The importance of modelling ballast particle shape in the discrete element method

The discrete element method has been used to model railway ballast. Particles have been modelled using both spheres and clumps of spheres. A simple procedure has been developed to generate clumps which resemble real ballast particles much more so than spheres. The influence of clump shape on the heterogeneous stresses within an aggregate has been investigated, and it has been found that more angular clumps lead to a greater degree of homogeneity. A box test consisting of one cycle of sleeper load after compaction has been performed on an aggregate of spheres and also on an alternative aggregate of clumps. The interlocking provided by the clumps provides a much more realistic load- deformation response than the spheres and the clumps will be the basis for future work on ballast degradation under cyclic loading.     

A modelling and verification approach for soybean seed particles using the discrete element method

To build a discrete element method (DEM) model of soybean seed particles, the shape and size of soybean seed particles were measured and analysed. The results showed that the shape of a soybean seed particle could be approximated to an ellipsoid and that the dispersity in size could be approximated by a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. On this basis, an approach for modelling soybean seed particles based on the multi-sphere (MS) method was proposed. The soybean seed particle was simplified to an ellipsoid with the averaged size of one hundred randomly selected soybean seeds. The model of a single soybean seed particle was built by filling spheres within the ellipsoid. For modelling soybean seed assembly, the primary dimension was generated according to the normal distribution, and the other secondary dimensions were calculated based on their relationships with the primary dimension. In this way, the model of soybean seed assembly with different sizes and distributions was built. In this paper, four varieties of soybean seed were used. By comparing the simulated results and experimental results both in piling tests and “self-flow screening” tests, when the number of filling spheres was five, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modelling method for soybean seed particles that we proposed were verified. Finally, an application case was employed to show how to use the soybean seed particle model and the discrete element method to analyse the discharging process of a silo.     

Deformation localisation modelling of polymer foam microstructure under compression: A new approach by discrete element modelling

A discrete element model (DEM) has been developed to represent the behaviour of the microscopic structure of polymer cellular material, consisting of closed-cells. In DEM, the polymer foam is represented as an assembly of particles which model the closed-cells. The behaviour of the particle is based on the Gibson model and depends on morphologic and mechanical parameters. The present numerical study demonstrates the effect of deformation localisation on the microstructure. It is noted that the cell morphologic parameters and the distribution of various size cells in the specimen have a significant influence of the local deformation. The effect of macroscopic faults is also studied.     

Discrete element modelling of railway ballast

The discrete element method has been used to simulate the behaviour of railway ballast under different test conditions. Single particle crushing tests have been simulated using agglomerates of bonded balls, and the distribution of strengths correctly follows the Weibull distribution, and the size effect on average strength is also consistent with that measured in the laboratory. Realistic fast fracture can be obtained if non-viscous damping is reduced. Oedometer tests on aggregates of crushable ballast particles have also been simulated and compared with the results from laboratory tests. Finally, box tests which simulate traffic loading have been simulated using both spherical balls and 8-ball clumps. It is found that the 8-ball clumps give much more realistic behaviour due to particle interlocking.     

A discrete element approach to evaluate stresses due to line loading on an elastic half-space

A new approach to computing sub-surface stresses in an elastic half-space subjected to a line loading is presented. The approach is based on the discrete element method (DEM) in which the material continuum is replaced by a set of convex, rigid, interacting elements connected through visco-elastic fibers. A Hertzian pressure profile with, and without surface traction is applied to a semi-infinite domain created by gluing together discrete elements. Stresses are calculated from the inter-element joint forces that develop due to relative motion of the elements. Newton’s laws are employed to simulate the motion of each element. The stress distribution obtained from the discrete element model compares very well with that obtained from continuum elasticity models. The paper illustrates the applicability of the DEM to analysis of contacts at the microlevel and serves as a foundation to further studies in fracture and fatigue of bearing materials.     

Micromechanical finite element framework for predicting viscoelastic properties of asphalt mixtures

A micromechanical finite element (FE) framework was developed to predict the viscoelastic properties (complex modulus and creep stiffness) of the asphalt mixtures. The two-dimensional (2D) microstructure of an asphalt mixture was obtained from the scanned image. In the mixture microstructure, irregular aggregates and sand mastic were divided into different subdomains. The FE mesh was generated within each aggregate and mastic subdomain. The aggregate and mastic elements share nodes on the aggregate boundaries for deformation connectivity. Then the viscoelastic mastic with specified properties was incorporated with elastic aggregates to predict the viscoelastic properties of asphalt mixtures. The viscoelastic sand mastic and elastic aggregate properties were inputted into micromechanical FE models. The FE simulation was conducted on a computational sample to predict complex (dynamic) modulus and creep stiffness. The complex modulus predictions have good correlations with laboratory uniaxial compression test under a range of loading frequencies. The creep stiffness prediction over a period of reduced time yields favorable comparison with specimen test data. These comparison results indicate that this micromechanical model is capable of predicting the viscoelastic mixture behavior based on ingredient properties.     

