L’utilisation de structures fines est croissante dans bon nombre d’industries. En ce sens, leur représentation mécanique et optimisation est un enjeu majeur de la recherche actuelle. De façon classique, l’optimisation s’effectue avec un critère de contrainte, obtenue à partir d’une modélisation éléments-finis en déplacements. L’idée de ces travaux est de construire un modèle éléments-finis mixte déplacements-contraintes et de développer des méthodes de réduction adaptées, de façon à améliorer l’efficacité des méthodes d’optimisation existantes. On construit d’une part deux modèles élément-finis mixtes déplacements-contraintes généralisées, pour des analyses dynamiques de structures “plaque” fines et épaisses. Ces derniers présentent l’avantage de donner des résultats identiques aux modèles classiques en déplacements, avec un meilleur temps de reconstruction des champs de contraintes. Cependant, ils s’avèrent être délicats pour plusieurs raisons : la taille des matrices associées, la difficulté de faire une analyse modale rapide, et un temps d’assemblage accru. C’est la raison pour laquelle nous développons par la suite des méthodes de sous-structuration et de double synthèse modale spécifiquement dédiées aux modèles mixtes. L’idée est d’utiliser des bases modales tirées du modèle équivalent en déplacements pour composer une nouvelle base mixte réduite. Dix méthodes sont implémentées, basées sur des modes encastrés, libres et de branche, parmi lesquelles certaines s’avèrent très efficaces pour réduire le nombre de degrés de liberté du système mixte, sans passer par ses modes propres. Enfin, nous intégrons les modèles mixtes sous-structurés sous forme de super- éléments mixtes dans un algorithme génétique, dans le but de mener une optimisation multi-objectif de structures “plaque” académiques sous chargement dynamique, avec critères de contrainte et paramètres d’épaisseur. Les modèles précédemment définis sont ainsi paramétrés en épaisseur, et ne nécessitent plus d’être ré-assemblés pour chaque configuration. Nous disposons désormais d’un modèle mixte “plaque”, qui conserve les avantages d’un accès direct aux contraintes, tout en étant affranchi de sa taille importante par le biais des méthodes de réduction, et de son assemblage grâce au paramétrage. Il en résulte des modèles mécaniques originaux et efficaces, permettant de réduire les coûts de calcul des algorithmes d’optimisation classiques. Ce type de méthode, couplé à de puissants algorithmes génétiques, permet d’avoir une bonne vue d’ensemble des solutions optimales, et laissent augurer des perspectives intéressantes pour une utilisation industrielle. / The use of thin structures is increasing in many industries. Their mechanical representation and optimization is therefore a major challenge in modern research. Usually, the optimization is done with a stress criterion which is determined through displacements finite-element model. The idea of this work is to build a mixed displacements-stresses finite-element model and to develop adapted reduction procedures, in order to improve the efficiency of existing optimization methods. On the one hand, we build two mixed displacements-generalized stresses finite element models, for thin and thick dynamic plate structures analysis. They afford the advantage of giving identical results as classical displacements models with a better computational time to re-build the stress fields. Nevertheless, they turn out to be tricky for some reasons : the bigger matrices size, the difficulty of modal analysis and an assembling time higher. That is the reason why we develop afterwards some sub-structuring methods and double modal synthesis specifically dedicated to mixed models. The idea is to use modal basis taken from the equivalent displacement model so as to build a new mixed reduced basis. Ten methods are implemented, based on fixed modes, free modes, and branch modes. Some of them turn out to be very efficient to drastically reduce the amount of degrees of freedom of the mixed model, without using its eigenmodes. Finally, we embed the sub-structured mixed model in the form of Mixed Super- Element in a genetic algorithm, with the aim of conducting a multi-objective optimization of academic plate structures under dynamic loads, with stresses criterion and thicknesses parameters. The models previously defined are configured with thicknesses as parameters, and therefore don’t need to be re-assembled for each configuration. We now dispose of a powerful thickness-parametrized mixed reduced plate finite element model : it keeps the advantages of an easy access to the stresses and is free of its important size thanks to the reduction method and of its assembling thanks to the parametrization. The result is an original and efficient mechanical model that reduces the computational cost of classical optimization algorithms. That type of model, coupled with powerful genetic algorithms, permits a global optimization with a good overview of the solutions and promises interesting perspectives for industrial uses.

