Composites are materials which cater to the present and future needs of many demanding industries, such as aerospace, as they are weight-sensitive for a given requirement of strength and stiff ness, corrosion resistant, potentially multi-functional and can be tailored according to the application. However, they are in particular difficult to join as they cannot be easily machined, without introducing damages which can eventually grow. Any structure is as strong as its weakest joint. Most of the joints belong to the category of mechanically-fastened joints and they pose enormous challenges in modeling due to contact phenomena, nonlinearity and stress concentration factors. It is therefore a necessity to construct an efficient model that would include all the relevant contact phenomena in the joints, as it has been pointed out in literature that damage typically initiates near the joint holes. The focus of this work is to describe the construction of an asymptotically-correct model using the Variational Asymptotic Method (VAM). Amongst its many potential applications, VAM is a well-established analytical tool for obtaining the stress and strain fields for beams and shells. The methodology takes advantage of the small parameter that is inherent in the problem, such as the ratio of certain characteristic dimensions of the structure. In shells and beams, VAM takes advantage of the dimension-based small parameter(s), thereby splitting the problem into 2-D + 1-D (for beams) and 1-D + 2-D (for shells), in turn offering very high computational efficiency with very little loss of accuracy compared to dimensionally unreduced 3-D models. In this work, the applicability of VAM is extended to two-dimensional (2-D) and three-dimensional (3-D) frictionless contact problems. Since a generalised VAM model for contact has not been pursued before, the `phantom0 step is adopted for both 2-D and 3-D models. The development of the present work starts with the construction of a 2-D model involving a large rectangular plate being pressed against a rigid frictionless pin. The differential equations governing the problem and the associated boundary conditions are obtained by minimizing the reduced strain energy, augmented with the appropriate gap function, by using a penalty method. The model is developed for both isotropic and orthotropic cases. The boundary value problem is solved numerically and the displacement field obtained is compared with the one obtained using commercial software (ABAQUSr) for validation at critical regions such as the contact surfaces. Banking on the validation of the 2-D model, a 3-D model with a pin and a finite annular cylinder was constructed. The strain energy for the finite cylinder was derived using geometrically exact 3-D kinematics and VAM was applied leading to the reduction in the strain energy for isotropic and orthotropic materials in rectangular and cylindrical co-ordinates. As in the 2-D case, the reduced strain energy, subject to the inequality constraint of the gap function, is minimized with respect to the displacement field and the corresponding boundary value problem is solved numerically. The displacements of the contact surface and the top surface of the annular cylinder are compared with those from ABAQUS and thus validated. The displacement fields obtained using the current 2-D and 3-D models show very good agreement with those from commercial finite element software packages. The model could be re ned further by using the gap function derived in this work and applying it to a plate model based on VAM, which could be explored in the future.

Este trabalho apresenta uma metodologia de análise da heterogeneidade do concreto a partir de modelos computacionais desenvolvidos com o método de Galerkin livre de elementos. Esse método se caracteriza pela discretização de um domínio de interesse por um conjunto de partículas sem que exista explicitamente uma malha de elementos no sentido convencional. O objetivo é a previsão das propriedades mecânicas macroscópicas do material resultante a partir das fases individuais e do arranjo geométrico. O concreto foi admitido, na escala mesoscópica, como um composto formado por inclusões (agregado graúdo) imersas em uma matriz (argamassa). Para a simulação foi desenvolvida uma formulação multiregiões onde se admitiu que cada agregado e a argamassa são domínios distintos interligados nas suas interfaces. Para isto foram utilizadas técnicas de subdivisões do domínio (elemento representativo) ao ponto que os seus comportamentos mecânicos não foram comprometidos. Para simular o processo das perdas de rigidez com a formação da fissuração no concreto foi admitido o efeito da mecânica do dano contínuo através do modelo de Mazars. Para as análises foram desenvolvidos modelos computacionais bidimensionais e tridimensionais da heterogeneidade do concreto. A geometria dos agregados foi aproximada por circunferências e elipses no caso 2D e por esferas e elipsoides no caso 3D. Como conclusão a metodologia de multiregiões com o método de Galerkin livre de elementos foi satisfatória e os modelos apresentaram caminhos preferenciais de ruptura adequados durante a evolução da danificação. / This thesis presents a methodology for analyzing the heterogeneity of concrete from computational models developed with the element free Galerkin method. This method is characterized by discretization of a domain of interest by a set of particles with no explicit mesh in the conventional sense. The goal is to predict the macroscopic mechanical properties of the material resulting from the individual phases and the geometric arrangement. The concrete was assumed, in the mesoscopic scale, as a compound formed by inclusions (coarse aggregate) embedded in a matrix (mortar). For the simulation, a formulation was developed where multi regions were admitted, assuming that each aggregate and mortar are distinct domains connected by their interfaces. For this we used techniques of subdivisions of the domain (representative elements) to the point that their mechanical behaviors were not compromised. To simulate the process of loss of stiffness with the formation of cracks in the concrete, continuum damage mechanics was admitted through Mazars model. For the analysis, two-dimensional and three-dimensional computer models of the heterogeneity of the concrete were developed. The shape of the aggregates was approximated by circles and ellipses in the two-dimensional case, and by spheres and ellipsoids for the 3D problems. In conclusion the multi region methodology with the element free Galerkin methods was satisfactory and the models presented suitable preferred paths for the rupture during the evolution of damage.

