O processo de dano em materiais quasi-frágeis pode ser caracterizado pela perda de isotropia para certos níveis de carga. A localização de deformações, o efeito cooperativo entre regiões danificadas e a avalanche de rupturas são características particulares na medição do dano neste tipo de material. As características mencionadas criam diferentes formas de dissipação de energia, que não são fáceis de representar utilizando métodos baseados na hipótese dos meios contínuos. No presente trabalho uma versão do Método dos Elementos Discretos Formado por Barras é empregado. Neste método a massa do contínuo é concentrada nos nós, os quais são interconectados por barras sem massa. Essas barras possuem uma lei constitutiva bilinear, que é usada para simular a ruptura da estrutura em estudo. A distribuição dos nós permite formar uma treliça tridimensional regular, e a partir dessa discretização espacial é possível chegar a um sistema de equações de movimento, que é resolvido com um esquema explícito de integração numérica (diferenças finitas centrais). Neste método a fratura e a fragmentação são levadas em conta de forma natural, já que as barras que rompem durante o processo são desativadas, respeitando o balanço energético. É possível introduzir heterogeneidade no modelo considerando as propriedades do material como campos espaciais aleatórios com distribuição de probabilidades de Weibull e comprimento de correlação conhecido. Nessa dissertação, é analisado o processo de dano que aparece em estruturas de geometria simples quando solicitadas até o colapso. Diferentes índices são apresentados para realizar a medição do dano. O desempenho desses índices, e a maneira com que eles ajudam na interpretação da evolução do dano, são discutidos nesse trabalho. / The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method is employed. In this method the mass of the solid is concentrated on node points, which are interconnected by uniaxial elements. These elements have a bilinear constitutive law, which is used to simulate the rupture of the structure under study. The node distribution allows the formation of a regular three-dimensional lattice, and from this spatial discretization it is possible to arrive at a system of equations of motion, which is solved by an explicit numerical integration scheme (central difference). In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. In this dissertation, the damage process, which appears in structures of simple geometry, when they are loaded until collapse, is analysed. Different indexes are presented to perform the measurement of the damage. The performance of those indexes, and the way they help in the interpretation of the damage evolution, are discussed in this paper.

Dans la fabrication de lentilles asphériques pour la photolithographie, l’étape delissage est critique. C’est aujourd’hui le seul procédé qui peut corriger les défauts de hautesfréquences spatiales responsables de diffusions parasites, de diminutions de transmittance etde contraste. Cette opération doit préserver la forme asphérique basse fréquence tout enlissant les défauts de hautes fréquences. Un tel comportement peut être obtenu pour des outilscombinant une couche continue flexible pour le suivi basse fréquence et une couche de poixfractionnée pour le lissage de défauts hautes fréquences. Les buts principaux de cette étudesont de prédire l’efficacité de lissage et le suivi de forme de différents outils et ensuite dedéterminer l’outil permettant le meilleur compromis. A cette fin, un modèle multi-échelles estdéveloppé. A l’échelle de l’outil entier, une étude paramétrique par éléments finis permet dedéterminer les caractéristiques de la couche flexible ainsi que la force appliquée optimale afind’obtenir l’homogénéité de la pression à l’échelle de la forme asphérique globale. A l’échelle dela couche de poix, la Méthode par Eléments Discrets est utilisée pour investiguer l’interfaceoutil-pièce. Un modèle basé sur le concept de la poutre cohésive viscoélastique est développé,prenant en compte la réponse fréquentielle de la couche de poix. La comparaison avecl’Analyse Mécanique Dynamique montre la capacité de la DEM à modéliser le comportementviscoélastique. L’opération de lissage est ensuite modélisée par DEM et analytiquement. Lesdonnées expérimentales obtenues par la méthode de la Densité Spectrale de Puissancemettent en évidence l’impact des propriétés de la poix sur l’efficacité de lissage. Lacomparaison entre les résultats numériques et expérimentaux montre que le modèle DEMdonne des résultats prometteurs pour la modélisation du lissage de défauts. / In aspherical photolithography optics manufacturing, the smoothing step iscritical. So far, it is the only process that can correct high spatial frequency defects, responsiblefor flare and transmission, contrast decrease. This operation must preserve the low frequencyaspherical shape while smoothing high frequency defects. That behavior can be obtained withtools that combine a continuous flexible layer for low frequency compliance and a fractionatepitch layer for high frequency defect polishing. The main goals of this study are predicting thesmoothing efficiency and form control of different tools, and then determining the best tool toachieve a good balance between them. To do this, a multi-scale model is developed. First, atthe whole tool scale, a finite-element parametric study yields the best characteristics for theflexible layer as well as the optimal applied force to achieve pressure homogeneity at the globalaspherical shape level. Second, at the pitch layer level, the Discrete Element Method is used toinvestigate the tool-workpiece interface. A model based on the viscoelastic cohesive beamconcept is developed, taking into account the pitch layer’s frequency response. Comparisonwith Dynamic Mechanical Analysis shows the ability of DEM to model viscoelastic behavior. Thesmoothing operation is then modeled both by DEM and analytically. Experimental data obtainedby the Power Spectral Density Method highlight the impact of pitch properties on the smoothingefficiency. Comparison between numerical and experimental data shows that the DEM modelyields promising results in defect smoothing modeling

