La plus part des matériaux présentant un intérêt en ingénierie et sciences physiques sont intrinsèquement hétérogènes, comme par example les composites renforcés, les matériaux poreux, et les solides polycristallins (e.g., métaux, glace, plusieurs roches). Un problème fondamental en mécanique des matériaux réside dans l'estimation de la réponse macroscopique de tels matériaux hétérogènes à partir des propriétés et de l'arrangement géométrique (microstructure) de leurs constituants. En plus, l'incorporation de l'effet des processus locaux (e.g., évolution de la microstructure, endommagement, ecruisage, recristallisation) sur la réponse macroscopique exige des connaissances statistiques sur la distribution spatiale des champs locaux dans le matériau. A cet effet, nous avons développé des méthodes non-linéaires d'homogénéisation capables de fournir des estimations non seulement du comportement macroscopique mais également des statistiques des champs dans les composites viscoplastiques. Ces méthodes sont basées sur des principes variationnels convenablement conçus, qui se servent d'un composite linéaire de comparaison choisi de façon optimale, permettant une conversion directe des estimations linéaires aux estimations correspondantes pour les potentiels effectifs des composites non-linéaires. Afin d'extraire des estimations des statistiques des champs à partir de ces méthodes, nous proposons une nouvelle procédure basée sur l'utilisation de potentiels effectifs convenablement perturbés. Au moyen de cette procédure sont obtenues des estimations pour les premiers moments des champs locaux dans chaque phase, qui sont conformes aux estimations correspondantes pour le comportement effectif. De plus, contrairement aux approches précédantes, cette procédure n'est pas limité aux premiers et seconds moments, et peut être employée pour estimer les moments d'ordre supérieur, aussi bien que la moyenne par phase des fonctions (convexes) plus générales des champs. Des résultats sont donnés pour des composites biphasés à microstructures particulaires et aléatoires, isotropes transverse ou isotropes. La pertinence de ces résultats est évaluée en les comparant aux résultats exacts correspondant à des matériaux stratifiés séquentiels non-linéaires. Les estimations obtenues s'avèrent en bon accord avec les résultats exacts, même pour des non-linéarités élevées pour lesquelles les champs de déformation sont fortement hétérogènes.

<p align="justify">In a context of restoration of historical masonry structures, it is crucial to properly estimate the residual strength and the potential structural failure modes in order to assess the safety of buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry presents preferential damage orientations, strongly localised failure modes and damage-induced anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms. As a consequence, both the membrane and the flexural behaviours of masonry walls have to be taken into account for a proper estimation of the structural stability.</p> <p align="justify">Macrosopic models used in structural computations are based on phenomenological laws including a set of parameters which characterises the average behaviour of the material. These parameters need to be identified through experimental tests, which can become costly due to the complexity of the behaviour particularly when cracks appear. The existing macroscopic models are consequently restricted to particular assumptions. Other models based on a detailed mesoscopic description are used to estimate the strength of masonry and its behaviour with failure. This is motivated by the fact that the behaviour of each constituent is a priori easier to identify than the global structural response. These mesoscopic models can however rapidly become unaffordable in terms of computational cost for the case of large-scale three-dimensional structures.</p> <p align="justify">In order to keep the accuracy of the mesoscopic modelling with a more affordable computational effort for large-scale structures, a multi-scale framework using computational homogenisation is developed to extract the macroscopic constitutive material response from computations performed on a sample of the mesostructure, thereby allowing to bridge the gap between macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic homogenisation-based multi-scale approach for quasi-brittle thin shell failure.</p> <p align="justify">For the numerical treatment of damage localisation at the structural scale, an embedded strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks using average cohesive zones including mixed cracking modes and presenting evolving orientation related to fine-scale damage evolutions.</p> <p align="justify">A first originality of this research work is the definition and analysis of a criterion based on the homogenisation of a fine-scale modelling to detect localisation in a shell description and determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale transition incorporating strong embedded discontinuities driven by the damaging mesostructure is proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous homogenisation scheme is extended to a shell description in order to model the localised behaviour of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical masonry wall tests and verified against three-dimensional full fine-scale computations in which all the bricks and the joints are discretised.</p>

