Mit der vorliegenden Arbeit wird der Einfluss von Temperaturfeldern, des Interkonnektors, der Zellsinterung sowie des Aufbaus einer Solid Oxide Cell (SOC) auf die Beanspruchung der Membran-Elektroden-Einheit (MEA) untersucht. Dazu wurde ein dreidimensionales, thermo-elektro-chemisches Modell in Comsol Multiphysics entwickelt und validiert. Das Modell ist in der Lage ein dreidimensionales Temperaturfeld für einen stationären und instationären Betriebspunkt einer SOC im Brennstoffzellenmodus oder Elektrolysemodus zu berechnen. Die berechneten Temperaturfelder werden auf ein linear-elastisches thermomechanisches Modell einer Wiederholeinheit projiziert. Da der Auflagerzustand einer Wiederholeinheit im Stack nicht bekannt ist, werden die Extremfälle freie Biegung und verhinderte Biegung betrachtet. Zusätzlich wird die MEA ohne Interkonnektor modelliert um den vom Interkonnektor losgelösten Einfluss von Temperaturfelder zu ermitteln.

Transiente Simulationen im Rahmen von Parameterstudien oder Optimierungsprozessen erfor-dern die Anwendung der Modellordnungsreduktion zur Minimierung der Berechnungs¬zeiten. Die aus der Wärmestrahlung resultierende Nichtlinearität bei der Analyse thermischer Felder wird hier als äußere Last betrachtet, wodurch die entkoppelte Ermittlung der strahlungs-beding¬ten Wärmeströme gelingt. Darüber hinaus ermöglichen die infolgedessen konstanten System¬matrizen die Reduktion des Temperaturvektors mit etablierten Verfahren für lineare Systeme, wie beispielsweise den Krylov-Unterraummethoden. Die aus der in der Regel großflächigen Verteilung der thermischen Lasten folgende hohe Anzahl von Systemeingängen limitiert allerdings die erzielbare reduzierte Dimension. Deshalb werden zustandsunabhängige, sich synchron verändernde Lasten zu einem Eingang zusammengefasst. Die aus der Strahlung resultierenden Wärmeströme sind im Gegensatz dazu durch die aktuelle Temperaturverteilung bestimmt und lassen sich nicht derart gruppieren. Vor diesem Hintergrund wird ein Ansatz basierend auf der Singulärwertzerlegung von aus Trai¬ningssimulationen gewonnenen Beispiellastvektoren vorgeschlagen. Auf diese Weise gelingt eine erhebliche Verringerung der Eingangsanzahl, sodass im reduzierten System ein sehr geringer Freiheitsgrad erreicht wird. Im Vergleich zur Proper Orthogonal Decomposition (POD) genügen dabei deutlich weniger Trainingsdaten, was den Rechenaufwand während der Offline-Phase erheblich vermindert. Darüber hinaus dehnt das entwickelte Verfahren die Gültigkeit des reduzierten Modells auf einen weiten Parameterbereich aus. Die Berechnung der strahlungsbedingten Wärmeströme in der Ausgangsdimension bestimmt dann den numerischen Aufwand. Mit der Discrete Empirical Interpolation Method (DEIM) wird die Auswertung der Nichtlinearität auf ausgewählte Modellknoten beschränkt. Schließlich erlaubt die Anwendung der POD auf die Wärmestrahlungsbilanz die schnelle Anpassung des Emissionsgrades. Somit hängt das reduzierte System nicht mehr vom ursprünglichen Freiheitsgrad ab und die Gesamt-simulationszeit verkürzt sich um mehrere Größenordnungen. / Transient simulations as part of parameter studies or optimization processes require the appli-cation of model order reduction to minimize computation times. Nonlinearity resulting from heat radiation in thermal analyses is considered here as an external load. Thereby, the determi-nation of the radiation-induced heat flows is decoupled from the temperature equation. Hence, the system matrices become invariant and established algorithms for linear systems, such as Krylov Subspace Methods, can be used for the reduction of the temperature vector. However, in general the achievable reduced dimension is limited as the thermal loads distributed over large parts of the surface lead to a high number of system inputs. Therefore, state-independent, synchronously changing loads are combined into one input. In contrast, the heat flows resulting from radiation are determined by the current temperature distribution and cannot be grouped in this way. Against this background, an approach based on the singular value decomposition of snapshots obtained from training simulations is proposed allowing a considerable decreased input number and a very low degree of freedom in the reduced system. Compared to Proper Orthogonal Decomposition (POD), significantly less training data is required reducing the computational costs during the offline phase. In addition, the developed method extends the validity of the reduced model to a wide parameter range. The computation of the radiation-induced heat flows, which is performed in the original dimension, then determines the numerical effort. The Discrete Empirical Interpolation Method (DEIM) restricts the evaluation of the nonlinearity to selected model nodes. Finally, the application of the POD to the heat radiation equation enables a rapid adjustment of the emissivity. Thus, the reduced system is no longer dependent on the original degree of freedom and the total simulation time is shortened by several orders of magnitude.

