La thèse est consacrée à l'étude d'un analogue du problème de Riemann-Hilbert et de déformations isomonodromiques pour les solutions de l'équation de Dirac sur le cylindre. L'objectif est de faire un lien entre la théorie de déformation et les fonctions de corrélation dans certains modèles intégrables en théorie quantique des champs dans le volume fini. Dans une première partie, nous étudions des solutions multivaluées de l'équation de Dirac, qui réalisent une représentation unitaire de dimension 1 du groupe fondamental du cylindre avec n points marqués. Nous introduisons et étudions la base canonique des solutions, la fonction de Green et la fonction tau de l'opérateur de Dirac singulier. Dans une seconde partie, nous obtenons, de deux facons différentes, les équations différentielles nonlinéaires satisfaites par les fonctions de corrélation du modéle d'Ising sur le cylindre.

Le but de ces travaux est de proposer une contribution au recalage d'images TDM-TEP dans les régions thoraciques et abdominales. Notre méthodologie est fondée sur l'introduction de contraintes anatomiques au recalage non linéaire appliqué sur les intensités. Cette introduction est faite d'une manière explicite, en divisant la procédure en une phase d'initialisation recalant les structures segmentées dans les deux images, et une deuxième phase de recalage à niveaux de gris, raffinant l'étape précédente de l'algorithme. Les transformations sont modélisées dans les deux étapes à partir de Free Form Deformations (FFD). La segmentation est réalisée selon une procédure hiérarchique de reconnaissance de formes. La mesure fournie par le protocole d'évaluation que nous avons développé indique une erreur inférieure à 1cm pour les structures les plus significatives (poumons, foie, reins, coeur), sauf pour le stomach (erreur d'1.5cm).

Nous nous sommes intéresses a la restauration de la symétrie de réflexion droite-gauche brisée dans certains calculs effectues en utilisant l'approche HTDA (Higher Tamm-Danco Approximation). Cette approche a été proposée par le groupe de Bordeaux pour traiter de façon microscopique les corrélations en conservant explicitement les nombres de nucléons. La projection sur la parité par la méthode PAV (projection après variation) utilisant une généralisation du théorème de Wick de type Lowdin s'est avérée être très bien adaptée dans le cadre d'un modèle simple pour ce type de calcul et a permis de tourner certaines difficultés propres aux calculs qui utilisent la théorie de la fonctionnelle de la densité déduite par exemple de l'interaction de Skyrme. Les résultats obtenus pour des noyaux lourds manifestant une déformation octupôlaire ou a tout le moins une grande déformation pour ce mode, sont en gros tout a fait cohérents avec les calculs antérieurs effectues dans une approche HFB ou HF+BCS. D'autre part nos résultats montrent qu'on peut abaisser par projection sur la parité positive la hauteur de la seconde barrière de fission par une quantité de l'ordre de 1 MeV.

Sheet metal forming is used in a wide range of industrial processes ranging from tube manufacturing to automobile and aviation industry. It includes processes like stamping, bending, stretching, drawing and wheeling. In the past few years materials for sheet metal forming and, technology have improved a lot. The improved materials have higher strength and more ductility than conventional sheet steel and therefore they have to be worked differently. For such steels conventional methods can not be applied totally. So there is a need for constant improvement in technology. Trial and error method currently in use increases lead time and is not economic also. To overcome the problems, use of simulation software in metal forming processes has increased significantly. The rapid development of software technology accompanied with lower cost computer hardware have enabled many manufacturing operations to be modeled cost-effectively that only a few years ago would have been considered impractical. However there are some difficulties in simulation of sheet metal forming process. For example it is never an easy task to select the correct software for a particular process. Various authors ascribe different causes for the difficulties. Among them the prominent ones are lacunae in elasto-plastic modeling, material behaviour, involved complexities and a lack of good elements. Apart from that the demands of sheet metal processes are increasing both with respect to the tolerance requirements of the finished part and with regard to geometric complexity of the part to be formed. A few years ago finite elements have been developed using Papcovitch-Neuber solutions of the Navier equation for the displacement function. Among these elements PN5X1 has the abilities to predict both displacements and stresses accurately. And recently the element is extended to include material nonlinearity and is working well for the small deformation range. To use this element for sheet metal forming it is necessary that the element should predict correct results for large deformations. In the present work we have further extended this element for large displacements and large rotation. In the literature there are various algorithms recommended for use with large deformation. Among them we have selected a suitable algorithm and verified its usefulness. First we have taken a simple truss and applied loads to cause large deflection. We observe adequate convergence with the chosen algorithm and then we extend it to PN5X1. in large deformation analysis, equilibrium is computed about the deformed shape. In the chosen algorithm we apply incremental loading and within each load step loop we iterate for equilibrium. We ensure error free solution (equilibrium) before additional loading is introduced. With the help of flowchart these processes have been depicted. A computer program in C, based on the above incremental method and equilibrium check has been written. For the purpose of verification of the program, we have solved some benchmark tests. We start with linear cases and then attempt a number of geometric nonlinear problems like- cantilever subjected to end shear, pinched cylinder with open end etc. We have also included the classical benchmark problem of the cantilever subjected to end moment. The present algorithm gives solutions which are in excellent agreement with those reported in the literature. Finally, we look at some aspects of the problem which require further investigation.

