Universität Stuttgart
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Item Open Access On the computational modeling of micromechanical phenomena in solid materials(2013) Linder, Christian; Miehe, Christian (Prof. Dr.-Ing. habil.)This work aims to contribute to the research on the constitutive modeling of solid materials, by investigating three particular micromechanical phenomena on three different length scales. The first microscopic phenomenon to be considered on the macroscopic scale is the process of failure in solid materials. Its characteristic non-smoothness in the displacement field results in the need for sophisticated numerical techniques in case one aims to capture those failure zones in a discrete way. One of the few finite element based methods successfully applied to such challenging problems is the so called strong discontinuity approach, for which failure can be described within the individual finite elements. To avoid stress locking, a higher order approximation of the resulting strong discontinuities is developed in the first part of this work for both, purely mechanical as well as electromechanical coupled materials. A sophisticated crack propagation concept relying on a combination of the widely used global tracking algorithm and the computer graphics based marching cubes algorithm is employed to obtain realistic crack paths in three dimensional simulations. Secondly, materials with an inherent network microstructures such as elastomers, hydrogels, non-woven fabrics or biological tissues are considered. The development of advanced homogenization principles accounting for such microstructures is the main focus in the second part of this work to better understand the mechanical and time-dependent effects displayed by such soft materials. Finally, the incorporation of wave functions into finite element based electronic structure calculations at the microscopic scale aims to account for the fact that the properties of condensed matter as for example electric conductivity, magnetism as well as the mechanical response upon external excitations are determined by the electronic structure of a material.Item Open Access Modeling the long-term behavior of structural timber for typical serviceclass-II-conditions in South-West Germany(2010) Schänzlin, Jörg; Kuhlmann, Ulrike (Prof. Dr.-Ing.)Creep deformation influences the serviceability limit state as well as the ultimate limit state of timber structures. In order to consider this time-dependent behavior, creep coefficients and rheological models have been developed by various researchers. Comparing the rheological models, quite different temporal deformations are evaluated for a duration of load of 50 ears. In order to find the model, which is most suitable to the situation in the region of Tübingen, South-West Germany, the existing deformations of several beams in roof structures in opened, protected but not heated buildings are measured. By loading the structure the elastic global stiffness of the particular element is determined. So creep coefficients can be evaluated, which should have been used by the engineer in order to get the existing deflection fter 50 years. Within the region of Tübingen, on average a creep coefficient of 2.23 was found based on these measurements. However, the standard deviation of 0.97 is quite large. For the numerical evaluation of the time-dependent behavior Toratti’s model is modified, so that it matches the measured deformations. This modified model is verified by an additional set of measurements in the region of Breisgau-Hochschwarzwald, where the influence of the snow on the creep coefficient has to be taken into account. However, the application of the modified model takes too much time due to the numerical solutions of the single time steps. By means of a case study, functions are fitted to the results of the models in order to develop “simple” functions for the determination of the creep coefficient with respect to the main influences. The creep deformation influences the ultimate limit state especially in composite structures or elements subjected to compression. For this reason, the influence of the increased creep strain is approximated for columns, in order to reach the same safety level as proposed in the current regulations in DIN 1052. Additionally, the design procedure for timber-concrete-composite structures is modified in order to consider the increased creep coefficients.Item Open Access Weak or strong : on coupled problems in continuum mechanics(2010) Markert, Bernd; Ehlers, Wolfgang (Prof. Dr.-Ing.)The present work aims at giving a concise introduction to the vast field of coupled problems, particularly to those of importance in engineering and physics. Therefore, the common terminology and an appropriate classification of coupled equation systems is presented accompanied by some mathematical and computational issues. Attention is focused on volumetrically coupled multi-field formulations arising from the continuum mechanical treatment of multi-physics problems, but also geometrically coupled problems are addressed. Based on actual problems in the areas of poroelastodynamics, continuum biomechanics, and fluid-saturated porous media in general both the theoretical modeling by means of coupled continuum equations as well as the efficient numerical solution in the context of the finite element method (FEM) are presented and discussed in a problem-oriented fashion.Item Open Access Perceptions of threat and policy attitudes : the case of support for anti-terrorism policies in Germany(2019) Trüdinger, Eva-Maria; Bernhagen, Patrick (Prof. Dr.)Item Open Access General properties of ionic complex fluids(2016) Bier, Markus; Dietrich, Siegfried (Prof. Dr.)Item Open Access Kraft-Wärme-Kopplung im Wärmemarkt Deutschlands und Europas : eine Energiesystem- und Technikanalyse(2014) Blesl, Markus; Voß, Alfred (Prof. Dr.