This DPhil project is set in the context of single crystal elasticity-plasticity finite element modelling. Its core objective was to develop and implement a methodology for predicting the evolution of texture in single and dual-phase material systems. This core objective has been successfully achieved. Modelling texture evolution entails essentially modelling large deformations (as accurately as possible) and taking account of the deformation mechanisms that cause texture to change. The most important deformation mechanisms are slip and twinning. Slip has been modelled in this project and care has been taken to explore conditions where it is the dominant deformation mechanism for the materials studied. Modelling slip demands that one also models dislocations since slip is assumed to occur by the movement of dislocations. In this project a model for geometrically necessary dislocations has been developed and validated against experimental measurements. A texture homogenisation technique which relies on interpretation of EBSD data in order to allocate orientation frequencies based on representative area fractions has been developed. This has been coupled with a polycrystal plasticity RVE framework allowing for arbitrarily sized RVEs and corresponding allocation of crystallographic orientation. This has enabled input of experimentally measured initial textures into the CPFE model allowing for comparison of predictions against measured post-deformation textures, with good agreement obtained. The effect of texture on polycrystal physical properties has also been studied. It has been confirmed that texture indeed has a significant role in determining the average physical properties of a polycrystal. The thesis contributes to the following areas of micro-mechanics materials research: (i) 3D small deformation crystal plasticity finite element (CPFE) modelling, (ii) geometrically necessary dislocation modelling, (iii) 3D large deformation CPFE modelling, (iv) texture homogenisation methods, (v) single and dual phase texture evolution modelling, (vi) prediction of polycrystal physical properties, (vii) systematic calibration of the power law for slip based on experimental data, and (viii) texture analysis software development (pole figures and Kearns factors).

Este trabalho apresenta uma ferramenta de simulação computacional de canal de propagação para ambiente macro-celular baseada em modelos geométricos e no modelo estatístico apresentado no relatório COST 259 DCM. Para a implementação desta ferramenta é realizada, inicialmente, uma abordagem dos principais modelos de predição de perda por propagação, utilizados atualmente, assim como, um estudo dos modelos geométricos que fornecem as informações de distribuição de potência temporal e angular para diferentes tipos de distribuições estatísticas de espalhadores. A modelagem geométrica utiliza grupos independentes no qual os espalhadores são distribuídos com uma densidade Gaussiana. A utilização desta distribuição Gaussiana leva a distribuições de atraso e ângulo de chegada mais próximas dos resultados de medições do que o usando distribuição uniforme. A base geométrica define o conceito direcional e temporal. A base estatística define o número de grupo de espalhadores adicionais e suas localizações, quando estes existiram. Efeitos como: direção e potência de chegada de cada grupo de espalhadores, a presença ou não de visada direta entre transmissor e receptor a medida que a estação móvel percorre uma célula e a variação da polarização cruzada foram implementados nesse simulador. Desta forma, essa ferramenta computacional simula tanto a dispersão temporal, presente nos modelos de banda larga, como a dispersão angular, utilizadas em sistemas de comunicação móveis que exploram a diversidade espacial. / This work present a simulation tool for macro cell environment based on geometrical and statistical representation of the scatterers and on the COST 259 Directional Channel Model (DCM). A comprehensive review of the propagation prediction models for terrestrial wireless communication systems and geometric channel models, that provide, times of arrival (TOA) and the angle of arrival (AOA) for diferents statistics scatterers distribution is realized. This tool uses gaussianly distributed scatterers for each cluster. This distribution is naturally more realistic than the uniform distribution leading closer to experimental results. This geometrically based model simulates the TOA dispersion present in wide band channel models and the AOA dispersion necessary for systems that explore spatial diversity. This tool also incorporates the concept of line-of-sight and non-line-of-sight and its birth and death as the mobile station moves in a cell, as well as the appearance and disappearance of additional clusters of scatterers. The output provided by this simulation tool is comprised of all the complex amplitudes, delays and angles of arrival of all multipath components associated with each cluster of scatterers. Mean attenuation and slow fading effects are also incorporated to the model and fast fading appears as a consequence of the multipath interference.

