CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions 1. Basic differential equations of thermoelasticity theory 2. Fundamental matrices 3. Thermo-radiating conditions. Somigliana type integral representations CHAPTER II. Formulation of Boundary Value and Interface Problems 4. Functional spaces 5. Formulation of basic and mixed BVPs 6. Formulation of crack type problems 7. Formulation of basic and mixed interface problems CHAPTER III. Uniqueness Theorems 8. Uniqueness theorems in pseudo-oscillation problems 9. Uniqueness theorems in steady state oscillation problems CHAPTER IV. Potentials and Boundary Integral Operators 10. Thermoelastic steady state oscillation potentials 11. Pseudo-oscillation potentials CHAPTER V. Regular Boundary Value and Interface Problems 12. Basic BVPs of pseudo-oscillations 13. Basic exterior BVPs of steady state oscillations 14. Basic interface problems of pseudo-oscillations 15. Basic interface problems of steady state oscillations CHAPTER VI. Mixed and Crack Type Problems 16. Basic mixed BVPs 17. Crack type problems 18. Mixed interface problems of steady state oscillations 19. Mixed interface problems of pseudo-oscillations

The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.

We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ordinary differential equation (ODE). Following this line of reasoning, we propose another model which is entirely an abstract ODE.We also highlight an alternative method for a two-temperature model, which might be of independent interest.

Lightweight structures became more and more important over the last years. One special class of such structures are short fibre reinforced composites, produced by injection moulding. To avoid expensive experiments for testing the mechanical behaviour of these composites proper material models are needed. Thereby, the stochastic nature of the fibre orientation is the main problem. In this thesis it is looked onto the simulation of such materials in a linear thermoelastic setting. This means the material is described by its heat conduction tensor κ(p), its thermal expansion tensor T(p), and its stiffness tensor C(p). Due to the production process the internal fibre orientation p has to been understood as random variable. As a consequence the previously mentioned material quantities also become random. The classical approach is to average these quantities and solve the linear hermoelastic deformation problem with the averaged expressions. Within this thesis the incorpora- tion of this approach in a time and memory efficient manner in an existing finite element software is shown. Especially for the time and memory efficient improvement several implementation aspects of the underlying software are highlighted. For both - the classical material simulation as well as the time efficient improvement of the software - numerical results are shown. Furthermore, the aforementioned classical approach is extended within this thesis for the simulation of the thermal stresses by using the stochastic nature of the heat conduc tion. This is done by developing it into a series w.r.t. the underlying stochastic. For this series known results from uncertainty quantification are applied. With the help of these results the temperature is developed in a Taylor series. For this Taylor series a suitable expansion point is chosen. Afterwards, this series is incorporated into the computation of the thermal stresses. The advantage of this approach is shown in numerical experiments.

CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions 1. Basic differential equations of thermoelasticity theory 2. Fundamental matrices 3. Thermo-radiating conditions. Somigliana type integral representations CHAPTER II. Formulation of Boundary Value and Interface Problems 4. Functional spaces 5. Formulation of basic and mixed BVPs 6. Formulation of crack type problems 7. Formulation of basic and mixed interface problems CHAPTER III. Uniqueness Theorems 8. Uniqueness theorems in pseudo-oscillation problems 9. Uniqueness theorems in steady state oscillation problems CHAPTER IV. Potentials and Boundary Integral Operators 10. Thermoelastic steady state oscillation potentials 11. Pseudo-oscillation potentials CHAPTER V. Regular Boundary Value and Interface Problems 12. Basic BVPs of pseudo-oscillations 13. Basic exterior BVPs of steady state oscillations 14. Basic interface problems of pseudo-oscillations 15. Basic interface problems of steady state oscillations CHAPTER VI. Mixed and Crack Type Problems 16. Basic mixed BVPs 17. Crack type problems 18. Mixed interface problems of steady state oscillations 19. Mixed interface problems of pseudo-oscillations

Die Temperaturverhältnisse beim Ziehen und Wärmebehandeln von Draht werden mit mathematisch-analytischen Methoden auf der Grundlage der FOURIERschen Wärmeleitungsgleichung eingehend untersucht. Insbesondere wird unter den spezifischen Wärmeübergangsbedingungen zwischen Draht und Ziehdüse sowie zwischen Draht und Ziehtrommel deren thermische Wechselwirkung analysiert. Ein Näherungsverfahren zur Berechnung der Drahttemperaturen in Zugfolgen unter Berücksichtigung des Ziehdüseneinflusses wird angegeben und mit einem Beispiel zum Nassziehen stark verzinkten Stahldrahts illustriert. Aus geschwindigkeitsabhängig gemessenen Änderungen des Drahtdurchmessers werden unter thermoelastischer Ziehringdurchmesserkorrektur Schmierfilmdicken bestimmt. Diffusionsgleichungen werden analysiert und ein Zusammenhang zur Reaktionskinetik wird hergestellt. Ein neues reaktionskinetisches Werkstoffmodell, das insbesondere auch im Falle stärker anisothermer Verhältnisse, also bei Kurzzeitwärmebehandlung anwendbar ist, wird vorgestellt.

In the present work, we shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models allowing for more general material properties such as anisotropies, inhomogeneities, etc.