Thin structures exist as one dimensional slender objects (hairs, tendrils, telephone cords, etc.) and two dimensional thin sheets (tree leaves, Mobius bands, eggshells, etc.). Geometric and material nonlinearities can conspire together to create complex phenomena in thin structures. This dissertation studies snap-through, multi-stability, and localization in thin rods and sheets through a combination of experiments and numerics. The first work experimentally explores the multi-stability and bifurcations of buckled elastic strips subject to clamping and lateral end translations, and compares these results with numerical continuation of a perfectly anisotropic Kirchhoff rod model. It is shown that this naive Kirchhoff rod model works surprisingly well as an organizing framework for thin bands with various widths. Thin sheets prefer to bend rather than to stretch because of the high cost of stretching energy. Knowing the bending response of thin sheets can aid in simulating deformations such as creasing. The second work introduces an exact pure bending linkage mechanism for potential use in a bend tester that measures the moment-curvature relationship of soft sheets and filaments. Mechanical rotary pleating is a bending-deformation-dominant process that deforms nonwoven materials into zigzag filter structures. The third work studies what combinations of processing and material parameters lead to successful rotary pleating. The rotary pleating process is formulated as a multi-point variable-arc-length boundary value problem for an inextensible rod, with a moment-curvature constitutive law, such as might be measured by a bend tester, as input. Through parametric studies, this work generates pleatability surfaces that may help avoid pleating failure in the real pleating process. Creased thin sheets are generally bistable. The final work of this dissertation studies bistability of creased thin disks under the removal of singularities. A hole is cut in the disk and, through numerical continuation of an inextensible strip model, this work studies how the crease stiffness, crease angle, and hole geometry affect the bistability. / Doctor of Philosophy / Thin structures are those that have at least one dimension smaller than the other dimensions, such as hairs, telephone cords, and tree leaves, to name just a few. They can generate rich mechanical behaviors (e.g., snapping, crumpling) and complex shapes. A simple example is to rotate the two ends of a thin strip that has been deformed into an arch. Snapping will happen at a certain rotation angle. The first work studies snapping behaviors of thin bands subject to rotations and displacements at the two ends. This work employs a mechanical model based on force and moment balance on a spatial curve to solve the shapes of thin strips and capture the rich snapping behaviors. It is much harder to stretch a thin sheet than to bend it, which can be easily seen by deforming a piece of paper. The physics behind this is that stretching requires more energy than bending in thin objects. Knowing the bending response of thin sheets can aid in simulating deformations of thin structures. The second work introduces a new pure bending mechanism that can subject a sheet to pure bending and measure its bending response through a moment-curvature relationship. Thin sheets find broad applications in engineering. Mechanical pleating is a long-standing technique that deforms thin sheets into zigzag filter structures, but the mechanics behind it is unclear. The third work studies a rotary pleating process and aims to answer a basic question: What combinations of processing and material parameters lead to successful pleating? This work employs a one-dimensional model of an inextensible rod, with a moment-curvature constitutive law as input. The moment-curvature relationship of pleating materials can be measured by the pure bending mechanism developed in the second work. Thin sheets with prescribed crease patterns can create complicated and targeted shapes, such as origami (paper folding) and kirigami (paper cutting). A simple creased thin sheet is bistable: A stable configuration can be obtained by inverting the crease, which leads to a conical vertex/singularity. The fourth work of this dissertation finds that the bistability of creased thin sheets will be destroyed if a large hole is made around the vertex. This work studies the loss of bistability of creases under removal of singularities by quantifying how the hole size, hole geometry, and other factors such as the crease angle and crease stiffness affect the bistability.