Este trabalho investiga o comportamento dúctil de aços microligados classe API utilizado em tubulações na indústria do petróleo, e apresenta um estudo exploratório da aplicação da abordagem local e do modelo micromecânico de células computacionais para modelar a extensão estável de trinca em Modo I de abertura em aço ARBL. Ensaios laboratoriais na temperatura ambiente do aço API 5L X70 (utilizando corpos-de-prova normalizados) fornecem a curva de resistência à fratura (curva-R) do material. Esta curva foi utilizada para calibrar os parâmetros micromecânicos de células computacionais empregados no modelo. Este modelo foi utilizado para prever a pressão de colapso de dutos de paredes finas utilizados no transporte de gás, que apresentam defeitos longitudinais de diferentes razões entre profundidade de trinca e espessura de parede (a/t). As análises numéricas realizadas demonstram a capacidade da metodologia de células computacionais 2D em simular o rasgamento dúctil e o crescimento estável de trincas em corpos-de-prova de mecânica da fratura, assim como prever a pressão de colapso de estruturas tubulares contendo defeitos (trincas). / This study presents the experimental investigation of the ductile behaviour of microalloyed pipeline steel. Additionally, it extends the computational cell methodology to model Mode I crack extension in a high strength low alloy HSLA steel. Laboratory testing of an API 5L X70 steel at room temperature using standard, deep crack C(T) specimens provides the crack growth resistance curve to calibrate the micromechanics cell parameters for the material. The cell model incorporating the calibrated material-specific parameters is then applied to predict the burst pressure of a thin-walled gas pipeline containing longitudinal cracks with varying crack depth to thickness ratios (a/t). The numerical analyses demonstrate the capability of the computational cell approach to simulate ductile crack growth in fracture specimens and to predict the burst pressure of thin-walled tubular structures containing crack-like defects.

This works presents a study about effective properties of porous solids with nonlinear elastic and elastoplastic matrix. For macroscopic mechanics properties evaluation, micromechanics models are used with effective strain concept relative to the modified second method. The porous are assumed as randomly distributed in the matrix, which presents a constitutive law with linear behavior in dilatation and nonlinear in shear. The results are compared with those provided by finite element methods program ABAQUS, assuming porous with spherical geometry for three dimensional solids. Numerical results from ABAQUS were obtained by an implementation of an external subroutine which incorporates at analysis the nonlinear constitutive law. / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / Este trabalho apresenta um estudo sobre as propriedades efetivas de sólidos porosos com matriz elástica não linear e elastoplástica. Na avaliação das propriedades mecânicas macroscópicas empregam-se modelos micromecânicos lineares em conjunto com o conceito de deformação efetiva correspondente ao método secante modificado. Os poros são admitidos como distribuídos randomicamente na matriz, a qual apresenta uma lei constitutiva caracterizada por um comportamento linear em dilatação e não linear em cisalhamento. Os resultados obtidos são confrontados com aqueles fornecidos pelo programa comercial de elementos finitos ABAQUS, admitindo-se que os poros exibem geometrias esféricas para sólidos tridimensionais. A geração dos resultados numéricos oriundos do programa ABAQUS foi viabilizada mediante a implementação de uma sub-rotina externa que incorpora a relação constitutiva não linear considerada nas análises.