Open-cell ceramic foams are used in metal melt filtration processes to clean and calm the liquid melt. Due to the high temperatures and pressure of the melt, thermo-mechanical stresses occur in the filter structures, which require a corresponding evaluation of strength, deformation, and failure. The ceramic materials used no longer behave elastically and brittle at operating temperatures of up to 1650 ◦ C, but exhibit viscoplastic behavior. Experimental investigations of the deformation of filter structures during the filtration process are difficult or even impossible, which is why simulation methods are used to investigate the filtration process and the filter loading. The filters considered in this work are manufactured using a replica process in which a ceramic slurry is applied to an open-cell polyurethane foam, which is dried and fired in a thermal process. Real filter structures consist of a network of several thousand struts with varying geometries. Direct numerical simulation of these geometries is possible in principle, but it is very complex and expensive, which is why homogenization methods are used. Representative volume elements of the ceramic foams are generated and analyzed using the finite element method. The micro-macro relations determined in the process are mapped using corresponding continuum mechanical models. These models allow the evaluation of the thermo-mechanical behavior of filter materials and filter structures. This thesis provides a critical overview of methods for generating, characterizing, and homogenizing foam structures. The generation of realistic foam structures is carried out using various methods from the fields of mathematics and mechanics and is described in detail. Analytical and data-driven approaches are used for the actual homogenization. The analytical approaches use adaptations of continuum mechanical models from the field of granular media. The data-driven approaches use neural networks, which replace or supplement hard-to-describe thermodynamic potentials used in material modeling. Both approaches can be used in a developed general framework for the modeling of any porous structures. As a result of the research and modeling work carried out, generic and real foams are compared in terms of their topological and geometrical properties. It is discussed how local geometrical variations of foam structures affect the macroscopic behavior, considering different thermo-mechanical properties such as elasticity, viscoplasticity, and fracture strength. The developed homogenization concepts are compared with each other and with other concepts from the scientific literature and evaluated with respect to their accuracy, flexibility, and efficiency. Finally, possible further developments and applications are discussed.:1. Introduction 1.1. Motivation and objectives 1.2. Structure of the thesis 2. State of the art research 2.1. Integration of sub-project B05 into the CRC 920 2.2. Manufacture of open-cell foam structures 2.2.1. Schwartzwalder process 2.2.2. Additive manufacturing 2.2.3. Additional coatings 2.2.4. Bulk material properties 2.3. Characterization of open-cell foam structures 2.3.1. Topological and geometrical characteristics 2.3.2. Thermo-mechanical characteristics 2.3.3. Fluid dynamical characteristics 2.4. Modeling of open-cell foam structures 2.4.1. Geometrical models of foams 2.4.2. Direct numerical simulation 2.4.3. Homogenization approaches 2.4.4. Data-driven and machine-learning approaches 2.4.5. Constitutive models for open-cell foam structures 3. Modeling of open-porous ceramic foams 3.1. Foam surfaces of strut networks based on implicit functions 3.2. Sphere packings and Laguerre tessellations 3.3. Surface evolver, dry foams, wet foams, and foam froth 3.4. Voxel models and isosurfaces of foams 3.5. Finite element model 3.5.1. Models with structural elements 3.5.2. Unstructured tetrahedral meshes 3.5.3. Structured meshes 3.6. Generating foam structures using FoamGUI 3.7. Homogenized constitutive models 3.7.1. Scale bridging, meso and micro models 3.7.2. Effective elastic properties 3.7.3. Elastic limit surfaces 3.7.4. Effective yield surfaces 3.7.5. Modified Ehlers model 3.7.6. Constitutive model for viscoplastic behavior 3.7.7. Constitutive