Material damage such as dislocations and microcracks are characteristic of early stages of fatigue. Accumulation of these nascent cracks leads to non-linear elastic response of the material. These non-linearities can be detected from harmonic generation for propagating elastic waves. The long term goal of this study is to investigate the non-linear elastic propagation in parts with complex geometry. Cellular Automata is introduced as a new simulation method, in order to develop new analysis on quadratic non-linearities. An existing linear code was progressively modified to take into account a different constitutive law. Also the boundary conditions need to be reviewed to ensure free stress with the non-linear behavior. The propagation of the longitudinal wave is investigated in detail. Numerical accuracy is validated from comparison with a closed, for both linear and non-linear code. The reflection of the non-linear P-wave gives confirmation for the correct treatment of the boundary condition. Finally the capabilities of the Cellular Automata code are underlined for reflection of Lamb waves for various boundary conditions.

Les difficultés de mise en œuvre d'expériences de terrain ou de laboratoire, ainsi que les coûts associés, conduisent les sociétés industrielles à se tourner vers des codes numériques de calcul. Ces codes, censés être représentatifs des phénomènes physiques en jeu, entraînent néanmoins tout un cortège de problèmes. Le premier de ces problèmes provient de la volonté de prédire la réalité à partir d'un modèle informatique. En effet, le code doit être représentatif du phénomène et, par conséquent, être capable de simuler des données proches de la réalité. Or, malgré le constant développement du réalisme de ces codes, des erreurs de prédiction subsistent. Elles sont de deux natures différentes. La première provient de la différence entre le phénomène physique et les valeurs relevées expérimentalement. La deuxième concerne l'écart entre le code développé et le phénomène physique. Pour diminuer cet écart, souvent qualifié de biais ou d'erreur de modèle, les développeurs complexifient en général les codes, les rendant très chronophages dans certains cas. De plus, le code dépend de paramètres à fixer par l'utilisateur qui doivent être choisis pour correspondre au mieux aux données de terrain. L'estimation de ces paramètres propres au code s'appelle le calage. Cette thèse propose dans un premier temps une revue des méthodes statistiques nécessaires à la compréhension du calage Bayésien. Ensuite, une revue des principales méthodes de calage est présentée accompagnée d'un exemple comparatif basé sur un code de calcul servant à prédire la puissance d'une centrale photovoltaïque. Le package appelé CaliCo qui permet de réaliser un calage rapide de beaucoup de codes numériques est alors présenté. Enfin, un cas d'étude réel d'une grande centrale photovoltaïque sera introduit et le calage réalisé pour effectuer un suivi de performance de la centrale. Ce cas de code industriel particulier introduit des spécificités de calage numériques qui seront abordées et deux modèles statistiques y seront exposés. / Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of problems. The code intends to be as close as possible to the physical system. It turns out that, despite continuous code development, the difference between the code outputs and experiments can remain significant. Two kinds of uncertainties are observed. The first one comes from the difference between the physical phenomenon and the values recorded experimentally. The second concerns the gap between the code and the physical system. To reduce this difference, often named model bias, discrepancy, or model error, computer codes are generally complexified in order to make them more realistic. These improvements lead to time consuming codes. Moreover, a code often depends on parameters to be set by the user to make the code as close as possible to field data. This estimation task is called calibration. This thesis first proposes a review of the statistical methods necessary to understand Bayesian calibration. Then, a review of the main calibration methods is presented with a comparative example based on a numerical code used to predict the power of a photovoltaic plant. The package called CaliCo which allows to quickly perform a Bayesian calibration on a lot of numerical codes is then presented. Finally, a real case study of a large photovoltaic power plant will be introduced and the calibration carried out as part of a performance monitoring framework. This particular case of industrial code introduces numerical calibration specificities that will be discussed with two statistical models.

[pt] Este trabalho tem como objetivo apresentar detalhes do desenvolvimento de um código numérico tridimensional para simulação de processos de fraturamento e fragmentação em geomateriais. O código se baseia no método combinado dos elementos finitos e discretos, sendo capaz de simular a transição do contínuo para o descontínuo. A princípio é apresentada uma breve introdução ao método combinado dos elementos finitos e discretos, e as suas principais implementações são destacadas. Além disso, são apresentados os conceitos básicos dos modelos de zona coesiva, ressaltando o modelo baseado em potencial PPR (Park-Paulino-Roesler). Em seguida, são apresentados os detalhes do desenvolvimento do código. O desenvolvimento do código foi dividido em quatro partes: modelagem do contínuo, transição entre o contínuo e o descontínuo, detecção e interação entre contatos e a resolução das equações de equilíbrio. As implementações feitas no código são verificadas mediante a simulação de três tipos de ensaios de laboratório comumente empregados na mecânica das rochas (ensaio brasileiro, ensaio de compressão simples e ensaio de tenacidade à fratura), cujos parâmetros utilizados e os resultados para comparação foram obtidos da literatura. Por fim, são apresentados os resultados exibindo os padrões de fraturamento para cada tipo de ensaio e suas curvas força-deslocamento, ou tensão-deformação, bem como as considerações finais e sugestões para trabalhos futuros. / [en] This work aims to detail the development of a three-dimensional numerical code for simulating fracturing and fragmentation processes in geomaterials. The code is based on the combined finite-discrete element method, being able to simulate the transition from continuum to discontinuum. At first, a brief introduction to the combined finite-discrete element method is presented, and its main implementations are highlighted. In addition, the basic concepts of the cohesive zone models are shown, emphasizing the PPR (Park-Paulino-Roesler) potential based cohesive model. Then, the details of the code development are presented. The development of the code was divided into four parts: modelling of the continuum, transition from continuum to discontinuum, detection and interaction between contacts, and the solution of the equilibrium equations. The implementations made on the code are verified upon the simulation of three types of laboratory tests commonly employed in rock mechanics (Brazilian test, uniaxial compressive strength test, fracture toughness test), in which the parameters used and the results for comparison were obtained from the literature. At last, the results exhibiting the fracture patterns for each type of test and its force-displacement, or stress-strain, curves are displayed, as well as the final considerations and suggestions for future works.