The mechanical behaviour of geomaterials (e.g. soils, rocks and concrete) under plastic deformation is highly complex due to that fact that they are granular materials consisting of discrete non-uniform particles. Failure of geomaterials is often related to localisation of deformation (strain-localisation) with excessive shearing inside the localised zones. The microstructure of the material then dominates the material behaviour in the localised zones. The formation of the localised zone (shear band) during plastic deformation decreases the material strength (softening) significantly and initiates the failure of the material. There are two main approaches to the numerical modelling of localisation of deformation in geomaterials; discrete and continuum. The discrete approach can provide a more realistic material description. However, in the discrete approach, the modelling of all particles is complicated and computationally very expensive for a large number of particles. On the other hand, the continuum approach is more flexible, avoids modelling the interaction of individual particles and is computationally much cheaper. However, classical continuum plasticity models fail to predict the localisation of deformation accurately due to loss of ellipticity of the governing equations, and spurious mesh-dependent results are obtained in the plastic regime. Generalised plasticity models are proposed to overcome the difficulties encountered by classical plasticity models, by relaxing the local assumptions and taking into account the microstructure-related length scale into the models. Among generalised plasticity models, Cosserat (micropolar) and stain-gradient models have shown significant usefulness in modelling localisation of deformation in granular materials in the last few decades. Currently, several elastoplastic models are proposed based on Cosserat and strain-gradient theories in the literature. The individual formulation of the models has been examined almost always in isolation and are paired with specific materials in a mostly arbitrary fashion. Therefore, there is a lack of comparative studies between these models both at the theory level and in their numerical behaviour, which hinders the use of these models in practical applications. This research aims to enable broader adoption of generalised plasticity models in practical applications by providing both the necessary theoretical basis and appropriate numerical tools. A detailed comparison of some Cosserat and strain-gradient plasticity models is provided by highlighting their similarities and differences at the theory level. Two new Cosserat elastoplastic models are proposed based on von Mises and Drucker- Prager type yield function. The finite element formulations of Cosserat and strain-gradient models are presented and compared to better understand their advantages and disadvantages regarding numerical implementation and computational cost. The finite elements and material models are implemented into the finite element program ABAQUS using the user element subroutine (UEL) and an embedded user material subroutine (UMAT) respectively. Cosserat finite elements are implemented with different Cosserat elastoplastic models. The numerical results show how the Cosserat elements behaviour in the plastic regime depends on the models, interpolation of displacement and rotation and the integration scheme. The effect of Cosserat parameters and specific formulations on the numerical results based on the biaxial test is discussed. Two new mixed-type finite elements as well as existing ones (C1, mixed-type and penalty formulation), are implemented with different strain-gradient plasticity models to determine the numerical behaviour of the elements in the plastic regime. A detailed comparison of the numerical results of Cosserat and strain-gradient elastoplastic models is provided considering specific strain-localisation problems. Finally, some example problems are simulated with both the Cosserat and strain-gradient models to identify their applicability.

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.

Under loading conditions found in many geotechnical structures, it is common to observe failure in zones of high localized strain called shear bands. Existing models predict these localizations, but provide little insight into the micromechanics within the shear bands. This research captures the variation in microstructure inside and outside of shear bands that were formed in laboratory plane strain and two-dimensional discrete element method (DEM) biaxial compression experiments. Plane strain compression tests were conducted on dry specimens of Ottawa 20-30 sand to calibrate the device, assess global response repeatability, and develop a procedure to quantitatively define the onset of localization. A new methodology was employed to quantify and correct for the additional stresses imparted by the confining membrane in the vicinity of the shear band. Unsheared and sheared specimens of varying dilatancy were solidified using a two-stage resin impregnation procedure. DEM tests were performed using an innovative servo-controlled flexible lateral confinement algorithm to provide additional insights into laboratory results. The solidified specimens were sectioned and the resulting surfaces prepared for microstructure observation using bright field microscopy and morphological analysis. Local void ratio distributions and their statistical properties were determined and compared. Microstructural parameters for subregions in a grid pattern and along predefined inclined zones were also calculated. Virtual surfaces parallel to the shear band were identified and their roughnesses assessed. Similar calculations were performed on the DEM simulations at varying strain levels to characterize the evolution of microstructure with increasing strain. The various observations showed that the mean, standard deviation, and entropy of the local void ratio distributions all increased with increasing strain levels, particularly within regions of high local strains. These results indicate that disorder increases within a shear band and that the soil within the shear band does not adhere to the classical concept of critical state, but reaches a terminal void ratio that is largely a function of initial void ratio. Furthermore, there appears to be a transition zone between the far field and the fully formed shear block, as opposed to an abrupt delineation as traditionally inferred.