Discrete element modelling of cyclic loading of crushable aggreates

This paper examines the discrete element modelling of cyclic loading of an aggregate of crushable sand grains. Each grain of sand is modelled as an agglomerate of balls bonded together. The aggregate is subjected to compaction followed by isotropic normal (plastic) compression, and then unloaded to half the maximum applied stress. The aggregate is then subjected to cyclic loading to a maximum stress ratio of 0.8. The aim of the paper is to examine the reduction of the rate of axial strain with number of cycles, and to determine the relative influences of volumetric strain and shear strain rates on the axial strain rate. In particular, the paper aims to show whether particle breakage is mainly related to the accumulation of volumetric strain. This is found to be the case, which is consistent with proposals by other authors that plastic hardening under monotonic loading is due to particle fracture.     

Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test

Cracks in asphalt pavements create irreversible structural and functional deficiencies that increase maintenance costs and decrease lifespan. Therefore, it is important to understand the fracture behavior of asphalt mixtures, which consist of irregularly shaped and randomly oriented aggregate particles and mastic. A two-dimensional clustered discrete element modeling (DEM) approach is implemented to simulate the complex crack behavior observed during asphalt concrete fracture tests. A cohesive softening model (CSM) is adapted as an intrinsic constitutive law governing material separation in asphalt concrete. A homogenous model is employed to investigate the mode I fracture behavior of asphalt concrete using a single-edge notched beam (SE(B)) test. Heterogeneous morphological features are added to numerical SE(B) specimens to investigate complex fracture mechanisms in the process zone. Energy decomposition analyses are performed to gain insight towards the forms of energy dissipation present in fracture testing of asphalt concrete. Finally, a heterogeneous model is used to simulate mixed-mode crack propagation.     

Modelling of CFRP–concrete bond using smeared and discrete cracks

This paper presents a finite element study of the bond characteristic between CFRP and concrete. The behaviour of twelve shear-lap specimens was modelled using a combination of smeared and discrete cracks. The smeared crack model is based on Rankine’s failure criterion, whereas the discrete crack model is based on nonlinear fracture mechanics, where both mode I and II fractures are accounted for. The finite element model proved to be able to predict the ultimate loads, crack patterns at failure and CFRP strain distributions reasonably well. The same method was then used to simulate debond failures in retrofitted beams which also showed good correlation with the experimental results.     

Aggregate distribution influence on the indirect tensile test of asphalt mixtures using the discrete element method

The purpose of this study is to investigate the effect of horizontal aggregate distribution, i.e. aggregate distribution in horizontal cross sections, on the indirect tensile (IDT) test of asphalt mixtures. An index of aggregate homogeneity, used to evaluate the aggregate distribution in a two-dimensional (2D) cross section, was comprehensively described; the horizontal aggregate distribution was evaluated by the index. A microstructure-based discrete element model for predicting the IDT test results was established by a discrete element program called particle flow code in two dimensions (PFC2D). Based on this model and by loading horizontal cross sections of asphalt mixtures along different directions, the effects of horizontal aggregate distribution on the splitting strength and maximum horizontal stress with regard to an IDT test were numerically simulated by means of the discrete element method; the obtained results were verified by performing an actual IDT test. Results reveal that the splitting strengths and maximum horizontal stresses in the IDT test exhibit anisotropy. Furthermore, it is revealed that there is an insignificant correlation between the horizontal aggregate distributions and the average splitting strengths and average maximum horizontal stresses, as well as a significant correlation between the horizontal aggregate distributions and the variations in the splitting strengths and maximum horizontal stresses.     

A study of transverse ply cracking using a discrete element method

We study the transverse cracking of the 90° ply in [0/90]_S cross-ply laminates by means of a discrete element method. To model the 90° ply a two-dimensional triangular lattice of springs is constructed where nodes of the lattice model fibers, and springs with random breaking thresholds represent the disordered matrix material in between. The spring-lattice is coupled by interface springs to two rigid bars which represent the two 0° plies in the model, which could be sublaminate as well. Molecular dynamics simulation is used to follow the time evolution of the model system. It was found that under gradual loading of the specimen, after some distributed cracking, segmentation cracks occur in the 90° ply which then develop into a saturated state where the ply cannot support additional load. The stress distribution between two neighboring segmentation cracks was determined, furthermore, the dependence of the microstructure of damage on the ply thickness was also studied. To give a quantitative characterization of stiffness degradation, the Young modulus of the system is monitored as a function of the density of segmentation cracks. The results of the simulations are in satisfactory agreement with experimental findings and with the results of analytic calculations.     