Crystallographic texture in polycrystalline materials are known to play an important role in tailoring suitable properties for various technological applications. In addition, the evolution of texture provides a profound basis to develop scientific understanding of physical processes occurring in the material during deformation and annealing. Between the two, the understanding of deformation texture is much broader. However, certain issues pertaining to the evolution of deformation texture evolution are yet to be explored or not uniquely agreed upon. A few notable examples are the effects of extreme grain sizes and strain rates. Moreover, most of the studies are pertaining to single phase metals and alloys. While many engineering alloys consist of two phase microstructures, the effect of second phase in the microstructure on the evolution of texture in the individual phases has not been studied in a comprehensive manner. The present thesis is an attempt to addresses these issues in a more generic manner. The studies have been specifically aimed at examining the aforesaid issues in the close packed Face Centre Cubic (FCC) and Hexagonal Close Packed (HCP) metals and alloys. In brief, this thesis addresses the following problems pertaining to deformation texture: (i) the effect of extreme grain sizes, (ii) the effect of extreme strain rates and (iii) the effect of a second ductile phase. Chapter 1 of the thesis gives a detailed survey of literature pertaining to the evolution of deformation textures in different metals and alloys, while chapter 2 includes the details of the experimental techniques and simulation procedures, which are mostly common for the entire work. The issue of grain size is addressed in chapter 3. In the present investigation, the evolution of deformation texture in nickel (FCC) and titanium (HCP) with the extreme grain sizes (nanometre and millimetre) has been studied. Nanocrystalline nickel with the grain size ~ 20 nm was obtained by pulse electro-deposition while the other extreme of the grain size in nickel was obtained by annealing of a cold rolled sheet at 1373 K. The rolling texture in nanocrystalline nickel had a higher volume fraction of Brass component than in nickel with normal grain size. These results have been explained on the basis of inhibition of cross slip in small grain sizes and the operation of planar slip. This has been validated by viscoplastic self-consistent simulations. The texture of coarse grain nickel samples (typified as oligocrystalline, owing to the lesser number of grains in the thickness direction) also had higher Brass component like the nanocrystalline sample. A detailed analysis was performed by examining misorientation development in the grain interior and in the vicinity of the grain boundaries. The similarity at the two extreme length scales has been explained on the basis of lower “Grain Boundary Affected Zone” at the extreme length scales. To examine the effect of grain size in the case of HCP materials, commercially pure titanium with ultra-fine (500 nm) and normal grain size (~50 μm), was investigated. A monotonic evolution of texture was observed in the former, which has been attributed to the absence of twinning, a situation that could arise due to the lack of coordinated movement of twinning partials in the sub-micron grain size regime. Thus, a reasonable understanding of the evolution of deformation texture in hitherto unexplored regime of grain sizes was developed for the two materials. The chapter 4 of the thesis is dedicated to the study of strain rate effects in both FCC and HCP materials. The issue of strain rate has been addressed by two ways: (a) deforming the materials at extreme strain rates, namely 10-3 s-1 to 10+3 s-1 under compression up to a reasonable strain, and (b) deforming the materials under torsion within a reasonable range of strain rates, but up to large strains. In this case, in addition to nickel, copper was also investigated owing to the different strain hardening behaviour of the two materials. The compression texture in nickel and copper was characterized by the presence of <101> component at low strain rates. At high strain rate, ~10+3 s-1, there was a decrease in the intensity of the <101> component for nickel but it strengthened for copper. This has been explained on the basis of continuous dynamic recrystallization in copper. The torsion texture evolution in nickel and copper was similar at low strain rate (10-3 s-1) and was characterized by the presence of important shear texture components. At high strain rate (1 s-1), texture weakened for nickel, while for copper a rotated cube component was observed which has been attributed to dynamic recrystallization. The effect of strain rate was studied more comprehensively in hexagonal titanium by adding one more variable, that is, the initial texture. Extreme strain rates were imparted using static and dynamic compression tests. It was found that different initial textures led to different mechanical response in terms of yield strength and strain hardening as well as microstructural response in terms of twin fractions. The samples deformed at high strain rate showed increased twinning that led to some scatter in the texture components compared to low strain rate deformed samples. VPSC simulations were able to successfully capture the evolution of texture as well as microstructural evolution in terms of twin activity in the deformed samples at the extreme strain rates. Torsion tests on titanium at different strain rates indicated evolution of inhomogeneous nature of fibre texture components with increase in strain rate. Thus, weakening of texture was observed irrespective of the strain path (compression or torsion) and crystal structure (FCC or HCP) unless additional restoration mechanism like recrystallization (continuous or discontinuous) intervened. In chapter 5, the evolution of rolling texture in two phase FCC + BCC (Ni-Fe-Cr alloys) and HCP + BCC (Ti-13Nb-13Zr ) alloys has been studied. This study was aimed at examining the effect of second deforming phase on the texture evolution in the primary phase. The effect of various parameters like volume fraction and morphology of the second phase on deformation texture evolution was studied experimentally as well as by VPSC simulations. A reduction in the Brass component of texture was observed in the austenite phase due to the presence of harder ferrite phase while a characteristic rolling texture evolved in the ferrite phase. It has been established that the softer austenite phase carried maximum strain at low volume fractions of ferrite while the harder ferrite phase carried the maximum strain at higher volume fractions of ferrite. In case of the two phase HCP+BCC alloy Ti-13Nb-13Zr, both the hexagonal α and the cubic β phases showed a characteristic rolling texture irrespective of two different morphologies. For both the equiaxed and colony microstructures, the softer β phase carried the maximum strain. VPSC simulations were able to model the deformation texture evolution as well as microstructural parameters like strain partitioning and twin fraction satisfactorily for both the microstructural conditions. It was found that the deformation mechanism in one phase could be affected by the presence of the second phase and that a characteristic change in deformation texture could be produced in the presence of the second phase. Thus, a comprehensive perspective has been developed pertaining to the evolution of texture in FCC and HCP phases in the presence of a second ductile phase. The overall findings of the three investigations carried out for the thesis are summarised in chapter 6.