Der vorliegende Bericht beschreibt das Verhalten von ultrahochfestem Beton unter zweiaxialer Druckbeanspruchung. Bisher wurden ein Feinkornbeton und zwei Grobkornbetone mit unterschiedlichen Faserzusätzen untersucht. Die Zylinderdruckfestigkeiten nach 28 Tagen betragen rund 150, 160 und 170 N/mm². Besonders bei dem Feinkornbeton wurde eine überwiegend horizontale Ausrichtung der Stahlfasern festgestellt, die zu einer Anisotropie im Materialverhalten führte. Zusammenfassend muss festgestellt werden, dass die zweiaxiale Druckfestigkeit von UHPC nur geringfügig größer ist als die einaxiale. Für die Mischungen mit 2,5 Vol.-% Fasergehalt übersteigt die Festigkeit bei einem Spannungsverhältnis von Spannung 1 zu Spannung 2 gleich Eins die einaxiale Festigkeit um 7 bzw. 10 %. Bei dem Beton mit 0,9 Vol.-% Fasergehalt lag diese zweiaxiale Festigkeit sogar geringfügig unter der einaxialen. Bei der Bemessung von UHPC dürfen somit die vom Normalbeton bekannten Festigkeitssteigerungen unter mehraxialer Druckbelastung, wie sie z.B. bei reinen Druckknoten von Stabwerkmodellen angesetzt werden, nicht verwendet werden! Für die Beschreibung der Bruchkurve kann nach jetzigem Erkenntnisstand das Bruchkriterium nach OTTOSEN als eine gute Näherung empfohlen werden. Die Versuche haben gezeigt, dass sich UHPC in vielen, zum Teil sicherheitsrelevanten Bereichen anders verhält als Normalbeton. Für eine umfassende Beschreibung des Tragverhaltens sind weitere Versuche unter dreiaxiale Druckbelastung und kombinierter Druck-Zug-Belastung notwendig.

This thesis deals with the transport properties and critical current limitations found in YBa2Cu3O7[-delta] coated conductors prepared by the "rolling assisted biaxially textured substrate" (RABiTS) approach. For this purpose a buffer layer system composed of CeO2 and yttria-stabilised zirconia, and subsequently a YBa2Cu3O7[-delta] film were epitaxially grown by pulsed laser deposition on a biaxially textured metallic substrate. The resulting texture of the YBa2Cu3O7[-delta] film is crucial for the achievement of high critical current densities. A propagation of the granular structure of the metallic substrate into the YBa2Cu3O7[-delta] film was detected, which leads to the formation of a YBa2Cu3O7[-delta] grain boundary network and limits the critical current density of the samples. In order to study this limitation, critical current measurements were performed on the prepared samples at different temperatures and magnetic fields, detecting a transition between intergrain and intragrain current limitation that occurs at the so-called crossover magnetic field. The crossover magnetic field was found to shift to lower values as the temperature was increased. It was concluded that the grain boundary network limits the critical current density of the YBa2Cu3O7[-delta] coated conductor only for magnetic fields below the crossover field. / In der vorliegenden Dissertation werden Transporteigenschaften und die Limitierung der kritischen Stromdichte von YBa2Cu3O7[-delta] Bandleitern untersucht. Für die Präparation wird das epitaktische Schichtwachstum auf biaxial texturierten Substraten genutzt (RABiTS-Technik). Dabei wird mittels gepulster Laserdeposition eine Pufferschicht aus CeO2 und Yttrium-stabilisiertem Zirkonoxyd (YSZ) und anschließend eine YBa2Cu3O7[-delta] Schicht epitaktisch auf ein Substrat aufgebracht. Die resultierende biaxiale Textur der YBa2Cu3O7[-delta]-Schicht spielt eine Hauptrolle, um möglichst hohe Stromdichten zu erreichen. Es zeigte sich, daß die granulare Struktur des Substrates in die YBa2Cu3O7[-delta]-Schicht übertragen wird und zur Ausbildung eines Korngrenzennetzwerkes führt, welches wiederum die zu erwartende kritische Stromdichte begrenzt. Um die Wirkung des Korngrenzennetzwerkes zu untersuchen, wurden kritische Ströme der gewachsenen Schichten in Abhängigkeit der Temperatur und des angelegten Magnetfeldes gemessen. Es stellte sich heraus, daß die Limitierung des Stroms bei schwachen Magnetfeldern zwischen den einzelnen Körnern bestimmend ist, die dann bei größeren Feldern einer Strombegrenzung innerhalb der Körner weicht. Das beide Bereiche trennende Magnetfeld wird als Übergangsfeld bezeichnet. Daraus kann geschlußfolgert werden, daß das Korngrenzennetzwerk von YBa2Cu3O7[-delta] Bandleitern den Strom nur für magnetische Felder unterhalb des Übergangsfeldes begrenzt.