O propósito principal do presente trabalho é estabelecer diretrizes para o uso de elementos finitos sólidos na modelagem de estruturas delgadas submetidas à flexão. Por meio de um conjunto de problemas estudou-se o travamento de elementos finitos da elasticidade bi e tridimensionais, quando usados para modelar estruturas delgadas submetidas à flexão. Foram usados elementos planos de 4, 8 e 9 nós e elementos tridimensionais de 4, 10, 11, 8, 20 e 27 nós, considerando elementos não distorcidos e distorcidos. A análise dos resultados nesses modelos permitiram entender melhor o comportamento e o uso de elementos sólidos em estruturas delgadas. / The main objective of the present work is to establish guidelines for the use of solid finite elements in the modeling of thin structures submitted to bending. By means of a set of problems the locking of elements three-dimensional and two-dimensional elasticity was studied, when used to model problems thin structures subjected to bending. We use 2-D displacements-based elements of 4, 8 and 9 nodes and 3-D displacement based of 4, 10, 11, 8, 20 and 27 nodes, considering undistorted and distorted elements. The analysis of the results of these models lead to the understanding of the behavior and the use of solid elements in thin structures.

O propósito principal do presente trabalho é estabelecer diretrizes para o uso de elementos finitos sólidos na modelagem de estruturas delgadas submetidas à flexão. Por meio de um conjunto de problemas estudou-se o travamento de elementos finitos da elasticidade bi e tridimensionais, quando usados para modelar estruturas delgadas submetidas à flexão. Foram usados elementos planos de 4, 8 e 9 nós e elementos tridimensionais de 4, 10, 11, 8, 20 e 27 nós, considerando elementos não distorcidos e distorcidos. A análise dos resultados nesses modelos permitiram entender melhor o comportamento e o uso de elementos sólidos em estruturas delgadas. / The main objective of the present work is to establish guidelines for the use of solid finite elements in the modeling of thin structures submitted to bending. By means of a set of problems the locking of elements three-dimensional and two-dimensional elasticity was studied, when used to model problems thin structures subjected to bending. We use 2-D displacements-based elements of 4, 8 and 9 nodes and 3-D displacement based of 4, 10, 11, 8, 20 and 27 nodes, considering undistorted and distorted elements. The analysis of the results of these models lead to the understanding of the behavior and the use of solid elements in thin structures.

This thesis considers applications of gradient-based optimization algorithms to the design and control of some mechanics systems. The material distribution approach to topology optimization is applied to design two different acoustic devices, a reactive muffler and an acoustic horn, and optimization is used to control a ball pitching robot. Reactive mufflers are widely used to attenuate the exhaust noise of internal combustion engines by reflecting the acoustic energy back to the source. A material distribution optimization method is developed to design the layout of sound-hard material inside the expansion chamber of a reactive muffler. The objective is to minimize the acoustic energy at the muffler outlet. The presence or absence of material is represented by design variables that are mapped to varying coefficients in the governing equation. An anisotropic design filter is used to control the minimum thickness of materials separately in different directions. Numerical results demonstrate that the approach can produce mufflers with high transmission loss for a broad range of frequencies. For acoustic devices, it is possible to improve their performance, without adding extended volumes of materials, by an appropriate placement of thin structures with suitable material properties. We apply layout optimization of thin sound-hard material in the interior of an acoustic horn to improve its far-field directivity properties. Absence or presence of thin sound-hard material is modeled by a surface transmission impedance, and the optimization determines the distribution of materials along a “ground structure” in the form of a grid inside the horn. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration. The surface impedance is handled by a new finite element method developed for Helmholtz equation in the situation where an interface is embedded in the computational domain. A Nitschetype method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles both vanishing and non-vanishing interface conditions. We show the stability of the method for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. The thesis also presents a method for optimal control of a two-link ball pitching robot with the aim of throwing a ball as far as possible. The pitching robot is connected to a motor via a non-linear torsional spring at the shoulder joint. Constraints on the motor torque, power, and angular velocity of the motor shaft are included in the model. The control problem is solved by an interior point method to determine the optimal motor torque profile and release position. Numerical experiments show the effectiveness of the method and the effect of the constraints on the performance.