Este trabalho apresenta uma ferramenta de simulação computacional de canal de propagação para ambiente macro-celular baseada em modelos geométricos e no modelo estatístico apresentado no relatório COST 259 DCM. Para a implementação desta ferramenta é realizada, inicialmente, uma abordagem dos principais modelos de predição de perda por propagação, utilizados atualmente, assim como, um estudo dos modelos geométricos que fornecem as informações de distribuição de potência temporal e angular para diferentes tipos de distribuições estatísticas de espalhadores. A modelagem geométrica utiliza grupos independentes no qual os espalhadores são distribuídos com uma densidade Gaussiana. A utilização desta distribuição Gaussiana leva a distribuições de atraso e ângulo de chegada mais próximas dos resultados de medições do que o usando distribuição uniforme. A base geométrica define o conceito direcional e temporal. A base estatística define o número de grupo de espalhadores adicionais e suas localizações, quando estes existiram. Efeitos como: direção e potência de chegada de cada grupo de espalhadores, a presença ou não de visada direta entre transmissor e receptor a medida que a estação móvel percorre uma célula e a variação da polarização cruzada foram implementados nesse simulador. Desta forma, essa ferramenta computacional simula tanto a dispersão temporal, presente nos modelos de banda larga, como a dispersão angular, utilizadas em sistemas de comunicação móveis que exploram a diversidade espacial. / This work present a simulation tool for macro cell environment based on geometrical and statistical representation of the scatterers and on the COST 259 Directional Channel Model (DCM). A comprehensive review of the propagation prediction models for terrestrial wireless communication systems and geometric channel models, that provide, times of arrival (TOA) and the angle of arrival (AOA) for diferents statistics scatterers distribution is realized. This tool uses gaussianly distributed scatterers for each cluster. This distribution is naturally more realistic than the uniform distribution leading closer to experimental results. This geometrically based model simulates the TOA dispersion present in wide band channel models and the AOA dispersion necessary for systems that explore spatial diversity. This tool also incorporates the concept of line-of-sight and non-line-of-sight and its birth and death as the mobile station moves in a cell, as well as the appearance and disappearance of additional clusters of scatterers. The output provided by this simulation tool is comprised of all the complex amplitudes, delays and angles of arrival of all multipath components associated with each cluster of scatterers. Mean attenuation and slow fading effects are also incorporated to the model and fast fading appears as a consequence of the multipath interference.

Made available in DSpace on 2014-07-29T16:02:16Z (GMT). No. of bitstreams: 1 Dissertacao ana paula faria machado.pdf: 253816 bytes, checksum: 17cd09106048916ae2c14d5f373c0dff (MD5) Previous issue date: 2008-02-15 / In this dissertation we define geometrically uniform codes in Euclidean spaces, presenting some symmetrical properties of these codes. Build geometrically uniforme partitions and starting these we define generalized coset codes. We generalize the concept of geometrically uniform codes to hyperbolic spaces. We show a characterization of generalized coset codes through the concept of G-linear codes. / Nesta dissertação definimos códigos geometricamente uniformes em espaços euclideanos, apresentando algumas propriedades simétricas destes códigos. Construímos partições geometricamente uniformes e a partir destas definimos classes laterais de códigos generalizadas. Estendemos aos espaços hiperbólicos o conceito de códigos geometricamente uniformes. Mostramos também uma caracterização de classes laterais generalizadas através do conceito de códigos G-lineares.

