Ossos trabeculares possuem uma microestrutura porosa e podem ser modelados como um sólido elástico linear, heterogêneo e anisotrópico. A microtomografia tridimensional por raios-x (&#956CT) tem sido mundialmente utilizada para a caracterização de osso trabecular em pesquisas relacionadas à qualidade óssea e a doenças do metabolismo ósseo como a osteoporose. Na literatura existem poucas investigações sobre a influência de diferentes subvolumes amostrais na caracterização de propriedades mecânicas de osso trabecular humano através de &#956CT e ensaio mecânico computacional pelo método de Elementos Finitos. Nesta investigação doze vértebras humanas da região lombar foram utilizadas para a caracterização das propriedades mecânicas do osso trabecular através de &#956CT e modelagem computacional por elementos finitos. Uma amostra cúbica virtual com 18,5 mm de lado foi extraída de cada vértebra e quatro cubos menores centrais foram obtidos a partir dela com reduções de 20%, 40%, 60%, 80% do volume original de cada cubo. A abordagem Direct Mechanics por meio de análise de elementos finitos foi realizada através do Software FAIM (v6.0, Numerics88 Solutions Ltd). Os valores médios nas três direções principais de carregamento para os módulos de Young, Poisson e Torção obtidos foram, respectivamente, E1 = 294 MPa , E2 = 258 MPa , E3 = 153 MPa, G23 = 86 MPa, G31 = 103 MPa, G12 = 100 MPa, v21 = 0,121, v31 = 0,076, v12 = 0,137, v32 = 0,077, v13 = 0,141 e v23 = 0,140. O teste estatístico de Kruskal - Wallis ANOVA fator único foi aplicado com os procedimentos de comparação aos pares (teste de Tukey) mostrou que E1 &#8800 E3, E2 &#8800 E3 e E1 = E2. Isso indica que há a tendência para duas direções diferentes de carregamento mecânico nas amostras de osso trabecular das vértebras humanas analisadas, caracterizando uma simetria transversalmente isotrópica. Entretanto, os autovalores da matriz M (tensor anisotropia) expressaram uma tendência da microestrutura trabecular das vértebras humanas para a simetria ortotrópica, mostrando que a análise do fabric não classifica adequadamente a simetria da estrutura. A avaliação dos parâmetros microestruturais mostrou a tendência de um aumento do grau de conectividade das trabéculas a medida que ocorre uma redução dos subvolumes analisados (100% para 20% ou em milímetros de 18,5 para 3,7) acompanhado de um acréscimo dos valores da fração de volume ósseo. Esta tendência reforça a ideia de analisar-se as possíveis variações dos parâmetros morfométricos e mecânicos em domínios específicos. Em outras palavras, uma avaliação local com a escolha de volumes menores dos parâmetros microestruturais fração de volume, conectividade, espessura trabecular, separação trabecular, número trabecular e parâmetros mecânicos (Módulos de Young, Poisson e Torção) podem melhorar o prognóstico da resistência óssea, a qual prediz o risco de fratura de estruturas de osso esponjoso com precisão. Quando as propriedades mecânicas estão associadas com informações microestruturais por &#956CT são gerados mais parâmetros para se avaliar a qualidade óssea no diagnóstico de doenças do metabolismo ósseo. Portanto, a microtomografia de raios-X e análise de elementos finitos oferecem uma técnica não-invasiva com grande potencial para a avaliação da qualidade óssea. / Trabecular bone structures have a porous microstructure and can be modeled as linear elastic solid with a heterogeneous and anisotropic structure. The X-ray microtomography (&#956CT) has been used worldwide for the characterization of trabecular bone and its relationship with bone quality in metabolism diseases such as osteoporosis. In the literature there are few investigations regarding the influence of trabecular samples subvolumes in the assessment of microstructure and mechanical properties using &#956CT and finite element analysis. In this investigation twelve human vertebraes were used for the characterization of mechanical properties of trabecular bone using CT and computational modeling by finite elements. A cube sample with 18.5 mm sides was computationally extracted from each vertebrae and four smaller central cubes were obtained from it, with a 20%, 40%, 60%, 80% reduction from the original volume. The Direct Mechanics approach by finite element analysis was performed through the FAIM Software (v6.0, Numerics88 Solutions Ltd.). The mean values on three main directions of loading for Youngs Modulus, Poissons Modulus and Shears Modulus, were: E1 = 294 MPa , E2 = 258 MPa , E3 = 153 MPa G23 = 86 MPa, G31 = 103 MPa e G12 = 100 MPa, v21 = 0,121, v31 = 0,076, v12 = 0,137, v32 = 0,077, v13 = 0,141 e v23 = 0,140. The Kruskal-Wallis One Way Analysis of Variance on Ranks was applied with pairwise multiple comparison procedures (Tukey Test) showing that E1 &#8800 E3, E2 &#8800 E3 e E1 = E2. This indicates that there are two different main directions of loading on the trabecular bone samples of human vertebrae which is related to a transversely