Estruturas do tipo linha/curva (line-like, curve-like), alongadas e ramificadas são comumente encontradas nos ecossistemas que conhecemos. Na biomedicina e na biociências, por exemplo, diversas aplicações podem ser observadas. Justamente por este motivo, extrair este tipo de estrutura em imagens é um constante desafio em problemas de análise de imagens. Porém, diversas dificuldades estão envolvidas neste processo. Normalmente as características espectrais e espaciais destas estruturas podem ser muito complexas e variáveis. Especificamente as mais \"finas\" são muito frágeis a qualquer tipo de processamento realizado na imagem e torna-se muito fácil a perda de informações importantes. Outro problema bastante comum é a ausência de parte das estruturas, seja por motivo de pouca resolução, ou por problemas de aquisição, ou por casos de oclusão. Este trabalho tem por objetivo explorar, descrever e desenvolver técnicas de detecção/segmentação de estruturas finas e ramificadas. Diferentes métodos são utilizados de forma combinada, buscando uma melhor representação topológica e perceptual das estruturas e, assim, melhores resultados. Grafos são usados para a representação das estruturas. Esta estrutura de dados vem sendo utilizada com sucesso na literatura na resolução de diversos problemas em processamento e análise de imagens. Devido à fragilidade do tipo de estrutura explorado, além das técnicas de processamento de imagens, princípios de visão computacional são usados. Busca-se, desta forma, obter um melhor \"entendimento perceptual\" destas estruturas na imagem. Esta informação perceptual e informações contextuais das estruturas são utilizadas em um modelo de campos aleatórios de Markov, buscando o resultado final da detecção através de um processo de otimização. Finalmente, também propomos o uso combinado de diferentes modalidades de imagens simultaneamente. Um software é resultado da implementação do arcabouço desenvolvido e o mesmo é utilizado em duas aplicações para avaliar a abordagem proposta: extração de estradas em imagens de satélite e extração de raízes em imagens de perfis de solo. Resultados do uso da abordagem proposta na extração de estradas em imagens de satélite mostram um melhor desempenho em comparação com método existente na literatura. Além disso, a técnica de fusão proposta apresenta melhora significativa de acordo com os resultados apresentados. Resultados inéditos e promissores são apresentados na extração de raízes de plantas. / Line- curve-like, elongated and ramified structures are commonly found inside many known ecosystems. In biomedicine and biosciences, for instance, different applications can be observed. Therefore, the process to extract this kind of structure is a constant challenge in image analysus problems. However, various difficulties are involved in this process. Their spectral and spatial characteristics are usually very complex and variable. Considering specifically the thinner ones, they are very \"fragile\" to any kind of process applied to the image, and then, it becomes easy the loss of crucial data. Another very common problem is the absence of part of the structures, either because of low image resolution and image acquisition problems or because of occlusion problems. This work aims to explore, describe and develop techniques for detection/segmentation of thin and ramified structures. Different methods are used in a combined way, aiming to reach a better topological and perceptual representation of the structures and, therefore, better results. Graphs are used to represent the structures. This data structure has been successfully used in the literature for the development of solutions for many image processing and analysis problems. Because of the fragility of the kind of structures we are dealing with, some computer vision principles are used besides usual image processing techniques. In doing so, we search for a better \"perceptual understanding\" of these structures in the image. This perceptual information along with contextual information about the structures are used in a Markov random field, searching for a final detection through an optimization process. Lastly, we propose the combined use of different image modalities simultaneously. A software is produced from the implementation of the developed framework and it is used in two application in order to evaluate the proposed approach: extraction of road networks from satellite images and extraction of plant roots from soil profile images. Results using the proposed approach for the extraction of road networks show a better performance if compared with an existent method from the literature. Besides that, the proposed fusion technique presents a meaningful improvement according to the presented results. Original and promising results are presented for the extraction of plant roots from soil profile images.