L’acier à double phase (DP) a été développé par l'industrie automobile pour le but de réduire le poids, l'amélioration de la performance de la sécurité et l'efficacité énergétique. Habituellement, l'acier DP contient des îlots de martensite dure noyée dans une matrice de ferrite doux. La synergie entre ces deux phases avec la microstructure inhomogène présente d'excellentes propriétés mécaniques. Les propriétés mécaniques (comportements de plasticité et de dégâts) d'acier DP sont principalement dérivés de sa microstructure, par exemple, la fraction de volume, la taille, la distribution et la morphologie de chaque phase constituante. Les approches micromécaniques sont largement appliquées pour prédire la plasticité et d'autres propriétés mécaniques de l'acier DP selon divers scénarios de chargement. Dans ce travail, la modélisation micromécanique de l'acier DP a été réalisée en utilisant des microstructures réelles ou artificielles. Une véritable microstructure est obtenue à partir de l'image métallographique, tandis qu'un générateur de microstructure artificielle à l'aide d'un algorithme d'affectation de phase améliorée basée sur l'optimisation de la topologie matériau est proposé d'étudier les propriétés mécaniques. Dans ce générateur artificiel, un processus d'affectation de phase est réalisé sur une mosaïque de Voronoï modifié pour obtenir une mesure représentative de l'élément de volume (VER) avec une bonne convergence. La méthode proposée comprend également une réduction appropriée décomposition orthogonale (POD) des courbes de débit (instantanés), qui sont calculés en utilisant le schéma asymptotique homogénéisation d'extension (AEH), pour identifier le contrôle des paramètres optimaux pour l'acier DP. Cette méthode numérique est vérifiée en utilisant DP590 et DP980 aciers qui indiquent un bon accord avec la contrainte d'écoulement à partir de mesures et prédiction de RVE basés sur de vraies microstructures. Les prédictions des modèles de déformation plastique, y compris des bandes de cisaillement en utilisant la microstructure artificielle ressemblent étroitement le comportement mécanique réel dans des conditions de chargement similaires. En outre, une interpolation a été adoptée pour obtenir une corrélation entre ces paramètres de contrôles basés sur l'identification des différents aciers DP. En outre, un modèle de substitution bi-niveau réduit est élaboré et présenté pour identifier les paramètres matériels du critère de rupture de Mohr-Coulomb (MMC). En utilisant cette méthode, le processus d'identification devient possible avec un nombre limité de tests Expérimentaux. La méthode combine des éléments critiques locaux associés à des modèles globaux. Le modèle de substitution de la souche de fracture construit en utilisant l'approximation diffuse et les éléments locaux, réduit le coût de calcul pour la recherche des paramètres matériels. Des simulations de fracturation sont effectuées globales pour mettre à jour la déformation à la rupture de la cible et pour calculer le déplacement de l'apparition de la panne correspondante. Des résultats probants sont obtenus par application successive de la conception de l'expérience (DOE) et l'amélioration des algorithmes de transformation de l'espace de conception. Le protocole d'identification proposée est validé avec de l'acier DP590. Robustesse de la méthode est confirmée par des valeurs initiales différentes. Ces investigations numériques fournissent nouvelle direction pour les simulations multi-échelles de la plasticité et de dégâts des comportements d'acier DP. De plus, ils contribuent efficacement à combler le fossé entre la recherche scientifique et à l'application de l'ingénierie des matériaux hétérogènes. / Dual-phase (DP) steel has been developed by automotive industry for the purpose of weight reduction, improvement in safety performance and fuel efficiency. Usually, DP steel contains hard martensite islands embedded in a soft ferrite matrix. Synergy between these two phases with the inhomogeneous microstructure exhibits excellent mechanical properties. The mechanical properties (plasticity and damage behaviors) of DP steel are mostly derived from its microstructure, e.g., volume fraction, size, distribution and morphology of each constituent phase. Micromechanical approaches are vastly applied to predict plasticity and other mechanical properties of DP steel under various loading scenarios. In this work, micromechanical modelling of DP steel has been performed using real or artificial microstructures. A real microstructure is obtained from metallographic image, while an artificial microstructure generator with an enhanced phase assignment algorithm based on material topology optimization is proposed to investigate the mechanical properties. In this artificial generator, phase assignment process is performed on a modified Voronoï tessellation to achieve the tailored representative volume element (RVE) with a good convergence. The proposed method also includes a proper orthogonal decomposition (POD) reduction of flow curves (snapshots), which are computed using the asymptotic extension homogenization (AEH) scheme, to identify the optimal controlling parameters for DP steel. This numerical method is verified using DP590 and DP980 steels that indicate a good agreement with the flow stress from measurements and RVE prediction based on real microstructures. Predictions of plastic strain patterns including shear bands using the artificial microstructure closely resemble the actual mechanical behavior under similar loading conditions. Moreover, an interpolation has been adopted to obtain a correlation between these controlling parameters based on the identification for various DP steels. Additionally, a bi-level reduced surrogate model is developed and presented to identify the material parameters of the Mohr-Coulomb (MMC) fracture criterion. Using this method, the identification process becomes feasible with a limited number of experimental tests. The method combines local critical elements associated with global models. The surrogate model of fracture strain constructed using the diffuse approximation and the local elements, reduced the computational cost for searching material parameters. Global fracture simulations are performed to update the target fracture strain and to compute the corresponding failure onset displacement. Convincing results are obtained via successive application of design of experiment (DOE) and enhanced design space transformation algorithms. The proposed identification protocol is validated with DP590 steel. Robustness of the method is confirmed with different initial values. These numerical investigations provide new direction for multiscale simulations of the plasticity and damage behaviors of DP steel. Moreover, they efficiently contribute to bridge the gap between scientific research and engineering application of heterogeneous materials.

Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain. Three major problems have been addressed: • Homogenization and analysis of RVE without any defects • Homogenization and analysis of RVE with fiber-matrix de-bonding • Homogenization and analysis of RVE with radial matrix cracking. Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems analytically. The results have been compared against standard results in the literature and against 3D FEA. At the end, results for “Radial deformation due to torsion” problem will be presented which was solved “accidentally.”

<div>As the use of fiber-reinforced polymer composites grows in aerospace structures, there is an emerging need to implement damage tolerant approaches. The use of <i>in-situ</i> synchrotron X-ray tomography enables direct observations of progressive damage relative to the microstructural features, which is studied in a T650/5320 laminate composite with varying layup orientations (using 45^o and -45^o plies) in a compact tension specimen geometry. Specifically, the interactions of micromechanical damage mechanisms at the notch tip were analyzed through 3D image processing as the crack grew. First, monotonic tests were conducted where X-ray tomography was acquired incrementally between the unloaded state and maximum load. The analysis of the monotonic tension specimens showed intralaminar cracking was dominant during crack initiation, delamination became prevalent during the later stages of crack progression, and fiber breakage was, in general, largely related to intralaminar cracking. After the monotonic tension analysis, modifications were made to the specimen geometry and the loading assembly, and fatigue tests were conducted, also using <i>in-situ</i> synchrotron X-ray tomography. Specifically, tomography images were acquired after select intervals of cyclic loading to examine the crack growth behavior up to 5802 cycles. The analysis of the fatigue tests showed that intralaminar cracking was also dominant, while localized delamination allowed ply cross-over. A finite element analysis was conducted by comparing the crack profile at varying intervals of loading, and the change in stored energy per cycle, dU/dN, was calculated. The combined experimental and simulation analysis showed that when the per ply values of dU/dN were examined, the intralaminar cracking rate collapsed to one curve regardless of the ply orientation, where direct observations of fiber bridging were characterized and associated with a reduction in crack growth rate for the influenced ply. Overall, this work provides a physical understanding of the micromechanics facilitating intralaminar crack growth in composites, providing engineers the necessary assessments for slow crack growth approaches in structural composite materials.<br></div>

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Dans ce travail, la caractérisation mécanique de l’interphase entre les zones amorphes et cristallines dans le polyéthylène a été abordée. La caractérisation élastique est effectuée en appliquant deux approches micromécaniques à partir des données de la simulation moléculaire pour la zone interlamellaire. Ces approches micromécaniques sont d’une part le modèle étendu d’inclusion composite, et d’autre part la méthode de double inclusion. Les résultats des deux approches s’accordent parfaitement. Il a été mis en évidence que le tenseur de rigidité de l’interphase n’est pas défini positif, l’interphase est donc mécaniquement instable. La comparaison avec les résultats expérimentaux valide la méthodologie proposée. Pour la caractérisation hyperélastique, l’algorithme hybride proposé consiste à appliquer la loi de comportement d’un milieu continu isotrope, compressible et hyperélastique aux résultats de la simulation de la dynamique moléculaire d’un élément unitaire de polyéthylène. La notion d’optimisation d’un ensemble de fonctions coûts non négatives est l’idée clé de cette partie. Les paramètres hyperélastiques identifiés sont en bon accord avec ceux qui ont été estimés expérimentalement. L’évolution des frontières de l’interphase avec la déformation est le second résultat de cette analyse. La fin du travail est dédiée à la simulation numérique de la grande déformation viscoplastique d’un agrégat de polyéthylène. Le modèle de Gent adopté pour la contrainte de rappel, le tenseur de projection proposé pour l’approche modifiée de Taylor, et l’optimisation multiniveau font parties des contributions apportées. / Elastic characterization of the interphase layer in polyethylene is implemented by applying the