isotropic symmetry. However the eigenvalues of the matrix M (tensor anisotropy) expressed a tendency to orthotropic symmetry of the trabecular microstructure of human vertebrae, showing that the fabric assumption does not adequately classify the symmetry of the structure. The assessment of microstructural properties showed a tendency to increase the connectivity of the trabeculae with the reduction of the analyzed subvolumes (100% to 20% or 18.5 mm to 3.7 mm) as well as an increase of the bone volume fraction values. Those results highlight the idea that mechanical properties are better described in local regions. In other words, a local assessment of the microstructure parameters volume fraction, connectivity, trabecular thickness, trabecular separation, trabecular number and mechanical parameters (Youngs Modulus, Poissons Modulus and Shears Modulus) can improve the prediction of bone strength, which predicts the risk of cancellous bone fracture accurately. When the mechanical properties are associated with microstructural information more bone quality parameters are generated for the diagnosis of bone metabolism diseases and they can predict the fracture risk of cancellous bone structures with higher accuracy. Therefore, the X-ray microtomography and finite element analysis offer a non-invasive technique with great potential for the assessment of bone quality.

This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared.

Advances in the design and manufacturing technologies have greatly enhanced the utility of fiber reinforced composite materials in aircraft, helicopter and space- craft structural components. The special characteristics of composites such as high strength and stiffness, light-weight corrosion resistance make them suitable sub- stitute for metals/metallic alloys. However, composites are very sensitive to the anomalies induced during their fabrication and service life. Also, they are suscepti- ble to the impact and high frequency loading conditions because the epoxy matrix is at-least an order of magnitude weaker than the embedded reinforced carbon fibers. On the other hand, the carbon based matrix posses high electrical conductivity which is often undesirable. Subsequently, the metal matrix produces high brittleness. Var- ious forms of damage in composite laminates can be identified as indentation, fiber breakage, matrix cracking, fiber-matrix debonding and interply disbonding (delam- ination). Among all the damage modes mentioned above, delamination has been found to be serious for all cases of loading. They are caused by excessive interlaminar shear and normal stresses. The interlaminar stresses that arise in the case of composite materials due to the mismatch in the elastic constants across the plies. Delamination in composites reduce it’s tensile and compressive strengths by consid- erable margins. Hence the knowledge of these stresses is the most important aspect to be looked into. Basic theories like the Euler-Bernoulli’s theory and Timoshenko beam theory are based on many assumptions which poses limitation to determine these stresses accurately. Hence the determination of these interlaminar stresses accurately requires higher order theories to be considered. Most of the conventional methods of determination of the stresses are through the solutions, involving the trigonometric series, which are available only to small and simple problems. The most common method of solution is by Finite Element (FE) Method. There are only few elements existing in the literature and very few in the commercially available finite element software to determine the interlaminar stresses accurately in the composite laminates. Accuracy of finite element solution depends on the choice of functions to be used as interpolating polynomials for the field variable. In-appropriate choice will manifest in the form of delayed convergence. This delayed convergence and accuracy in predicting these stresses necessiates a formulation of elements with a completely new concept. The delayed convergence is sometimes attributed to the shear locking phenomena, which exist in most finite element formulation based on shear deformation theories. The present work aims in developing finite elements based on higher order theories, that alleviates the slow convergence and achieves the solutions at a faster rate without compromising on the accuracy. The accuracy primarily depends on the theory used to model the problem. Thus the basic theories (such as Elementary Beam theory and Timoshenko Beam theory) does not suffice the condition to accuratley determine the interlaminar stresses through the thickness, which is the primary cause for delamination in composites. Two different elements developed on the principle of super-convergence has been presented in this work. These elements are subjected to several numerical experiments and their performance is assessed by comparing the solutions with those available in