02 Fakultät Bau- und Umweltingenieurwissenschaften
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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 Rottweil - Untersuchungen zur Stadtbaugeschichte im Hochmittelalter(1970) Meckseper, Cord; Hanson, Harald (Prof.)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 Mikropolare Zweiphasenmodelle : Modellierung auf der Basis der Theorie Poröser Medien(2000) Diebels, Stefan; Ehlers, Wolfgang (Prof. Dr.)In der vorliegenden Arbeit wird eine Theorie zur Beschreibung von Mehrphasenmaterialien vorgestellt. Grundlage der Modellierung ist die Theorie Poröser Medien, die um Elemente der mikropolaren Theorie erweitert wird, um den Einfluß der Mikrostruktur erfassen zu können. Dazu werden für Mischungen aus einer beliebigen Anzahl von Konstituierenden die kinematischen Beziehungen einer finiten Theorie und die notwendigen Bilanzgleichungen diskutiert. Besondere Berücksichtigung kommt dabei den Erweiterungen aufgrund der vom Verschiebungsfeld unabhängigen Rotationen zu, die durch die mikropolare Erweiterung Eingang in die Theorie finden. Aus einer allgemeinen Bilanz können in einfacher Weise die Strukturen abgeleitet werden, die die Partialbilanzen der einzelnen Konstituierenden mit den Bilanzen der Mischung als Ganzes verknüpfen. Für ein Zweiphasenmodell bestehend aus einem elastischen porösen Festkörperskelett und einem viskosen Porenfluid wird dann durch die Auswertung der Clausius-Duhem-Ungleichung ein thermodynamisch konsistentes Modell formuliert. Dabei kommt der Aufstellung einer Evolutionsgleichung für die Volumenanteile besondere Bedeutung zu, da diese im Fall kompressiblen Materialverhaltens der Konstituierenden nicht aus kinematischen Überlegungen folgt. Schließlich wird das Modell konkretisiert. Für das Festkörperskelett wird eine Verzerrungsenergiefunktion angegeben, während anhand einer Dimensionsanalyse gezeigt wird, daß die Extraspannungen des Porenfluids gegenüber den Wechselwirkungskräften zwischen Fluid und Festkörper vernachlässigbar sind. Einige numerische Beispiele zeigen die Anwendbarkeit des Modells und demonstrieren den Einfluß der verschiedenen bei der Modellierung berücksichtigten Effekte.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 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 Scale dependence of flow and transport parameters in porous media(2006) Neuweiler, Insa; Helmig, Rainer (Prof. Dr.)The study discusses the problem of the influence of spatial scales on modeling of flow and transport processes in porous media. As soil and rock formations are usually heterogeneous, this problem is strongly coupled to the question as to how information about structure is transported over length scales. On different length scales different driving forces determine flow and transport processes. In order to derive an appropriate model for a certain scale of interest it is crucial to include information about the impact of structure on smaller scales into the model. The transfer from a detailed heterogeneous model to an equivalent model on a larger scale, where averaged properties are described, is called upscaling. To derive an upscaled model the following questions have to be addressed: • What are the relevant time scales and length scales? • What are the relevant processes on the scale, where heterogeneities are resolved? • How does the upscaled model look like? • What are the effective parameters for the upscaled model? As detailed information about the parameter distribution in the heterogeneous model is in most cases not known or it is not possible to deal with the exact distribution, further questions have to be addressed: • How can the effective parameters be approximated based on incomplete knowledge about the parameter distribution? • What are the relevant quantities to characterize the heterogeneous distribution and how can they be taken into account? Upscaling for different two-phase flow problems in porous media is discussed in the study.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 Efficient modeling of environmental systems in the face of complexity and uncertainty(2014) Oladyshkin, Sergey; Helmig, Rainer (Prof. Dr.-Ing.)Strong industrial development of the last century has led to a significant increase in public demand for different types of energy and, as a consequence, to an enormous increase in demand for natural resources. Naturally, all types of nature resources form a part of our surrounding environment. In order to extract natural resources a wide variety of technologies has been developed. This has led to a strong rise in interventions in the environment continuing up to the present days. At the same time, environmental systems form one of the largest and most important classes of complex dynamic systems. For this reason, society needs a better understanding of the environment in order to have an efficient and safe interaction for the sake of maximized welfare and sustainability in resources management. In particular, the ability to predict how the environment changes over time or how it will react to planned interventions is indispensable. However our surroundings behave non-trivially in various time and spatial scales. Moreover, many environmental systems are heterogeneous, non-linear and dominated by real-time influences of external driving forces. Unfortunately, a complete picture of environmental systems is not available, because many of these systems cannot be observed directly and only can be derived using sparse measurements. Moreover, environmental data is hardly available and expensive to acquire. Overall, this leads to limited observability, and an inherent uncertainty in all modeling endeavors. Still, research over several decades has showed that modeling plays a very important role in reconstructing (as far as possible) the complete and complex picture of the environment systems and offers a unique way to predict behavior of such multifaceted systems. The current thesis contains research in the field of environmental modeling in the face of complexity and uncertainty. The presented thesis is divided into three parts and refers to diverse applications such as underground petroleum reservoirs, groundwater flow, radioactive waste deposits and storage of energy relevant gases. Part 1 focuses on physical concepts and offers several possibilities to accelerate the modeling process. Part 2 deals with efficient model reduction methodologies for uncertainty quantification. Part 3 demonstrates application to the storage of energy relevant gases in geological formations and discusses related challenges.Item Open Access Models for non-isothermal compositional gas-liquid flow and transport in porous media(2007) Class, Holger; Helmig, Rainer (Prof.)Multiphase flow processes in porous media occur in many different fields of applications. One may basically distinguish between natural and technical porous media. A classical porous medium is the natural subsurface while there is still a number of technical porous media where flow and transport plays an important role and for which some basic model concepts developed for subsurface problems can be applied or at least adapted. One such technical porous medium is, for example, the gas diffusion layer of a fuel cell where the porous layer has the purpose of controlling the gas transport from the gas discharge channel to the reaction layer and concurrently the displacement of liquid water that is produced by the reaction. Major subsurface applications treated in this work are contaminant spreading in the saturated and unsaturated zone, thermally enhanced in-situ remediation methods, and the large topic of carbon dioxide storage in deep geologic formations. The latter got recently much attention in the discussions how to mitigate greenhouse gas concentrations and global warming. This work deals in particular with the numerical modeling of gas-liquid flow in porous media, thereby considering non-isothermal and compositional effects. The basic characteristics of the processes and different applications are explained and discussed. The fundamental concepts for the physical and mathematical models are introduced including their specific adaption to certain problems and a brief discussion of numerical solution algorithms. A large chapter presents example applications that illustrate the basic processes and phenomena by simulation results.