Carbon nanotube (CNT) forests are an important class of nanomaterials with many potential applications due to their unique properties such as mechanical compliance, thermal and electrical conductance, etc. Their deformation and failure in compression loading is critical in any application involving contact because the deformation changes the nature of the contact and thus impacts the transfer of load, heat, and charge carriers across the interface. The micro- and nano-structure of the CNT forest can vary along their height and from sample to sample due to different growth parameters. The morphology of CNTs and their interaction contribute to their mechanical behavior with change of load distribution in the CNT forest. However, the relationship is complicated due to involvement of many factors such as density, orientation, and entanglement of CNTs. None of these effects, however, are well understood. This dissertation aims to advance the knowledge of the structure-property relation in CNT forests and find methodologies for tuning their mechanical behavior. The mechanical behavior of CNT forests grown with different methodologies is studied. Furthermore, the effects of coating and wetting of CNT forests are investigated as methods to tailor the degree of interaction between CNTs. In situ micro-indentation of uncoated CNT forests with distinct growth-induced structures are performed to elucidate the effects of change of morphology along the height of CNT forests on their deformation mechanism. CNT aerial density and tortuosity are found to dictate the location of incipient deformation along height of CNT forests. Macro-compression testing of uncoated CNT forests reveals mechanical failure of CNT forests by delamination at the CNT-growth substrate. Tensile loading of CNT roots due to post-buckling bending of CNTs is proposed to be the cause of this failure and simple bending theory is shown to estimate the failure load to be on the same order of magnitude as experimental measurements. Furthermore, delamination is observed to occur in the in situ micro-indentation of CNT forests coated with aluminum on the top surface, which demonstrates the role of the mechanical constraints within the CNT forest in the occurrence of delamination at the CNT-substrate interface. In addition, this dissertation explores the mechanical behavior of CNT forests coated conformally (from top to bottom) with alumina by atomic layer deposition. In situ micro-indentation testing demonstrates that the deformation mechanism of CNT forests does not change with a thin coating (2 nm) but does change with a sufficiently thick coating (10 nm) that causes fracturing of the hybrid nanotubes. Ex situ flat punch and Berkovich indentations reveal an increase in stiffness of the CNT forests that are in range with those predicted by compression and bending theories. An increase in the recoverability of the CNTs is also detected. Finally, solvent infiltration is proposed as a method of decreasing stiffness of CNT forests and changing the deformation mechanism from local to global deformations (i.e., buckling in the entire height). Presence of solvents between CNTs decreases the van der Waals forces between them and produces CNT forests with lower stiffness. The results demonstrate the effect of interaction between CNTs on the mechanical behavior. This dissertation reveals important information on the mechanical behavior of CNT forests as it relates to CNT morphology and tube-to-tube interactions. In addition, it provides a framework for future systematic experimental and theoretical investigations of the structure-property relationship in CNT forests, as well as a framework for tuning the properties of CNT forests for diverse applications.

