slider model

AbstractThe spring-dashpot-slider is a common way to include solid friction for discrete element method simulations of granular matter. However, the most popular model that is currently in use has a number of problems, including the spontaneous creation of energy. The main cause for these problems is the discontinuous evolution of the spring displacement. In this paper, we derive a differential equation for the displacement that yields a continuous time evolution, that fixes the problems of the discontinuous model and is simpler to implement.

Modelling deformable boundary by spherical particle for normal contact

The normal contact of the elastic spherical particle with deformable boundary is investigated in terms of the Discrete Element Method (DEM). The particle of the prescribed radius is moving under gravity and the initial velocity. The deformable boundary is treated as rigidly fixed spherical particle with variable elasticity modulus and variable radius. The limit case, approaching the infinite radius presents an elastic half-space, while increasing of the elasticity modulus presents the rigid boundary, respectively.
 The linear model and the nonlinear Hertz contact model used in the discrete element method are investigated numerically by applying the 5th-order Gear’s  predictorcorrector integration scheme. The numerical model is tested by comparing it with analytical solution. The time variations of the particle positions, velocities and  accelerations are presented. On the basis of simulation results the limit values of the boundary particle parameters are evaluated and recommendations for the boundary  article parameters required in DEM simulation are drown.

Systematic investigation into the role of particle multi-level morphology in determining the shear behavior of granular materials via DEM simulation

This study aims to numerically investigate the dependence of shear behaviors of granular materials on particle multi-level morphology, encompassing form (mean of elongation and flatness), angularity, and roughness. To this end, four series of particles—ellipsoidal particles with varying elongation indices (EI) and flatness indices (FI), and equiaxed concave particles with varying angularity indices (AI) and roughness (RG)—are adopted to isolate the effects of particle morphology at each level. Through discrete element method (DEM) simulations, granular assemblies with varying values of EI, FI, AI, and RG are consolidated to achieve the maximum packing density under the same confining pressure. Subsequently, they are subjected to triaxial drained compression tests until reaching a critical state. Based on numerical results, the independent effects of EI, FI, AI, and RG on the macro- and micro-mechanical response of granular materials are examined and compared in detail. Furthermore, using the ‘Stress-force-fabric’ (SFF) relationship, the anisotropic origins of the peak- and critical-state shear strengths induced by EI, FI, AI, and RG are also analyzed.

Particle Size Effect on Powder Packing Properties and Molten Pool Dimensions in Laser Powder Bed Fusion Simulation

Various defects are produced during the laser powder bed fusion (L-PBF) process, which can affect the quality of the fabricated part. Previous studies have revealed that the defects formed are correlated with molten pool dimensions. Powder particles are thinly spread on a substrate during the L-PBF process; hence, powder packing properties should influence the molten pool dimensions. This study evaluated the influence of particle size on powder packing properties and molten pool dimensions obtained through numerical simulations. Using particles with different average diameters (Dav) of 24, 28, 32, 36, and 40 μm, a series of discrete-element method (DEM) simulations were performed. The packing fraction obtained from DEM simulations became high as Dav became small. Several particles piled up for small Dav, whereas particles spread with almost one-particle diameter thickness for large Dav. Moreover, the packing structure was inhomogeneous and sparse for large Dav. As a result of multiphysics computational fluid dynamics (CFD) simulations incorporating particles’ positions as initial solid metal volume, the molten pool width obtained was hardly dependent on the Dav and was roughly equivalent to the laser spot size used in the simulations. In contrast, the molten pool depth decreased as Dav decreased. Even if the powder bed thickness is the same, small particles can form a complex packing structure by piling up, resulting in a large specific surface area. This can lead to a complex laser reflection compared to the large particles coated with almost one-particle thickness. The complex reflection absorbs the heat generated by laser irradiation inside the powder bed formed on the substrate. As a result, the depth of the molten pool formed below the substrate is reduced for small particles.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure, this study proposed a novel approach combining numerical simulation and machine learning algorithms. Initially, 3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional (3D) discrete element method (DEM) were conducted to construct a database. In this process, the positions of the particles were randomly altered, and the particle assemblages changed. Interestingly, besides confirming the influence of particle size distribution parameters, the stress-strain curves differed despite an identical gradation size statistic when the particle position varied. Subsequently, the obtained data were partitioned into training, validation, and testing datasets at a 7:2:1 ratio. To convert the DEM model into a multi-dimensional matrix that computers can recognize, the 3D DEM models were first sliced to extract multi-layer two-dimensional (2D) cross-sectional data. Redundant information was then eliminated via gray processing, and the data were stacked to form a new 3D matrix representing the granular soil's fabric. Subsequently, utilizing the Python language and Pytorch framework, a 3D convolutional neural networks (CNNs) model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil's fabric. The mean squared error (MSE) function was utilized to assess the loss value during the training process. When the learning rate (LR) fell within the range of 10-5-10-1, and the batch sizes (BSs) were 4, 8, 16, 32, and 64, the loss value stabilized after 100 training epochs in the training and validation dataset. For BS = 32 and LR = 10-3, the loss reached a minimum. In the testing set, a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error (MAPE) of 4.43% under the optimized condition, demonstrating the accuracy of this approach. Thus, by combining DEM and CNNs, the variation of soil's mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Hydraulic heave in granular soils under hypergravity conditions

A series of discrete element method (DEM) simulations have been conducted to investigate the initiation and development of hydraulic heave for granular soils under hypergravity. During the development of hydraulic heave, local failure can occur when the stress-reduction factor (α) is <0.8, in which the particles are reorganized by the fluid and subsequently regain stability as particles settle down. However, if α is >0.8, global failure occurs, causing the mobilization of the entire soil. The triggering mechanism of the hydraulic heave is the force equilibrium between the contact force and critical fluid force, which scales up proportionally with g-level. The non-linear variation of critical hydraulic gradient (icr) with g-levels is attributed to the non-linear relationship between fluid force and hydraulic gradient. Finally, an analytical model along with a fitting formula, is proposed to predict this non-linear relationship between icr and g-level.

A simple gradation-state-dependent model for granular materials

This paper proposes a gradation-state-dependent constitutive model to capture the granular materials' mechanical behaviours considering the granular crushing's influence. Firstly, a gradation evolution law is developed to reflect the change in grain size distribution (GSD) with the growth of stress levels, and then, based on the evolution law, the elastic compliance matrix is modified to reflect the effects of particle breakage. Secondly, as the critical state line (CSL) exhibits gradation dependence, a novel method is developed to describe the family of CSLs under different fixed gradations. Subsequently, by combining the gradation evolution law with the CSL equation, the paper explains the steepening of the slope of the critical state line when the crushing is activated. With the improvement of CSL, the material's shear dilatancy and contraction properties are better reflected, assisting in establishing a plastic compliance matrix. Employing the derived elastic and plastic compliance matrix, the elastic–plastic model reflecting the influence of gradation and state effects is established and verified with a series of experimental and discrete element method (DEM) simulation results.