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

This research focuses on modelling reflectors in typical material testing reactors (MTRs). Reflectors present some challenges to the usual approach to full-core calculational models. Diffusion theory is standardly used in full-core calculations and is known to be inaccurate in regions where the flux is anisotropic, for example within the reflectors. Thus, special consideration should be given to reflector models. In this research, normalised generalised equivalence theory is used to homogenise cross-sections and calculate equivalent nodal parameters and albedo boundary conditions for the reflector surrounding a typical MTR reactor. Various studies have shown that equivalence theory can be used to accurately generate equivalent nodal parameters for the core and reflector regions of large reactors, such as pressurised and boiling water reactors, in one dimension and for two neutron energy groups. This has not been tested for smaller reactors where leakage, environment sensitivity and multi-group spectrum dependency are much larger. The SAFARI-1 MTR reactor is modelled in this work. A thirty day operational cycle is simulated for this reactor, using the nodal diffusion code MGRAC. NGET reflector equivalent nodal parameters are calculated using the codes NEWT and EQUIVA. The impact of different reflector models are evaluated, based on their effect on the core power, flux distribution, reactivity and neutron leakage over the duration of the operational cycle. It is found that homogenisation introduces some environment dependencies in the reflector parameters, particularly in the corners of the reactor core. In full-core calculations, the reflector parameters show some sensitivity to the in-core reflector structures, but not the fuel composition. A practical reflector model for SAFARI-1 is proposed, which proves that NGET equivalence theory can be used for multi-group reflector modelling in a small MTR reactor. This approach to reflector modelling simplifies the core model, increases the accuracy of a diffusion calculation, and increases the efficiency (shorter calculational time and better convergence behaviour) of computer simulations. / Thesis (MSc (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

Temperature is one of the parameters that limits the output torque and reduces the lifespan of electrical machines. Models that can provide accurate estimation of the temperature field in the most critical components (e.g. windings) at lower computational effort can be useful to improve the design process and reduce the time to market. Depending on the application, engineers usually rely on hi-fidelity models, e.g. based on the finite elements method (FEM), or lower order models, e.g. thermal equivalent circuits (TECs). The aim of the present work is to provide new tools and methodologies to obtain the temperature distribution within the windings using reduced order hi-fidelity models or improved TEC that could account for any working condition, including AC effects. A new methodology, based on the multiple scales method (MSM), is introduced which homogenises the complex windings domain and allows for the estimation of its effective thermal properties. The homogenisation through the MSM is performed solving a single elementary cell. The MSM also allows for the reconstruction of the actual thermal field. Extensive numerical and experimental validation is provided, in particular for the case of electrical windings encapsulated with epoxy. The thermal homogenisation is then combined with an electromagnetic homogenisation technique to estimate winding losses including AC effects, such as proximity and skin effects. The coupled analysis is validated numerically on reference test problems, and experimentally, on a suitably built "motorette". The method is proven to correctly predict losses including thermal effects and to estimate magnitude and location of the temperature hotspot within the winding domain. This work also introduces a new approach for building thermal equivalent circuits that represents the most commonly employed modelling technique for electrical machine thermal analysis. Here the TEC approaches are thoroughly analysed, highlighting limitations. The proposed new technique extends the range of numerical accuracy, accounting for high Biot numbers (up to Bi = 2) and internal heat generation. The result of this approach is higher spatial resolution about the temperature field within the winding domain and thus enables improved information on hotspot location and magnitude. The method is experimentally validated and also applied to model an electrical machine for full-electric in-wheel vehicle propulsion.