Estruturas do tipo linha/curva (line-like, curve-like), alongadas e ramificadas são comumente encontradas nos ecossistemas que conhecemos. Na biomedicina e na biociências, por exemplo, diversas aplicações podem ser observadas. Justamente por este motivo, extrair este tipo de estrutura em imagens é um constante desafio em problemas de análise de imagens. Porém, diversas dificuldades estão envolvidas neste processo. Normalmente as características espectrais e espaciais destas estruturas podem ser muito complexas e variáveis. Especificamente as mais \"finas\" são muito frágeis a qualquer tipo de processamento realizado na imagem e torna-se muito fácil a perda de informações importantes. Outro problema bastante comum é a ausência de parte das estruturas, seja por motivo de pouca resolução, ou por problemas de aquisição, ou por casos de oclusão. Este trabalho tem por objetivo explorar, descrever e desenvolver técnicas de detecção/segmentação de estruturas finas e ramificadas. Diferentes métodos são utilizados de forma combinada, buscando uma melhor representação topológica e perceptual das estruturas e, assim, melhores resultados. Grafos são usados para a representação das estruturas. Esta estrutura de dados vem sendo utilizada com sucesso na literatura na resolução de diversos problemas em processamento e análise de imagens. Devido à fragilidade do tipo de estrutura explorado, além das técnicas de processamento de imagens, princípios de visão computacional são usados. Busca-se, desta forma, obter um melhor \"entendimento perceptual\" destas estruturas na imagem. Esta informação perceptual e informações contextuais das estruturas são utilizadas em um modelo de campos aleatórios de Markov, buscando o resultado final da detecção através de um processo de otimização. Finalmente, também propomos o uso combinado de diferentes modalidades de imagens simultaneamente. Um software é resultado da implementação do arcabouço desenvolvido e o mesmo é utilizado em duas aplicações para avaliar a abordagem proposta: extração de estradas em imagens de satélite e extração de raízes em imagens de perfis de solo. Resultados do uso da abordagem proposta na extração de estradas em imagens de satélite mostram um melhor desempenho em comparação com método existente na literatura. Além disso, a técnica de fusão proposta apresenta melhora significativa de acordo com os resultados apresentados. Resultados inéditos e promissores são apresentados na extração de raízes de plantas. / Line- curve-like, elongated and ramified structures are commonly found inside many known ecosystems. In biomedicine and biosciences, for instance, different applications can be observed. Therefore, the process to extract this kind of structure is a constant challenge in image analysus problems. However, various difficulties are involved in this process. Their spectral and spatial characteristics are usually very complex and variable. Considering specifically the thinner ones, they are very \"fragile\" to any kind of process applied to the image, and then, it becomes easy the loss of crucial data. Another very common problem is the absence of part of the structures, either because of low image resolution and image acquisition problems or because of occlusion problems. This work aims to explore, describe and develop techniques for detection/segmentation of thin and ramified structures. Different methods are used in a combined way, aiming to reach a better topological and perceptual representation of the structures and, therefore, better results. Graphs are used to represent the structures. This data structure has been successfully used in the literature for the development of solutions for many image processing and analysis problems. Because of the fragility of the kind of structures we are dealing with, some computer vision principles are used besides usual image processing techniques. In doing so, we search for a better \"perceptual understanding\" of these structures in the image. This perceptual information along with contextual information about the structures are used in a Markov random field, searching for a final detection through an optimization process. Lastly, we propose the combined use of different image modalities simultaneously. A software is produced from the implementation of the developed framework and it is used in two application in order to evaluate the proposed approach: extraction of road networks from satellite images and extraction of plant roots from soil profile images. Results using the proposed approach for the extraction of road networks show a better performance if compared with an existent method from the literature. Besides that, the proposed fusion technique presents a meaningful improvement according to the presented results. Original and promising results are presented for the extraction of plant roots from soil profile images.

