Energy dissipation in granular materials in DEM simulations

Soil has generally been treated as a continuum from as early as the eighteenth century. Since then the analysis of soil behaviour in practical engineering analyses and development of constitutive models has depended on a continuum assumption. However, in order to gain a deeper understanding of the behaviour of soils and their particulate nature, there is a need to move from continuum mechanics to discrete models. Such modelling is possible using the Discrete Element Method (DEM). In this thesis an open source DEM particle simulation software, LIGGGHTS is used to study the relationships between grain scale parameters and energy dissipation in granular media in one-dimensional compression. In order to measure the dissipated energy, changes in energy terms are traced at every time step and the principle of energy conservation applied. The influence of particle size distribution, initial void ratio, and inter-particle friction coefficient on energy dissipation are studied and discussed. It is shown that increasing the coefficient of uniformity decreases the energy dissipated; lowering the initial voids ratio results in steeper energy dissipation curves; and a higher inter-particle coefficient of friction yields more energy dissipation. It is hoped that the knowledge gained of the relationship between grain scale parameters and energy dissipation can be built upon to formulate constitutive relationships within the hyperplasticity framework. It is envisioned that relating grain scale parameters to constitutive models will allow the formulation of models that are purely based on the micro-mechanics of granular media

Advances in the development of the discrete element method for excavation processes

This work presents new developments of the discrete element method improving e ciency and accuracy of modelling of rock-like materials, especially in excavation processes.Postprint (published version

Advances in the development of the discrete element method for excavation processes

Modelling of granular materials, soils and rocks has been a challenging topic of investigation for decades. Classical continuum mechanics has been used to idealize soils and rocks, and numerical solution techniques such as finite element method (FEM) has been used to model these materials. Considering the idealization of the material, continuum mechanics allows the analysis of phenomena with discontinuous nature such as fracture in rock or soil via damage models. However, in more complex processes like rock milling or crushing, this kind of models are usually not suitable. Discrete models are more appropriate for problems with multiple discontinuities and particulate materials. The discrete element method (DEM) has been gaining popularity in analysis of granular materials, soils and rocks. Many aspects of this method still require more profound investigation. This thesis presents new developments of the discrete element method improving effi ciency and accuracy of modelling of rock-like materials, especially in excavation processes. All the numerical algorithms has been implemented in an in-house software, which was then used to run numerical examples. The basic formulation of DEM with linear elastic-perfectly brittle contact model is presented. The main di erence with other models found in the literature is the consideration of global sti ness and strength parameters that are constants in the whole model. The result of a simulations is strongly related with the con guration of the particle assembly used. Particle assemblies should be su ciently compact and ensure the isotropy to reproduce the physical properties of the modelled material. This thesis presents a novel technique for the generation of highly dense particle assemblies in arbitrary geometries, satisfying all the requirements for accurate discrete element simulations. One of the key issues in the use of the DEM is the estimation of the contact model parameters. A methodology is proposed for the estimation of the contact model parameters yielding required macroscopic properties of the material. The relationships between the contact model parameters and the mechanical properties of brittle materials, as well as the influence of the particles assembly con guration on the macroscopic properties, are analysed. A major di culty in the application of the DEM to real engineering problems is the high computational cost in simulation involving a large number of particles. The most common way to solve this is the use of parallel computing techniques, where multiple processors are used. As an alternative, a coupling scheme between DEM and the finite element method (FEM) is proposed in the thesis. Within the hybrid DEM/FEM model, DEM is only used in the region of the domain where it provides an advantage over a continuum-based approach, as the FEM. The coupling is dynamically adapted, starting with the whole domain discretized with FEM. During the simulation, in the regions where a high stress level are found, a change of modelling method from continuum FEM to the discrete DEM is employed. Finally, all the developments are applied to the simulation of a real excavation process. An analysis of the rock cutting process with TBM disc cutters is performed, where DEM and the DEM/FEM coupling technique presents an important advantage over other simulation techniques.La modelación de materiales granulares, terrenos y rocas ha sido un desafío para la investigación por décadas. La mecánica del continuo clásica ha sido utilizada para idealizar terrenos y rocas, y técnicas numéricas de solución, como el método de los elementos finitos (FEM), han sido usadas para modelar estos materiales. Considerando la idealización del material, la mecánica del continuo permite el análisis de fenómenos de naturaleza discontinua como la fractura en rocas y terreno mediante modelos de daño. Sin embargo, en procesos mas complejos como la molienda o trituración de roca, este tipo de modelos no suelen ser adecuados. Los modelos discretos son mas apropiados para problemas con múltiples discontinuidades y material particulado. El método de los elementos discretos (DEM) ha ido ganando popularidad en el análisis de materiales granulares, terrenos y rocas. Sin embargo, muchos aspectos de este método todavía requieren una investigación mas profunda. Esta tesis presenta nuevos desarrollos del método de los elementos discretos para mejorar su eficiencia y precisión en el modelado de materiales como roca, especialmente para procesos de excavación. Todos los algoritmos numéricos se han implementado en el programa propio, que ha sido utilizado para probar distintos ejemplos. La formulación básica del DEM, con un modelo lineal de contacto elástico perfectamente frágil ha sido utilizado en el presente trabajo. La principal diferencia con otros modelos de la literatura es la consideración de que los parámetros de rigidez y fuerzas máximas son valores globales y constantes en todo el modelo. El resultado de la simulación está fuertemente relacionado con la configuración del ensamblaje de partículas utilizado. El ensamblaje de partículas debe ser suficientemente compacto y asegurar la isotropía de las propiedades físicas del material modelado. La tesis presenta una nueva técnica para la generación de ensamblajes de partículas de alta densidad para geometrías arbitrarias, satisfaciendo todos los requisitos para una simulación con elementos discretos correcta. Uno de los temas clave en el uso del DEM es la estimación de los parámetros del modelo de contacto. Se propone una metodología para la estimación de los parámetros del modelo de contacto siguiendo las propiedades macroscópicas requeridas en el material Las relaciones entre los parámetros del modelo y las propiedades mecánicas de materiales frágiles, así como su la influencia de la configuración del ensamblaje de partículas son analizadas. Una gran dificultad en la aplicación del DEM en problemas reales de ingeniería es el alto costo computacional de simulaciones que consideran un gran número de partículas. La solución mas común para resolver esto es el uso de técnicas de computación paralela, donde se utiliza un gran número de procesadores. Como vía alternativa, un esquema acoplado entre el DEM y el FEM expuesto en la tesis. Con el modelo híbrido DEM/FEM, el DEM es usado solo en las partes del dominio donde presenta ventajas sobre el enfoque continuo del FEM. El acoplamiento puede ser adaptado dinámicamente, comenzando con todo el dominio discretizado con FEM, y durante la simulación, en las regiones donde se encuentran altos niveles de tensión, se emplea un cambio del método de simulación de continuo (FEM) a discreto (DEM). Finalmente, todos los desarrollos son aplicados a la simulación de un proceso excavación real. Se realiza un estudio del proceso de corte de roca con discos costadores, utilizados en tuneladoras, donde el DEM y la técnica de acoplamiento presentan una importante ventaja sobre otras técnicas de simulación

