L'objectif de cette thèse est de proposer une démarche de modélisation à partir de niveau microstructure pour obtenir un modèle d'endommagement à gradient. Elle se fonde, d'une part, sur la méthode d'homogénéisation pour construire un milieu effectif à partir de la microstructure donnée, et d'autre part, sur la formulation variationnelle, à l'échelle macroscopique, d'une loi d'évolution d'endommagement à partir du milieu homogénéisé. Nous construisons dans un premier temps une approche basée sur le développement asymptotique et de la méthode variationnelle pour homogénéiser un milieu élastique périodique. Afin de modéliser le phénomène de localisation d'endommagement , cette approche a été étendue à un milieu hétérogène quasi périodique. Par un exemple du milieu micro fissuré quasi périodique, nous obtenons une énergie élastique qui dépend non seulement du gradient de l'endommagement mais aussi du gradient de déformation. Dans la deuxième partie, nous construisons un modèle d'endommagement à gradient à partir de l'énergie élastique homogénéisé en se basant sur la principe de minimisation d'énergie. En ajoutant des hypothèse pour simplifier le modèle, nous pouvons construit explicitement des états localisés d'endommagement et de déformation. Enfin, un schéma de résolution numérique, basé sur un algorithme de minimisation alternée, a été proposé pour le cas d'un barre en traction. A partir des résultats numériques, les avantages et les inconvénients du modèle sont discutés. / The aim of this work is to propose a general framework to obtain a gradient damage model from the micro-structural level. It is based, firstly, on the homogenization method to derive an effective medium from the microstructure, and secondly, on the variational formulation of a damage evolution law from the homogenized medium. We propose, as a first step, an approach based on asymptotic expansion and the variational method for homogenizing a periodic elastic medium. To model the localization of damage, this approach has been extended to a quasi-periodic heterogeneous medium. From an example of quasi periodically micro-cracked solid, we obtain an elastic energy that not only depends on the gradient of the damage but also the strain gradients. Based on the principle of energy minimization, we propose the construction of a gradient damage model from the elastic energy homogenized in the second part. By adding some hypothesis to simplify the model, we can construct localized damage and strain solutions in closed form. Finally, a numerical resolution scheme, which is based on an alternate minimization algorithm, is proposed for the one-dimensional traction bar test. From the numerical results, the advantages and disadvantages of the model are discussed.

The interdependencies that exist within and between infrastructures can cause unexpected system properties to emerge when their components fail due to large disruptions. As witnessed following emergencies such as Hurricane Katrina, the complexities of these interdependencies make it very difficult to effectively recover infrastructure because of the challenges they create in prioritizing the most critical components for repair. The Joint Infrastructure Interdependencies Research Program was initiated by Public Safety Canada (PSC) and the Natural Sciences and Engineering Research Council of Canada (NSERC) in 2005 to research methods for remedying this problem. As a part of this research, the University of British Columbia (UBC) is developing an infrastructure interdependency simulator, named I2Sim, to simulate disasters and develop strategies for dealing with emergencies. Part of this development is to construct a model of the UBC electrical distribution system and interface it with I2Sim. In this research, a general methodology for such a model is presented, which employs an off-the-shelf powerflow modeling tool. In addition, a model of the UBC information technology infrastructure is developed to provide a second infrastructure model to demonstrate the electrical model's usefulness in multi-infrastructure disaster recovery simulations. Simulations with these models have shown that the recovery of this two-infrastructure system can be carried out more effectively following an earthquake if both infrastructures are considered together in the repair approach, rather than individually. This difference was on the order of thirty percent. To extend this research from electrical distribution systems to electrical bulk systems, an interdependency model of the British Columbia Transmission Corporation bulk power network and its communications system was also developed, along with a post-blackout restoration procedure. Using these, simulations of a post-blackout recovery were carried out to study the level of risk that communications outages may pose to the electrical network's recovery. These simulations revealed a correlation between restoration time and the number of communication points lost. This research also demonstrates there is value in combining the results of such simulations with risk evaluation tools. Together these results provided a clearer indication of where vulnerabilities exist. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis studies the strain response of mastic asphalt to arbitrary tension, arbitrary compression, alternating tension/compression, loading, zigzag loading and sinusoidal loading. In order to model the strain response to different loading histories, the scissors model is employed. Matlab modules are developed that are able to predict strain response not only for creep loading but also for other types of non constant stress loading such as zigzag loading and sinusoidal loading. In addition, another phenomological model, i.e. the viscoelastoplastic continuum damage model, is summarized and discussed in detail with respect to its applicability for the available data set.

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Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom. The transient temperature distribution within the region is simulated using a two-dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem. The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range. Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models. / Master of Science

Yes / Finite element (FE) analysis of fiber-reinforced polymer (FRP) reinforced concrete beams cast in U-shaped ultra-high performance concrete (UHPC) permanent formworks is presented in this paper. Concrete damage plasticity (CDP) and FRP brittle damage models were used to simulate the damage behavior of concrete and FRP bars. The results of FE simulation are in good agreement with the experimental results. Furthermore, parametric studies were conducted to investigate the effect of concrete and UHPC strengths, yield strength of steel bars, elastic modulus of FRP bars, ultimate tensile strength of FRP bars, types of UHPC normal strength concrete (NSC) interface and thickness of UHPC under different reinforcement conditions. Flexural performances, in terms of cracking, yield, ultimate loads and corresponding deflections, failure mode, energy dissipation and ductility, were investigated. Traction-separation model was used to describe the bonding degradation and the maximum slip of two types of bonding interfaces (smooth surface and medium-rough surface). Both flexural capacity and resistance to deformation of composite beams are significantly improved by the utilization of hybrid FRP/steel reinforcement. The UHPC formwork can also delay the occurrence and development of cracks. By appropriately increasing the strength of UHPC or elastic modulus of FRP bar, the flexural capacity of composite beams is effectively improved. It is expected that the results presented in this paper can guide the design and construction of U-shaped UHPC permanent formwork-concrete composite beams reinforced with FRP bars.

