Cemented carbides based on tungsten carbide and cobalt arecommonly produced by a powder metallurgy route including liquidphase sintering. The pressed compact densifies to almost halfits volume during sintering due to pore elimination. Thesintering behaviour changes with material composition, such ascarbide grain size, binder fraction, carbon content andaddition of cubic carbides. This thesis is devoted to the study of constitutivebehaviour, in particular densification, and the microstructuralevolution during cemented carbide sintering. Dimensionalchanges are monitored using dilatometry with and withoutapplied external load. The microstructural evolution isinvestigated with light optical microscopy and scanningelectron microscopy. Thermodynamic calculations are used asreference. Constitutive relations are derived for uniaxial viscosity,viscous equivalent of Poisson’s ratio and sintering stressbased on relative density and temperature. The relations areextended to a model describing sintering shrinkage withexplicit dependencies on carbide grain size and binder content.The model is divided in three stages of which two pertain tothe solid state and the third to liquid phase sintering. Solidstate shrinkage is suppressed in a material with coarsecarbides and in the stage of liquid phase sintering grain sizestrongly influences the uniaxial viscosity. The binder contentaffects primarily the later densification. The effects of carbon content and grain size distribution onshrinkage have been studied. High carbon content enhancesshrinkage rate, but the effect of grain size distribution israther small. The mean carbide grain size is insufficient todescribe densification for very broad distributions only. Shrinkage occurs through rearrangement andsolution-reprecipitation. Rearrangement is studied through theevolution of the pore size distribution and simulatedgenerically using a discrete element method. Keywords:Cemented carbides, Sintering, Constitutiverelations, Microstructure, Densification, Modelling

<p>Cemented carbides based on tungsten carbide and cobalt arecommonly produced by a powder metallurgy route including liquidphase sintering. The pressed compact densifies to almost halfits volume during sintering due to pore elimination. Thesintering behaviour changes with material composition, such ascarbide grain size, binder fraction, carbon content andaddition of cubic carbides.</p><p>This thesis is devoted to the study of constitutivebehaviour, in particular densification, and the microstructuralevolution during cemented carbide sintering. Dimensionalchanges are monitored using dilatometry with and withoutapplied external load. The microstructural evolution isinvestigated with light optical microscopy and scanningelectron microscopy. Thermodynamic calculations are used asreference.</p><p>Constitutive relations are derived for uniaxial viscosity,viscous equivalent of Poisson’s ratio and sintering stressbased on relative density and temperature. The relations areextended to a model describing sintering shrinkage withexplicit dependencies on carbide grain size and binder content.The model is divided in three stages of which two pertain tothe solid state and the third to liquid phase sintering. Solidstate shrinkage is suppressed in a material with coarsecarbides and in the stage of liquid phase sintering grain sizestrongly influences the uniaxial viscosity. The binder contentaffects primarily the later densification.</p><p>The effects of carbon content and grain size distribution onshrinkage have been studied. High carbon content enhancesshrinkage rate, but the effect of grain size distribution israther small. The mean carbide grain size is insufficient todescribe densification for very broad distributions only.</p><p>Shrinkage occurs through rearrangement andsolution-reprecipitation. Rearrangement is studied through theevolution of the pore size distribution and simulatedgenerically using a discrete element method.</p><p><b>Keywords:</b>Cemented carbides, Sintering, Constitutiverelations, Microstructure, Densification, Modelling</p>