Density relaxation of granular matter through Monte Carlo and granular dynamics simulations

Granular materials are the principal ingredients of the industrial complex involved with the handling and processing of bulk solids including pharmaceuticals, chemicals, agricultural and mining materials. Despite the enormous importance of these materials in society, their behavior is not well-understood; in fact, there is no known model available that is capable of predicting the wide range of phenomenon that have been observed. One of the most important of these is known as density relaxation. Here, a granular material undergoes an increase in solids fraction as a result of the application of discrete taps or continuous vibrations. In this dissertation, the density relaxation phenomenon is promoted by the application of discrete taps to a periodic system of monodisperse spheres. Both stochastic ( Monte Carlo) and deterministic (granular dynamics) simulations are employed in this work. The granular microstructure of the system particles was analyzed via radial distribution function, coordination number, and the distribution of sphere centers in the vertical direction. In the MC simulations, the effect of a tap applied to the system is modeled using two different approaches: (1) vertical position-dependent expansion of the particles, and (2) uniformly lifting the entire ensemble on a small displacement above the supporting floor. Both methods resulted in an increase in the system density after numerous thousands of taps. However, method (1) exhibited a strong dependence of the final system density on the fill height, which has not been experimentally reported in the literature. On the other hand, this dependency was not seen when the expansion of type (2) was used. The MC evolution of the bulk solids fraction was found to be in qualitative agreement with an inverse log form that has been reported in the experimental literature. The simulated results illustrated that the bulk density is related to amount of the lift in method (2), with a critical value producing the most favorable results. Most striking is the finding that as the taps evolve, the particles self-organize into quasi-crystalline layers, initiated by the planar floor. The granular dynamics approach makes use of uniform, inelastic, and frictional spheres that interact via laws from well-founded collision-mechanics principles. The equations of motion are numerically integrated to obtain the positions and velocities of the particles. The tapping disturbance consisted of a harmonic intermittent oscillation of the floor. The same type of self-organization into quasi-crystalline layers first identified in the MC simulations was also found here, strongly supporting the conjecture that this is a universal mechanism of the density relaxation process