-Ing.)Im Wärmemarkt stehen seit Jahren unterschiedlichste Wärmeversorgungstechnologien auf Basis fossiler und erneuerbarer Energieträger, sowie Strom und Fernwärme untereinander als auch mit Einsparoptionen im Wettbewerb. Ein Großteil des Endenergieverbrauchs in Deutschland und der EU27 wird heute und zukünftig für die Deckung der Wärmenachfrage aufgewendet. Der Wärmemarkt steht damit im Fokus energiepolitischer und –wirtschaftlicher Fragestellungen. Ziel der Ausführungen ist es, mögliche Einflussfaktoren auf den Wärmemarkt in Deutschland und Europa zu analysieren. Die Auswirkungen hinsichtlich der Struktur der eingesetzten Energieträger und Technologien bis zum Jahr 2050 werden untersucht. Ein Schwerpunkt wird hierbei auf die Untersuchung der Rolle der Kraft-Wärme-Kopplung (KWK) und Fernwärme gelegt. Die Bewertung der KWK und Fernwärme und deren Vergleich zur getrennten Erzeugung hängen von der gewählten Versorgungsaufgabe ab. Entsprechend werden unterschiedliche Rangfolgen gekoppelter und ungekoppelter Wärmeversorgungstechnologien bei einer Analyse mit Hilfe von CO2-Vermeidungskosten, der ganzheitlichen Bilanzierung und einer para-metrisierten Versorgungsaufgabe ermittelt. Für die Beurteilung der energetischen, umweltseitigen und kostenseitigen Implikationen un-terschiedlicher Versorgungssysteme im Wärmemarkt wird eine detaillierte länderspezifische Untersuchung mittels einer Energiesystemanalyse durchgeführt. Hierfür wird das paneuropäi-sche Energiesystemmodell TIMES PanEU entwickelt, in welchem sowohl länderspezifische und sektoral differenzierte Versorgungstechnologien des Wärmemarktes als auch die beste-henden Versorgungsstrukturen modelliert sind. Die Entwicklung der Wärmenachfrage auf Nutzenergieebene wird basierend auf Simulationsergebnissen vorgegeben. So reduziert sich beispielsweise der spezifische Wärmebedarf des Gebäudebestandes in Deutschland bis zum Jahr 2050, trotz regulatorischer Vorgaben z. B. hinsichtlich des Gebäudestandards sowie de-ren Fortschreibung, aufgrund der aktuellen energetischen Sanierungszyklen und -quoten le-diglich auf Neubaustandard des Jahres 2007. Die Ergebnisse der Szenarienanalysen mit dem Energiesystemmodell TIMES PanEU zeigen, dass fossile Energieträger in wesentlich größerem Maße als Elektrowärmeanwendungen und der Einsatz von erneuerbaren Energien im Wärmemarkt von politischen Vorgaben (z.B. einem Treibhausgasminderungsziel) beeinflusst werden. Die Rolle der Fernwärme wird in erheblicher Weise dadurch bestimmt, ob diese quasi CO2-frei erzeugt werden kann. Optionen hierfür bestehen in Form von KWK-Anlagen auf Basis fossiler Energieträger mit CO2-Abscheidung und Speicherung, auf Basis von Geothermie oder Biomasse sowie durch Wärmepumpen und Solarthermie. Das technische und wirtschaftliche Potenzial dieser Erzeugungsoptionen ist ein limitierender Faktor für den Ausbau der Fern- und Nahwärmeversorgung in Deutschland.Item Open Access The role of interfacial areas in two-phase flow in porous media : bridging scales and coupling models(2010) Niessner, Jennifer; Helmig, Rainer (Prof. Dr.-Ing. habil.)This habilitation deals with a thermodynamically consistent modeling of two-phase flow in porous media which is extremely relevant for the understanding, the prediction, and optimization of the processes in many environmental, technical, and biological systems. Among these are the storage of carbon dioxide in the subsurface, methane migration from abandoned coal mines, the migration of radioactive gases from nuclear waste disposal sites (environmental systems), the processes in fuel cells and heat exchangers (technical systems) or the interaction between blood vessels and interstitial space (biological systems) which is very important for cancer therapy. The presented thermodynamically consistent model of two-phase flow in porous media is the first to numerically account for the extremely important role of phase-interfacial areas. This is put into practice through use of a rational thermodynamics approach by Hassanizadeh and Gray [1990] which not only includes interfaces as parameter in the equations, but additionally as entities allowing the formulation of conservation equations for interfaces. To be exact, conservation equations of mass, momentum, energy, and entropy are formulated on the pore scale for phases and interfaces and volume-averaged to the macro scale. The entropy productions of the entropy conservation equations are used to formulate the second law of thermodynamics. A speciality of the approach is the fact that thus, constitutive relationships do not need to be empirically formulated, but can be obtained by exploiting the residual entropy inequality. The aim of this work is to make the thermodynamically consistent and physically-based model accessible to numerical modeling allowing to represent effects which could otherwise not (or only using completely empirical approaches) be described. Among these are capillary hysteresis as well as the kinetics of mass and energy transfer between phases as these transfer processes take place across interfaces and thus, are highly dependent on them. Based on indicators and dimensionless quantities, the integration of the interfacial-area-based model into a multi-scale multi-physics framework is shown. This allows for the solution of the physically-based and thermodynamically consistent model whenever this is necessary and the solution of the empirical, but less costly, classical model wherever and whenever the physical situation allows. With such an approach, computing times and the amount of data needed can be drastically reduced.Item Open Access Tackling coupled problems in porous media : development of numerical models and an open source simulator(2013) Flemisch, Bernd; Helmig, Rainer (Prof. Dr.