Dans de nombreux domaines industriels et scientifiques, en particulier dans les domaines du génie civil et de génie mécanique, des matériaux à l’échelle de la microstructure, un très hétérogène par rapport à la nature du comportement mécanique. Cette fonctionnalité peut faire la prédiction du comportement de la structure soumise à différents types de chargement, nécessaires pour la conception durable, assez difficile. Le contrôle du comportement des ouvrages de génie civil est très complexe en raison de la diversité de la charge à laquelle ils sont soumis. La construction est maintenant réglementée partout dans le monde: les normes sont plus strictes et pris en compte, jusqu’à un état limite, en raison de différentes charges, par exemple des charges sévères tels que l’impact ou tremblement de terre. Modèles de comportement des matériaux et des structures doivent inclure l’élaboration de ces critères de conception et deviennent plus complexe. Ces modèles sont souvent basées sur des approches phénoménologiques, sont capables de reproduire la réponse du matériau au niveau ultime. Réponses de contrainte-déformation des matériaux sous sollicitations cycliques, dont de nombreuses recherches ont été exécutées dans les années précédentes afin de caractériser et le modèle, sont définies par différents types de propriétés de plasticité cycliques tels que l’écrouissageue, l’effet rochet et de de relaxation. En utilisant les modèles de comportement existants, ces réponses mentionnées peuvent être simulés d’une manière raisonnable. Cependant, il peut y avoir échec dans certains simulation des réponses structurelles et la déformation locale et globale. Insuffisance de ces études peut être résolu par le développement de solides modèles de comportement à l’aide d’expériences et de la connaissance des principes de fonctionnement des différents mécanismes de comportement inélastique ensemble. Dans ce travail, nous présentons un modèle phénoménologique constitutive qui est capable de coupler deux principaux mécanismes de comportement inélastique, plasticité et endommagement. Le modèle vise les applications de chargement cycliques. Ainsi, dans une partie de plasticité ou de dommages, les effets de durcissement isotropes et linéaires cinématiques à la fois sont pris en compte. Le principal avantage de ce modèle est l’utilisation de la plasticité indépendante contre les critères de l’endommagement pour décrire les mécanismes inélastiques. Un autre avantage concerne la mise en oeuvre numérique d’un tel modèle fourni en hybride-stress variationnel, obtenu avec une précision très améliorée et calcul efficace du stress et des variables internes dans chaque élément. Plusieurs exemples sont présentés afin de confirmer l’exactitude et l’efficacité de la formulation proposée en application à un chargement cyclique. / In many industrial and scientific domains, especially in civil engineering and mechanical engineering fields, materials that can be used on the microstructure scale, are highly heterogeneous by comparison to the nature of mechanical behavior. This feature can make the prediction of the behavior of the structure subjected to various loading types, necessary for sustainable design, difficult enough. The construction of civil engineering structures is regulated all over the world: the standards are more stringent and taken into account, up to a limit state, due to different loadings, for example severe loadings such as impact or earthquake. Behavior models of materials and structures must include the development of these design criteria and thereby become more complex, highly nonlinear. These models are often based on phenomenological approaches, are capable of reproducing the material response to the ultimate level. Stress-strain responses of materials under cyclic loading, for which many researches have been executed in the previous years in order to characterize and model, are defined by different kind of cyclic plasticity properties such as cyclic hardening, ratcheting and relaxation. By using the existing constitutive models, these mentioned responses can be simulated in a reasonable way. However, there may be failure in some simulation for the structural responses and local and global deformation. Inadequacy of these studies can be solved by developing strong constitutive models with the help of the experiments and the knowledge of the principles of working of different inelastic behavior mechanisms together. This dissertation develops a phenomenological constitutive model which is capable of coupling two basic inelastic behavior mechanisms, plasticity and damage by studying the cyclic inelastic features. In either plasticity or damage part, both isotropic and linear kinematic hardening effects are taken into account. The main advantage of the model is the use of independent plasticity versus damage criteria for describing the inelastic mechanisms. Another advantage concerns the numerical implementation of such model provided in hybrid-stress variational framework, resulting with much enhanced accuracy and efficient computation of stress and internal variables in each element. The model is assessed by simulating hysteresis loop shape, cyclic hardening, cyclic relaxation, and finally a series of ratcheting responses under uniaxial loading responses. Overall, this dissertation demonstrates a methodical and systematic development of a constitutive model for simulating a broad set of cycle responses. Several illustrative examples are presented in order to confirm the accuracy and efficiency of the proposed formulation in application to cyclic loading.