L'enrichissement des modèles numériques de l'être humain est un enjeu majeur dans la recherche en biomécanique des chocs. Dans le cas des os longs, les propriétés mécaniques sont le plus souvent déterminées à partir de caractéristiques macroscopiques sans prendre en compte l'influence de l'architecture du tissu. Ce manque de considération explique les limites de la biofidélité des modèles proposés actuellement. Fort de ce constat, une approche multi-échelle semble être pertinente pour une amélioration des prédictions obtenues. Cette thèse s'intéresse plus particulièrement au comportement de l'humérus humain dans le cadre de sollicitations dynamiques et propose le développement d'une loi micromécanique pour le décrire. Cette loi est un couplage entre le schéma d'homogénéisation linéaire de Mori-Tanaka pour l'estimation des propriétés mécaniques apparentes de l'humérus avec un raisonnement thermodynamique décrivant la progression de l'endommagement au sein de l'os cortical à l'aide d'une loi de croissance des porosités. La validité de ce modèle a été faite à travers l'estimation de l'effort ultime lors d'essais de type impacts. Pour ce faire, cette étude repose sur les résultats de campagnes expérimentales explorant à différentes échelles les propriétés mécaniques de 13 humérus prélevés de 10 sujets humains post-mortem. Ainsi des essais d'impact ont été réalisés sur pièces anatomiques, les propriétés élastiques mésoscopiques et l'influence de l'endommagement sur ces dernières ont été caractérisées à travers des tests de traction/compression ou de flexion sur éprouvettes et les propriétés microscopiques de la matrice osseuse ont été mesurées par nanoindentation. / The relevant of the human numerical models is a major issue in biomechanical researches. The long bones' mechanical properties are often identified from macro-scale characteristics without taking account of bone structure. This lack of consideration explains the limit of the proposed models biofidelity. A multi-scale approach seems to be relevant for the prediction's improvement, in light of this. This thesis studied the human humerus behavior during dynamical solicitations and propose a micromechanical law to describe it. This law is coupling the linear homogenization scheme of Mori-Tanaka to evaluate the apparent mechanical properties of humerus with a thermo dynamical reasoning to describe the cortical bone damaging by porosities growing. The model validity has been established by the estimation of the maximal load during a impact test. This study is based on the results from multi-scale experimental campaigns exploring the mechanicals properties of 13 humerus from 10 post-mortem human cadavers. So impacts tests have been realized on anatomical specimens, the mesoscopic elastic properties and the damaging influence on them have been characterized by traction, compression or flexion tests and the microscopic properties of bone matrix have been measured by nanoindentation.

Die Arbeit beschreibt die skalenübergreifende Modellierung und Simulation des Werkstoffverhaltens von Faser-Kunststoff-Verbunden mit textiler Verstärkungsstruktur, die ausgehend von den konstitutiven Eigenschaften der Verbundbestandteile (Mikroskala) und ihrer geometrischen Anordnung im Verbund (Mesoskala) die rechnerische Vorhersage des effektiven Materialverhaltens des Verbundes (Makroskala) ermöglicht. Neben Schädigungsprozessen beeinflusst insbesondere das dehnratenabhängige Materialverhalten der polymeren Matrix das mechanische Verhalten des Verbundes. Dieser Einfluss wird anhand verschiedener Glasfaser-Polypropylen-Verbunde numerisch untersucht. Ein viskoplastisches Materialmodell bildet dabei das nichtlineare Materialverhalten von Polypropylen ab. Die Modellierung der textilen Verstärkungsstruktur erfolgt durch Anwendung der erweiterten Finiten-Elemente-Methode (XFEM). Anhand des Vergleichs von rechnerisch und experimentell gewonnenen Ergebnissen erfolgt schließlich die Verifikation der vorgeschlagenen Modellierungsstrategie. / This contribution covers the trans-scale modelling and simulation of the mechanical behaviour of textile-reinforced polymers. Starting from the material properties of the individual constituents (micro-scale) and their geometrical arrangement (meso-scale), the effective material behaviour of the composite (macro-scale) is numerically predicted. In addition to damage processes, the inelastic deformation behaviour of the composite is influenced by the strain-rate dependent material behaviour of the polymeric matrix. This influence is numerically investigated for different glass-fibre-polypropylene composites. A viscoplastic material model accounts for the nonlinear mechanical behaviour of polypropylene. The complex textile reinforcement is modelled by the eXtended finite element method (XFEM). A comparison of computed and experimental results allows for the verification of the proposed modelling strategy.