Jamming in granular media:modeling of experimental data

This thesis studies the phenomenon of jamming in granular media, such as when a salt shaker gets clogged. We use modern instrumentation, like X-ray synchrotron tomography, to look inside real jamming experiments. High performance computers allow simulating mathematical models of jamming, but we are also able to treat some of them just using paper and pencil. One main part of this thesis consists of an experimental validation of the distinct-element-method (DEM). In this model, grains are modeled separately, their trajectories obey Newton's laws of motion and a model of the contacts between grains is given. Real experiments of jamming of glass beads flowing out of a container were carried out. 3D snapshots of the interior of the media were taken using X-ray synchrotron tomography. These snapshots were computer processed using state of the art image analysis. It was found that 3D DEM is capable of predicting quite well the final positions of the grains of the real experiments. Indeed, in cases of instant jamming (jamming without a substantial previous flow of beads) the simulations agree well with the real experiments. However, in cases of non instant jamming, because of chaotic behavior of the model and the system, the results do not agree. Furthermore, a sensitivity analysis to grain location and size perturbations was carried out. In a second part, we describe results on 2D DEM simulations of jamming in a hopper. We focus on the jamming probability J, the average time T before jamming and the average number ψ of beads falling through the hole when jamming occurs. These quantities were related to global parameters such as the number of grains, the hole size, the friction coefficient, grain length or the angle of the hopper (in opposition to fine-scale parameters that are the positions and radii of the grains). In agreement with intuition, a monotonic behavior of J and ψ as a function of the number of grains, the hole size, the friction coefficient was found. However, surprising results were also found such as the non-monotonicity of the average number of beads falling through the hole when jamming occurs as a function of the grain length and the hopper angle. In the third part, we study simple probabilistic 2D models called SPM, in which non-interacting particles move with constant speed towards the center of a circular sector. Formulas giving the jamming probability or the average time before jamming when jamming occurs as a function of global parameters were found. SPM and 2D DEM were compared and a locally good correspondence between the global parameters of the two was established. SPM led us to study some combinatorial problems, in particular two bi-indexed recurrence sequences. One gives the number of ways of placing identical balls in fixed-size numbered urns and the other the number of subsets of a given ordered set without a certain number of consecutive elements. Several different ways of computing the sequences, each advantageous in certain cases, were found

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd

Developing Fundamental Models of Colloid Transport and Absorption in Sand Filters

This work was undertaken as part of an Industrial Collaborative Awards in Science and Engineering (iCASE) research programme, jointly funded by the National Nuclear Laboratory (NNL) and the Engineering and Physical Sciences Research Council (EPSRC). The aim was to probe the mechanisms of clogging of sand bed filters using particle based computer simulation methods. Existing models take a top down approach, making use of an empirical clogging parameter. Simulation holds the prospect of relating this parameter to properties of the effluent and the sand bed. The problem was approached using two computational methods: molecular dynamics, and smooth particle applied mechanics. The molecular dynamics model yielded successful results, qualitatively agreeing with existing experimental data with regards to the rate of deposition within the bed, and the associated observed pressure drop. The model was systematically explored by varying the nature of the colloidfluid-sand forces, the geometry and packing fraction of the sand bed, and the concentration of the colloids. An investigation into the fractal nature of the deposits was also performed, suggesting that a lower fractal dimension creates greater physical hinderance to the flow. This serves as additional validation for existing theories. The smooth particle model yielded less successful results. Substantial parameterisation of the model was undertaken, however, the model still showed signs of instability under certain conditions. Again, it produced qualitative agreement with existing literature, but showed substantial deviation from the results gained from the molecular dynamics model. Ultimately, further parameterisation of this model is required to allow for a more effective comparison of the models

Novel Shear-Thinning of Aged PDMS/Fumed Silica Admixtures and Properties of Related Silicone Elastomers