The mechanical and physical properties of polymers are determined primarily by the underlying nano-scale structures and characteristics such as entanglements, crystallites, and molecular orientation. These structures evolve in complex manners during the processing of polymers into useful articles. Limitations of available and foreseeable computational capabilities prevent the direct determination of macroscopic properties directly from atomistic computations. As a result, computational tools and methods to bridge the length and time scale gaps between atomistic and continuum models are required. In this research, an internal state variable continuum model has been developed whose internal state variables (ISVs) and evolution equations are related to the nano-scale structures. Specifically, the ISVs represent entanglement number density, crystal number density, percent crystallinity, and crystalline and amorphous orientation distributions. Atomistic models and methods have been developed to investigate these structures, particularly the evolution of entanglements during thermo-mechanical deformations. A new method has been created to generate atomistic initial conformations of the polymer systems to be studied. The use of the hyperdynamics method to accelerate molecular dynamics simulations was found to not be able to investigate processes orders of magnitude slower that are typically measurable with traditional molecular dynamics simulations of polymer systems. Molecular dynamics simulations were performed on these polymer systems to determine the evolution of entanglements during uniaxial deformation at various strain rates, temperatures, and molecular weights. Two methods were evaluated. In the first method, the forces between bonded atoms along the backbone are used to qualitatively determine entanglement density. The second method utilizes rubber elasticity theory to quantitatively determine entanglement evolution. The results of the second method are used to gain a clearer understanding of the mechanisms involved to enhance the physical basis of the evolution equations in the continuum model and to derive the models material parameters. The end result is a continuum model that incorporates the atomistic structure and behavior of the polymer and accurately represents experimental evidence of mechanical behavior and the evolution of crystallinity and orientation.