Pile foundations that support offshore structures are required to resist not only static loading, but also dynamic loading from waves, wind and earthquakes. The purpose of this study is to gain a better understanding of the behavior of offshore piles under cyclic or dynamic loading using the finite element approach. To achieve this goal, an appropriate constitutive model is required to simulate the behavior of soils and interfaces. The DSC constitutive model is developed for saturated interfaces to study the behavior under severe shear deformation at the soil-pile interface. Monotonic and cyclic simple shear experiments are conducted on Ottawa sand-steel interfaces under drained and undrained conditions using the Cyclic-Multi-Degree-of-Freedom shear device with porewater pressure measurement (CYMDOF-P). The effect of various parameters such as normal stress, surface roughness of steel, type of loading, and the amplitude and frequency of the applied displacement in two-way cyclic loading are investigated. The data from the simple shear tests on saturated interfaces are used to calculate the parameters in the DSC model. The resulting parameters are then used to verify the DSC model by back predicting tests from which parameters are determined and independent tests that are not used in parameters determination. The model predictions, in general, were found to provide a highly satisfactory correlation with the observations. In the context of DSC, the concept of critical disturbance is developed to identify initiation of liquefaction in saturated Ottawa sand-steel interfaces. This method is based on using microstructural changes in material as an indication of liquefaction identification. The finite element method, along with DSC constitutive model, is used to investigate the response of offshore piles to dynamic loading. These include cyclic loading of axially loaded instrumented pile in clay and full-scale laterally loaded pile in sand. The DSC model is used to model the nonlinear behavior of saturated soils and interfaces. A nonlinear dynamic finite element program DSC-DYN2D based on the DSC modeling approach and the theory of nonlinear porous media is used for this purpose. Results from numerical solutions are compared with field measurements. Strong agreement between numerical predictions and field measurements are an indication of the ability to solve challenging soil-structure interaction problems.Based on the results of this research, it can be stated that the finite element-DSC model simulation allows realistic prediction of complex dynamic offshore pile-soil interaction problems, and is capable of characterizing behavior of saturated soils and interfaces involving liquefaction.

In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. / In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können.

In the thesis, we study the Navier-Stokes-like and the Navier-Stokes-Fourier- like problems for the flows of homogeneous incompressible fluids. In the first part of the thesis, we introduce a new type of boundary condition for the shear stress tensor, which includes the time derivative of the velocity. Therefore, we are able to capture the dynamic response of the fluid on the boundary. As the second part of the thesis, we include the published journal article co-authored by J. Žabenský on the Navier-Stokes-Fourier-like problem formulated in the complete thermodynamic setting. In both parts, the constitutive relations are formulated implicitly with the use of maximal monotone graphs. The main result of the thesis is the existence analysis for the above mentioned problems.

This study has two parts. In the first part we develop a computational approach to the solution of an inverse modelling problem concerning the material properties of electrolytes used in Lithium-ion batteries. The dependence of the diffusion coefficient and the transference number on the concentration of Lithium ions is reconstructed based on the concentration data obtained from an in-situ NMR imaging experiment. This experiment is modelled by a system of 1D time-dependent Partial Differential Equations (PDE) describing the evolution of the concentration of Lithium ions with prescribed initial concentration and fluxes at the boundary. The material properties that appear in this model are reconstructed by solving a variational optimization problem in which the least-square error between the experimental and simulated concentration values is minimized. The uncertainty of the reconstruction is characterized by assuming that the material properties are random variables and their probability distribution estimated using a novel combination of Monte-Carlo approach and Bayesian statistics. In the second part of this study, we carefully analyze a number of secondary effects such as ion pairing and dendrite growth that may influence the estimation of the material properties and develop mathematical models to include these effects. We then use reconstructions of material properties based on inverse modelling along with their uncertainty estimates as a framework to validate or invalidate the models. The significance of certain secondary effects is assessed based on the influence they have on the reconstructed material properties. / Thesis / Doctor of Philosophy (PhD)

