13 Zentrale Universitätseinrichtungen
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/14
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Item Open Access Simulation and modeling of mono- and bidisperse suspensions(2000) Höfler, Kai; Herrmann, H. J. (Prof. Dr.)We present a numerical simulation technique which allows us to study three-dimensional, non-Brownian particle suspensions at low Reynolds numbers. We use this simulation technique to study mono- and bidisperse suspensions. And extend the Kynch theory of sedimentation to a advection-diffusion model, which is able to describe the evolution of the concentrations of polydisperse suspensions. The simulation technique couples the particles and the fluid by means of constraint forces and is verified on various test cases like fluid flow through a bed of fixed spheres and the calculation of the volume fraction dependency of the mean sedimentation velocity. We study the velocity fluctuations of monodisperse suspensions and find that the velocity fluctuations in systems with periodic boundary conditions diverge with the system size L. The increase of the velocity fluctuations is in agreement with theoretical arguments. In the case of monodisperse suspensions where the container is bounded by walls in the directions perpendicular to gravity no such scaling is found. Based on Kynch's one-dimensional theory for the evolution of concentrations in monodisperse suspension, we formulate an extension for polydisperse suspensions. The choice of the flux function is based on Batchelor's sedimentation coefficients, which reproduces the basic features of the results of three-dimensional simulations of batch sedimentation. We extended the Kynch model to an advection-diffusion model, where the volume fraction dependency of the diffusion coefficient is described by a phenomenological expression, which shows a good agreement with experimental data. The system of coupled partial differential equations resembles the results of simulations to a high degree and allows to describe the experimental concentration profiles of monodisperse particle suspensions of a given size distribution.Item Open Access Fast algorithms for the simulation of granular particles(2001) Müller, Matthias S.; Herrmann, Hans J. (Prof. Dr.)The goal of this work was the design, implementation and analysis of a fast simulation method for granular materials. The starting point was the Direct Simulation Monte Carlo Method. Since DSMC was designed for the field of dilute gas flow, it has of course several limitations for dense flows. For dense systems several improvements like CBA, CUBA or ESMC exist. The most serious disadvantage of DSMC for dissipative systems is the missing excluded volume''. In contrast to all other DSMC variations, is was not the collision step that has been modified , but the advection step. In order to be more efficient than molecular dynamics, which naturally incorporates the excluded volume, the excluded volume is only enforced on a coarse grained level. Although there have been large modifications to the original DSMC algorithms, HSMC is identical to DSMC in the limit of dilute systems. In order to test and verify the algorithm several test cases have been selected. Every test case covers specific properties of granular materials. As a whole they cover a wide spectrum of phenomena. Among the test cases are homogeneous cooling, the clustering instability, shear flow, pipe flow and heap formation.Item Open Access Statistical failure properties of fiber-reinforced composites(2003) Cruz Hidalgo, Raul; Herrmann, Hans J. (Prof. Dr.)A composite material or composite is a complex solid material composed of two or more constituents. On macroscopic scale, they have structural or functional properties not present in any individual component and generally they are designed to exhibit the best properties or qualities of its constituents. Nature has provided composite materials in biomatter such as seaweed, wood, and human bone and there are several artificial structures as reinforced concrete, fiber-reinforced composites and so on. Surprisingly, they are not new in common life, even the ancient Egyptians made plywood and the Romans had concrete. Nowadays, the new carbon-fiber composites weigh about five times less than steel, but can be comparable or better in terms of stiffness and strength, depending on fiber orientation. These composites do not rust or corrode like steel or aluminum. Perhaps most important, the automobile industry could reduce vehicle weight by as much as 60%, significantly saving vehicle fuel. A fiber-reinforced composite is a system made of fibers embedded in a protective material called a matrix, with a coupling agent applied to the fiber to improve the adhesion of the fiber to the matrix material. The functions of a matrix, whether