Design optimization is a method that can be used to automate the design process to obtain better results. When applied to aeroelastic structures, design optimization often leads to the creation of highly flexible aeroelastic structures. There are, however, a number of conventional design procedures that must be modified when dealing with highly flexible aeroelastic structures. First, the deformed geometry must be the baseline for weight, structural, and stability analyses. Second, potential couplings between aeroelasticity and rigid-body dynamics must be considered. Third, dynamic analyses must be modified to handle large nonlinear displacements. These modifications to the conventional design process significantly increase the difficulty of developing an optimization framework appropriate for highly flexible aeroelastic structures. As a result, when designing these structures, often either gradient-free optimization is performed (which limits the optimization to relatively few design variables) or optimization is simply omitted from the design process. Both options significantly decrease the design exploration capabilities of a designer compared to a scenario in which gradient-based optimization is used. This dissertation therefore presents various contributions that allow gradient-based optimization to be more easily used to optimize highly flexible aeroelastic structures. One of our primary motivations for developing these capabilities is to accurately capture the design constraints of solar-regenerative high-altitude long-endurance (SR-HALE) aircraft. In this dissertation, we therefore present a SR-HALE aircraft optimization framework which accounts for the peculiarities of structurally flexible aircraft while remaining suitable for use with gradient-based optimization. These aircraft tend to be extremely large and light, which often leads to significant amounts of structural flexibility. Using this optimization framework, we design an aircraft that is capable of flying year-round at \SI{35}{\degree} latitude at \SI{18}{\kilo\meter} above sea level. We subject this aircraft to a number of constraints including energy capture, energy storage, material failure, local buckling, stall, static stability, and dynamic stability constraints. Critically, these constraints were designed to accurately model the actual design requirements of SR-HALE aircraft, rather than to provide a rough approximation of them. To demonstrate the design exploration capabilities of this framework, we also performed several parameters sweeps to determine optimal design sensitivities to altitude, latitude, battery specific energy, solar efficiency, avionics and payload power requirements, and minimum design velocity. Through this optimization framework, we demonstrate both the potential of gradient-based optimization applied to highly flexible aeroelastic structures and the challenges associated with it. One challenge associated with the gradient-based optimization of highly flexible aeroelastic structures, is the ability to accurately, efficiently, and reliably model the large deflections of these structures in gradient-based optimization frameworks. To enable large-scale optimization involving structural models with large deflections to be performed more easily, we present a finite-element implementation of geometrically exact beam theory which is designed specifically for gradient-based optimization. A key feature of this implementation of geometrically exact beam theory is its compatibility with forward and reverse-mode automatic differentiation, which allows accurate design sensitivities to be obtained with minimal development effort. Another key feature is its native support for unsteady adjoint sensitivity analysis, which allows design sensitivities to be obtained efficiently from time-marching simulations. Other features are also presented that build upon previous implementations of geometrically exact beam theory, including a singularity-free rotation parameterization based on Wiener-Milenkovi\'c parameters, an implementation of stiffness-proportional structural damping using a discretized form of the compatibility equations, and a reformulation of the equations of motion for geometrically exact beam theory from a fully implicit index-1 differential algebraic equation to a semi-explicit index-1 differential algebraic equation. Several examples are presented which verify the utility and validity of each of these features. Another challenge associated with the gradient-based optimization of highly flexible aeroelastic structures is the ability to reliably track and constrain individual dynamic stability modes across the design iterations of an optimization framework. To facilitate the development of mode-specific dynamic stability constraints in gradient-based optimization frameworks we develop a mode tracking method that uses an adaptive step size in order to maintain an arbitrarily high degree of confidence in mode correlations. This mode tracking method is then applied to track the modes of a linear two-dimensional aeroelastic system and a nonlinear three-dimensional aeroelastic system as velocity is increased. When used in a gradient-based optimization framework, this mode tracking method has the potential to allow continuous dynamic stability constraints to be constructed without constraint aggregation. It also has the potential to allow the stability and shape of specific modes to be constrained independently. Finally, to facilitate the development and use of highly flexible aeroelastic systems for use in gradient-based optimization frameworks, we introduce a general methodology for coupling aerodynamic and structural models together to form modular monolithic aeroelastic systems. We also propose efficient methods for computing the Jacobians of these coupled systems without significantly increasing the amount of time necessary to construct these systems. For completeness we also discuss how to ensure that the resulting system of equations constitutes a set of first-order index-1 differential algebraic equations. We then derive direct and adjoint sensitivities for these systems which are compatible with automatic differentiation so that derivatives for gradient-based optimization can be obtained with minimal development effort.

<p> This thesis reports a systematic study of geometrically frustrated f.c.c. double perovskites with both monoclinic (P2₁/n) La₂LiMO₆ and cubic (Fm3m) Ba₂YMO₆ symmetries, where M=Mo (S=1/2), Re (S=1) and Ru (S=3/2). The roles of both the spin quantum number, i.e. quantum spin fluctuations, and the local site symmetry, i.e. orbital ordering, on the determination of the ground magnetic state were studied. All the compounds were prepared by solid state reaction and the structural information and magnetic properties of the compounds were collected using diffraction techniques (X-ray and neutron), de susceptibility, heat capacity, muon spin relaxation (μSR) and solid state NMR. </p> <p> The S=3/2 materials, La₂LiRuO₆ and Ba₂YRuO₆, while highly frustrated with frustration indices f ~ 16 and 8, respectively, both show antiferromagnetic (AF) long range ordering at 24K and 37K, respectively. The Neel temperature of the latter compound was determined for the first time by the heat capacity and neutron diffraction. This compound shows an unusual AF transition as two broader peaks were observed in the susceptibility while La₂LiRuO₆ shows a typical AF behavior. There is about 1 % of Y/Ru site mixing observed by 89Y MAS NMR in Ba₂YRuO₆. </p> <p> For the S=1 materials, monoclinic La₂LiReO₆ shows collective singlet like behavior as zero magnetization was observed in the ZFC susceptibility and a static and diluted spin system was indicated by μSR. On the other hand, the cubic phase, Ba₂YReO₆ surprisingly shows a spin glass behavior confirmed by μSR while no Y/Re site mixing was observed by MAS NMR. It is also a surprising observation that this compound retains cubic symmetry down to 3K where it would have a structure transition subject to the Jahn-Teller theorem. </p> <p> Finally, the S=1/2 compounds, La₂LiMoO₆ and Ba₂YMoO₆, show quite different magnetic behavior. Monoclinic La₂LiMoO₆ shows the presence of at least short range order achieved at 18K according to the heat capacity and μSR measurements. Ba₂YMoO₆ retains cubic symmetry down to 3K and no Jahn-Teller distortion was observed at the limit of the resolution of neutron diffraction. This compound surprisingly appears to remain paramagnetic down to 2K, yet evidence for a collective singlet state was observed by a paramagnetic Knight shift measurement in NMR. This is consistent with an existing theoretical prediction. </p> <p> An extended study on other S=1/2 Mo analogues, Ba₂LuMoO₆ and Ba₂ScMoO₆ is also presented. Both compounds show cubic structure confirmed by X-ray diffraction and paramagnetic behavior down to 2K in the susceptibility. </p> / Thesis / Doctor of Philosophy (PhD)