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Doctor of Philosophy / Department of Grain Science and Industry / R. P. Kingsly Ambrose / Praveen V. Vadlani / Wheat flour processing involves gradual size reduction and size-based fractionation of milled components. The size-based separation efficiency of wheat flour particles, with minimum bran contamination, is an important flour mill operational parameter. The flour particles often behave as imperfect solids with discontinuous flow and agglomerates during the separation process due to their differences in physical and chemical characteristics. Noticeable loss in throughput has been observed during sieving of soft wheat flour compared to that of hard wheat flour due to differences in inter-particle cohesion. However, there is limited understanding on the factors that influence the inter-particulate forces. Direct and indirect methods were applied to investigate the effects of moisture content, particle size, sifter load, and chemical composition on the cohesion behavior of flours from different wheat classes. Image analysis approach was used to quantify the particle characteristics such as surface lipid content, roughness, and morphology with respect to particle size to better understand the differences between hard and soft wheat flours. Surface lipid content and roughness values showed that the soft wheat flours are more cohesive than hard wheat flours. The morphology values revealed the irregularity in flour particles, irrespective of wheat class and particle size, due to nonuniform fragmentation of endosperm particles. The chemical composition significantly contributes to the differences in cohesion and flowability of wheat flours. Based on the particle parameters, a granular bond number (GBN) model was developed to predict the dynamic flow of wheat flour. In order to further understand the wheat flour flow behavior during size-based separation, a correlation was developed using the discrete element method (DEM). The error of predictions demonstrated that this correlation can be used to estimate the sieving performance and sieve blinding phenomenon of wheat flour. The experimental results from this dissertation work and the numerical model could eventually be instrumental to improve the efficiency of size-based separation of flour from various wheat classes. In addition, the models developed in this study will contribute significantly to understand the inter-particle cohesion as influenced by chemical composition.