Almost all research on biorefinery concepts are based on chemical pulping processes and ways of utilising lignin, hemicelluloses and extractives as well as a part of the remaining cellulose for production of nano materials in order to create more valuable products than today. Within the Forest as a Resource (FORE) research program at FSCN we are utilising the whole chain of unit processes from forestry to final products as paper and board, where the pulping process research focus on high yield process as TMP and CTMP. As these process solutions are preserving or only slightly changing the properties of the original wood polymers and extractives, the idea is to find high value adding products designed by nature. From an economic perspective, the production of nanocellulose from a chemical pulp is quite expensive as the pulp has to be either enzymatically (e.g. mono-component endoglucanase) pre-treated or chemically oxidised using the TEMPO (2,2,6,6 - tetramethyl-piperidine-1-oxil) - mediated oxidation method in order to make it possible to disrupt the fibres by means of homogenisation. In high yield pulping processes such as in TMP and CTMP, the idea with this study was to investigate the possibility to use fractions of low quality materials from fines fractions for the production of nano-ligno-cellulose (NLC). The integration of a NLC unit process in a high yield pulping production line has a potential to become a future way to improve the quality level of traditional products such as paper and board grades. The intention of this research work was that, by using this concept, a knowledge base can be created so that it becomes possible to develop a low-cost production method for its implementation. In order to study the potential of this concept, treatment of thermo-mechanical pulp (TMP) fines fractions were studied by means of homogenisation It seems possible to homogenise fine particles of thermo-mechanical pulp (1% w/v) to NLC. A correspond fines fraction from bleached kraft pulp (BKP) was tested as a reference at 0.5% w/v concentration. The objective presented in this work was to develop a methodology for producing mechanical pulp based NLC from fines fractions and to utilise this material as strength additives in paper and board grades. Laboratory sheets of CTMP and BKP, with addition of their respective NLC, were made in a Rapid Köthen sheet former. It was found that handsheets of pulp fibres blended with NLC improved the z-strength and other important mechanical properties for similar sheet densities. The characterisation of the particle size distribution of NLC is both important and challenging and the crill methodology developed at Innventia (former STFI) already during the 1980s was tested to see if it would be both fast and reliable enough. The crill measurement technique is based on the optical responses of a micro/nano particle suspension at two wavelengths of light; UV and IR. The crill value of TMP and CTMP based nano-ligno-cellulose were measured as a function of the homogenisation time. Results showed that the crill value of both TMP-NLC and CTMP-NLC correlated with the homogenisation time.

Grâce à leurs bonnes propriétés mécaniques spécifiques, les matériaux cellulaires architecturés présentent un fort intérêt pour répondre aux problématiques du secteur aéronautique. Cependant, la modélisation d'une structure macroscopique incluant un matériau cellulaire nécessite, soit de modéliser complètement l'architecture à l'échelle mésoscopique - ce qui est coûteux en temps de calcul - soit d'utiliser un Milieu Homogène Equivalent (MHE). Ainsi, cette thèse propose de caractériser un matériau cellulaire modèle constitué d'un empilement de tubes, selon un motif carré ou hexagonal, puis d'identifier un modèle phénoménologique rendant compte du comportement mécanique inélastique du matériau. Dans un premier temps, le matériau est caractérisé sous chargements multi-axiaux à l'aide de simulations éléments finis périodiques en petites déformations. Le comportement homogénéisé en petites déformations est ensuite utilisé pour l'identification d'une Loi Homogène Equivalente (LHE) compressible et anisotrope, qui permet la modélisation de structures sandwichs en remplaçant le coeur cellulaire par son MHE. Une comparaison est réalisée entre les réponses mécaniques des simulations de référence complètement maillées et celles utilisant l'approche par MHE, validant ainsi la pertinence de la méthode multi-échelle de modélisation proposée. La caractérisation en grandes déformations des deux types d'empilement est ensuite menée. D'abord, les effets de bords et les instabilités qui gouvernent le comportement macroscopique sont étudiés. Puis, après une étude du volume élémentaire représentatif des empilements, la caractérisation du comportement inélastique par la technique de l'homogénéisation périodique est réalisée. Le comportement adoucissant en compression de l'empilement hexagonal est ainsi étudié. Finalement, une extension des LHE identifiées en petites déformations est proposée pour rendre compte du comportement en compression du matériau observé en grandes déformations. / Cellular materials have excellent specific properties, which make them attractive for aeronautical applications. However, modelling macroscopic structures including a cellular material is either very costly in terms of computational time if the whole mesoscopic structure is considered or a Homogeneous Equivalent Medium (HEM) has to be used. This Ph.D. dissertation presents, the characterisation of a cellular material built from a stacking of tubes with a square or hexagonal based pattern and the identification of a phenomenological model of their inelastic mechanical behaviour. First, the material is characterised for multi-axial loadings through a periodic finite element model in small deformations for each tube stacking pattern. The macroscopic behaviour is then used to identify a compressible anisotropic Homogeneous Equivalent Law (HEL). Within the infinitesimal strain hypothesis, a comparison is carried out between reference full scale models and HEM based ones of sandwich structures with a cellular core, confirming the relevance of the proposed multi-scale method. Then, the mechanical behaviour of each tube stacking is characterised for large deformations in order to study the influence of the boundary size effects and the instabilities in the core on the macroscopic behaviour of sandwich structures. After a study on the representative volume element, the macroscopic inelastic behaviour is characterised through the periodic homogenisation technique, especially the softening observed in compression for the hexagonal pattern. Finally, an extension of the HELs identified in small deformations is proposed to model the behaviour observed in large deformations.