framework for plastic behavior 3.7.8. General return algorithm 3.7.9. Application to the phenomenological models 3.7.10. Hybrid models 3.7.11. Neural networks 3.7.12. Data sampling for the neural network training 3.7.13. Parameter identification for the modified Ehlers model 4. Results 4.1. Geometrical foam models 4.1.1. Foam models based on implicit functions 4.1.2. Foam models based on sphere packings 4.2. Effective thermo-mechanical properties 4.2.1. Geometry dependent elastic properties 4.2.2. Yield and failure surfaces 4.2.3. Fracture mechanical properties 4.2.4. Fracture mechanical properties for thermo-shock loading 4.2.5. Visco-plastic properties 4.2.6. Effective plastic properties 5. Conclusions & Discussion

The phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics. The finite element formulation is derived starting from the variational principle of total virtual power. The intention of this manuscript is to demonstrate the potential of the framework for multi-physical fracture models and complex processes inside the crack. The present model at hand allows to predict realistic deformation kinematics and heat fluxes at cracks. At the application of fully coupled, transient thermo-elasticity to a pre-cracked plate, the opened crack yields thermal isolation between both parts of the plate. Inhomogeneous thermal strains result in a curved crack surface, inhomogeneous recontact and finally heat flow through the crack regions in contact. The novel phase-field framework further allows to study processes inside the crack, which is demonstrated by heat radiation between opened crack surfaces. Finally, numerically calculated crack paths at a disc subjected to thermal shock load are compared to experimental results from literature and a curved crack in a three-dimensional application are presented.

In den letzten Jahren intensivierten sich die Bemühungen, anisotropes Verhalten von Gesteinen in numerischen Modellen abzubilden. Für ein tiefgreifendes Verständnis dieser Prozesse sind numerische Modelle gut geeignet, da hier die Rand- und Anfangsbedingungen sehr exakt vorgegeben werden können, um das Verhalten eines pkysikalischen Systems unter vollständig kontrollierbaren Bedingungen zu studieren. Am Beispiel von Gneis wird ein numerisches Modell für die Modellierung einaxialer Druck- und Spaltzugversuche vorgestellt. Dieses nutzt den Diskreten-Element-Code 3DEC der Fa. Itasca Consulting Group, Inc. um gekoppeltes nichtlinear-anisotropes thermo-mechanisches Materialverhalten zu simulieren. In dieser Arbeit wird sowohl der Modellaufbau anhand eines GBM gezeigt, als auch ein Stoffgesetz zur Simulation eines nichtlinearen orthotropen thermischen Expansionsverhaltens entwickelt. Die dafür benötigten Modellparameter werden anhand von durchgeführten Laborversuchen kalibriert. Das entwickelte Modell wird dann angewendet, um die Modellierung einaxialer Druck- und Spaltzugversuchen für ein anisotropes Material (Gneis) durchzuführen, um das Modell zu validieren. Am Ende der Arbeit wird eine praktische Anwendung des Modells in Form eines Schneidversuchs gezeigt. / In recent years, efforts have intensified to simulate the anisotropic behavior of rocks in numerical models. Numerical models are well suited for a profound understanding of these processes, since the boundary and initial conditions can be specified very precisely in order to study the behavior of a physical system under fully controllable conditions. Using the example of gneiss, a numerical model is presented for the modeling of uniaxial compression and Brazilian tensile tests. The discrete element code 3DEC from the company Itasca Consulting Group, Inc. is used to simulate coupled nonlinear- anisotropic thermo-mechanical material behavior. In this thesis the model generation is shown using Grain-Based Models and a material law for the simulation of a nonlinear orthotropic thermal expansion behavior is developed. The model parameters required for this are calibrated based on performed laboratory tests. The developed model is then applied to perform modeling of uniaxial compression and Brazilian tensile tests for an anisotropic material (gneiss) to validate the model. Lastly, a practical application of the model is shown in the form of a cutting test.