abstract: Polymer and polymer matrix composites (PMCs) materials are being used extensively in different civil and mechanical engineering applications. The behavior of the epoxy resin polymers under different types of loading conditions has to be understood before the mechanical behavior of Polymer Matrix Composites (PMCs) can be accurately predicted. In many structural applications, PMC structures are subjected to large flexural loadings, examples include repair of structures against earthquake and engine fan cases. Therefore it is important to characterize and model the flexural mechanical behavior of epoxy resin materials. In this thesis, a comprehensive research effort was undertaken combining experiments and theoretical modeling to investigate the mechanical behavior of epoxy resins subject to different loading conditions. Epoxy resin E 863 was tested at different strain rates. Samples with dog-bone geometry were used in the tension tests. Small sized cubic, prismatic, and cylindrical samples were used in compression tests. Flexural tests were conducted on samples with different sizes and loading conditions. Strains were measured using the digital image correlation (DIC) technique, extensometers, strain gauges, and actuators. Effects of triaxiality state of stress were studied. Cubic, prismatic, and cylindrical compression samples undergo stress drop at yield, but it was found that only cubic samples experience strain hardening before failure. Characteristic points of tensile and compressive stress strain relation and load deflection curve in flexure were measured and their variations with strain rate studied. Two different stress strain models were used to investigate the effect of out-of-plane loading on the uniaxial stress strain response of the epoxy resin material. The first model is a strain softening with plastic flow for tension and compression. The influence of softening localization on material behavior was investigated using the DIC system. It was found that compression plastic flow has negligible influence on flexural behavior in epoxy resins, which are stronger in pre-peak and post-peak softening in compression than in tension. The second model was a piecewise-linear stress strain curve simplified in the post-peak response. Beams and plates with different boundary conditions were tested and analytically studied. The flexural over-strength factor for epoxy resin polymeric materials were also evaluated. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2011

This dissertation proposes a new framework to characterize the nonlinear behavior of anisotropic materials in an on-line manner. The proposed framework applies recursive estimation and a multi-linear model to characterize the nonlinear behavior of anisotropic materials on-line using full-field strains, which are capable of capturing the multi-axial information of anisotropic materials. A stochastic method is developed to characterize the linear behavior of anisotropic materials under the influence of full-field strain measurement noise. This method first derives stochastic equations based on the formulas of energy-based characterization that utilizes the principle of ener-gy conservation, and then recursively estimates elastic constants at every acquisition of measure-ment using a Kalman filter (KF). Since the measurement model is expressed nonlinearly, the KF utilizes a Kalman gain, which is newly derived in this dissertation through variance minimization, to achieve optimal characterization. The aforementioned method, namely stochastic linear characteri-zation in this dissertation, becomes a basis of the multi-linear characterization method. This method utilizes a multi-linear model, which is defined by partitions, to characterize the nonlinear constitu-tive relations. The multi-linear characterization scales up the number of estimates and identifies the coefficients of each linear partition using the previously derived KF. The recursive updates in measurements not only removes uncertainty through sensor measurements, but also enables the on-line capability of the nonlinear characterization of anisotropic materials. A series of numerical and experimental studies were performed to demonstrate the performance of the proposed framework in characterizing the nonlinear behavior of anisotropic materials. The validity and applicability of the proposed framework were confirmed by the comparison with the known values of the characterized constitutive relations. It was found that the proposed framework identified elastic constants that were in good agreement with known values irrespective of the spec-imen geometry. The results of the multi-linear characterization method were well correlated with known nonlinear stress-strain relations and concluded that the proposed framework is capable of characterizing adequate nonlinear behavior on-line. / Ph. D.

In this study, a laminated glass unit which consists of two glass sheets bonded together by PVB is analyzed as a curved beam and as a cylindrical shell. Laminated glass curved beams and shells are used in architecture, aerospace, automobile and aircraft industries. Curved beam and shell structures differ from straight structures because of their initial curvature. Because of mathematical complexity most of the studies are about linear behavior rather than nonlinear behavior of curved beam and shell units. Therefore it is necessary to develop a mathematical model considering large deflection theory to analyze the behavior of curved beams and shells. Mechanical behavior of laminated glass structures are complicated because they can easily perform large displacement since they are very thin and the materials with the elastic modulus have order difference. To be more precise modulus of elasticity of glass is about 7*104 times greater than the modulus of elasticity of PVB interlayer. Because of the nonlinearity, analysis of the laminated glass has to be performed by considering large deflection effects. The mathematical model is developed for curved beams and shells by applying both the variational and the minimum potential energy principles to obtain nonlinear governing differential equations. The iterative technique is employed to obtain the deflections. Computer programs are developed to analyze the behavior of cylindrical shell and curved beam. For the verification of the results obtained from the developed model, the results from finite element models and experiments are used. Results used for verification of the model and the explanation of the bahavior of the laminated glass curved beams and shells are presented in figures.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21081号 / 工博第4445号 / 新制||工||1691(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 杉浦 邦征, 教授 KIM Chul-Woo, 教授 清野 純史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

