This dissertation introduces new methodologies for the analysis of neural spike trains. Biological properties of the nervous system, and how they are reflected in neural data, can motivate specific analytic tools. Some of these biological aspects motivate multiscale frameworks, which allow for simultaneous modelling of the local and global behaviour of neurons. Chapter 1 provides the preliminary background on the biology of the nervous system and details the concept of information and randomness in the analysis of the neural spike trains. It also provides the reader with a thorough literature review on the current statistical models in the analysis of neural spike trains. The material presented in the next six chapters (2-7) have been the focus of three papers, which have either already been published or are being prepared for publication. It is demonstrated in Chapters 2 and 3 that the multiscale complexity penalized likelihood method, introduced in Kolaczyk and Nowak (2004), is a powerful model in the simultaneous modelling of spike trains with biological properties from different time scales. To detect the periodic spiking activities of neurons, two periodic models from the literature, Bickel et al. (2007, 2008); Shao and Li (2011), were combined and modified in a multiscale penalized likelihood model. The contributions of these chapters are (1) employinh a powerful visualization tool, inter-spike interval (ISI) plot, (2) combining the multiscale method of Kolaczyk and Nowak (2004) with the periodic models ofBickel et al. (2007, 2008) and Shao and Li (2011), to introduce the so-called additive and multiplicative models for the intensity function of neural spike trains and introducing a cross-validation scheme to estimate their tuning parameters, (3) providing the numerical bootstrap confidence bands for the multiscale estimate of the intensity function, and (4) studying the effect of time-scale on the statistical properties of spike counts. Motivated by neural integration phenomena, as well as the adjustments for the neural refractory period, Chapters 4 and 5 study the Skellam process and introduce the Skellam Process with Resetting (SPR). Introducing SPR and its application in the analysis of neural spike trains is one of the major contributions of this dissertation. This stochastic process is biologically plausible, and unlike the Poisson process, it does not suffer from limited dependency structure. It also has multivariate generalizations for the simultaneous analysis of multiple spike trains. A computationally efficient recursive algorithm for the estimation of the parameters of SPR is introduced in Chapter 5. Except for the literature review at the beginning of Chapter 4, the rest of the material within these two chapters is original. The specific contributions of Chapters 4 and 5 are (1) introducing the Skellam Process with Resetting as a statistical tool to analyze neural spike trains and studying its properties, including all theorems and lemmas provided in Chapter 4, (2) the two fairly standard definitions of the Skellam process (homogeneous and inhomogeneous) and the proof of their equivalency, (3) deriving the likelihood function based on the observable data (spike trains) and developing a computationally efficient recursive algorithm for parameter estimation, and (4) studying the effect of time scales on the SPR model. The challenging problem of multivariate analysis of the neural spike trains is addressed in Chapter 6. As far as we know, the multivariate models which are available in the literature suffer from limited dependency structures. In particular, modelling negative correlation among spike trains is a challenging problem. To address this issue, the multivariate Skellam distribution, as well as the multivariate Skellam process, which both have flexible dependency structures, are developed. Chapter 5 also introduces a multivariate version of Skellam Process with Resetting (MSPR), and a so-called profile-moment likelihood estimation of its parameters. This chapter generalizes the results of Chapter 4 and 5, and therefore, except for the brief literature review provided at the beginning of the chapter, the remainder of the material is original work. In particular, the contributions of this chapter are (1) introducing multivariate Skellam distribution, (2) introducing two definitions of the Multivariate Skellam process in both homogeneous and inhomogeneous cases and proving their equivalence, (3) introducing Multivariate Skellam Process with Resetting (MSPR) to simultaneously model spike trains from an ensemble of neurons, and (4) utilizing the so-called profile-moment likelihood method to compute estimates of the parameters of MSPR. The discussion of the developed methodologies as well as the ``next steps'' are outlined in Chapter 7.