relationships of two micromechanical approaches, “Extended Composite Inclusion Model” and “Double-Inclusion Method”, to the Monte Carlo molecular simulation data for the interlamellar domain. The results of the two approaches match perfectly. The interphase stiffness lacks the common feature of positive definiteness, which indicates its mechanical instability. Comparison with experimental results endorses the proposed methodology. For the hyperelastic characterization of the interlamellar domain and the interphase layer, the proposed hybrid algorithm consists in applying the constitutive equations of an isotropic, compressible, hyperelastic continuum to the molecular dynamics simulation results of a polyethylene stack. Evolution of the interphase boundaries are introduced as auxiliary variables and the notion of minimizing a set of nonnegative objective functions is employed for parameter identification. The identified hyperelastic parameters for the interlamellar domain arein good agreement with the ones that have been estimated experimentally. Finally, the large, viscoplastic deformation of an aggregate of polyethylene is reexamined. The Gent model adopted for the back stress of the noncrystalline phase, correcting the projection tensor for the modified Taylor approach, and the idea of multilevel optimization are among the contributions made.

Le travail présenté dans ce document vise à mettre en évidence et à comprendre l'effet de la taille nanométrique des renforts sur les propriétés des nanocomposites avec une approche expérimentale. Des nanocomposites de PMMA et particules de silice (15nm, 25nm, 60nm, 150nm et 500nm) de fractions volumiques 2 0/0, 40/0 et 6 0/0 ont été fabriqués. Des analyses multi-échelles (MET et DRX-WAXS) ont montré que les paramètres caractéristiques de la microstructure des nanocomposites varient avec la taille des nanoparticules. En effet, la diminution de la taille des nanoparticules à fraction volumique constante a entrainé une diminution de la distance intermoléculaire. Cette diminution a induit une densification de la matrice et une réduction de la mobilité des chaînes de la matrice. Des essais mécaniques (traction, DMA) ont montré que les modules de Young (E) et de conservation (E') des nanocomposites augmentent avec la diminution de la taille des nanoparticules à fraction volumique constante. Et que l'augmentation de E' est conservée avec l'augmentation de la température. Une augmentation des températures de transition vitreuse (Tg) et de dégradation (Td) a également été observée avec les essais DSC, DMA et ATG. Le modèle de la borne inférieure d'Hashin-Shtrikman étendue aux nanocomposites à renforts sphériques proposé par Brisard a été utilisé. La modélisation des modules élastiques des nanocomposites a montré que pour reproduire les données expérimentales, il faut que d'une part que les modules surfaciques caractérisant l'interface soient dépendants de la taille des nanoparticules. Et d'autre part, tenir compte de l'état de dispersion des nanoparticules. / The work presented in this paper aims to highlight and to understand the size effect of nano-reinforcements on nanocomposite properties With an experimental approach. Nanocomposites of PMMA and silica particles With different sizes (15nm, 25nm, 60nm, 150nm and 500nm) and volume fractions (20/0, 4 0/0 and 60/0) were manufactured. Multiscale analysis (MET and DRX-WAXS) have shown that the characteristic parameters of the microstructure of nanocomposites vary With the size of the nanoparticles. Indeed, the decrease in the size of nanoparticles at a given volume fraction implies a decrease of the intermolecular distance. This decrease has induced a densification of the matrix and a decrease of the matrix chain mobility. Mechanical tests (tensile, DMA) have shown that the young (E) and the conservation (E') moduli of the nanocomposites increase With the decrease in the size of the nanoparticles With a constant volume fraction. And the increase of E l is kept when temperature growing. An increase in glass transition (Tg) and degradation temperature (Td) was also observed With the DSC, DMA and ATG tests. Experimental elastic properties of the nanocomposites were used to assess the relevance of size effect micromechanical models, particularly the Hashin-Shtrikman bounds With interface effects proposed by Brisard. The modeling has shown that to reproduce the experimental elastic moduli of nanocomposites, the elastic coefficients of the interface must be dependents on particle sizes. And the state of dispersion of particles must be taken into account.