-Ing.)Flow and transport processes in porous media are the governing processes in a large variety of geological, technical and biological systems. For many interesting and important applications, these processes cannot be treated in an isolated manner or adequately described by means of a single-scale, single-physics mathematical model, and the coupling of two or more models is required. The development of coupled numerical models poses severe challenges on the conceptual, analytical and computational level. This habilitation thesis aims to describe a number of these challenges and solve some of the problems they pose. It is divided into three parts: Part A "Model Coupling" deals with uncoupled and coupled porous-media models in general and describes some of these models in detail. "Locally Conservative Discretization Methods," as treated in Part B, are a fundamental ingredient of reasonable numerical models for porous media flow and transport processes. A numerical model is realized by its implementation in the form of computer code. Part C "Open-Source Porous-Media Simulation" deals with the idea of developing such a computer code by means of open-source development techniques.Item Open Access On the elementary theory of Heller triangulated categories(2013) Künzer, Matthias; König, Steffen (Prof. Dr.)Verdier's formalism of triangulated categories works with triangles, which fit into octahedra. These triangles enjoy a morphism prolongation property, but those octahedra do not. We establish a formalism of n-triangles such that the 2-triangles coincide with Verdier's triangles, such that the 3-triangles are particular Verdier octahedra, and such that n-triangles appear for all n. Now morphism prolongation holds for all n. Following Heller, we let the n-triangles be governed by an isotransformation between two shift functors on the stable category of n-pretriangles.Item Open Access Quantum systems with balanced gain and loss, signatures of branch points, and dissociation effects(2014) Cartarius, Holger; Wunner, Günter (Prof. Dr.)Gain and loss to the wave function of quantum mechanics can in a convenient way be modelled by effective non-Hermitian Hamiltonians. Imaginary contributions to the potential introduce source and drain terms for the probability amplitude. A special class of non-Hermitian Hamiltonians are those which possess a parity-time symmetry. In spite of their non-Hermiticity these Hamiltonians allow for real energy eigenvalues, i.e. the existence of stationary states in the presence of balanced gain and loss. This effect has been identified theoretically in a large number of quantum systems. Its existence has also been proved experimentally in coupled optical wave guides. The wave guides are, however, only optical analogues of quantum systems. In the first part of this thesis it is shown from the theoretical side that Bose-Einstein condensates in a double-well setup are an ideal candidate for a first experimental realisation of a genuine quantum system with parity-time symmetry. When particles are removed from one well and coherently injected into the other the external potential is parity-time symmetric. To investigate the system the underlying time-independent and time-dependent Gross-Pitaevskii equations are solved numerically. It turns out that a subtle interplay between the nonlinearity of the Gross-Pitaevskii equation and the gain-loss effect leads to a complicated dynamics of the condensate wave function. However, the most important result is the existence of stationary states that are sufficiently stable to be observable in an experiment. Two suggestions for experimental realisations are presented. They are based on the idea of embedding the non-Hermitian parity-time-symmetric system into a larger structure described by a Hermitian Hamiltonian. A further effect of non-Hermitian Hamiltonians are so-called exceptional points, at which two resonances coalesce such that both their eigenvalues and wave functions become identical. It is shown that an exceptional point can unambiguously be identified by a characteristic non-exponential decay of the resonances. With numerically exact calculations for the hydrogen atom in crossed electric and magnetic fields this effect is verified in an experimentally accessible quantum system. The second part of the thesis is devoted to semiclassical Gaussian approximations to the Boltzmann operator, which have become an important tool for the investigation of thermodynamic properties of clusters of atoms at low temperatures. A numerically cheap frozen Gaussian approximation to the imaginary time propagator with a width matrix especially suited for the dynamics of clusters is developed. It is applied to the cases of Ar3 and Ar6. For these clusters classical-like transitions in one step from a bounded moiety to free particles are found for increasing temperatures. Additionally, the structure of the Ar6 cluster is studied in the bound configuration and during the dissociation. Quantum effects, i.e. differences with the purely classical case, manifest themselves in the low-temperature behaviour of the mean energy and specific heat as well as in a slight shift of the transition temperature. A first-order correction to the semiclassical propagator is used to improve the results of the calculation for Ar3, and it is shown how the correction can be used to objectively assess the validity of the frozen Gaussian approximation.