Este trabalho de pesquisa apresenta um modelo numérico para a análise de estruturas planas sob excitação aleatória induzida pelo vento. O comportamento não-linear da estrutura é considerado adotando-se um modelo constitutivo elasto-plástico para o material, aço estrutural. Os elementos das estruturas estudadas estão sujeitos ao surgimento e desaparecimento de rótulas plásticas, levando a um dimensionamento mais econômico. O conhecimento a respeito de vibrações aleatórias de estruturas lineares encontra-se estabelecido. Por outro lado, poucos resultados encontram-se disponíveis para o caso não linear considerado. Para a simulação de vibrações aleatórias uma análise de Monte Carlo é utilizada. Uma função de densidade espectral de potência das velocidades do vento é usada para gerar um certo número de funções harmônicas de carregamento. Os ângulos de fases destes harmônicos são gerados por um algoritmo pseudo-aleatório. Para cada função de carregamento realiza-se uma integração direta no tempo pelo método de Newmark. A grande quantidade de dados de resposta é tratada estatisticamente de modo a permitir a obtenção de conclusões, a respeito da possibilidade de ocorrência de eventos desfavoráveis, do ponto de vista da engenharia. / This work presents a numerical model to analyze structures under random dynamic excitation induced by the wind. The structure is considered to have nonlinear behavior due to the elastic-plastic constitutive law adopted for the material, structural steel. The members of the studied structures may experience formation or disappearance of plastic hinges, leading to a more economic design. Random vibrations of linear structures is a well established subject. On the other hand, very few results are available for the nonlinear case as the one considered. To simulate random vibrations a Monte Carlo type analysis is used. A power spectral density function for wind velocity is used to generate a large number of harmonic input functions. Their phase angles are generated via a pseudo-random algorithm. Numerical time integration using Newmark’s method is performed for each input function. The large amount of response data obtained is statistically treated to allow for useful engineering conclusions on the probability of occurrence of unfavorable events.

Este trabalho de pesquisa apresenta um modelo numérico para a análise de estruturas planas sob excitação aleatória induzida pelo vento. O comportamento não-linear da estrutura é considerado adotando-se um modelo constitutivo elasto-plástico para o material, aço estrutural. Os elementos das estruturas estudadas estão sujeitos ao surgimento e desaparecimento de rótulas plásticas, levando a um dimensionamento mais econômico. O conhecimento a respeito de vibrações aleatórias de estruturas lineares encontra-se estabelecido. Por outro lado, poucos resultados encontram-se disponíveis para o caso não linear considerado. Para a simulação de vibrações aleatórias uma análise de Monte Carlo é utilizada. Uma função de densidade espectral de potência das velocidades do vento é usada para gerar um certo número de funções harmônicas de carregamento. Os ângulos de fases destes harmônicos são gerados por um algoritmo pseudo-aleatório. Para cada função de carregamento realiza-se uma integração direta no tempo pelo método de Newmark. A grande quantidade de dados de resposta é tratada estatisticamente de modo a permitir a obtenção de conclusões, a respeito da possibilidade de ocorrência de eventos desfavoráveis, do ponto de vista da engenharia. / This work presents a numerical model to analyze structures under random dynamic excitation induced by the wind. The structure is considered to have nonlinear behavior due to the elastic-plastic constitutive law adopted for the material, structural steel. The members of the studied structures may experience formation or disappearance of plastic hinges, leading to a more economic design. Random vibrations of linear structures is a well established subject. On the other hand, very few results are available for the nonlinear case as the one considered. To simulate random vibrations a Monte Carlo type analysis is used. A power spectral density function for wind velocity is used to generate a large number of harmonic input functions. Their phase angles are generated via a pseudo-random algorithm. Numerical time integration using Newmark’s method is performed for each input function. The large amount of response data obtained is statistically treated to allow for useful engineering conclusions on the probability of occurrence of unfavorable events.

This study provides an overview of the implementation of a nonlinear microstructural constitutive model in ABAQUS employing a user subroutine at the level of the biomedical engineer. Two different element formulations are employed: a continuum incompressible and a plane stress incompressible. All examples are validated by performing a number of deformations on 2D and 3D square elements and comparing the analytical formulation in a programming language and the user subroutine in ABAQUS. Application models will be presented that provide a deeper look into the impacts of soft tissue deformation, damage, and fracture. Additionally, we investigate the mechanical behavior of skin layers in terms of the nominal stress-strain curve using uniaxial and cyclic loading tests on porcine skin specimens in two forms: dermis integrating epidermis and hypodermis. Experiments were performed on specimens from the belly and breast of the pigs and under both orthogonal orientations with respect to the spine direction. All tests were carried out at room temperature with cyclic loading at a constant strain rate and increasing stretch increments. Finally, data is fitted using microstructural constitutive model.