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Thin-walled structures are major components in many engineering applications. When a thin-walled slender beam is subjected to lateral loads, causing moments, the beam may buckle by a combined lateral bending and twisting of cross-section, which is called lateral-torsional buckling. A generalized analytical approach for lateral-torsional buckling of anisotropic laminated, thin-walled, rectangular cross-section composite beams under various loading conditions (namely, pure bending and concentrated load) and boundary conditions (namely, simply supported and cantilever) was developed using the classical laminated plate theory (CLPT), with all considered assumptions, as a basis for the constitutive equations. Buckling of such type of members has not been addressed in the literature. Closed form buckling expressions were derived in terms of the lateral, torsional and coupling stiffness coefficients of the overall composite. These coefficients were obtained through dimensional reduction by static condensation of the 6x6 constitutive matrix mapped into an effective 2x2 coupled weak axis bending-twisting relationship. The stability of the beam under different geometric and material parameters, like length/height ratio, ply thickness, and ply orientation, was investigated. The analytical formulas were verified against finite element buckling solutions using ABAQUS for different lamination orientations showing excellent accuracy.

Call number: LD2668 .T4 1986 L43 / Master of Science / Civil Engineering

During this thesis work a coupled thermo-mechanical finite element model (FEM) was builtto simulate hot rolling in the blooming mill at Sandvik Materials Technology (SMT) inSandviken. The blooming mill is the first in a long line of processes that continuously or ingotcast ingots are subjected to before becoming finished products. The aim of this thesis work was twofold. The first was to create a parameterized finiteelement (FE) model of the blooming mill. The commercial FE software package MSCMarc/Mentat was used to create this model and the programing language Python was used toparameterize it. Second, two different pass schedules (A and B) were studied and comparedusing the model. The two pass series were evaluated with focus on their ability to healcentreline porosity, i.e. to close voids in the centre of the ingot. This evaluation was made by studying the hydrostatic stress (σm), the von Mises stress (σeq)and the plastic strain (εp) in the centre of the ingot. From these parameters the stress triaxiality(Tx) and the hydrostatic integration parameter (Gm) were calculated for each pass in bothseries using two different transportation times (30 and 150 s) from the furnace. The relationbetween Gm and an analytical parameter (Δ) was also studied. This parameter is the ratiobetween the mean height of the ingot and the contact length between the rolls and the ingot,which is useful as a rule of thumb to determine the homogeneity or penetration of strain for aspecific pass. The pass series designed with fewer passes (B), many with greater reduction, was shown toachieve better void closure theoretically. It was also shown that a temperature gradient, whichis the result of a longer holding time between the furnace and the blooming mill leads toimproved void closure.

Preterm birth (PTB) is the leading cause of childhood death and effects 10% of babies worldwide. First-time diagnosis is difficult, and as many as 95% of all PTBs are intractable to current therapies. The processes of both preterm labor and normal parturition are poorly understood, in part because pregnancy is a protected environment where experimentation contains the risk of causing harm to the gestation and fetus. This proposes the need for non-invasive investigations to understand both normal and high-risk pregnancies. Furthermore, each pregnancy can vary significantly which adds the complex need for patient-specific investigations. To address this need, we propose the development of parameterized ultrasound-based finite element analyses to study the mechanics of the womb. As a first step, this dissertation work conducts sensitivity analyses on cervical, uterine, and fetal membrane parameters as well as model boundary conditions to determine which factors have the greatest impact on cervical tissue stretch. The effects of the range of patient geometries and material properties are reported. Findings show that a soft and short cervix result in greatest stretch at the internal os, and fetal membrane detachment increases cervical stretch. Additionally, patient-specific finite element analyses are performed on low- and high-risk cohorts and results between the two are compared. Patient geometries are documented at various gestational timepoints, and the effect of a cervical pessary is determined based on changes in cervical geometry and stiffness. Findings showed that a soft cervix correlates with sooner delivery, and that high pessary placement is ideal to decrease stretch at the internal os.