This study aims to deduce an appropriate shape and density for an electronic free-cell that could be placed into a silo so that position and other desired physical parameters could be recorded. To determine how density and shape affects the trajectory and displacement of free cells, the trajectory and displacement of cylindrical, cuboid and triangular prism free-cells of equivalent volume was investigated in a discharging quasi 3D silo slice. The free-cells were placed at twelve different starting positions spread evenly over one half of the 3D slice. Tests were conducted using a monosized batch of spherical particles with a diameter of approximately 5 mm. Tests were also conducted in a binary mixture consisting of particles of different sizes (5 mm/4 mm) and the same density (1.28 g/cm3) and a binary mixture consisting of particles of different size (6 mm/5 mm) and different densities (1.16 g/cm3/1.28 g/cm3).The rotation of the free cells was also briefly discussed.Computer simulations were conducted using the Discrete Element Method (DEM). The simulation employed the spring-slider-dashpot contact model to represent the normal and tangential force components and the modified Euler integration scheme was applied to calculate the particle velocities and positions at each time step. One trial of each of the metal and plastic, cylindrical, cuboid and triangular prism free cells was compared with the average of three experimental trials. The trajectory and displacement of a representative particle positioned at the same starting position as the free cell was also obtained from DEM simulation and compared with the path and displacement of each of the free cells to determine which free cell followed the particle most closely and hence to determine a suitable free cell that would move with the rest of the grains. Spherical particles are idealised particles. Therefore tests were also conducted with a small number of polyhedral particles, to deduce their flow rate and the critical orifice width at which blockages were likely to form. Simulations were also conducted to test the feasibility of the DEM in modelling the behaviour of these polyhedral particles.Results indicate that for a free cell to move along the same trajectory and have the same displacement and velocity as an equivalent particle in the batch it should have a similar density to the majority of the other particles. A cylindrical free cell of similar density to the particles was found to follow the path of the representative particle more closely than the cuboid or triangular prism. Polyhedral particles were found to have a greater flow rate than spherical particles of equivalent volume.

Integral bridges are designed without expansion joints or bearings to eliminate the maintenance and repair costs associated with them. Thus, the expansion and contraction due to daily and seasonal temperature variations of the deck of the bridge are restricted by the abutments, causing the abutments to move cyclically towards and away from the granular material used as backfill. This movement results in a stress accumulation in the backfill retained by the abutments. The Discrete Element Method (DEM) was used was used to perform a numerical sensitivity analysis, investigating the effect of granular particle shape on the response of backfill material retained by integral bridge abutments.   Two DEM software suites were used to perform the simulations, namely STAR-CCM+, a commercial code, and Blaze-DEM, a research code under development at the University of Pretoria. Blaze-DEM makes use of Graphics Processing Unit (GPU) computing as opposed to traditional Central Processing Unit (CPU) computing. Blaze-DEM delivered computational times over 150 times faster than the equivalent simulation in STAR-CCM+. The results from the numerical sensitivity analysis showed that the particles with lower sphericities (higher angularities) experienced larger accumulations of stresses on the abutment as opposed to the more spherical particles. This was suggested to be a result of particle interlocking and reorientation. / Dissertation (MEng)--University of Pretoria, 2018. / Civil Engineering / MEng / Unrestricted

The goal of the project was to characterize the granular flows impact on the gas flow in a packed-bed-reactor. The study was created at Swerim as a master's thesis for Luleå University of Technology. The packed-bed-reactor geometry used in this study is a scaled down blast furnace model. The granular flow was modelled using the discrete element method (DEM) in LS-DYNA. Four models were created with different sizes and size distribution of the particles. To study the granular flows impact on gas flow, porosity is extracted from the DEM models and analyzed, since porosity has a direct impact on the gas flow. The supervisors form Swerim, Joakim Eck and Martin Flemström created computational fluid dynamics (CFD) models in Ansys Fluent using the porosity from the DEM models. The DEM results are presented as granular flow profiles. This flow profile is created by injecting particles with alternating colors to see this profile. A total of 6 images are taken over the whole process. The porosity results are presented as a porosity field plots of the extracted porosity data using MATLAB. The CFD results are presented as plots of gas velocity and absolute pressure. The results show the different characteristics of the flow in the different DEM models, and how it relates to the different porosity fields that were found. Furthermore, the CFD models show how the flow of the gas is dependent on the porosity.