Non-Aqueous Phase Liquids (NAPLs) include commonly occurring organic contaminants such as gasoline, diesel fuel and chlorinated solvents. When released to subsurface environments their spreading is a complex process of multi-component, multi-phase flow. This work has strived to develop new models and methods to describe the spreading of NAPLs in heterogeneous geological media. For two-phase systems, infiltration and immobilisation of NAPL in stochastically heterogeneous, water-saturated media were investigated. First, a methodology to continuously measure NAPL saturations in space and time in a two-dimensional experiment setup, using multiple-energy x-ray-attenuation techniques, was developed. Second, a set of experiments on NAPL infiltration in carefully designed structures of well-known stochastic heterogeneity were conducted. Three detailed data-sets were generated and the importance of heterogeneity for both flow and the immobilised NAPL architecture was demonstrated. Third, the laboratory experiments were modelled with a continuum- and Darcy’s-law-based multi-phase flow model. Different models for the capillary pressure (Pc) – fluid saturation (S) – relative permeability (kr) constitutive relations were compared and tested against experimental observations. A method to account for NAPL immobility in dead-end pore-spaces during drainage was introduced and the importance of accounting for hysteresis and NAPL entrapment in the constitutive relations was demonstrated. NAPL migration in three-phase, water-NAPL-air systems was also studied. Different constitutive relations used in modelling of three-phase flow were analysed and compared to existing laboratory data. To improve model performance, a new formulation for the saturation dependence of tortuosity was introduced and different scaling options for the Pc-S relations were investigated. Finally, a method to model the spreading of multi-constituent contaminants using a single-component multi-phase model was developed. With the method, the migration behaviour of individual constituents in a mixture, e.g. benzene in gasoline, could be studied, which was demonstrated in a modelling study of a gasoline spill in connection with a transport accident. / Flerfasföroreningar innefattar vanligt förekommande organiska vätskor som bensin, dieselolja och klorerade lösningsmedel. Spridningen av dessa föroreningar i mark är komplicerad och styrs av det samtidiga flödet av organisk vätska, vatten och markluft samt utbytet av komponenter (föroreningar) mellan de olika faserna. Detta arbete syftade till att utveckla nya metoder och modeller för att studera spridningen av flerfasföroreningar i mark: (i) En metodik utvecklades för att i laboratorium noggrant och kontinuerligt mäta hur en organisk vätska är rumsligt fördelad i en tvådimensionell experimentuppställning. Metoden baserades på röntgenutsläckning för olika energinivåer. (ii) Infiltration av organisk vätska i vattenmättade medier studerades för olika konfigurationer av geologisk heterogenitet. I experimentuppställningen packades olika sandmaterial noggrant för att konstruera en välkänd, stokastiskt heterogen struktur. Spridningsprocessen dokumenterades i tre detaljerade mätserier och heterogenitetens påverkan på flöde och kvarhållning av den organiska vätskan påvisades. (iii) Experimenten simulerades med en numerisk modell. Olika modeller prövades för att beskriva de grundläggande relationerna mellan kapillärtryck (Pc) vätskehalt (S) och relativ permeabilitet (kr) för detta tvåfassystem av vatten och organisk vätska. En relation infördes för att beskriva partiell orörlighet hos den organiska vätskan i porer vars halsar tillfälligt blockeras av vatten då mediet avvattnas. Vikten av att i de grundläggande relationerna ta hänsyn till hysteresis och kvarhållning av organisk fas visades. (iv) Olika Pc-S-kr relationer för trefassystem av vatten, organisk vätska och markluft testades mot befintliga experimentella data. En ny relation för hur slingrigheten (eng. tortuosity) beror av vätskehalten infördes i kr-S relationen och olika möjligheter för att skala Pc-S relationen analyserades. (v) En modelleringsmetodik utvecklades för att studera spridningen av flerkomponentsföroreningar. Med metoden kunde spridningsbeteendet hos enskilda, särskilt skadliga komponenter som t.ex. bensen särskiljas då ett bensinutsläpp i samband med en transportolycka simulerades.

We study behavior of incompressible non-Newtonian fluids with a relation be- tween the shear stress and the shear rate given by a non-monotone S-shaped curve. These fluids are described with a special class of implicit constitutive relations that may be derived in a thermodynamically consistent manner us- ing the entropy production maximization principle or gradient dynamics. In the latter approach, the constitutive relation is given as the derivative of a non-convex dissipation potential. The concept of dissipation potential allows us to discuss stability of the constitutive relation and explain the experimen- tally observed response discontinuities. We are also concerned with hydrody- namic stability of flows of implicitly constituted fluids. Finally, we propose a numerical scheme for simulation of transient flows of fluids with a specific non-monotone constitutive relation. We employ the numerical scheme in a simulation of two-dimensional Taylor-Couette flow and the numerical results confirm our theoretical observations concerning the admissible flow states.

We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.

<p>In this work we propose and validate a computational method for reconstructing constitutive relations (material properties) in complex multiphysics phenomena based on incomplete and noisy measurements which is applicable to different problems arising in nonequilibrium thermodynamics and continuum mechanics. The parameter estimation problem is solved as PDE–constrained optimization using a gradient–based technique in the optimize–then–discretize framework. The reconstructed material properties taken as an example here are the transport coefficients characterizing diffusion processes such as the viscosity and the thermal conductivity, and we focus on problems in which these coefficients depend on the state variables in the system. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. This research is motivated by questions arising in the computational analysis and optimization of advanced welding processes which involves modelling complex alloys in the liquid phase at high temperatures.</p> / Doctor of Philosophy (PhD)