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2017 / The scientific requirements for Radio Frequency (RF) receivers especially for Radio Astronomy have become more demanding, requiring: compact, low-profile, multi and wideband antennas and more sensitive receivers. Integration of the antenna into the receiver system is often critical to meet these demands. Noise theory to model these more complex systems is well developed but is not implemented in commercial solvers, given the niche market of the receivers it is only available using specialised software. If the system is closely coupled, it becomes necessary for design to incorporate Electromagnetic (EM) and Microwave (MW) modelling into the multi port noise modelling. CAESAR, a combined noise and EM/MW modelling code is available, but to use it requires the exclusive use of the CAESAR software, which is impractical given the utility and wide use of commercial solvers. Mathematical methods are developed to incorporate commercial solvers into the more specialised CAESAR, validated using a folded dipole and applied to a wideband Eleven antenna system, a compact form of a log periodic dipole array. The Eleven antenna consist of eight single ended or four differential ports, with a closely coupled feeding arrangement. Cryogenic measurements are done to verify the modelling, the measured sensitivity matches with the model closely in amplitude and shape, giving confidence to the approach, and allowing modelling but not system optimisation. Optimising the antenna based on receiver design and still being able to use commercial code requires the external scripting of a commercial solver. The EDITFEKO (card based) module of FEKO (a powerful and versatile solver) is used along with the meshing software GMSH and GNU Octave. Optimisation of system sensitivity is demonstrated on a choke horn fed reflector system at 1420MHz. This optimisation method is applied to a practical application, an octave band system (4:5 GHz to 9 GHz) for the Hartebeesthoek Radio Observatory. The design is split into smaller simulations using waveguide modes and the associated S–parameters, the techniques are presented and checked on a truncated system. Initial design and optimisation are given. The combining of specialised multiport noise modelling design and optimisation within commercial EM/MW solvers allows more sensitive and specialised receivers to be built. Index terms— noise modelling, wideband, multiport, corrugated horn, octave band receiver, EM/MW optimisation / MT2018

Lors du fonctionnement des packages électroniques, ceux ci sont exposés à diverses sollicitations d'ordres thermiques et mécaniques. De même, la combinaison de ces sources de contraintes constitue l'origine de la quasi majorité des défaillances des packages électroniques. Pour s'assurer de la bonne résistance des packages électroniques, les fabricants pratiquent des tests de fiabilité et des analyses de défaillance avant toute commercialisation. Toutefois, les essais expérimentaux, lors de la phase de conception et de l'élaboration des prototypes, s'avèrent contraignants en termes de temps et de ressources matérielles. En revanche, la simulation numérique à l'aide de la méthode des éléments finis constitue une option alternative en termes de temps et de ressources. Les objectifs dévolus aux travaux de recherche visent à élaborer quatre modèles éléments finis en 3D, validés/calibrés par des essais expérimentaux, intégrant les recommandations JEDEC (1) en vue de : - Procéder à la caractérisation thermique et thermomécanique des packages électroniques ; - Et prédire la durée de vie en fatigue thermique des joints de brasures et ce, en lieu et place de la caractérisation expérimentale normalisée. Or, la mise en œuvre des modèles éléments finis présente certains inconvénients liés aux incertitudes au niveau de la géométrie, des propriétés matériaux, les conditions aux limites ou les charges. Ceux ci ont une influence sur le comportement thermique et thermomécanique des systèmes électroniques. D'où la nécessité