Depuis des décennies, le processus d'enlèvement de matière des composites à matrices polymères (CMP) ne cesse de susciter des interrogations. La complexité et la multitude des phénomènes physiques activés par la coupe constituent encore un défi d'actualité pour la compréhension et la maitrise du comportement des structures composites. Ce travail propose une analyse multiéchelle fine des phénomènes élémentaires émanant du comportement de chacune des phases constituantes du matériau afin de modéliser leurs couplages multiphysiques potentiels conduisant à la formation du copeau. L'étude est alors hybride conjuguant l'approche expérimentale exprimée par l'essai instrumenté et l'approche numérique exprimée par la modélisation par éléments finis (EF). La formulation du couplage multiphysique a fait l'objet d'une routine VUMAT alliant la mécanique de l'endommagement continu à la mécanique de la rupture par le biais du triptyque élasticité-endommagement-rupture. A la différence des approches binaires de la littérature, le modèle développé dans ce travail s'appuie sur un concept d'endommagement progressif pour prédire la rupture physique des phases, et par conséquent, la formation du copeau. Les mécanismes d'initiation et de propagation de la fissure sont pilotés par les énergies de rupture des phases identifiées selon les normes en vigueur. La gestion du contact par une routine VFRIC a permis d'assurer la synergie entre les propriétés locales de l'interface et les frottements générés. Les calculs ont démontré la pertinence du modèle tridimensionnel proposé dans la simulation des mécanismes de formation du copeau sensiblement à l'orientation et la nature des fibres. La bonne concordance entre les mesures et les prédictions d'efforts de coupe a mis en évidence l'intérêt d'un pilotage rigoureux du contact outil-pièce pour la simulation multiphysique de la coupe. / Since several decades, the material removal process of Fiber Reinforced Polymers (FRP) continues to raise technical and scientific queries. The understanding of the multiple and complex phenomena generated when cutting still remains challenging for controlling the behavior of composite structures. This study addresses a multiscale analysis of elementary phenomena associated to each of the composite constituents in order to model the chip formation mechanisms owing to the multiphysical coupling. An investigation combining the experimental approach resulting in the instrumented test and numerical approach allowing to the finite element (FE) development was hence conducted. A VUMAT subroutine was built to express the constitutive formulation coupling the continuum damage mechanics to the failure mechanics by means of the triptych elasticity-damage-failure. Unlike to the binary approaches proposed by the open literature, the model proposed herein bases on the progressive damage concept for predicting the physical failure allowing to the formation of the chip. The crack initiation and growth mechanisms are controlled by the failure energies determined experimentally for each material phase. The efficiency of the VFRIC subroutine to managing the contact properties, i.e. friction, at the tool-material interface was confirmed. The numerical results proved the reliability of the model to simulate the chip formation mechanisms with respect of fiber orientation. The good agreement between the measured and predicted forces proved the interest of the rigorous modeling of the tool-material interface.

Le rodage mécanique demeure encore le procédé industriel de référence pour la finition des cylindres de moteurs dans le cadre des productions de grande série. La voie actuelle de fabrication en rodage procède par frottement et abrasion à vitesse réduite pour imprimer une texture anisotrope et multi-échelle sur la surface du cylindre. La signature de cette texture a la particularité de satisfaire des exigences multifonctionnelles du cylindre (frottement, lubrification, usure, consommation d'huile, etc.). Elle est cependant générée par un rodage stratifié en production industrielle qui consiste en trois étapes successives avec effet d'échelle: ébauche (échelle macroscopique), finition (échelle mésoscopique) et superfinition (échelle microscopique). Plusieurs méthodes de rodage ont émergé cette dernière décennie et dont la différentiation technologique et économique se fait essentiellement par le choix des attributs texturaux et topographiques de surface de rodage. La présente étude analyse les processus de rodage industriel, du choix d'anisotropie possibles et paramètres texturaux dans une optique de fonctionnalisation de la surface rodée du cylindre. Une approche méthodologique sur la tribo-fonctionnalité multi-échelle de la surface de rodage du cylindre a été développée, puis validée par simulation numérique dans le cas du tribo-contact segment-cylindre. Elle s'appuie sur le triptyque suivant :- le couplage entre le processus de rodage et la fonctionnalité via la caractérisation de sa signature texturale multi-échelle,- l'exploitation de l'anisotropie contrôlée par simulation numérique qui conduit à la texture de fonction,- l'interaction surface – procédé de rodage qui devient indissociable, notamment dans la fabrication de la texture de fonction et sa qualification tribo-fonctionnelle par des essais tribométriques.Cette démarche méthodologique a été appliquée aux procédés de rodage industriel tel que le rodage plateau (PH), glissant (SH) et hélico-glissant (HSH). Cela a permis de démontrer qu'une texture anisotrope fine de type PH composée de plateaux et vallées de faible amplitude présente les meilleurs attributs fonctionnelles en frottement. Cependant, une texture anisotrope de type HSH avec un angle de striation de 130° est moins sensible en frottement à l'aspect plateau obtenu par écrêtage des pics de rugosité. Ce résultat ouvre une évolution potentielle du process HSH où la dernière étape de rodage peut être réduite voire supprimée. Par la suite, la démarche développée a été étendue aux textures innovantes à bas frottement de rodage en développement avec une anisotropie circulaire, ondulatoire, stratifiée mixte, ou assistée en trajectoire. Les résultats ont montré que des textures HSH optimisées en trajectoire (avec suppression de stries d'inversion au niveau des points mort haut (PMH) et point mort bas (PMB) du cylindre) ainsi que des textures stratifiées mixtes 45°-130°-45° (stries à 45° au PMB et PMH et 130° au milieu du cylindre) permettent une réduction significative du frottement segment-fût en régime de lubrification mixte en comparaison par rapport au texture de rodage HSH conventionnel. / Mechanical honing process is still the reference industrial process for high production engine liners. The current manufacturing way use reduced velocity friction and abrasion mechanisms to print a multiscale and anisotropic texture on the liner surface. The texture signature characteristics satisfy multifunctional requirements of the liner (friction, lubrication, wear, oil consumption etc.). It is generated by a stratified honing process for industrial production which consists of three stages with scale effect: rough (macroscopic scale), finish (mesoscopic scale) and super-finish honing (microscopic scale). Different honing methods emerged during last decade in which the technological and economic differentiation is essentially based on textural attributes of honed surfaces. The present study analyses the industrial honing processes, the possible surface anisotropy choices and texture parameters with a view to honed liner surface functionalisation. A methodological approach about multiscale honed surface tribofunctionality has been developed and then validated by numerical simulation in the case of ring-liner tribocontact. It builds on the following triptych:- the coupling between honing process and functionality through its multiscal textural signature,- the exploitation of the controlled anisotropy by numerical simulation which conducts to fonctionality,- the surface-process interaction which becomes indivisible, particularly in texture manufacturing and its tribofunctional qualification though tribometric trials.The methodology has been applied to industrial honing processes (plateau honing (PH), slide honing (SH) and helical slide honing (HSH)). The results show that smooth texture with lower plateau roughness and valley depth contributes to reduce frictional performances of honed surfaces. Nevertheless, Helical slide honed surfaces are less sensitive in friction to the plateaudness i.e., to superficial roughness comparatively to PH textures. This is promising for HSH process optimization, in which the third stage can be reduced or deleted. Then the developed approach has been extended to honing development for innovative texture anisotropy (circular, undulatory, mixed, trajectory assisted) for low-friction performances. The results show that assisted trajectory (without inversion grooves at top dead (TDC) and bottom dead centers (BDC)) and 45-130-45 mixed textures (with 45° cross-hatched grooves at TDC and BDC, 130° cross-hatched grooves at mid-height) enhance significantly frictional performances in comparison to HSH conventional process.

Content: Leather is a fairly durable and flexible material created by tanning animal rawhides and can be found in many household and personal products. However, ensuring that the product endures attack from the environmental elements that contribute to its wear and tear is the key concern of the general consumer. Animal rawhides are soft collagenous connective tissues. The most important function of collagen is a mechanical one - to withstand loads acting on the leather material. The purpose of this paper is to show how findings from recent studies on the mechanics of collagen in connective tissues lend to the goal of structural biologists to establish a complete understanding of the functional significance of collagen in connective tissues. In particular, 28 different types of collagen have been identified - about 90% being type 1 collagen - in the human body. Most types of collagen participate in higher-order assemblies such as networks, filaments, microfibrils, fibrils, fibres/fascicles. These assemblies collectively form a hierarchical architecture in the tissue from the molecular level to the macroscopic level. A complete understanding the functional significance of collagen in connective tissues could direct the development of new technology, e.g. leather design and production. In this paper, I shall discuss findings related to the higher-order assemblies. The conventional understanding of the collagenous fibre-like structures - embedded in a hydrated ground substance - in connective tissue finds an analogy to engineering fibres reinforcing composite materials such as carbon fibre reinforced polymer composites. The macroscopic stress- strain response of the connective tissue to external loads acting on it is consistent with fibre composite behaviour. A structure-mechanical framework, underpinning the hierarchical architecture of the connective tissue, is proposed to explain this mechanical response of the tissue. By integrating models specific to the different levels of the tissue to enable better understanding of the macroscopic nature of the tissue, the framework serves as a representation of reality for guiding further research, especially for the purpose of exploring hypotheses and revealing properties for which only sparse (or no observational data) is available. This paper ends with a discussion on the prospect and challenges for future studies on collagen in connective tissues. Take-Away: A fresh look at the degree of collagen fibril alignment in tissue Rethinking the mechanics of cross-linking between fibrils Interfibrillar mechanics is governed by plastic stress transfer Influence of fibril diameter on interfibrillar stress transfer

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[pt] Compósitos cimentícios estão ganhando cada vez mais relevância na indústria da construção civil. No entanto, as diretrizes para o projeto do material compósito e dos seus elementos estruturais são ainda incipientes, pois mecanismos de ponte de transferência de forças providos pelas fibras ainda estão sob investigação. Este trabalho apresenta uma estratégia de modelagem de elementos finitos que leva em consideração a estrutura de nível mesoestrutural do material cimentício reforçado com fibras. Desta forma, quatro fases do material são consideradas no modelo numérico: agregados graúdos, argamassa, zona de transição interfacial (ZTI) e fibras. A argamassa e os agregados são modelados usando elementos contínuos triangulares com comportamento linear-elástico. As fibras são incluídas usando elementos de treliça unidimensionais acopladas a elementos bidimensionais contínuos. Uma técnica de fragmentação de malha é usada para introduzir elementos de interface nas arestas dos elementos de argamassa e na interface entre agregados e argamassa para representar a ZTI. O método Take-and-Place, proposto por Wriggers e Moftah (2006), foi adotado neste estudo para incluir agregados no modelo. Primeiro, os agregados são gerados seguindo uma curva de Fuller, que define um empacotamento entre os agregados perfeitos. Na segunda fase, os agregados são introduzidos no modelo garantindo a não sobreposição entre eles. Finalmente, as fibras são adicionadas. Para validar a metodologia proposta, testes experimentais foram simulados com sucesso em um framework de simulação numérica – GeMA. Por fim, o trabalho explora a influência do empacotamento fibra-agregado na resposta mecânica e nos padrões de fraturamento de compósitos cimentícios fibrosos. / [en] Fiber Reinforced Concrete (FRC) materials are gaining more relevance in the construction industry. However, the guidelines for the design of the composite material and of structural elements thereof are incipient and the stress bridging mechanisms are still under investigation. This work presents a finite element modelling strategy that takes into account the material meso-level structure. Four phases of the FRC material are considered in the model: coarse aggregates, mortar, interfacial transition zone (ITZ), and fibers. The mortar and aggregates are modelled using triangular linear elements with linear–elastic behavior. Fibers are included using one-dimensional truss elements which are coupled to the matrix through the technique proposed by Congro (2021). Zero-thickness interface elements are introduced at the interface between mortar elements, and at the interface between aggregates and mortar to represent the ITZ. The Take-and-Place method, obtained from Wriggers and Moftah (2006), was adopted in this study to include aggregates in the model. First, the aggregates are generated following a Fuller s curve that means a perfect aggregate package. In the second phase, the aggregates are placed in the model without overlapping. Finally, fibers were added. A mesh fragmentation technique is used to introduced zero-thickness interface elements at the interface between mortar elements, and at the interface between aggregates and mortar to represent the ITZ. To validate the proposed methodology, direct tensile test models were successfully reproduced in finite element analyses performed in an in-house framework – GeMA. Based on the obtained results, the authors could explore the influence of the fibers-aggregate packing in the mechanical response of the composite material.

Les composites tissés 3D, à l'aide de leurs grandes libertés de conception, peuvent fournir des propriétés mécaniques adaptées aux besoins spécifiques d'une structure. La complexité architecturale de ces matériaux induit néanmoins des propriétés, des comportements ainsi que des endommagements très difficiles à prédire. Les travaux présentés dans ce manuscrit s'inscrivent directement dans cette problématique et cherchent à développer des outils permettant, par simulation numérique, de prévoir les caractéristiques mécaniques de ce type de matériaux. Afin de répondre à cet objectif, une approche multiéchelle, alliant essais expérimentaux et simulations numériques, a été adoptée. Cette démarche permet, en appliquant des sollicitations réelles, de considérer la géométrie des renforts et les hétérogénéités du matériau, observables à l'échelle mésoscopique, qui sont responsables du comportement macroscopique du composite tissé. Le travail d'investigation expérimentale s'est attaché à caractériser le comportement d'un composite interlock 2,5D et des ses constituants ainsi que les mécanismes et cinétiques de rupture, pour des sollicitations de traction/flexion, grâce à des observations tomographiques aux rayons X et au concept d'interzone. En ce qui concerne la modélisation numérique, un critère de rupture permettant de simuler la dégradation ultime du composite, en coupant les fils de renforts, a été présenté et testé sur une cellule représentative du composite expérimentale. Les résultats en termes de localisations, d'orientations et de cinétiques de l'endommagement sont en accord avec les observations expérimentales. Ensuite, après avoir estimé l'influence des différents paramètres architecturaux sur le critère de rupture avec une campagne de calcul éléments finis, des architectures optimisées, pour les sollicitations considérées, ont pu être proposées et comparées à l'interlock 2,5D. Toujours dans l'optique d'une meilleure prédiction du comportement des composites tissés, les travaux se sont également intéressés à une modélisation plus fine des mécanismes d'endommagement. Une approche fiabiliste a donc été introduite sur le critère de rupture à l'aide d'une distribution statistique de Weibull. De plus, un autre mécanisme d'endommagement a aussi pu être pris en compte dans la modélisation en simulant, avec le modèle GTN (Gurson-Tvergaard-Needleman), la cavitation de la matrice. Enfin, des techniques de réduction de modèle ont été employées pour diminuer le coût calcul de la modélisation multiéchelle afin d'identifier, par exemple, des propriétés matériaux par méthode inverse ou de simuler des essais de fatigue. / With their large flexibility of design , 3D woven composites can provide mechanical properties tailored specificially to structural needs. However, the architectural complexity of woven reinforcements presents serious challenges when predicting properties, behaviours and damage processes. The present work deals with these challenges and seeks to develop numerical tools which are able to foresee the mechanical characteristics of this kind of materials. For this purpose, a multiscale approach, which combines experimental tests and numerical simulations, has been adopted. This approach allows, simultaneously, to take into account the loads and composite behavior, at the macroscopic scale, also the reinforcement geometry and the material heterogeneities which are only visible at the mesoscopic scale. The experimental investigation has been carried out to characterize the behaviour of an 2.5D interlock composite and its constituents. Examinations of the damage mechanisms have also been performed, using tomography and the interzone concept, for this woven composite under loadings in tension and combined tension and bending. With regards to the numerical modeling part, the ultimate degradation of the composite was simulated by cutting the reinforcement yarns with a failure criterion, previously reported, on a 3D representative cell of the experimental composite. For the two kinds of macroscopic loadings, the locations, orientations and kinetics of the damage were found to be fully in agreement with the experimental results. The influence of the architectural parameters on the failure criterion was then evaluated by finite element calculation. Consequently, it has been possible to proposed optimized architectures and make a camparison, for the two macroscopic loadings, with the 2.5D interlock woven composite. Still motivated to improve the prediction of the behaviour of woven composites, this work has also been on developing a finer modeling approach to the understanding of damage mechanisms. A stochastic approach was therefore introduced to the failure criterion using a Weibull statistical distribution. In addition, matrix cavitation has also been taken into account in the modelling. This damage mechanism was simulated using the GTN (Gurson-Tvergaard-Needleman) model. Finally, model reduction techniques have been applied to lower the cost of computing multiscale modeling in order to identify, for example, material properties by an inverse method or to simulate fatigue tests.

Ein metrischer Graph mit einem selbstadjungierten, negativen Laplace-Operator wird Quantengraph genannt. In dieser Arbeit werden Transporteigenschaften zufälliger Laplace-Operatoren betrachtet. Dazu wird die Multiskalenanalyse (MSA) von euklidischen Räumen auf metrische Graphen angepasst. Eine Überdeckung der metrischen Graphen wird aus gleichmäßig polynomiellem Wachstum und der gleichmäßigen Beschränkung der Kantenlängen gewonnen. Als Hilfsmittel für die MSA werden eine Combes-Thomas-Abschätzung und eine Geometrische Resolventenungleichung bewiesen. Zusammen mit einer Wegner-Abschätzung und der Existenz von verallgemeinerten Eigenfunktionen wird mittels der modifizierten MSA spektrale Lokalisierung (d.h. reines Punktspektrum) mit polynomiell fallenden Eigenfunktionen am unteren Rand des Spektrums für negative Laplace-Operatoren mit zufälligem Potential geschlossen. Dabei sind alle Randbedingungen, die eine nach unten beschränkten Operator liefern, wählbar. / We prove spectral localization for infinite metric graphs with a self-adjoint Laplace operator and a random potential. Therefor we adapt the multiscale analysis (MSA) from the euclidean case to metric graphs. In the MSA a covering of the graph is needed which is obtained from a uniform polynomial growth of the graph. The geometric restrictions of the graph contain a uniform bound on the edge lengths. As boundary conditions we allow all settings which give a lower bounded self-adjoint operator with an associated quadratic form. The result is spectral localization (i.e. pure point spectrum) with polynomially decaying eigenfunctions in a small interval at the ground state energy.

<p>Composite materials have been invented and used to make all kinds of industrial products, such as automobiles, aircraft, sports equipment etc., for many years. Excellent properties such as high specific stiffness and strength have been recognized and studied for decades, motivating the use of composite materials. However, the design of composite structures still remains a challenge. Existing design tools are not adequate to exploit the full benefits of composites. Many tools are still based on the traditional material selection paradigm created for isotropic homogeneous materials, separated from the shape design. This will lose the coupling effects between composite materials and the geometry and lead to less optimum design of the structure. Hence, due to heterogeneity and anisotropy inherent in composites, it is necessary to model composite parts with appropriate microstructures  instead of simplistically replacing composites as black aluminum and consider materials and geometry at the same time.</p> <p><br></p> <p>This work mainly focuses on the design problems of complex material-structural systems through computational analyses. Complex material-structural systems are structures made of materials that have microstructures smaller than the overall structural dimension but still obeying the continuum assumption, such as fiber reinforced laminates, sandwich structures, and meta-materials, to name a few. This work aims to propose a new design-by-analysis framework based on the mechanics of structure genome (MSG), because of its capability in accurate and efficient predictions of effective properties  for different solid/structural models and three-dimensional local fields (stresses, strains, failure status, etc). The main task is to implement the proposed framework by developing new tools and integrating these tools into a complete design toolkit. The main contribution of this work is a new efficient high-fidelity design-by-analysis framework for complex material-structural systems.</p> <p><br></p> <p>The proposed design framework contains the following components. 1) MSG and its companion code SwiftComp is the theoretical foundation for structural analysis in this design framework. This is used to model the complex details of the composite structures. This approach provides engineers the flexibility to use different multiscale modeling strategies. 2) Structure Gene (SG) builder creates finite element-based model inputs for SwiftComp using design parameters defining the structure. This helps designers deal with realistic and meaningful engineering parameters directly without expert knowledge of finite element analysis. 3) Interface is developed using Python for easy access to needed data such as structural properties and failure status. This is used as the integrator linking all components and/or other tools outside this framework. 4) Design optimization methods and iteration controller are used for conducting the actual design studies such as parametric study, optimization, surrogate modeling, and uncertainty quantification. This is achieved by integrating Dakota into this framework. 5) Structural analysis tool is used for  computing global structural responses. This is used if an integrated MSG-based global analysis process is needed.</p> <p><br></p> <p>Several realistic design problems of composite structures are used to demonstrate the capabilities of the proposed framework. Parameter study of a simple fiber reinforce laminated structure is carried out for investigating the following: comparing with traditional design-by-analysis approaches, whether the new approach can bring new understandings on parameter-response relations and because of new parameterization methods and more accurate analysis results. A realistic helicopter rotor blade is used to demonstrate the optimization capability of this framework. The geometry and material of composite rotor blades are optimized to reach desired structural performance. The rotor blade is also used to show the capability of strength-based design using surrogate models of sectional failure criteria. A thin-walled composite shell structure is used to demonstrate the capability of designing variable stiffness structures by steering in-plane orientations of fibers of the laminate. Finally, the tool is used to study and design auxetic laminated composite materials which have negative Poisson's ratios.</p>

[pt] Nos últimos anos, os materiais compósitos cimentícios vêm ganhando destaque na indústria da construção civil. Suas excelentes propriedades mecânicas e contribuição para o controle de propagação de fissuras são um atrativo para seu emprego como material de construção. No entanto, normas técnicas para projeto envolvendo estes materiais e estruturas ainda não são consagradas. Uma melhor compreensão do comportamento de materiais cimentícios com adição de fibras requer o estudo de suas fases e da interação entre elas. Análises em diferentes escalas possibilitam esta representação. Tensões e deformações, dano e iniciação de fissuras ocorrem na escala das heterogeneidades e ajudam a explicar e prever o comportamento do concreto em uma escala macroscópica. A modelagem e simulação do comportamento destes compósitos é complexa e desafiadora. Para tal, é necessário definir os principais mecanismos que descrevem o comportamento do material de modo a escolher a descrição matemática adequada. Esta dissertação propõe metodologias para a modelagem numérica multiescala de materiais compósitos cimentícios. A partir de informações obtidas na escala do material, busca-se compreender melhor o comportamento global do compósito. Para isto, serão desenvolvidos métodos numéricos e computacionais baseados no Método dos Elementos Finitos, em técnicas de Inteligência Artificial e nos conceitos da Mecânica do Dano Computacional. Na macroescala, um modelo contínuo equivalente é desenvolvido através de técnicas probabilísticas e de Inteligência Artificial. Na mesoescala, duas abordagens são propostas. A primeira inclui as fibras através de elementos de interface, e a segunda através de um novo elemento compósito fibra-matriz. Os modelos desenvolvidos permitem avaliar a evolução do dano, o processo de propagação de fissuras, e o comportamento global carga-deslocamento do compósito até a ruptura. Resultados experimentais da literatura suportam as conclusões do trabalho. / [en] In recent years, fiber reinforced cement-based materials have gained relevance in the civil engineering industry. Due to its excellent mechanical properties and contribution to crack propagation control, there is a great appeal to its usage as a construction material. However, technical standards for fiber reinforced concrete are still not established. A better understanding of the behavior of cement composite materials requires the representation of the material phases and their interfacial behavior. Stresses and strain distributions, damage evolution and fracture initiation develop at the observation scale of the heterogeneities and help to explain and predict the behavior of concrete at a macroscopic level. The numerical modeling of these composites emerge as challenging and complex problems. For this, it is necessary to define the main mechanisms that describe the material behavior in order to choose the proper mathematical formulation. This dissertation proposes methodologies for the numerical modeling of cement composite materials in a multiscale approach. From the information obtained at the material scale, this work aims at assessing the global behavior of the composite. Numerical and computational procedures will be developed based on the Finite Element Method, Artificial Intelligence techniques and concepts of Computational Damage Mechanics. At the macroscale, an equivalent continuum model is developed through probabilistic and Artificial Intelligence techniques. At the mesoscale, two approaches are proposed. The first includes the fibers through interface elements. The second adopts a new fiber-matrix composite element. With the models developed here, it is possible to evaluate damage evolution, fracture propagation patterns, load-displacement global behavior of the composite upto failure. Experimental results from the literature give support to the conclusions.