The dissertation “Formation of wrinkles on a coated substate“ treats the finite element simulations of controlled wrinkle formation experiments conducted at the Leibniz Institute for Polymer Research. The systems used for the experiments consist of a soft polydimethylsiloxane (PDMS) layer with a thin, stiff layer on top. The wrinkling process is triggered by a stress mismatch between the bulk and the thin layer. To create the stress mismatch, the bulk material is first uni-axially stretched and then the thin layer is created by a low-pressure plasma treatment of the stretched bulk in a vacuum chamber. Under subsequent relaxation, wrinkles form. Their wavelength depends on the choice of the process gas and the duration of the treatment. The use of thin silicon masks placed directly on the PDMS allows to sharply restrict the plasma-exposed area. Sequential exposures of the same sample to multiple treatment processes with and without a mask allow to locally modify the layer thickness and stiffness. With this, we can locally control the wavelength of the resulting wrinkles and trigger the formation of branches and line defects at the boundary between areas of different wavelengths. The dissertation first covers the mathematical model for the coated substrate, a combination of a hyperelastic material model from three-dimensional elasticity for the bulk (an almost incompressible Mooney–Rivlin material model) and a Cosserat shell model for the film on top. A nonlinear and nonconvex minimization problem is deduced and transferred to a suitable finite element space. Existence of minimizers is proven in the continuous and the discrete case before the discrete problem is solved numerically. The numerical simulations show a good agreement with corresponding physical experiments.

Presented is an overview of a semi-analytical solution which was developed to study the response of internally pressurized elliptical composite cylinders with clamped boundaries. Using a geometrically linear analysis and the solution scheme, the response of a quasi-isotropic elliptical cylinder is compared with the response of a quasi-isotropic circular cylinder in order to study the effects of elliptical geometry. The distinguishing features of the response of an elliptical cylinder are the inward normal displacement of the cross section at the ends of the major diameter that occur despite the outward force of the internal pressure, the presence of circumferential displacements, and the presence of inplane shear strains. These effects lead to spatial variations, including sign reversals, of a number of displacement, strain, and curvature responses. The responses of a quasi-isotropic elliptical cylinder evaluated using a geometrically linear analysis are then compared to the responses evaluated using a geometrically nonlinear analysis. It is shown that geometric nonlinearities tend to flatten certain responses at the ends of the minor diameter, and reduce the magnitude of certain responses in the boundary region. To study the influence of material orthotropy, the responses of axially-stiff and circumferentially-stiff elliptical cylinders evaluated using geometrically nonlinear analyses are examined. It is shown that in some instances material orthotropy can be used to mitigate the influence of the elliptical geometry and make particular responses look like those of a circular cylinder. An evaluation of failure using the maximum stress and Hashin failure criteria and geometrically linear and nonlinear analyses is presented for elliptical cylinders. These failure criteria involve interlaminar shear stresses which are computed by integrating the equilibrium equations of elasticity through the thickness of the cylinder wall. The failure criteria are used to assess the mode of failure (e.g., tensile or compressive fiber or matrix modes), the location of failure, and the pressure at failure. Both criteria predict first failure to occur at the clamped boundaries because of matrix cracking. The predicted failure pressures and circumferential locations are very similar for the two criteria, and the nonlinear analyses predict slightly higher pressures at somewhat different circumferential locations. First fiber failure is also considered. For this failure the two criteria predict similar failure scenarios for the linear analyses, but they differ in their predictions for the nonlinear analyses. Specifically, using the maximum stress criterion, the circumferentially-stiff elliptical cylinder is predicted to fail due to fiber compression, but the Hashin criterion predicts failure to be due to fiber tension, and at a different circumferential location. Also, first fiber failure pressures are at least a factor of two greater than the first matrix failure pressure. / Master of Science