literature. Spacecraft and aircraft structures are light in weight and are also lightly damped because of low internal damping of the material of construction. This increased exibility may allow large amplitude vibration, which might cause structural instability. In addition, they are susceptible to impact loads of very short duration, which excites many structural modes. Hence, structural dynamics and wave propagation study becomes a necessity. The wave based techniques have found appreciation in many real world problems such as in Structural Health Monitoring (SHM). Wave propagation problems are characterized by high frequency loads, that sets up stress waves to propagate through the medium. At high frequency, the wave lengths are small and from the finite element point of view, the element sizes should be of the same order as the wave lengths to prevent free edges of the element to act as a free boundary and start reflecting the stress waves. Also longer element size makes the mass distribution approximate. Hence for wave propagation problems, very large finite element mesh is an absolute necessity. However, the finite element problems size can be drastically reduced if we characterize the stiffness of the structure accurately. This can accelerate the convergence of the dynamic solution significantly. This can be acheived by the super-convergent formulation. Numerical results are presented to illustrate the efficiency of the new approach in both the cases of dynamic studies viz., the free vibration study and the wave propagation study. The thesis is organised into five chapters. A brief organization of the thesis is presented below, Chapter-1 gives the introduction on composite material and its constitutive law. The details of shear locking phenomena and the interlaminar stress distribution across the thickness is brought out and the present methods to avoid shear locking has been presented. Chapter-2 presents the different displacement based higher order shear deformation theories existing in the literature their advantages and limitations. Chapter-3 presents the formulation of a super-convergent finite element formulation, where the effect of lateral contraction is neglected. For this element static and free vibration studies are performed and the results are validated with the solution available in the open literature. Chapter-4 presents yet another super-convergent finite element formulation, wherein the higher order effects due to lateral contraction is included in the model. In addition to static and free vibration studies, wave propagation problems are solved to demonstrate its effectiveness. In all numerical examples, the super-convergent property is emphasized. Chapter-5 gives a brief summary of the total research work performed and presents further scope of research based on the current research.

Les premiers recyclages d’enrobés bitumineux à 50% sont apparus sur autoroutes françaises dans les années 1990 – une charte de l’innovation spécifique aux enrobés drainants intégrant 50% de recyclés fut notamment délivrée début 2002 (SETRA - CSTR, 2002). Un nouveau cycle de recyclage à fort taux de ces tout premiers enrobés a été entrepris ici ou là, depuis quelques années. Le multirecyclage des agrégats d’en-robé (AE) dans les mélanges d’enrobés bitumineux est de ce fait une problématique actuelle, qui va se gé-néraliser dans l’avenir, lorsqu’il faudra recycler des enrobés contenant déjà des enrobés recyclés plusieurs fois. Le projet visant à étudier le MUlti-Recyclage des Enrobés tièdes a été labellisé projet national (PN MURE). Une part du projet MURE regroupant des aspects scientifiques particuliers a été regroupé au sein du projet « IMPROVMURE », financé par l’Agence Nationale de la Recherche, et qui a débuté en mars 2014. L’objectif du projet « Innovation en Matériaux et PROcédés pour la Valorisation du MUlti-Recyclage des En-robés » (IMPROVMURE) est de fournir des éléments de réponse raisonnés et quantifiés, en laboratoire et sur sites pilotes, afin de faire du multi-recyclage des enrobés fabriqués à chaud et tiède. Les questions sociétales, environnementales, règlementaires ou normatives sont également prises en compte dans le cadre du projet. Un des objectifs du projet IMPROVMURE est l’étude des propriétés thermomécaniques des enrobés. C’est dans le cadre de cet objectif que s’inscrit le travail de thèse présenté dans ce document. Cette thèse est le fruit d’une collaboration entre le Laboratoire Génie Civil et Bâtiment de l’ENTPE (LGCB)/Laboratoire de Tribologie et Dynamique des Systèmes (LTDS) et l’entreprise EIFFAGE Infrastructures. 