organic, ceramic, or metallic, are to support and protect the fibers, and to provide a means of distributing the load among and transmitting it between the fibers without itself fracturing. The tensile failure of fiber composites is generally dominated by failure of the fiber bundles. If an uniaxial load is applied in the direction parallel to the fibers the actual composite stress S_T can be obtained as S_T = S_f V_f + (1-V_f) S_m, where V_f denotes the fiber volume fraction, S_f is the mean stress carried by the fibers and S_m is the usually small stress carried by the matrix. The matrix can carry some load in a metal or polymer matrix composite but, after matrix cracking, carries almost zero load in ceramic matrix composites. So that, the matrix stress S_m can normally be neglected in damage modeling since already at relatively low load levels, the matrix gets multiply cracked or yields plastically limiting its load bearing capacity. However, stress transfers between the fibers by the matrix action continues despite gradual damage, therefore, it has a very important role in the load redistribution. In reconstituted artificial construction materials the range of load redistribution also called load sharing can be controlled by varying the properties of the matrix material and the fiber-matrix interface. To understand the failure of composites one has to concentrate on the breaking of the fibers. Hence, in fiber composites the two factors controlling fiber failure are 1. the statistical fiber strength 2. the stress re-distribution (load sharing) after the fiber fails. The stress along the fiber depends on the applied external stress, but also on precisely how stress is transferred from a broken fiber to the surrounding intact fibers and in the matrix environment. This stress transfer is governed by the elastic properties of the constituents and by the fiber/matrix interface, and is difficult to obtain in the presence of more than one broken fiber. For a realistic modeling of the damage process of fiber composites under an uniaxial load, the stress distribution would have to be calculated in the whole volume of the sample. Even limiting the number of independent variables needed to describe the internal microstructure of the specimen, an accurate prediction of the ultimate strength is a computationally demanding task. Hence, in general, the modeling of fiber composites is based on certain idealizations about the geometry of the fiber arrangement and the stress redistribution following fiber failures in the specimen. Moreover, in order to obtain reliable conclusions the number of fibers forming the system has to be very large which makes the numerical problem, in many cases, too time consuming as to perform the study in a reasonable amount of time. Thus, a lot of effort has been spent on analytical approaches and more simple numerical models which may also provide a solid ground. One of those models, the fiber bundle model, received a lot of attention because severals important quantities can be derivated analytically in their frameworks, furthermore, efficient simulation techniques can be developed which allow for the study of large samples. Despite their simplicity, they capture most of the main aspects of material damage and breakdown. They have provided a deeper understanding of fracture processes and have served as a starting point for more complex models of fiber reinforced composites and other micro-mechanical models.Item Open Access Clusterbildung in granularen Gasen(2004) Miller, Stefan; Luding, Stefan (PD Dr.)Diese Arbeit beschäftigt sich mit granularen Medien geringer Dichte - den so genannten granularen Gasen. Die Dynamik dieser dissipativen Systeme ist durch komplexe Strukturbildung gekennzeichnet: Aus einem anfänglich homogenen System bilden sich mit der Zeit Dichte- und Temperaturschwankungen heraus, die immer weiter anwachsen, bis sie schließlich Systemgröße erreicht haben. Im ersten Teil der Arbeit stellen wir mit der parallelisierten Ereignisdynamik ein Verfahren vor, mit dem sich granulare Gase effizient simulieren lassen. Im zweiten Teil der Arbeit untersuchen wir die Eigenschaften granularer Gase zum einen mit Hilfe theoretischer Konzepte wie kinetischer Gastheorie, linearer Stabilitätsanalyse der hydrodynamischen Bewegungsgleichungen, einer Clusterpopulationsdynamik und der Perkolationstheorie. Zum anderen führen wir umfangreiche Computersimulationen durch, um die Clusterbildung besser zu verstehen. Insgesamt erhalten wir mit Hilfe dieser Untersuchungsmethoden einen dreistufigen Verlauf des Clusterwachstums: Zunächst das homogene Regime das gut durch die Vorhersagen der kinetischen Gastheorie beschrieben wird, dann das Clusterwachstum, in dem sich ein großer Perkolationscluster herausbildet und schließlich das Sättigungsregime, wenn dieser Systemgröße erreicht hat.