En contrôle non-destructif par ultrasons, la simulation présente un intérêt majeur en permettant à la fois d’optimiser les configurations de contrôle des pièces et de simplifier l’analyse des données acquises. Cette thèse traite de la modélisation de la propagation des ultrasons dans les matériaux composites tissés. Ces matériaux sont constitués de fibres de Carbone (micrométriques) regroupées en mèches (millimétriques) qui sont ensuite tissées pour former une couche de matériau : leur structure est donc hétérogène à deux échelles distinctes. L’étude à l’échelle du tissage nécessite la connaissance préalable des propriétés mécaniques des mèches. Nous proposons deux méthodes visant à effectuer l’homogénéisation dynamique du matériau à l’échelle microscopique. Une première consiste à identifier les rigidités complexes d’un milieu effectif représentatif de la mèche en comparant les nombres d’ondes des modes guidés s’y propageant à ceux calculés dans un milieu hétérogène de même géométrie ; nous avons développé un algorithme génétique permettant de faire correspondre les jeux de nombres d’onde, dont l’application permet d’identifier certaine des rigidités recherchées. La seconde consiste à étendre un modèle existant permettant d’homogénéiser la structure de la mèche en tenant compte de la diffraction multiple des ondes de volume par les fibres. Le modèle initial (modèle à trois phases) ne traitant que le cas de l’incidence normale aux fibres est étendu au cas plus complexe de l’incidence oblique : un calcul de la diffraction multiple en incidence oblique par un réseau dense de fibres et tenant compte de l’anisotropie des différents milieux est donc proposé. Comme pour la première méthode, on utilise un algorithme génétique pour effectuer l’identification des rigidités effectives. Les résultats obtenus nous amènent à remettre en cause certaines hypothèses de base faites pour effectuer cette homogénéisation dynamique ; particulièrement, la dépendance des résultats à l’angle d’incidence semble remettre en cause le choix de la loi de Hooke comme loi fondamentale pour effectuer une homogénéisation dynamique des composites à structures complexes. / The simulation of nondestructive examinations is of great interest to optimize testing configurations and to help interpreting collected data. This thesis deals with the modeling of ultrasonic propagation into woven composite materials. These materials are made from Carbon fibers (micrometric) assembled into bundles (millimetric) which are woven to form a layer; their structure is thus heterogeneous at two scales. To study the material at the weave scale, one first needs to know the mechanical properties of bundles. We propose two methods aiming at dynamically homogenize the material at this scale. The first one achieves identification of complex rigidity coefficients of the effective material by comparing the wave numbers of guided waves propagating in the effective materials with those of guided waves propagating in the heterogeneous composite. A genetic algorithm is developed to match the sets of wave numbers, allowing to identify some of the coefficients. The second method extends an existing model that homogenizes bundles and takes into account multiple scattering of bulk waves on fibers. The existing model (3-phase model) was limited to waves at normal incidence; the extension deals with oblique incidence. For this, the problem of multiple scattering of waves under oblique incidence on fibers is solved; the solution takes into account the anisotropy and viscoelasticity of the various phases. A genetic algorithm (as already used in the first homogenization method) allows one to identify the complex effective rigidity coefficients. Results obtained using this method finally brings us to question some of the basic hypotheses made to proceed to dynamic homogenization.