La simulation numérique par la méthode des éléments finis (MEF) fournit de nos jours une grande aide pour les ingénieurs dans les processus de conception d’optimisation des produits. Malgré le développement croissant des ressources de calcul, la fiabilité et l’efficacité des simulations numériques par la MEF restent à améliorer. Ce travail de thèse consiste à développer une famille d’éléments solide-coque (SHB) pour la modélisation tridimensionnelle des structures minces. Cette famille d’éléments SHB est basée sur une formulation tridimensionnelle en grands déplacements et rotations. La technique dite “d’intégration réduite dans le plan”, en utilisant un nombre arbitraire de points d’intégration dans la direction de l’épaisseur, permet la modélisation des structures minces avec une seule couche d'éléments. Dans ce travail de thèse, deux éléments linéaires SHB prismatique et hexaédrique, ainsi que leurs contreparties quadratiques, ont été implantés dans le code par éléments finis ABAQUS pour l’analyse quasi-statique et dynamique des structures minces. La performance de ces éléments a été validée à travers une série de cas tests académiques, ainsi que sur des problèmes complexes de type impact/crash et des procédés de mise en forme de tôles minces. L'ensemble des résultats numériques obtenus révèle que les éléments SHB représentent une alternative intéressante aux éléments coques et solides traditionnels pour la modélisation tridimensionnelle des structures minces. / Nowadays, the finite element (FE) simulation provides great assistance to engineers in the design of products and optimization of manufacturing processes. Despite the growing development of computational resources, reliability and efficiency of the FE simulations remain the most important features. The current work contributes to the development of a family of assumed strain based solid-shell elements (SHB), for the modeling of 3D thin structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In the current contribution, a family of prismatic and hexahedral SHB elements with their linear and quadratic versions have been implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. The performance of the SHB elements is evaluated via a series of popular benchmarks as well as with impact/crash and sheet metal forming processes. All numerical results reveal that the SHB elements represent an interesting alternative to traditional shell and solid elements for the 3D modeling of thin structural problems.

Dans ce travail, des modèles thermomécaniques basés sur une approche non-locale sont proposés pour décrire le comportement des Alliages à Mémoire de Forme (AMF) avec la prise en compte des effets de la localisation et de la chaleur latente lors de la transformation de phase. Ces modèles sont obtenus comme des extensions d’un modèle local existant. Pour décrire la localisation de la transformation de phase, l’extension du modèle initial a consisté à le réécrire dans un contexte non-local par l’introduction d’une nouvelle variable, définie comme la contrepartie non-locale de la fraction volumique de martensite déjà présente dans le modèle local. L’exploitation de ce modèle a nécessité le développement d’un élément fini spécial dans ABAQUS avec la fraction volumique non-locale de martensite comme un degré de liberté supplémentaire. Les simulations réalisées montrent la pertinence d’une telle approche dans la description de la transformation de phase dans des structures minces en AMF, soumises à des chargements thermomécaniques. Pour décrire les effets de la chaleur latente, une équation d’équilibre thermique ayant comme terme source des contributions dépendant de la transformation de phase a été adjointe au modèle initial. Là encore, l’exploitation du modèle a nécessité le développement d’un élément fini qui prend en compte le couplage thermomécanique et la formulation proposée pour l’équilibre thermique. Les simulations numériques réalisées ont montré l’effet retardant sur la transformation de phase de la chaleur latente, et le caractère hétérogène possible de la transformation dans ce cas. Ces effets sont d’autant plus importants que la vitesse de déformation est élevée / In this Phd thesis, thermo-mechanical models based on a nonlocal approach are proposed in order to describe the behavior of Shape Memory Alloys (SMA), taking into account localization and latent heat effects during phase transformation. These models are obtained as extensions of an existing local model. In order to describe the localization of phase transformation, the extension of the initial model consisted of rewriting it in a nonlocal context through the introduction of a new variable, defined as the nonlocal counterpart of the martensite volume fraction. The use of this model has required the development of a specific finite element in ABAQUS with the nonlocal martensite volume fraction as an additional degree of freedom. The simulations show the relevance of