In dieser Arbeit wird ein Verfahren entwickelt (Infrared Transition Moment Orientational Analysis, IR-TMOA) um die dreidimensionale Ordnung auf molekularer Ebene in infrarot-durchlässigen Systemen zu quantifizieren. Es beruht auf der Messung zahlreicher Infrarotspektren, die unter systematisch variierender Polarisation des einfallenden Lichts und Ausrichtung der Probe relativ zur optischen Achse aufgenommen werden. So wird ein repräsentativer Ausschnitt des dreidimensionalen Absorptionsellipsoids gemessen. Die Tensordarstellung dieses Ellipsoids ist äquivalent zum quadratischen Mittel der Verteilungsfunktion der Orientierung der Übergangsmomente, was wiederum dem Ordnungsparameter entspricht. Von zentraler Bedeutung ist ebenfalls, dass die Ordnung (und Orientierung) spezifisch für verschiedene molekulare Untereinheiten angegeben werden kann, da im mittleren Infrarot die Übergangsdipolmomente definierten, lokalen Schwingungen zugeordnet sind. Im zweiten Teil der Arbeit wird IR-TMOA angewendet um die molekulare Ordnung von verschiedenen amorphen und kristallinen Untereinheiten in teil-kristallinen Polymeren (Polycaprolacton, PCL und Polyethylen, PE) zu bestimmen. So kann der Einfluss der Grenzflächen und der geometrischen Einschränkungen in PCL-Filmen auf Substraten in seiner Temperaturabhängigkeit charakterisiert werden. Ebenso wird erstmalig in freitragenden PCL-Filmen in durch mechanische Streckung plastisch deformierten Bereichen die stark biaxiale molekulare Ordnung quantifiziert. In industriell produzierten PE-Filmen, die unter dem Einfluss von äußerer mechanischer Spannung kristallisieren, wird die biaxiale Ordnung und Orientierung vollständig charakterisiert und in Abhängigkeit der Präparationsbedingungen analysiert. Des weiteren wird die Ordnung in einem System aus zwei Phasen untersucht: einer ferroelektrischen Polymermatrix mit mikrometer-großen Flüssigkristalleinschlüssen (Polymer Dispersed Liquid Crystals). Dies erlaubt es, den Einfluss eines äußeren elektrischen Feldes und des remanenten Feldes der Matrix auf die Flüssigkristalle zu quantifizieren. Durch IR-TMOA wird für alle Systeme, die infrarot aktive Vibrationen aufweisen, eine dreidimensionale molekulare Beschreibung der Orientierung und Ordnung ermöglicht. Dies stellt wiederum einen unverzichtbaren Beitrag zum Verständnis der unterliegenden strukturbildenden Prozesse dar und deren Beitrag zur resultierenden makroskopischen Struktur.