L’enjeu actuel pour les industriels de l’aéronautique est de diminuer la consommation en carburant et/ou d’augmenter le rendement des avions. A terme, Safran souhaite remplacer les aubes de turbine, actuellement en superalliage, par des aubes en matériau composite tissé de type SiC/SiBC. Il est alors important de prévoir leurs durées de vie. Ce travail a donc consisté à développer un modèle de durée de vie pour ces composites autocicatrisants. Ces matériaux tissés sont constitués de fibres Nicalon, d’une interphase de pyrocarbone et d’une matrice autocicatrisante multicouche (B4C, SiC et SiBC). La particularité de ces composites est l’oxydation de chaque constituant du matériau en fonction de l’environnement (température, atmosphère sèche ou humide). Le modèle de durée de vie développé offre un compromis entre des temps de calcul réduits, malgré la prise en compte de phénomènes physico-chimiques complexes, et une prévision de la durée de vie suffisamment précise. L’approche retenue est un couplage entre un modèle d'endommagement mécanique et un modèle physico-chimique. Un modèle de durée de vie uniaxial a été proposé afin de justifier les différents couplages nécessaires entre les parties mécanique et physico-chimique mais également pour optimiser les algorithmes de résolution. Ce modèle a permis d’identifier les coefficients pour deux nuances de matériaux. Afin de réaliser des essais de structures, un modèle de durée de vie multiaxial a été proposé et implanté dans le code de calcul ZéBuLoN. Un protocole d’identification a également été proposé dans ce travail même si les essais de caractérisation jusqu’ici réalisés ne sont pas suffisants pour identifier complètement le modèle 3D sur ces matériaux. / The current challenge for the aerospace industry is to decrease the fuel consumption and/or to increase the performance of planes. In the future, Safran Group wishes to replace the turbine blades, currently in superalloy, with woven composite SiC/SiBC material blades. Therefore, it is important to predict their life time. This work involved developing a life time model of these self-healing composites. These woven materials are made up of Nicalon fibers, and an interphase of pyrocarbone and a self-healing matrix (B4C, SIC and SiBC). The particularity of these composites is the oxidation of every constituent of the material depending on the environment (temperature, dry or wet atmosphere). The developed life time model offers a compromise between reduced calculating time, in spite considering complex physico-chemical phenomena, and an accurate enough prediction of the life time. The approach chosen is a coupling between a mechanical damage model and a physico-chemical model. A uniaxial life time model was proposed to explain the different necessary couplings between the mechanical and physico-chemical parts but also to optimize the resolution algorithms. This model enabled to identify the coefficients for two grades of materials. In order to carry out tests of structures, a multiaxial life time model was proposed and implemented in the ZéBuLoN Finite Element code. A protocol of identification was also proposed in this work even if the characterization tests so far realized are not sufficient to identify the 3D-Model for these materials.

O presente trabalho de pesquisa está relacionado à análise do progresso do fraturamento na zona tracionada de fundações rochosas de barragens de concreto e suas conseqüências nas avaliações de estabilidade global. Tomou-se como exemplo a barragem de Porto Primavera de propriedade da CESP (Companhia Energética de São Paulo), situada entre os estados de São Paulo e Mato Grosso do Sul, Brasil. Com a ajuda de modelos elaborados com elementos finitos e sob a ótica da mecânica da fratura não linear e da mecânica do dano, analisa-se o desenvolvimento da fratura mediante uma avaliação iterativa tensão-deformação e carga hidráulica. Devido ao carregamento progressivo de água, realiza-se a análise iterativa baseada no avanço da fratura e na aplicação de pressão hidráulica, até quando a fratura deixa de progredir. A simulação numérica proposta tem o objetivo de estudar o desenvolvimento de fraturas, determinar as deformações ocorridas sob a ação das forças de empuxo d'água, de subpressão, do peso próprio e das pressões de água na fratura do maciço rochoso fraturado. As deformações calculadas são comparadas com registros da instrumentação na fundação efetuados durante o enchimento do reservatório, o que permitirá o ajuste dos parâmetros adotados na simulação, assim como estabelecer as reais características da fundação / This study is related to the analysis of crack propagation in the tensioned zone of concrete dam foundation. The example of Porto Primavera dam owned by CESP (São Paulo State Power Company) Brazil is presented. Fracture growth is analyzed by mean iterative stress-strain and hydraulic head analysis with codes based on finite elements incorporating non-linear fracture mechanics and damage models. Due to progressive load of water, a step-by-step analysis is performed, based on the development of fracture and application of forces due of hydraulic pressure. The proposed numerical simulation has the purpose of studying the development of fracture, determining deformations due to the action of uplift pressure, self-weight and hydraulic pressure on the fracture walls. The computed deformations are compared with instrumentation data, obtained during the impoundment of the reservoir, from devices installed in the foundation, which will allow to adjust the adopted parameters in the simulation and to determine the real characteristics of the foundation