15 types d’enrobés ont été testés pour l’étude des propriétés thermomécaniques des enrobés multi-recyclés. Les enrobés diffèrent par leur condition de fabrication (Laboratoire ou chantier), leur procédé de fabrication (chaud ou tiède mousse), le taux d’agrégat d’enrobé introduit (0%, 40%, 70% ou100%) et le nombre de cycles de recyclage (un, deux ou trois). Trois caractéristiques ont été communes à tous les types d’enrobés fabriqués, sauf pour l’enrobé contenant 100% d’agrégats d’enrobé. La première est la même courbe granulométrique des granulats, la troisième est la teneur en liant de 5.4% en masse et la troisième est le type d’enrobé « Béton Bitumineux Semi-Grenu » (BBSG) de type 03 selon la norme EN 13108-1. Trois domaines du comportement des enrobés bitumineux ont été étudies : Viscoélasticité linéaire (VEL), couplage thermomécanique à basse température et fissuration à froid. Pour le domaine de comportement VEL, les enrobés bitumineux ont été étudiés à l’aide des essais de module complexe en traction-compression réalisés sur une large gamme de températures et de fréquences sur éprouvette cylindrique à l’ENTPE. Les résultats sont modélisés à l’aide du modèle analogique 2S2P1D qui a été développé au laboratoire LGCB de l’ENTPE. Des essais de propagation d’ondes ont aussi été réalisés. La méthode de détermination du temps de vol des ondes « P » et des ondes « S » et la méthode Impact Résonance sont utilisées. Ces essais utilisent des méthodes non destructives et faciles à réaliser. On peut ainsi calculer les valeurs de modules et de coefficients de Poisson des matériaux. Puis, le couplage thermomécanique à basse température est caractérisé à l’aide de l’essai de retrait thermique empêché (TSRST), qui utilise le même dispositif que l’essai de module complexe mais les éprouvettes utilisées sont de géométrie différente. Finalement des essais de propagation de fissure ont été réalisés avec des sollicitations monotones. La propagation de la fissure suivie utilisant la méthode de corrélation des images. Des estimations de la hauteur de fissure ont été faites sur la basse de la méthode DRCL développée à l’ENTPE. / Reuse of Reclaimed Asphalt Pavement (RAP) is considered as one of the main solutions to cope with the objectives of worldwide sustainable development. In this way, the reuse of RAP in bituminous mixtures has been matter of study in previous papers (Chen et al., 2009; Kaur et al., 2013; Mogawer et al., 2012; Ru-bio et al., 2012; Sias Daniel et al., 2013; Valdés et al., 2011) and had concluded be economically profitable as well as had demonstrated the durability of the tested materials. Nowadays, new topics overcome dealing with how increase the RAP content and how many times RAP could be recycled. In France, a collaborative research and development project called “Multi-recycling of warm foam bitu-minous mixtures” (MURE) have brought together all the stakeholders involved in road construction. The pro-gram has run since March 2014. The scientific part of MURE project is IMPROVMURE project (Innovation for Materials and Processes for Improving the Multi-Recycling of Mixes). The overall budget of the project were €4.7M, €2.3M of which been provided by the ANR (National Re-search Agency) in the framework of the IMPROVMURE project, which has gotten under way in March 2014 and its main goal of characterizing the remobilization of the binder from recycled materials was the evalua-tion of the durability of mixes with the addition of binder. Thus, one objective of this project is to determine the thermomechanical properties of multi-recycled bi-tuminous mixtures, so in the context of this goal the current study was made. Likewise this investigation was a collaboration between the Tribology and System Dynamics Laboratory (LTDS) of the University of Lyon/ENTPE (“Ecole Nationale des Travaux Publics de l’Etat” ) and the French company EIFFAGE Infra-structures. For this study 15 types of bituminous mixtures were tested, the bituminous mixtures were produced in the laboratory and construction site, also two different techniques were studied for mixtures elaboration: hot and warm using foamed bitumen in both cases, the RAP content on these were 0%, 40%, 70% and even close to 100% produced after several recycling operations (up to 3 cycles). All bituminous mixtures have 3 invariants: the first is the same aggregate grading curves (except the bituminous mixture with 100% of RAP). The second one is the total binder content (5.4% in total weight). The last is classified as BBSG-03 0/10 bitu- 15 minous mixture, as is specified in the European standards for classification of bituminous mixtures (NF EN 13108-1 - 2007). Three domains of behaviour were studied: Linear Viscoelastic behaviour (LVE), cracking behaviour at low temperature and the fracture behaviour at low temperature. The LVE was studied considering complex modulus tests on bituminous mixtures and were performed in tension/compression on cylindrical samples, thus LVE behaviour was then modelled with 2S2P1D rheological model, developed at Uni. of Lyon / ENTPE, for the other hand cracking behaviour at low temperature was studied considering Thermal Stress Restrained Specimen Tests (TSRST), and finally fracture behaviour at low temperature was studied with the crack propagation tests as a monotonic loading.