de formuler le problème en termes probabilistes et ce, dans le but de mener une étude de fiabilité et d’optimisation des packages électroniques. Pour remédier au temps de calcul énorme généré par les méthodes d’analyse de fiabilité classiques, nous avons développé des méthodologies spécifiques à cette problématique, via des méthodes d’approximation basées sur le krigeage avancé,qui nous ont permis de bâtir un modèle de substitution, qui rallie efficacité et précision. Par conséquent, une analyse de fiabilité a été menée avec exactitude et dans un temps extrêmement court, via les méthodes de simulation Monte Carlo et FORM/SORM, couplées avec le modèle de krigeage avancé. Ensuite, l’analyse de fiabilité a été associée dans le processus d’optimisation, en vue d’améliorer la performance et la fiabilité de la conception structurelle des packages électroniques. A la fin, nous avons procédé à l’applicabilité des dites méthodologies d’analyse de fiabilité aux quatre modèles éléments finis ainsi développés. Il résulte que les analyses de fiabilité menées se sont avérées très utiles pour prédire les effets des incertitudes liées aux propriétés matériaux. De même, l’analyse d’optimisation de fiabilité ainsi réalisée nous a permis d’améliorer la performance et la fiabilité de la conception structurelle des packages électroniques. (1) JEDEC (Joint Electron Device Engineering Council) est un organisme de normalisation des semi-conducteurs. / During operation, electronic packages are exposed to various thermal and mechanical solicitations. These solicitations combined are the source for most of electronic package failures. To ensure electronic packages robustness, manufacturers perform reliability testing and failure analysis prior to any commercialization. However, experimental tests, during design phase and prototypes development, are known to be constraining in terms of time and material resources. This research aims to develop four finite element models in 3D, validated/calibrated by experimental tests, integrating JEDEC recommendations to : - Perform electronic packages thermal and thermomechanical characterization ; - Predict the thermal fatigue life of solder joints in place of the standardized experimental characterization.However, implementation of the finite element model has some disadvantages related to uncertainties at the geometry, material properties, boundary conditions or loads. These uncertainties influence thermal and electronic systems thermomechanical behavior. Hence the need to formulate the problem in probabilistic terms, in order to conduct a reliability study and a electronic packages reliability based design optimization.To remedy the enormous computation time generated by classical reliability analysis methods, we developed methodologies specific to this problem, using approximation methods based on advanced kriging, which allowed us to build a substitution model, combining efficiency and precision. Therefore reliability analysis can be performed accurately and in a very short time with Monte Carlo simulation (MCS) and FORM / SORM methods coupled with the advanced model of kriging. Reliability analysis was associated in the optimization process, to improve the performance and electronic packages structural design reliability. In the end, we applied the reliability analysis methodologies to the four finite element models developed. As a result, reliability analysis proved to be very useful in predicting uncertainties effects related to material properties. Similarly, reliability optimization analysis performed out has enabled us to improve the electronic packages structural design performance and reliability. In the end, we applied the reliability analysis methodologies to the four finite element models developed. As a result, reliability analysis proved to be very useful in predicting uncertainties effects related to material properties. Similarly, reliability optimization analysis performed out has enabled us to improve the electronic packages structural design performance and reliability.