such an approach in the description of the phase transformation occurring in thin SMA structures subjected to thermo-mechanical loadings. To achieve the description of the latent heat effects, a heat balance equation with a source term depending on contributions of the phase transformation was added to the constitutive equations of the initial model. Even there, the use of the model required the development of a finite element which takes into account the thermo-mechanical coupling and considers the proposed formulation for the thermal balance. Numerical simulations have shown the delaying effect of the latent heat on phase transformation and the possible heterogeneous character of the phase transformation in this case. These effects are even more important as the strain rate is high

Dans un contexte où l'utilisation de structures déployables s'est généralisée, le département Recherche de la société Thales Alenia Space étudie un nouveau concept de télescope spatial dont le miroir secondaire est déployé grâce au déroulement de six mètres rubans. Des études antérieures ont permis la mise au point d'un prototype constitué de rubans métalliques dont le déploiement s'est avéré trop violent. Dans ce travail de thèse nous proposons d'une part un nouveau type de ruban à la vitesse de déroulement maîtrisable et d'autre part un modèle original décrivant le comportement dynamique de tels rubans, permettant de mieux appréhender les phénomènes complexes pouvant intervenir lors de scénarios de pliage, de déploiement ou de déroulement. La solution envisagée pour contrôler la vitesse de déroulement repose sur l'exploitation des propriétés mécaniques d'une couche de matériau viscoélastique collée à la surface du ruban. Ces propriétés variant avec la température permettent de garantir un maintien de la position enroulée à froid et assurent un déroulement régulé grâce à un réchauffage localisé. Ces phénomènes ont été mis en évidence expérimentalement et numériquement. La lourdeur des méthodes classiques de modélisation et le manque de richesse des méthodes simplifiées nous ont conduit à développer un modèle de poutre à section fortement déformable permettant de décrire le comportement dynamique des rubans en grands déplacements. Partant d'un modèle de coque, l'originalité de la méthode repose essentiellement sur l'introduction d'une cinématique de type elastica pour décrire les grandes variations de forme de la section. Un modèle énergétique 1D est obtenu en intégrant dans la section et le problème est résolu à l'aide du logiciel de modélisation par éléments finis COMSOL. On propose finalement un modèle continu 1D à 4 paramètres cinématiques qui permet de rendre compte d'une large gamme de phénomènes intervenant dans des scénarios complexes de pliage, de déroulement et de déploiement dynamique. / The research department of Thales Alenia Space is studying new concepts of space telescopes whose secondary mirror is deployed thanks to the unreeling of six tape-springs. A breadboard using metallic tape-springs has been built during preliminary studies and has exhibited a deployment that is too energetic and induce too important shocks.In this thesis a new kind of tape-spring with a controlled uncoiling speed is introduced. Secondly a rod model with highly deformable thin-walled cross-sections describing the dynamic behaviour of tape-springs is derived.In order to over come the deployment speed of a tape spring, a viscoelastic layer is stuck on its sides. Thanks to its properties varying with the temperature, the viscoelastic layer is used to maintain the tape-spring in a coiled configuration at low temperature whereas a local heating leads to a controlled uncoiling. These phenomenons have been underlined experimentally and numerically.Because of the high complexity of classical shell models and the lack of details of simplified models, smart modelling methods need to be developed to describe the highly non linear behaviour of a tape-spring. A planar rod model with highly deformable thin-walled cross-sections that accounts for large displacements and large rotations in dynamics is proposed. Starting from a classical shellmodel, the main additional assumption consists in introducing an elastica kinematics to describe thelarge changes of the cross-section shape with very few parameters. The expressions of the strain andkinetic energies are derived by performing an analytical integration over the section. The Hamilton principle is directly introduced in a suitable finite element software to solve the problem. Several examples (folding, coiling and deployment of a tape spring) are studied through the FEM software COMSOL to demonstrate the ability of the 4-parameter model to account for several phenomena: creation of a single fold and associated snap-through behaviour, splitting of a fold into two, motion of a fold along the tape during a dynamic deployment, scenarios of coiling and uncoiling of a bistable tape-spring.