Fumed silica filler has long been used to structurally reinforce silicone elastomers. Unfortunately, the combination of as little as a few weight percent of untreated fumed silica nanoparticles [uFSN] with a siloxane polymer, such as PDMS, forms a difficult to process waxy solid admixture that even long periods of high shear mixing will not thin. In the course of the current work it was noted that after a period of storage certain solid admixtures would become viscous liquids when subjected to additional high shear mixing. It was further found that the required aging period could be decreased if the admixture storage temperature were increased. The only known interaction of PDMS and uFSN at moderate conditions is the adsorption of polymer on filler, and this interaction is also known to occur more quickly at higher temperature. This study examines the relationship between polymer adsorption and admixture liquefaction. Further, the mechanical properties of cured elastomers containing liquefied admixtures are examined to assess the degree of reinforcement that these materials afford

The interactions between gold nanoparticles and their self-assembly

Gold nanoparticles (AuNPs) are one of the most promising building blocks to fabricate versatile nanostructures. Such nanostructures have the great potential to enable new gold-based nanomaterials or nanocomposites with specific properties by precisely controlling the interactions (potential energies and/or forces) between them. In other words, the interactions between AuNPs are therefore regarded as one of the key factors governing particles’ self-assembly process that can drive multiple AuNPs to form ordered structures as required. Quantifying the interactions between them and understanding of their self-assembly process are of great importance and yet still challenging. In this study, molecular dynamics (MD) simulations are performed to calculate the interactions (e.g., potential energies) between AuNPs. The MD results reveal that a more effective force model between AuNPs can be developed as a function of their surface separation compared with the conventional Hamaker equation. In addition, MD simulations examine several effects (i.e., particle size, shape, rotation, surface patch, surfactant, as well as configuration) on their interactions. The results demonstrate that the different impacts of these factors (e.g., the hindrance of surfactant). Apart from spherical gold nanoparticles, interactions between gold nanorods (AuNRs) are also be quantified by MD simulations. The interparticle forces of AuNRs can be expressed as a function of their surface separation and the rotation angle since the rotational movement is applied on AuNR. Further, the MD-derived interparticle force models of gold nanospheres are integrated into discrete element method (DEM) to explore their self-assembly process. To the best of our knowledge, this might be the first time that the MD-based interparticle force models are integrated into DEM to explore the self-assembly process of gold nanoparticles. The results show that ordered nanostructures are ultimately constructed. Specifically, the mean coordination number (CN) of AuNPs (3 nm in size) is up to 5.99 and two major large clusters is observed under the simulation conditions at the equilibrated state. The completion of this study not only allows us to evaluate the interactions between AuNPs by MD simulation, but profoundly, the MD-DEM coupling approach opens a new window to unfold the self-assembly process of AuNPs

Modelling techniques for the study of molecular self-organisation

In this thesis we develop computational techniques for modelling molecular selforganisation. After a short review of the current nanotechnological applications of molecular self-assembly and the main problems encountered in modelling the selforganised behaviour of chemical systems, we introduce a set of methods, from both chemistry and complexity science, for the prediction of self-assembled structures, with particular focus on Monte Carlo (MC) based methods. We apply the MC method to two systems of experimental interest. First we model the silica nanoparticles on the surface of spherical polystyrene latex droplets, synthesised by the S. Bon Group at the University of Warwick, as a set of soft spheres on a spherical surface, to study their packing patterns as a function of the broadening of the nanoparticle size distribution. Then we develop a hexagonal lattice model for the study of the two-dimensional self-organisation of planar molecules capable of complementary interactions, to study their phase diagrams as a function of the strength of their complementary interactions and bonding motif. In both cases, the phases are characterised using a number of order parameters. We show that these simplified models are able to reproduce the experimental observations. We then develop an Agent Based (AB) algorithm, traditionally used for the study of complex systems, for the modelling of molecular self-organisation. In this algorithm, an agent is identified with a stable portion of the system under investigation. The agents can then evolve following a set of rules which include elements of adaptation (new configurations induce new types of moves) and learning (past successful choices are repeated), in order to drive the system towards its lowest energy configuration. We first apply the method to the study of the packing of a set of idealised shapes, then we extend it to the study of a realistic system. The latter is achieved by linking the AB algorithm to an available molecular mechanics code, in order to calculate the interaction energies of atomistic models. In both cases we compare the AB result with that of MC based methods, showing that for all the systems studied, the AB method consistently finds significantly lower energy minima than the MC algorithms in less computing time. Finally, we show how the AB algorithm can be used as a part of the protocol to calculate the phase diagram of a rigid organic molecule (1,4-benzene-dicarboxylic acid or TPA) with less computational effort than standard techniques