Lors d'une transformation de phase à l’état solide d'un acier, l'interaction entre la phase naissante et la phase parente, chacune avec ses propriétés mécaniques propres, génère des contraintes au voisinage de l'interface entre phases. L’accommodation de ces contraintes est réalisée à travers la plastification de la phase parente notamment, celle dont la limite d'élasticité est la plus faible. La transformation se faisant, si une contrainte déviatorique - même faible- est exercée, la plasticité locale sera canalisée dans la direction de la contrainte appliquée et apparaît à l’échelle macroscopique. Cette déformation est appelée plasticité de transformation ou TRIP (TRansformation Induced Plasticity) ; seuls des modèles dédiés peuvent en rendre compte. Cette plasticité peut aussi apparaître sans charge externe durant la transformation, si la phase austénitique a été soumise à un pré-écrouissage juste avant sa transformation. Les modèles de plasticité de transformation actuels ne sont dans ce cas pas toujours à même de reproduire les observations expérimentales. Afin d'identifier les mécanismes responsables de la plasticité issue de transformations diffusives pour différents cas de chargement, une modélisation numérique des conséquences mécaniques de telles transformations est proposée dans ce travail. La résolution, à chaque instant de la transformation, du problème d'interaction mécanique entre phases utilise la méthode des éléments finis. Ceci donne accès à la description locale des champs de contrainte et de déformation dus à cette interaction. Une première approche de la modélisation porte, comme dans la plupart des modèles courants de plasticité de transformation, sur la croissance d'une particule unique de phase naissante interagissant avec la matrice mère. On peut ainsi analyser les hypothèses portées sur les champs mécaniques auxquelles il est fait appel dans les modèles analytiques. Cette approche est ensuite étendue au cas d'un milieu homogène où apparaissent des germes aléatoirement dans le temps et dans l'espace, avec des lois de distribution données. Cette deuxième approche met en évidence l'importance de la densité spatiale de germes et du taux de germination sur les prédictions de TRIP. Elle pose en outre les bases d'une modélisation de transformation diffusive dans un milieu cristallin hétérogène, où les propriétés effectives sont déterminées par moyennation d'ensemble sur des multicristaux. Avec l'une comme l'autre des approches, l'accord qualitatif avec les mesures expérimentales de TRIP est correct, pour le cas classique de chargements constants pendant la transformation comme pour les conséquences d'un pré-écrouissage. / During the solid-solid phase transformation of a steel, the interaction between new phase and parent phase, each having its own properties, leads to accommodation stresses in the vicinity of the interface between phases. Dislocations are thus produced in the parent phase, the one which has the lowest yield stress. If an external loading stress -even small- is exerted during the transformation, dislocations result to a permanent strain at the macroscopic scale, in the direction of the load. This strain is called transformation plasticity or TRIP (TRansformation Induced Plasticity); only dedicated models can predict it. This plasticity may also be observed without any external load during the transformation, if the austenitic phase as been pre-hardened just before the transformation. In this latter case, current transformation plasticity models do not always provide correct predictions as compared to experimental observations. A numerical modelling of the mechanical consequences of diffusive transformations is proposed in this work. It is meant to identify the mechanisms which are responsible for the plasticity induced by such transformations for all cases of loading. The finite elements method is used to solve the problem of the mechanical interaction between phases at any instant of the transformation. This gives access to a local description of the stress and strain fields due to this interaction. In a first approach of the modelling inspired from most current transformation plasticity models, a single growing particle interacting with its mother phase is considered. This allows to analyse the hypothesis on mechanical fields according to which analytical formulations of transformation plasticity can be obtained. This approach has then been extended to the case of a homogeneous medium in which nuclei appear randomly in time and space, with prescribed distribution laws. With this improved approach, the importance of the spatial density of nuclei and of the rate of nucleation on TRIP predictions could be evidenced. Besides, this approach provides the basis of a modelling of diffusive transformation in a crystalline heterogeneous material, where the effective properties are determined by ensemble averaging over multicrystals. With both approaches, a correct qualitative agreement with experimental measures could be obtained, in the classical case of constant load during the transformation as well as concerning the consequences of a pre-hardening.

Adaptive methods in finite element analysis are essential tools in the efficient computation and error control of problems that may exhibit singularities. In this paper, we consider solving a boundary value problem which exhibits a singularity at the origin due to both the structure of the domain and the regularity of the exact solution. We introduce a hybrid mixed finite element method using Lagrange Multipliers to initially solve the partial differential equation for the both the flux and displacement. An a posteriori error estimate is then applied both locally and globally to approximate the error in the computed flux with that of the exact flux. Local estimation is the key tool in identifying where the mesh should be refined so that the error in the computed flux is controlled while maintaining efficiency in computation. Finally, we introduce a simple refinement process in order to improve the accuracy in the computed solutions. Numerical experiments are conducted to support the advantages of mesh refinement over a fixed uniform mesh.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014. / In this dissertation we compute the anomalous dimensions for a class of operators, belonging to the SU(3) sector of the theory, that have a bare dimension of order N. For these operators the large N limit and the planar limit are distinct and summing only the planar diagrams will not capture the large N dynamics. Although the spectrum of anomalous dimensions has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this dissertation we explicitely compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators.