This thesis deals with determination of representative constitutive model for describing atherosclerotic carotid artery behavior. The first part of the thesis provides brief summary of medical knowledge needed as well as detailed describtion of current experimental methods for determination of mechanical properties of atherosclerotic arteries. The main part is focused on mechanical testing of atheroslecotic carotid arteries. The description of sample preparation, testing device and the experiment itself is involved. Statistical analysis of measured data is done, focusing on comparison of factors potentially influencing mechanical behavior. In conclusion, the FEA analysis on simplified geometry of carotid artery with atheroma is performed. Emphasis is placed on the impact of material model obtained from experiments on equivalent stress in fibrous cap.

Avec l’avènement des NEMS, MEMS, films minces et autres revêtements, la caractérisation des propriétés mécaniques à uneéchelle locale est primordiale. A cet effet, l’essai d’indentation instrumentée permet l’acquisition continue de la réponse (courbeforce – profondeur de pénétration) d’un matériau à la pénétration d’un indenteur de géométrie donnée. Le post-traitement d’unetelle courbe permet la détermination de propriétés telles que le module d’indentation ou la dureté. Cette analyse est basée surla théorie du contact élastique, qui suppose une géométrie axisymétrique parfaite de la pointe d’indentation, un comportementpurement élastique du matériau, et la non-prise en compte des déplacements radiaux dans la zone de contact. En pratique, ceshypothèses sont souvent mises en défaut : les indenteurs sont généralement des pyramides à 3 pans (Berkovich, Cube Corner)ou 4 pans (Vickers, Knoop) présentant un émoussement de la pointe, et le comportement mécanique des matériaux est souventcomplexe. La correction de la relation de Sneddon, utilisée dans la méthode d’Oliver et Pharr pour l’analyse des essais denanoindentation, est donc nécessaire. Dans le cadre de cette thèse, nous nous sommes intéressés à la détermination de ce facteurde correction, qui n’est pas une valeur universelle ni unique comme le préconisent certains auteurs. Il dépend notamment de lapression exercée par la pointe d’indentation et du matériau sollicité. Cette étude s’est faite sur la base de la détermination de laloi de comportement d’un des matériaux standards utilisés pour la calibration de l’essai de nanoindentation, la silice fondue.Ce matériau présente un comportement mécanique spécifique : sa déformation anélastique s’effectue par un mécanisme dedensification. Dans un premier temps, les paramètres de cette loi de comportement sont identifiés par une approche inversecombinant la simulation numérique 3D de l’essai d’indentation à l’optimisation de la fonction objectif au moyen d’unalgorithme génétique. Le facteur de correction est ensuite déterminé pour deux géométries de pointes et à différentes valeursdu rapport adimensionnel "profondeur de pénétration/rayon de pointe". La méthodologie proposée a été appliquée à ladétermination du module d’indentation d’un acier inox. / With the advent of NEMS, MEMS, thin films and other coatings, the characterization of local mechanical properties is achallenge. For this purpose, the instrumented indentation test allows for the continuous acquisition of the response (loadpenetration depth) of the material using an indenter of given geometry. The post-processing of such a curve allows thedetermination of the indentation modulus or the hardness of that material. This analysis relies on the elastic contact theory,which assumes an axisymmetric and perfect indenter, a purely elastic behaviour, and no radial displacements in the contactarea. In practice, those assumptions are defeated: indenters shapes are rather three-sided (Berkovich, Cube Corner) or foursided (Vickers, Knoop) pyramids, with blunted tips. Furthermore, mechanical behaviour is rather complex. The introductionof a correction factor in the Sneddon’s relationship, on which is based the Oliver and Pharr method for the analysis ofnanoindentation data is then necessary. Whithin the scope of this work, we aimed at determining this correction factor, whichhas not a unique nor a universal value, as recommended by some authors. It depends on the pressure distribution beneath theindenter and on the tested material. This study is based on the identification of the constitutive law of one of the referencespecimen used for calibration of the nanoindentation test, namely fused silica. The latter exhibits a specific mechanicalbehaviour, its anelastic deformation being achieved by a densification mechanism. In a first step we have determined the modelparameters by an inverse approach combining the 3D numerical simulation of the indentation test with the optimization of theobjective function using a genetic algorithm. The correction factor is then determined for two tip geometries and at severalpenetration depth over tip radius adimensional ratios. The proposed methodology was applied to the determination of theindentation modulus of an inox steel.

In this study, two major internal erosion initiation processes, suffusion and concentrated leak mechanisms, which lead to both defect formation in a dam’s body and its foundation and high throughflow in dams subjected to internal erosion were studied. This understanding has the potential to facilitate numerical modelling and expedite dam safety assessment studies.  The throughflow properties of coarse rockfill material were studied by; analysing filed pump test data, performing extensive laboratory experiments with a large-scale apparatus and numerically simulating the three-dimensional flow through coarse rock materials, replicating the material used in the laboratory experiments. Results from the tests demonstrate that the parameters of the nonlinear momentum equation of the flow depend on the Reynolds number for pore Reynolds numbers lower than 60000.  Numerical studies were also carried out to conduct numerical experiments. By applying a Lagrangian particle tracking method, a model for estimating the lengths of the flow channels in the porous media was developed.  The shear forces exerted on the coarse particles in the porous media were found to be significantly dependent on the inertial forces of the flow. Suffusion and concentrated leak mechanisms were also studied by means of laboratory experiments to develop a theoretical framework for continuum-based numerical modelling. An erosion apparatus was designed and constructed with the capability of applying hydraulic and mechanical loading. Results were then used to develop constitutive laws of the soil erosion as a function of the applied hydromechanical load for both suffusion and concentrated leak mechanisms. Both the initiation and mass removal rate of were found to be dependent on the soil in-situ stresses. A three-dimensional electrical-resistivity-based tomography method was also adopted for the internal erosion apparatus and was found to be successful in visualising the porosity evolution due to suffusion. / <p>QC 20161006</p>

La simulation interactive du corps humain est un problème crucial en informatique médicale. Les approches sont multiples pour arriver à cet objectif. Diminuer le temps de calcul est le leitmotiv d'un grand nombre de travaux ces dernières années. Pour les recherches qui utilisent des modèles physiques inspirés de la Mécanique des Milieux Continus pour la simulation des objets déformables, ce sont principalement les forces internes et leurs dérivées qui font l'objet d'études pour l'amélioration des performances au niveau du temps de calcul. Nous avons choisi de développer la Méthode des Masses-Tenseurs, modèle physique souvent utilisé pour son bon compromis temps de calcul — précision. Notre première contribution est l'utilisation du calcul formel pour la génération des équations des forces internes et de leurs dérivées. Notre deuxième contribution est la parallélisation de ce modèle physique en calculant les équations générées sur le GPU. Notre troisième contribution est l'extension de ce modèle physique à d'autres types d'éléments : triangle, quadrangle, hexaèdre, prisme et pyramide. Tenir compte des déformations pour utiliser la loi de comportement la plus efficace en temps de calcul lorsque c'est possible, est une stratégie que nous avons mis en place. Dans la même idée, nous prenons en compte la géométrie du modèle à simuler pour utiliser des éléments plus complexes mais en nombre réduit. Pour utiliser ces stratégies, nous avons développé et utilisé des modèles mixtes en loi de comportement et en type d'éléments. Nos travaux se placent dans le contexte du projet ETOILE pour le développement d'un modèle biomécanique du système respiratoire / Interactive simulation of the human body is a crucial issue in medical computer sciences. There are many approaches to reach this goal. Reducing the computation time is the leitmotiv of a large number of efforts in recent years. For researches which use physical models derived from continuum mechanics for the simulation of deformable objects, it is primarily the internal forces and their derivatives which are the subject of study for improving computation time. We chose to develop the Tensor Mass Method, a physical model often used for its good computation time vs accuracy trade-off. Our first contribution is the use of computer algebra to generate the internal forces and their derivatives. Our second contribution is the parallelization of this physical model by computing the generated equations on the GPU. Our third contribution is an extension of this physical model to other elements : triangle, quandrangle , hexahedron, prism and pyramid. Considering deformations to use the most effective constitutive law in terms of computation time whenever possible is a good strategy that we started developing. In the same idea, we take the geometry of the simulated model into account to introduce more complex elements, albeit in reduced numbers. To use these strategies, we have developed mixed models in constitutive laws and elements. Our research was performed in the framework of the ETOILE project, to develop a biomechanical model of the respiratory system

L'objectif de ce travail est d'analyser l'influence du renforcement du sol par la method Soil Mixing sur le comportement des fondations superficielles et profondes. Une étude numérique a été effectuée – avec des analyses éléments finis dans ABAQUS - dans le but d'acquérir une compréhension du fonctionnement et une estimation de la performance des fondations améliorées. Pour être en mesure d'utiliser des colonnes SM pour l'amélioration de la fondation, il est nécessaire de bien comprendre leur performance sous charge axiale statique. Par conséquent, une série de simulations reproduisant des essais de chargement d'une seule colonne, et d’un groupe de colonnes ont été réalisées. Les essais à pleine et petite échelle ont été modélisés et leurs résultats comparés avec les observations expérimentales. Un bon accord entre les prédictions numériques et les mesures confirme une bonne calibration des lois constitutives des sols, des colonnes et de l’interface sol/colonne en SM. En outre, cette étude a révélé que la colonne SM agit d'une manière similaire à un pieu en béton, son comportement est régi principalement par l'interface. Ensuite, la modélisation numérique d’une fondation superficielle à petite échelle a été menée. Deux types de renforcement ont été étudiés. Le premier consiste en une seule colonne, située au centre sous la semelle analysée. Le second cas correspond à un groupe de quatre colonnes SM. Deux densités de sol ont été analysés. L'objectif de la modélisation est d'identifier l'efficacité du renforcement en termes de capacité portante de la fondation et de la réduction de son déplacement vertical. Il a été trouvé que la densité du sable a un impact significatif sur le comportement de la semelle. La variation de densité a entraîné une différence significative entre les forces totales portées par les fondations. Mais, il a été constaté que le pourcentage de la force reprise par le sol par rapport à la force total, est indépendant de la densité. L'influence du renforcement obtenu par un groupe de colonnes SM sur une fondation profonde, a été étudiée. La modélisation numérique d'un seul pieu théorique installé dans le sol homogène, a été réalisée. L'objectif de l'étude est de détecter l'impact de divers paramètres, tels que la distance horizontale entre les colonnes de SM, la distance verticale entre les têtes de colonnes et la pointe de pieu, le diamètre et la longueur des éléments SM, sur la capacité portante de la fondation. On a montré que la distance entre les colonnes et leur diamètre ont la plus grande influence sur la force de charge, la longueur de renforcement conduit à une moindre influence. / The aim of this work is to analyse the influence of soil reinforcement executed by the Soil Mixing method on the behaviour of shallow and deep foundations. Numerical investigation has been carried out - with the use of Finite Element (FE) analyses in ABAQUS - in an attempt to identify the mechanisms guiding the performance of supported foundations. To be able to use SM columns as the foundation’s improvement, it is necessary to fully understand their performance under applied static, axial load. Therefore, a set of simulations reproducing loading tests of single and group of columns have been carried out. Full and small scale tests have been modelled and their results compared with experimental observations. Good agreement between numerical predictions and measurements, confirms proper calibration of the chosen constitutive laws of: soils, columns and interactions between them. Moreover, this study has revealed that the SM column acts in a similar way to concrete pile, hence its behaviour is governed mainly by the interface. Afterwards, numerical modelling of small scale shallow foundation has been accomplished. Two kinds of reinforcement have been investigated. The first one consists of a single column situated centrally under the analysed footing. The second kind of improvement involves group of four SM columns. Two densities of soil have been analysed. The goal of the modelling is to identify the efficiency of the reinforcement in terms of: bearing capacity of the foundation and reduction of its vertical displacement. Despite significant difference between total forces borne by the foundation tested on soil with different densities, it has been found that the percentage of the total force that was taken by the soil is density independent. The influence of reinforcement executed by group of SM columns on a deep foundation has been studied. Numerical modelling of a theoretical, single pile, installed in homogeneous soil, has been carried out. The aim of the investigation is to detect the impact of parameters such as: pattern of reinforcing elements, horizontal distance between SM columns, vertical distance between columns’ heads and tip of the pile, diameter and length of SM elements, on the bearing capacity of the foundation. It has been found that the distance between columns and their diameter has the biggest influence on the borne force. However, the length of the reinforcement has shown the least significant influence.

Nous présentons dans ce mémoire l'influence que peuvent avoir les écoulements de fluide au sein de la matrice rocheuse fracturée, laquelle est sujette aux variations locales ou régionales de l'état de contrainte in situ. Du fait de l'augmentation de la pression de pore, la longueur et l'ouverture de la (les) fracture(s) peuvent subir des variations significatives et conduire à la formation de chemins préférentiels pour l'écoulement du fluide dans le milieu géologique. Les modèles théorique et numérique évoqués ici sont des modèles de comportement hydro-mécanique pour le milieu poreux saturé en présence d'une seule phase fluide. La méthode des éléments finis étendue (XFEM) est utilisée afin de modéliser la dynamique des fractures ainsi que les écoulements de fluide dans la matrice rocheuse fracturée, sans être tributaire de la dépendance au maillage. Ainsi, nous considérons: (i) qu'il existe une pression fluide induite par l'écoulement au sein de la fracture, (ii) que la dynamique de la fracture est gérée grâce à un modèle de zone cohésive en supposant un chemin de propagation prédéfini, et (iii) que des échanges entre la fracture et la matrice poreuse peuvent se produire. Ce dernier aspect sera pris en compte en introduisant, dans la formulation du problème couplé, un champ de multiplicateur de Lagrange. Ce champ résulte de la dualisation de la condition d'égalité entre la pression de pore et de la pression de fluide au niveau des parois de la fracture. Afin de respecter les contraintes liées à XFEM, nous avons choisi d'introduire dans la formulation une loi cohésive non-régularisée de type Talon-Curnier. Ce type de loi est capable de gérer la propagation et/ou la refermeture de la fracture. Le modèle HM-XFEM a été validé à partir des solutions analytiques du modèle 2D de fracture KGD, et ce, pour différents régimes de propagation. Nous avons ensuite appliqué le modèle HM-XFEM au cas d'un réseau de fractures non connectées entre elles et évoluant sur des chemins de propagation prédéfinis, afin d'analyser comment les fractures d'un réseau peuvent influer les unes sur les autres lorsqu'elles sont soumises à un écoulement. En particulier, une étude paramétrique a été menée afin de montrer l'influence que peuvent avoir la viscosité, le débit d'injection et l'écartement entre les fractures sur leur propagation. Une attention particulière sera porté à l'évolution du stress-shadowing effect (i.e. modification de l'état de contrainte due à l'effet d'interaction entre les fractures). / In the present work, we address the issue of groundwater flow in the fractured porous media submitted to local or regional stress-state variations. Due to the increasing pore fluid pressure, the length and aperture distribution of the fractures are modified resulting in the formation of preferential flow channels within the geological formation. The numerical approach proposed is a fully coupled hydro-poro-mechanical model in saturated conditions involving single-phase flow both in fractures and in the porous matrix. The extended finite element method (XFEM) is employed for modeling fracture dynamics and flow calculation for fracture which do not lie on the mesh but cross through the elements. In this study: (i) we consider the pressure build up generated by fluid flow inside and through the fracture, (ii) the fracture dynamics by using a cohesive zone model (CZM) on pre-existing propagation path and (iii) fluid exchanges may occur in between fractures and porous medium. The last specification of the HM-XFEM model is taken into account through the introduction of a Lagrange multiplier field along the fracture path. These fields are the result of the dualised condition of pressure continuity between the pore pressure and the fluid pressure inside the fracture. As a function of the Lagrange multiplier value, both permeable and impervious fractures can be considered. The cohesive law employed is a non-regularized-type cohesive law to ensure propagation and eventually closure of the fracture. Validation of the model has been conducted by means of the well-known KGD fracture model when different propagation regimes are considered. We applied the HM-XFEM model to the case of multi-stage fracture network stimulated by the injection of incompressible fluid at constant rate. Fractures are not connected to each other and evolve on pre-existing propagation paths. We aim at appreciating the influence of the fluid viscosity, the injection rate and spacing between each fracture, on the fracture propagation. A peculiar attention is paid to the stress-shadowing effect (i.e. interaction between fractures).

In diesem Preprint werden grundlegende Gleichungen zur Behandlung von transversal isotropem Materialverhalten zusammengetragen. Wir betrachten ein transversal isotropes Materialgesetz mit linear elastischem Verhalten. Die angegebenen Materialgleichungen sind zur Beschreibung sowohl kleiner als auch großer Deformationen geeignet. Sie bilden eine wesentliche Grundlage zur Lösung statischer Probleme mit der Methode der finiten Elemente. Es werden Gleichungen für den ebenen Spannungszustand und den ebenen Verzerrungszustand hergeleitet.:1 Einführung 2 Energiefunktional 3 Umrechnung der Materialkonstanten 4 Elastizitätsmatrix 5 Eigenwerte 6 Ebener Verzerrungszustand 7 Ebener Spannungszustand 8 Anhang

Em geral, as formulações disponíveis na literatura para a análise de cascas laminadas reforçadas com fibras substituem o meio original heterogêneo por um homogêneo equivalente, que dificulta a identificação das tensões fibra-matriz, ou requerem que a malha de elementos finitos seja disposta de modo que os nós dos elementos finitos de fibra coincidam com os nós dos elementos finitos de casca, que é uma exigência bastante restritiva e que aumenta o número de graus de liberdade do sistema de equações resultante. Neste sentido, o objetivo geral desta tese consiste em desenvolver uma formulação para a inclusão de fibras longas e curtas aleatórias nas diversas lâminas de cascas laminadas anisotrópicas com não linearidade geométrica utilizando o método dos elementos finitos sem aumentar o número de graus de liberdade do sistema de equações resultante e sem a necessidade de coincidência de nós na discretização das fibras e da matriz. Nesta formulação, o elemento finito triangular de casca laminada utilizado para discretizar a matriz possui dez nós e sete graus de liberdade por nó, sendo três translações, três componentes do vetor generalizado e a taxa de variação linear da deformação ao longo da espessura. As fibras curvas, curtas aleatórias ou longas, são introduzidas, em qualquer camada do laminado, por meio de relações cinemáticas que garantem sua aderência à matriz sem a introdução de novos graus de liberdade no sistema de equações resultante. Para discretizá-las são utilizados elementos finitos unidimensionais de ordem qualquer com três graus de liberdade por nó e que consideram consistentemente a não linearidade geométrica. Todas as grandezas envolvidas são escritas em relação à configuração inicial do corpo, caracterizando a descrição Lagrangeana total ou material do movimento. Para modelar o comportamento do material adota-se a Lei Constitutiva de Saint-Venant-Kirchhoff que relaciona de forma linear o tensor de tensões de Piolla-Kirchhoff de segunda espécie e o tensor de deformações de Green-Lagrange. O equilíbrio é encontrado a partir do Princípio da Mínima Energia Potencial Total e o sistema não linear de equações resultante é resolvido utilizando-se o procedimento iterativo de Newton-Raphson. As ações externas podem ser introduzidas ao sistema de forma total ou incremental e a contribuição das fibras para a energia do sistema é adicionada na matriz global do problema. Os exemplos numéricos testados validam e demonstram as potencialidades da formulação proposta. / In general, the Finite Element (FE) formulations available in the literature for the analysis of fibre reinforced laminated shells replace the original heterogeneous medium by an equivalent homogeneous one, which makes difficult the identification of fiber-matrix stress distribution, or require that the finite element mesh is arranged in a way that the fibre finite element nodes coincide with the shell finite element ones, which is a very restrictive requirement and increases the number of degrees of freedom of the resulting system of equations. In this sense, the objective of this thesis is to develop a formulation for the inclusion of long and random short fibres in any layer of FE laminated anisotropic shells developing large displacement and rotations without increasing the number of degrees of freedom and the necessity of matching nodes in the discretization of the fibre and the matrix. In this formulation, the triangular laminated shell finite element used to discretize the matrix has ten nodes and seven degrees of freedom per node, that are, three translations, three components of a generalized vector and the linear rate of strain variation along the thickness. The curved fibres, long or random short, are introduced in any layer of the laminate shell by means of kinematic relation to ensure its adherence to the matrix without introducing new degrees of freedom in the resulting system of equations. To discretize them, any order one-dimensional finite elements with three degrees of freedom per node are used. These fibres elements are consistently considered by Geometric nonlinearity. All involved variables are written with respect to the initial configuration of the body, characterizing the Total Lagrangian description. To model the behavior of the material we use the Saint-VenantKirchhoff Constitutive Law that relates linearly the second Piolla-Kirchhoff stress tensor and Green-Lagrange strain tensor. The equilibrium is achieved from the Principle of Minimum Potential Energy and the non-linear system of equations is solved by the Newton-Raphson iterative procedure. External loads may be introduced to the system by one or various steps and the contribution of fibres to the energy of the system is added to the global matrix of the problem. The numerical examples validate and demonstrate the potential of the proposed formulation.

Durch die beanspruchungsgerechte Anordnung von Fasermaterialien wie Glas oder Carbon mit hervorragenden Trageigenschaften entstehen technische Textilien, die in eine Betonmatrix eingebracht werden können, so daß ein neuer, innovativer Verbundwerkstoff entsteht, der sowohl bei der Herstellung neuer Betonbauteile verwendet werden kann als auch für den Einsatz in der Instandsetzung und Verstärkung bestehender Bauwerke geeignet ist. Da die verwendeten Materialien im Gegensatz zum Stahl nicht korrosionsempfindlich sind und gleichzeitig hohe Festigkeiten aufweisen, können Verstärkungen aus textilbewehrtem Beton mit sehr geringen Abmessungen ausgeführt werden. Bei Holzkonstruktionen können textile Verstärkungen die durch die Anisotropie bedingten Festigkeits- und Steifigkeitsunterschiede kompensieren und die Dauerhaftigkeit erhöhen. Bei Verzicht auf Knotenbleche aus Stahl und durch Applikation von textilen Strukturen können beachtliche Steigerungen der Tragfähigkeit und der Duktilität von Verbindungen erreicht werden. In den fünf Projektbereichen werden in theoretischen und experimentellen Untersuchungen die Grundlagen für die Werkstoffe, die mechanische Beschreibung, die konstruktive Durchbildung und die Bemessung, die technologische Aufbringung, bautechnische Umsetzung und die Langzeiteigenschaften und damit für die Sicherheit und die Lebensdauer bei der Verwendung textiler Bewehrungen für die Instandsetzung und Verstärkung geschaffen. / The stress-oriented arrangement of fibre materials, such as glass or carbon, which have an excellent load-bearing capacity, leads to technical textiles that may be incorporated into a concrete matrix. So a new, innovative composite material is produced, which can be used for the production of new concrete members and also for the restoration and strengthening of existing structures. As the materials used are noncorrosive compared to steel and as they show great strength at the same time, textile-reinforced concrete can be used for strengthening tasks of small dimensions. With regard to timber structures, textile reinforcement can compensate the strength and stiffness differences caused by anisotropy and can increase durability. If textile structures are used instead of steel gussets this may lead to a considerable increase in the ultimate strength and the ductility of joints. The five fields of the project are designed that theoretical and experimental investigations are carried out to provide the fundamentals of the materials. Additionally information will be obtained about the mechanical description, the detailing and the dimensioning, the techniques of applying, the realisation on the site and the long-term behaviour. All leading to a safety concept and also a service life concept for the use of textile reinforcements for restoration and strengthening.

Em geral, as formulações disponíveis na literatura para a análise de cascas laminadas reforçadas com fibras substituem o meio original heterogêneo por um homogêneo equivalente, que dificulta a identificação das tensões fibra-matriz, ou requerem que a malha de elementos finitos seja disposta de modo que os nós dos elementos finitos de fibra coincidam com os nós dos elementos finitos de casca, que é uma exigência bastante restritiva e que aumenta o número de graus de liberdade do sistema de equações resultante. Neste sentido, o objetivo geral desta tese consiste em desenvolver uma formulação para a inclusão de fibras longas e curtas aleatórias nas diversas lâminas de cascas laminadas anisotrópicas com não linearidade geométrica utilizando o método dos elementos finitos sem aumentar o número de graus de liberdade do sistema de equações resultante e sem a necessidade de coincidência de nós na discretização das fibras e da matriz. Nesta formulação, o elemento finito triangular de casca laminada utilizado para discretizar a matriz possui dez nós e sete graus de liberdade por nó, sendo três translações, três componentes do vetor generalizado e a taxa de variação linear da deformação ao longo da espessura. As fibras curvas, curtas aleatórias ou longas, são introduzidas, em qualquer camada do laminado, por meio de relações cinemáticas que garantem sua aderência à matriz sem a introdução de novos graus de liberdade no sistema de equações resultante. Para discretizá-las são utilizados elementos finitos unidimensionais de ordem qualquer com três graus de liberdade por nó e que consideram consistentemente a não linearidade geométrica. Todas as grandezas envolvidas são escritas em relação à configuração inicial do corpo, caracterizando a descrição Lagrangeana total ou material do movimento. Para modelar o comportamento do material adota-se a Lei Constitutiva de Saint-Venant-Kirchhoff que relaciona de forma linear o tensor de tensões de Piolla-Kirchhoff de segunda espécie e o tensor de deformações de Green-Lagrange. O equilíbrio é encontrado a partir do Princípio da Mínima Energia Potencial Total e o sistema não linear de equações resultante é resolvido utilizando-se o procedimento iterativo de Newton-Raphson. As ações externas podem ser introduzidas ao sistema de forma total ou incremental e a contribuição das fibras para a energia do sistema é adicionada na matriz global do problema. Os exemplos numéricos testados validam e demonstram as potencialidades da formulação proposta. / In general, the Finite Element (FE) formulations available in the literature for the analysis of fibre reinforced laminated shells replace the original heterogeneous medium by an equivalent homogeneous one, which makes difficult the identification of fiber-matrix stress distribution, or require that the finite element mesh is arranged in a way that the fibre finite element nodes coincide with the shell finite element ones, which is a very restrictive requirement and increases the number of degrees of freedom of the resulting system of equations. In this sense, the objective of this thesis is to develop a formulation for the inclusion of long and random short fibres in any layer of FE laminated anisotropic shells developing large displacement and rotations without increasing the number of degrees of freedom and the necessity of matching nodes in the discretization of the fibre and the matrix. In this formulation, the triangular laminated shell finite element used to discretize the matrix has ten nodes and seven degrees of freedom per node, that are, three translations, three components of a generalized vector and the linear rate of strain variation along the thickness. The curved fibres, long or random short, are introduced in any layer of the laminate shell by means of kinematic relation to ensure its adherence to the matrix without introducing new degrees of freedom in the resulting system of equations. To discretize them, any order one-dimensional finite elements with three degrees of freedom per node are used. These fibres elements are consistently considered by Geometric nonlinearity. All involved variables are written with respect to the initial configuration of the body, characterizing the Total Lagrangian description. To model the behavior of the material we use the Saint-VenantKirchhoff Constitutive Law that relates linearly the second Piolla-Kirchhoff stress tensor and Green-Lagrange strain tensor. The equilibrium is achieved from the Principle of Minimum Potential Energy and the non-linear system of equations is solved by the Newton-Raphson iterative procedure. External loads may be introduced to the system by one or various steps and the contribution of fibres to the energy of the system is added to the global matrix of the problem. The numerical examples validate and demonstrate the potential of the proposed formulation.