Dans un contexte d’amélioration des dispositifs pour la réduction de bruit, l’étude sur le transfert d’énergie irréversible en utilisant des résonateurs purement acoustiques à comportement non linéaire a été réalisée. Les résonateurs acoustiques classiques en régime linéaire agissent comme un Amortisseur de Masse Accordée (TMD, en anglais) et ils sont efficaces pour une gamme de fréquence très étroite. Cependant, lorsqu’ils sont soumis à des excitations très fortes (régime non-linéaire) ils peuvent devenir efficaces pour une plus large gamme de fréquences si des termes non linéaires peuvent être activés. Dans un premier temps, une étude sur ce comportement non-linéaire d’un résonateur d’Helmholtz modifié a été réalisée expérimentalement. Ensuite, l’équation dynamique gouvernante de tels résonateurs ont été développées en prenant en compte les non-linéarités de la force de rappel et d’amortissement. Une approximation de la solution analytique de l’équation gouvernante du résonateur acoustique a été déterminée en utilisant les méthodes des échelles multiples du temps et de transformation du temps non régulière. Dans un deuxième temps, une étude du couplage entre un mode acoustique en basses fréquences et un résonateur (celui étudié précédemment) à comportement non-linéaire a été réalisée. Pour ce faire, des mesures expérimentales avec un montage du système couplé ont permis de vérifier l’atténuation acoustique produite par le résonateur en régime forcé et libre. Une modélisation analytique du couplage a permis d’identifier l’expression de la variété invariante lente, ce qui a permis d’étudier les possibles points d’équilibre et points singuliers du système. Les modèles analytiques développés ont également été vérifiés par des simulations numériques. / Nowadays, there is a need of new types of technologies for sound reduction because of the growing of different industries. In this context, we have studied the targeted energy transfer using a purely acoustic resonator. These acoustic resonators act, in the linear regime, as a Tuned Masse Damper (TMD) and they are efficient for a narrow frequency band. But, when they are excited with high forces, in the nonlinear regime, they are efficient for a wider frequency band if the nonlinear terms are activated. First, an experimental study about the nonlinear behavior of a modified Helmholtz Resonator was done. Then, the governing equation of such resonators were developed considering the nonlinearities in the restitution force and damping. An approximation of the analytical solution of the governing equation of the acoustical resonator is derived using the multiples scales of time method and the non-smooth time transformation method. In a second part, a study about the coupling between an acoustic mode in low frequencies and a resonator (the one studied in the previous part) with a nonlinear behavior is done. In order to do this, experimental measurements of the coupled system to confirm acoustic attenuation by the resonator in forced and free regime were done. Then, an analytical modelling of the coupled system allowed to derive the expression of the Slow Invariant Manifold (SIM), in order to identify the possible equilibrium points and singular points of the system. Derived analytical models were verified by numerical simulations.

Les matériaux composites à matrice organique sont largement utilisés dans l'industrie des transports et notamment dans le domaine aéronautique. Pour permettre un dimensionnement optimal des structures, il est nécessaire d'étudier le comportement des matériaux CMO sur une large gamme de vitesses et de températures.L'objectif de cette thèse est de proposer un modèle de comportement et de rupture permettant de prédire la réponse des CMO sur une large gamme de vitesses de sollicitation et de températures. Les recherches se sont intéressées dans un premier temps à la caractérisation de la transition entre les régimes de comportement linéaire et non linéaire du matériau unidirectionnel T700GC/M21 (renforts de fibres de carbone, résine époxy), ainsi qu'à la dépendance de cette transition à la vitesse de sollicitation et à la température. Les travaux se sont ensuite focalisés sur l'étude expérimentale du régime de comportement non linéaire endommageable du T700GC/M21. Enfin, au terme de ces deux étapes, une version améliorée du modèle disponible à l'ONERA pour les composites stratifiés (OPFM) a été proposée, version intégrant un critère de transition linéaire/non linéaire de comportement, et une prise en compte de l'influence de la vitesse de sollicitation et de la température sur la réponse du matériau / Nowadays, organic matrix composite materials are widely used in the transportation industry, and particularly in the aeronautical industry. To provide an optimal dimensioning of the structures, it is necessary to study the mechanical behavior of OMC on a large range of strain rates and temperatures. The aim of this PhD thesis is to propose a behavior and a rupture model to predict the mechanical response of OMC for a large range of strain rates and temperatures. The research was initially focused on the characterization of the transition between the linear and nonlinear behavior of the material T700GC/M21, a carbon / epoxy unidirectional laminate as well as the strain rate and temperature dependencies of this transition. The work was then focused on the experimental study of the nonlinear damaged behavior of the T700GC/M21. Finally, completing these first two steps, an updated version of the behavior model available at ONERA (OPFM) was proposed which includes the transition between linear and nonlinear behavior and the influence of strain rate and temperature on the mechanical response of the material.