In soil, where trees and crops grow, heavy vehicles shear and compact the soil, leading to reduced plant growth and diminished nutrient recycling. Computer simulations offer the possibility to improve the understanding of these undesired phenomena. In this thesis, soils were modelled as large collections of contacting spherical particles using the Discrete Element Method (DEM) and the physics engine AGX Dynamics, and these entities were analyzed. In the first part of the thesis, soils, which were considered to be continua, were subjected to various controlled deformations and fields for quantities such as stress and strain were visualized using coarse graining (CG). These fields were then compared against analytical solutions. The main goal of the thesis was to evaluate the usefulness, accuracy, and precision of this plotting technique when applied to DEM-soils. The general behaviour of most fields agreed well with analytical or expected behaviour. Moreover, the fields presented valuable information about phenomena in the soils. Relative errors varied from 1.2 to 27 %. The errors were believed to arise chiefly from non-uniform displacement (due to the inherent granularity in the technique), and unintended uneven particle distribution. The most prominent drawback with the technique was found to be the unreliability of the plots near the boundaries. This is significant, since the behaviour of a soil at the surface where it is in contact with e.g. a vehicle tyre is of interest. In the second part of the thesis, a vehicle traversed a soil and fields were visualized using the same technique. Following a limited analysis, it was found that the stress in the soil can be crudely approximated as the stress in a linear elastic solid.

This work aims to develop and implement a linear elastic grain-level micromechanical model based on the discrete element method using bonded contacts and an improved fracture criteria to capture both intergranular and transgranular microcrack initiation and evolution in polycrystalline ceramics materials. Gaining a better understanding of the underlying mechanics and micromechanics of the fracture process of brittle polycrystalline materials will aid in high performance material design. Continuum mechanics approaches cannot accurately simulate the crack propagation during fracture due to the discontinuous nature of the problem. In this work we distinguish between predominately intergranular failure (along the grain boundaries) versus predominately transgranular failure (across the grains) based on grain orientation and microstructural parameters to describe the contact interfaces and present the first approach at fracturing discrete elements. Specifically, the influence of grain boundary strength and stiffness on the fracture behavior of an idealized ceramic material is studied under three different loading conditions: uniaxial compression, brazilian, and four-point bending. Digital representations of the sample microstructures for the test cases are composed of hexagonal, prismatic, honeycomb-packed grains represented by rigid, discrete elements. The principle of virtual work is used to develop a microscale fracture criteria for brittle polycrystalline materials for tensile, shear, torsional and rolling modes of intergranular motion. The interactions between discrete elements within each grain are governed by traction displacement relationships.

Micromechanics of solidluid interactions can play a key role controlling macro-scale engineering behavior of granular media. The main objective of this study is to numerically investigate the micromechanics involved in solidluid mixtures to develop a better understanding of the macroscopic behavior of granular media for different applications. This is accomplished by developing a numerical model coupling the Discrete Element Method (DEM) and the Lattice Boltzmann Method (LBM) and employing it to study three distinct yet interrelated applications throughout the course of this research. In the first application, the DEM model is used to provide a clear relationship between energy dissipated by micro-scale mechanisms versus the traditional engineering definition based on macro-scale (continuum) parameters to develop a better understanding for the frictional behavior of granular media. Macroscopic frictional behavior of granular materials is of great importance for studying several complex problems such as fault slip and landslides. In the second application, the DEM-LBM model is employed for studying the undrained condition of dense granular media. While the majority of previous modeling approaches did not realistically represent non-uniform strain conditions that exist in geomechanical problems, including the LBM in the proposed model offers a realistic approach to simulate the undrained condition since the fluid can locally conserve the system volume. For the third application, the DEM-LBM model is used to study discontinuous shear thickening in a dense solidluid suspension. Shear thickening in a fluid occurs when the viscosity of the fluid increases with increasing applied strain rate. The DEM-LBM results for discontinuous shear thickening were compared to experimental data and proved to be an accurate approach at reproducing this phenomenon. The validated DEM-LBM model is then used to develop a physics-based constitutive model for discontinuous shear thickening-shear thinning in granular medialuid suspension. A closedorm model is then calibrated using the DEM-LBM model and validated against existing experimental test results reported in the literature. Findings of this research demonstrate how micromechanical modeling can be employed to address challenging problems in granular media involving solidluid interaction.