Zu Beginn des Forschungsvorhabens wurden im Rahmen der Teilprojekte B1 und B2 des SFB 532 alkalibeständige Glas- und Carbonrovings eingesetzt, die zu offenmaschigen 2D-Textilien verarbeitet wurden. Untersuchungen des Verbund- und des Tragverhaltens der Verstärkungsstrukturen in Pull-Out- und Dehnkörperversuchen haben gezeigt, dass das Potential der Verstärkungsfasern aufgrund einer unvollständiger Durchtränkung der Bewehrung nicht vollständig ausgeschöpft werden kann. Auch Defizite bei der Produktionstechnik wurden erkannt und für zukünftige Entwicklungen analysiert. Um das Potential der verwendeten Verstärkungsfaser vollständiger auszuschöpfen, wurden innovative Garnkonstruktionen, die sich positiv auf den inneren und/oder den äußeren Verbund auswirken, entwickelt und erprobt. Anhand von Versuchsreihen auf der Textilebene wurden unterschiedliche Textilparameter, wie Art der Bindung, Gittergröße und Wirkfadenspannung, identifiziert, die unmittelbar die Tragfähigkeit der Verbundbauteile beeinflussen. Für die gängigen Produktionstechniken Laminieren, Gießen, Spritzen, Schleudern und Extrudieren wurden entsprechende Bewehrungskonstruktionen abgeleitet, die den Anforderungen des jeweiligen Prozess angepasst wurden. Ein weiterer Punkt der Forschungsaktivitäten stellte die Entwicklung der Maschinentechnik zur Herstellung von Verstärkungstextilien dar. Am Institut für Textiltechnik (ITA) der RWTH Aachen University wurde in Zusammenarbeit mit Industriepartnern ein Maschinenkonzept entwickelt und umgesetzt, das die Herstellung von 3D-Abstandsgewirken mit einer freien Gestaltung der Deckflächen mit marktrelevanten Produktionsgeschwindigkeiten ermöglicht. Zur gezielten Einstellung der Wirkfadenspannung wurde ein Regelungssystem konzipiert und technisch umgesetzt, mit dem eine reproduzierbare Fertigung von textilen Verstärkungsstrukturen möglich wird.

Zur Bemessung und Simulation von flächigen Textilbetonstrukturen werden Berechnungsmodelle benötigt, die das Materialverhalten unter biaxialer Beanspruchung abbilden können. Für eindimensionale Strukturen existieren einige Modelle, zu deren Weiterentwicklung eine Erweiterung zur Abbildung des biaxialen Materialverhaltens vorgeschlagen wird. In diesem Beitrag werden die notwendigen Erweiterungen und deren Umsetzbarkeit bei der Modellierung diskutiert und bewertet. / For design and simulation of plane textile reinforced concrete structures mechanical models representing the material behaviour under biaxial loading are necessary. For one-dimensional structures several models were presented in the past. For their further development an extension for biaxial material behaviour is usually proposed. In this paper the required extensions are discussed and their feasibility for modelling is assessed.

A determinação das propriedades mecânicas em materiais hiperelásticos constitui uma atividade complexa, a qual requer a realização de ensaios mecânicos em laboratório, seleção de modelos matemáticos adequados a cada tipo de comportamento e ajuste de curva sobre os dados experimentais. O ensaio biaxial por inflação se caracteriza pela inflação de uma membrana fina após a aplicação de uma pressão uniforme agindo na direção normal a superfície e tem sido utilizado para obter a curva tensão versus deformação. O objetivo do presente trabalho é estudá-lo como um teste para a caracterização mecânicas de borrachas incompressíveis. É proposta uma metodologia e aspectos como a aplicabilidade da teoria de cascas finas, geometria esférica no topo da amostra, instabilidade e processo de deformação são investigados. Um código computacional foi desenvolvido para identificação de parâmetros da amostra deformada através de aquisição de imagem. A validação da metodologia foi realizada tanto através de análises numéricas por elementos finitos como através de ensaios experimentais realizados em laboratório. Um novo método analítico para a determincação da deformação no topo membrana inflada (ou bolha) foi proposto e testado. / The determination of mechanical properties of hyperelastic materials is a complex activity, which requires mechanical laboratory tests to obtain the stress-strain curve, selection of the appropriate mathematical model and curve fitting of the experimental data. The biaxial inflation test is characterized by the inflation of a thin membrane by applying uniform pressure acting on the normal direction of the surface. The purpose of this paper is to study it as a test for characterization of incompressible rubberlike materials. A methodology is proposed and aspects such as the applicability of the theory of thin shell, spherical geometry on top of the sample, instability and kinematic deformation process are investigated. A computer code was developed for identification of parameters of the deformed specimen by image acquisition. The validation of the methodology was carried out through both numerical analysis by finite elements and through experimental testing performed in laboratory. A new analytic method to determine the deformation of the apex of the inflated membrane (or bubble) is proposed and tested.