Dans le domaine du génie civil, le dimensionnement des structures en béton armé est essentiellement basé sur des démarches déterministes. Cependant, les informations fournies par des analyses déterministes sont insuffisantes pour étudier la variabilité de la réponse de la dalle. Le manque de connaissance des charges appliquées ainsi que les incertitudes liées à la géométrie de la dalle et les caractéristiques des matériaux nécessitent donc l’utilisation d’une approche fiabiliste qui permet la propagation de ces incertitudes dans les analyses déterministes. L'approche fiabiliste est basée sur le principe de couplage mécano-fiabiliste qui consiste à coupler un modèle stochastique et un modèle déterministe. Cependant un couplage mécano-fiabiliste peut être très exigeant en temps de calcul. Dans le cadre de cette thèse, la méthodologie propre aux problématiques des ouvrages du génie civil est développée et validée tout d'abord sur un cas simple de structures en béton armé. Le cas d'une poutre encastrée en béton armée est proposé. Le système est modélisé sous CASTEM par une approche aux éléments finis de type multifibre. Puis la fiabilité d'une dalle en béton armé impactée par une masse rigide à faible vitesse est étudiée en couplant OpenTURNS à Abaqus. Enfin, une enceinte de confinement en béton précontrainte modélisée sous ASTER est étudiée d'un point de vue probabiliste. Seul le problème physique des dalles en béton armé soumises à une chute de colis dans les centrales nucléaires est examiné en détail. Deux modèles déterministes sont utilisés et évalués afin d’étudier les phénomènes dynamiques appliqués aux dalles en béton armé sous impact : un modèle par éléments finis en 3D modélisé sous Abaqus et un modèle simplifié de type masse-ressort amorti à deux degrés de liberté. Afin d’étudier la fiabilité des dalles en béton armé, nous avons couplé les méthodes Monte Carlo et simulation d’importance avec le modèle de type masse-ressort. FORM est utilisée avec le modèle par éléments finis. L’objectif de cette étude est de proposer des solutions pour diminuer le temps de calcul d'une analyse fiabiliste en utilisant deux stratégies dans le cas des dalles impactées. La première stratégie consiste à utiliser des modèles analytiques qui permettent de prédire avec précision la réponse mécanique de la dalle et qui sont moins coûteux en temps de calcul. La deuxième consiste à réduire le nombre d’appels au modèle déterministe, surtout dans le cas des modèles par éléments finis, en utilisant des méthodes probabilistes d'approximation. Ces deux stratégies sont comparées afin de vérifier l’efficacité de chacune pour calculer la probabilité de défaillance. Enfin, une étude paramétrique est réalisée afin d’étudier l’effet des paramètres d’entrées des modèles déterministes sur le calcul de la probabilité de défaillance. / Reinforced concrete structures (RC) are subjected to several sources of uncertainties that highly affect their response. These uncertainties are related to the structure geometry, material properties and the loads applied. The lack of knowledge on the potential load, as well as the uncertainties related to the features of the structure shows that the design of RC structures could be made in a reliability framework. This latter allows propagating uncertainties in the deterministic analysis. However, in order to compute failure probability according to one or several failure criteria, mechanical and stochastic models have to be coupled which can be very time consuming and in some cases impossible. The platform OpenTURNS is used to perform the reliability analysis of three different structures . OpenTURNS is coupled to CASTEM to study the reliability of a RC multifiber cantilever beam subjected to a concentrated load at the free end, to Abaqus to study the reliability of RC slabs which are subjected to accidental dropped object impact during handling operations within nuclear plant buildings, and to ASTER to study the reliability of a prestressed concrete containment building. Only the physical problem of reinforced concrete impacted by a free flying object is investigated in detail. Two deterministic models are used and evaluated: a 3D finite element model simulated with the commercial code “Abaqus/Explicit” and an analytical mass-spring model. The aim of this study is to address this issue of reliability computational effort. Two strategies are proposed for the application of impacted RC slabs. The first one consists in using deterministic analytical models which predict accurately the response of the slab. In the opposite case, when finite element models are needed, the second strategy consists in reducing the number of simulations needed to assess the failure probability. In order to examine the reliability of RC slabs, Monte Carlo and importance sampling methods are coupled with the mass-spring model, while FORM is used with the finite element model. These two stategies are compared in order to verify their efficiency to calculate the probability of failure. Finally, a parametric study is performed to identify the influence of deterministic model parameters on the calculation of failure probability (dimensions of slabs, impact velocity and mass, boundary conditions, impact point, reinforcement.