The presentation describes partial results from an industrial project in which a transmission test bench from ZF Prüfsysteme was decoupled from the foundation in terms of vibration using commercial PU foam material ('Sylomer' SR220 from Getzner). The presentation shows how this material was extensively tested by the manufacturer and characterized in numerous data sheets in order to enable the engineer to perform a simple, operating point-dependent dynamic design using clear diagrams and the classic equation for a single-mass oscillator. However, if a more complex analysis is to be carried out using the finite element method, e.g. to determine all 6 rigid body shapes and natural frequencies of the dynamically decoupled test rig and not just the purely vertical natural shape/frequency, the apparent elasticity and shear moduli specified in the manufacturer's data sheets must be converted into true values for the corresponding operating points, which can then be used in a linear FE calculation. For this purpose, FEM models of the elastomer test specimens are generated for different shape factors. The conversion of the apparent to the true characteristic values is then carried out using the optimizer available in the PTC software “Creo Simulate” in a so-called 'feasibility study' and the results are discussed. It can be seen that the true moduli of elasticity and transverse strain coefficients are only slightly or no longer dependent on the form factor. Depending on the density of the PU foam, the transverse strain coefficient is also significantly lower than 0.5. The true shear modulus is practically identical to the measured shear modulus, as a pure biaxial stress and strain state occurs in the shear specimens, in which strain restraints due to transverse strain plays no role - quite unlike in the specimens loaded in the normal (compression) direction, in which triaxial compression stress states occur due to transverse strain restraints. Finally, the true material properties determined in this way are used for an exemplary modal analysis of the entire, idealized test rig on the strip foundation using the finite element method. The error is evaluated if the apparent modulus of elasticity and a Poisson ratio of zero is used instead, so that a simple evaluation and error estimation of analysis results is possible in practical applications. / Der Vortrag beschreibt Teilergebnisse aus einem industriellen Projekt, in dem ein Getriebeprüfstand der ZF Prüfsysteme schwingungstechnisch über kommerzielles PU- Schaummaterial („Sylomer“ SR220 der Firma Getzner) vom Fundament abgekoppelt wurde. Der Vortrag stellt dar, wie dieser Werkstoff vom Hersteller umfangreich getestet und in zahlreichen Datenblättern charakterisiert wurde, um dem Ingenieur schließlich eine einfache, betriebspunktabhängige dynamische Auslegung mittels übersichtlicher Diagramme und der klassischen Gleichung für einen Einmassenschwinger zu ermöglichen. Soll jedoch eine aufwendigere Analyse mittels der Methode der Finiten Elemente durchgeführt werden, z.B. um alle 6 Starrkörperformen und Eigenfrequenzen des dynamisch abgekoppelten Prüfstandes zu bestimmen und nicht nur die rein vertikale Eigenform/Eigenfrequenz, müssen die in den Herstellerdatenblättern angegeben formzahlabhängigen scheinbaren Elastizitäts- und Schubmoduli in wahre Werte für die entsprechenden Betriebspunkte umgerechnet werden, die dann in einer linearen FE-Rechnung verwendet werden können. Dafür werden FEM-Modelle der Elastomer-Probekörper für verschiedene Formfaktoren erzeugt. Die Umrechnung der scheinbaren in die wahren Kennwerte wird anschließend mittels des in der PTC-Software „Creo Simulate“ vorhandenen Optimierers in einer sogenannten „Machbarkeitsstudie“ durchgeführt und die Ergebnisse diskutiert. Es zeigt sich, dass die wahren E-Moduli und Querdehnzahlen nur noch gering bzw. nicht mehr vom Formfaktor abhängen. Je nach Dichte des PU-Schaums stellt sich auch eine Querdehnzahl von deutlich kleiner als 0,5 ein. Der wahre Schubmodul ist praktisch identisch wie der gemessene Schubmodul, da in den Schubproben ein reiner zweiachsiger Spannungs- und Dehnungszustand auftritt, in dem Dehnungsbehinderung durch Querdehnung keine Rolle spielt – ganz anders als in den in Normalenrichtung (Druck-) belasteten Proben, in denen durch die Querdehnungs- behinderung dreiachsige Spannungszustände auftreten. Schließlich werden die so bestimmten wahren Werkstoffkennwerte für eine exemplarische Modalanalyse des gesamten, idealisierten Prüfstandes auf den Streifenfundamenten mittels der Methode der Finiten Elemente verwendet. Der Fehler wird bewertet, wenn man stattdessen den scheinbaren E-Modul und eine Querdehnzahl von Null verwendet, so dass in der Anwendungspraxis eine einfache Bewertung und Fehlerabschätzung von Analyseergebnissen möglich ist.