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Performance modelling of a solar road panel prototype using finite element analysis

Performance prediction is a critical step towards the acceptance of a new pavement structure. This is true for both conventional and innovative designs; however, it is particularly important for innovative designs that attempt to redefine pavement design practices. One such innovative design concept is the solar road panel; a road panel with a transparent surface that generates electricity through embedded solar cells. Despite the work completed by multiple organisations towards the development of this concept, questions exist about the viability of these panels as a structural pavement surface. This paper investigates these questions through a finite element modelling approach that assesses a prototype panel's performance on a variety of structural bases. Overall, this paper finds that it is possible to design a solar road panel to withstand traffic loading and that a concrete structural base allows for substantial optimisation to the analysed prototype design.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Modelling and estimation of tensile behaviour of polylactic acid parts manufactured by fused deposition modelling using finite element analysis and knowledge-based library

With the rise of the Fused Deposition Modelling (FDM) industry, a better understanding of the relationship between FDM process parameters and mechanical behaviour —especially tensile behaviour —of designed parts is needed to enable development of industry specifications. To optimise and control the deposition process, modelling and predicting the mechanical behaviour of a manufactured part under various process parameters is required. Existing numerical modelling approaches either require input of extensive experimental data or lack cross-validation. In this paper, the mechanical behaviour of polylactic acid manufactured parts under tensile conditions was studied both experimentally and numerically, and the effects of printing pattern and infill density on ultimate tensile strength (UTS)-weight ratio and the modulus of elasticity were evaluated. The experimental results revealed that minimising air gaps and using a triangular infill pattern are beneficial for obtaining a good UTS/weight ratio. Of all the specimens considered, the 20% triangular pattern had the highest UTS/weight ratio. The numerical investigation revealed that the meso-structure approach described in this paper can be used to predict the modulus of elasticity and the breaking point, and does not require input from the unidirectional specimen stress-strain curves. Finally, the meso-structure numerical model and artificial neural network were used to construct a knowledge-based library that can predict the modulus of elasticity of FDM manufactured polylactic acid with three infill patterns and any infill density with an average prediction error of 14.80%.     

Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third-order zigzag theory

The new improved discrete Kirchhoff quadrilateral element based on the third-order zigzag theory developed earlier by the present authors for the static analysis of composite and sandwich plates is extended for dynamics and assessed for its performance for the free vibration response. The element is free from the shear locking. The finite element formulation is validated by comparing the results for simply supported plates with the analytical Navier solution of the zigzag theory. Comparison of the present results for the natural frequencies with those of a recently developed triangular element based on the zigzag theory, for composite and sandwich plates, establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The accuracy of the zigzag theory is assessed for composite and sandwich plates with various boundary conditions and aspect ratio by comparing the finite element results with the 3D elasticity analytical and finite element solutions.     

A calibration framework for discrete element model parameters using genetic algorithms

In this research, a universal framework for automated calibration of microscopic properties of modeled granular materials is proposed. The proposed framework aims at industrial scale applications, where optimization of the computational time step is important. It can be generally applied to all types of DEM simulation setups. It consists of three phases: data base generation, parameter optimization, and verification. In the first phase, DEM simulations are carried out on a multi-dimensional grid of sampled input parameter values to generate a database of macroscopic material responses. The database and experimental data are then used to interpolate the objective functions with respect to an arbitrary set of parameters. In the second phase, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the calibration multi-objective optimization problem. In the third phase, the DEM simulations using the results of the calibrated input parameters are carried out to calculate the macroscopic responses that are then compared with experimental measurements for verification and validation.The proposed calibration framework has been successfully demonstrated by a case study with two-objective optimization for the model accuracy and the simulation time. Based on the concept of Pareto dominance, the trade-off between these two conflicting objectives becomes apparent. Through verification and validation steps, the approach has proven to be successful for accurate calibration of material parameters with the optimal simulation time.     

Prediction of hopper discharge rate using combined discrete element method and artificial neural network

An Artificial Neural Network (ANN) was developed to predict the mass discharge rate from conical hoppers. By employing Discrete Element Method (DEM), numerically simulated flow rate data from different internal angles (20°–80°) hoppers were used to train the model. Multi-component particle systems (binary and ternary) were simulated and mass discharge rate was estimated by varying different parameters such as hopper internal angle, bulk density, mean diameter, coefficient of friction (particle-particle and particle-wall) and coefficient of restitution (particle-particle and particle-wall). The training of ANN was accomplished by feed forward back propagation algorithm. For validation of ANN model, the authors carried out 22 experimental tests on different mixtures (having different mean diameter) of spherical glass beads from different angle conical hoppers (60° and 80°). It was found that mass discharge rate predicted by the developed neural network model is in a good agreement with the experimental discharge rate. Percentage error predicted by ANN model was less than ±13%. Furthermore, the developed ANN model was also compared with existing correlations and showed a good agreement.     

Modelling of elastic continua using a grillage of structural elements based on discrete element concepts

A framework is described for modelling an elastic continuum using a grillage of beam‐like structural elements derived from discrete element concepts. The beam element properties are derived in detail and implemented in a structural analysis code for validation against classical two‐dimensional plane elasticity solutions. The framework offers the possibility of modelling the onset and propagation of fracture in materials that are initially continuous, without the need for specialized elements or remeshing in the context of traditional finite elements. Copyright © 2001 John Wiley & Sons, Ltd.     

On the central difference algorithm in discrete element modelling of impact

The paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach. It is revealed that the algorithm exhibits some different behaviour due to the inherent non‐linearity/discontinuity of the impact system. Particularly, for an elastic or slightly inelastic impact, the stable/unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion, and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability. Copyright © 2005 John Wiley & Sons, Ltd.