Owing to continuous miniaturization, many modern high-technology applications such as medical and optical devices, thermal barrier coatings, electronics, micro- and nano-electro mechanical systems (MEMS and NEMS), gems industry and semiconductors increasingly use components with sizes down to a few micrometers and even smaller. Understanding their deformation mechanisms and assessing their mechanical performance help to achieve new insights or design new material systems with superior properties through controlled microstructure at the appropriate scales. However, a fundamental understanding of mechanical response in surface-dominated structures, different than their bulk behaviours, is still elusive. In this thesis, the size effect in a single-crystal Ti alloy (Ti15V3Cr3Al3Sn) is investigated. To achieve this, nanoindentation and micropillar (with a square cross-section) compression tests were carried out in collaboration with Swiss Federal Laboratories for Materials Testing and Research (EMPA), Switzerland. Three-dimensional finite element models of compression and indentation with an implicit time-integration scheme incorporating a strain-gradient crystal-plasticity (SGCP) theory were developed to accurately represent deformation of the studied body-centered cubic metallic material. An appropriate hardening model was implemented to account for strain-hardening of the active slip systems, determined experimentally. The optimized set of parameters characterizing the deformation behaviour of Ti alloy was obtained based on a direct comparison of simulations and the experiments. An enhanced model based on the SGCP theory (EMSGCP), accounting for an initial microstructure of samples in terms of different types of dislocations (statistically stored and geometrically necessary dislocations), was suggested and used in the numerical analysis. This meso-scale continuum theory bridges the gap between the discrete-dislocation dynamics theory, where simulations are performed at strain rates several orders of magnitude higher than those in experiments, and the classical continuum-plasticity theory, which cannot explain the dependence of mechanical response on a specimen s size since there is no length scale in its constitutive description. A case study was performed using a cylindrical pillar to examine, on the one hand, accuracy of the proposed EMSGCP theory and, on the other hand, its universality for different pillar geometries. An extensive numerical study of the size effect in micron-size pillars was also implemented. On the other hand, an anisotropic character of surface topographies around indents along different crystallographic orientations of single crystals obtained in numerical simulations was compared to experimental findings. The size effect in nano-indentation was studied numerically. The differences in the observed hardness values for various indenter types were investigated using the developed EMSGCP theory.

La déformation visco-plastique de la glace est fortement anisotrope, le plan de glissement préferé étant la plan de base. Le fait que dans un polycristal chaque grain possède sa propre direction de déformation produit des incompatibilités et un champ de contrainte complexe. La déformation à été étudiée expérimentellement en mésurant la dis- tortion des plans cristallins de mono- et polycristaux de glace artificielle. Les expériences ont été réalisées à l'aide d'un faisceau synchrotron. Une nouvelle procédure éxperimental, basée sur les méthodes de l'imagerie en diffraction de Bragg, comme lumière blanche, im- agerie sur la courbe de diffraction et topographie laminaire et ponctuelle, a été dévéloppée. Les désorientations angulaires, les largeurs à mi-hauteur et les intensités intégrées ont été mésurées dans les trois dimensions spatiales de l'échantillon et avec une résolution de 50× 50 × 50µm3. Les algorithmes d'analyse de données ont été écrits pour extraire des données des résultats quantitatifs, et pour calculer les neuf composantes du tenseur de courbure ainsi que la distortion entière des plans cristallins. Les résultats ont permis d'observer les premières étappes de la déformation de la glace. Par example la polygonisation d'un grain à été observée. / The viscoplastic deformation of ice is strongly anisotropic. The preferred glide system is on the basal plane. In a polycrystal each grain exhibits its own deformation direction. As a result the deformation of polycrystalline ice is associated with strain in- compatibilities, especially at the grain boundaries and the triple junction. The deforma- tion process was experimentally investigated by measuring crystal lattice distortions of single- and polycrystalline, artificially grown ice crystals. The experiments were benefic- ing from a synchrotron X-ray beam. A new experimental method, based on Bragg diffrac- tion imaging (X-ray topography) methods, as white beam X-ray diffraction topography, rocking curve imaging, section- and pinhole X-ray topography was used. Angular mis- orientations, full-width-half-maxima and integrated Bragg diffracted intensities have been measured along the three spatial dimensions of the sample and with a spatial resolution of around 50µm × 50µm × 50µm. Data analysis algorithms were written in order to extract quantitative results from the data and to calculate all nine components of the curvature ten- sor, as well as the entire lattice distortion in the sample. The results give an insight into the early stages of plastic deformation of ice, i.e. the polygonisation of a grain was observed.