Determination of the relation between the bulk or rheological properties of a particle suspension and its microscopic structure is an old and important problem in physical science. In general, the rheology of particle suspension is quite complex, and the problem becomes even more complicated if the suspending particle is deformable. Despite these difficulties, a large number of theoretical and experimental investigations have been devoted to the analysis and prediction of the rheological behavior of particle suspensions. However, among these studies there are very few investigations that focus on the role of particle deformability. A novel method for full coupling of the fluid-solid phases with sub-grid accuracy for the solid phase is developed. In this method, the flow is computed on a fixed regular 'lattice' using the lattice Boltzmann method (LBM), where each solid particle, or fiber, is mapped onto a Lagrangian frame moving continuously through the domain. The motion and orientation of the particle are obtained from Newtonian dynamics equations. The deformable particle is modeled by the lattice-spring model (LSM).The fiber deformation is calculated by an efficient flexible fiber model. The no-slip boundary condition at the fluid-solid interface is based on the external boundary force (EBF) method. This method is validated by comparing with known experimental and theoretical results. The fiber simulation results show that the rheological properties of flexible fiber suspension are highly dependent on the microstructural characteristics of the suspension. It is shown that fiber stiffness (bending ratio BR) has strong impact on the suspension rheology in the range BR < 3. The relative viscosity of the fiber suspension under shear increases significantly as BR decreases. Direct numerical simulation of flexible fiber suspension allows computation of the primary normal stress difference as a function of BR. These results show that the primary normal stress difference has a minimum value at BR ∼ 1. The primary normal stress differences for slightly deformable fibers reaches a minimum and increases significantly as BR decreases below 1. The results are explained based on the Batchelor's relation for non-Brownian suspensions. The influence of fiber stiffness on the fiber orientation distribution and orbit constant is the major contributor to the variation in rheological properties. A least-squares curve-fitting relation for the relative viscosity is obtained for flexible fiber suspension. This relation can be used to predict the relative viscosity of flexible fiber suspension based on the result of rigid fiber suspension. The unique capability of the LBM-EBF method for sub-grid resolution and multiscale analysis of particle suspension is applied to the challenging problem of platelet motion in blood flow. By computing the stress distribution over the platelet, the "blood damage index" is computed and compared with experiments in channels with various geometries [43]. In platelet simulation, the effect of 3D channel geometry on the platelet activation and aggregation is modeled by using LBM-EBF method. Comparison of our simulations with Fallon's experiments [43] shows a similar pattern, and shows that Dumont's BDI model [40] is more appropriate for blood damage investigation. It has been shown that channels with sharp transition geometry will have larger recirculation areas with high BDI values. By investigating the effect of hinge area geometry on BDI value, we intend to use this multiscale computational method to optimize the design of Bileaflet mechanical heart valves. Both fiber simulations and platelet simulations have shown that the novel LBM-EBF method is more efficient and stable compare to the conventional numerical methods. The new EBF method is a two-Cway coupling method with sub-grid accuracy which makes the platelet simulations possible. The LBM-EBF is the only method to date, to the best of author's knowledge, that can simulate suspensions with large number of deformable particles under complex flow conditions. It is hoped that future researchers may benefit from this new method and the algorithms developed here.

Existing numerical techniques for modeling saturated deformable porous media are based on homogenization techniques and thus are incapable of performing micro-mechanical investigations, such as the effect of micro-structure on the deformational characteristics of the media. In this research work, a numerical scheme is developed based on the parallelized hybrid lattice-Boltzmann finite-element method, that is capable of performing micro-mechanical investigations through direct numerical simulations. The method has been used to simulate compression of model saturated porous media made of spheres and cylinders in regular arrangements. Through these simulations it is found that in the limit of small Reynolds number, Capillary number and strain, the deformational behaviour of a real porous media can be recovered through model porous media when the parameters porosity, permeability and bulk compressive modulus are matched between the two media. This finding motivated research in using model porous geometries to represent more complex real porous geometries in order to perform investigations of deformation on the latter. An attempt has been made to apply this technique to the complex geometries of ªfeltº, (a fibrous mat used in paper industries). These investigations lead to new understanding on the effect of fiber diameter on the bulk properties of a fibrous media and subsequently on the deformational behaviour of the media. Further the method has been used to investigate the constitutive relationships in deformable porous media. Particularly the relationship between permeability and porosity during the deformation of the media is investigated. Results show the need of geometry specific investigations.

The load-carrying and energy-dissipation capacities of ultra-high-performance concrete (UHPC) under dynamic loading are evaluated in relation to microstructure composition at strain rates on the order of 10⁵ s⁻¹ and pressures of up to 10 GPa. Analysis focuses on deformation and failure mechanisms at the mesostructural level. A cohesive finite element framework that allows explicit account of constituent phases, interfaces, and fracture is used. The model resolves essential deformation and failure mechanisms in addition to providing a phenomenological account of the effects of the phase transformation. Four modes of energy dissipation are tracked, including pressure-sensitive inelastic deformation, damage through the development of distributed cracks, interfacial friction, and energy released through phase transformation of the quartz silica constituent. Simulations are carried out over a range of volume fractions of constituent phases to quantify trends that can be used to design materials for more damage-resistant structures. Calculations show that the volume fractions of the constituents have more influence on the energy-dissipation capacity than on the load-carrying capacity, that inelastic deformation is the source of over 70% of the energy dissipation, and that the presence of porosity changes the role of fibers in the dissipation process. The results also show that the phase transformation has a significant effect on the load-carrying and energy-dissipation capacities of UHPC for the conditions studied. Although transformation accounts for less than 2% of the total energy dissipation, the phase transformation leads to a twofold increase in the crack density and yields nearly an 18% increase to the overall energy dissipation. Microstructure-behavior relations are established to facilitate materials design and tailoring for target-specific applications.