Cette thèse s'inscrit dans le cadre d'un projet globalde collaboration avec le groupe Cobra Europe. La motivation principale estde comprendre et de modéliser les mécanismes physiques de dégradations etde rupture d'un tissu préalablement conçu pour répondre à un cahier des charges identifié.Ce travail poursuit alors les acquis de la thèse de Piezelen s'intéressant aux mécanismes de dégradation conduisantà la ruine d'un tissu et en introduisant des grandeurs susceptibles d'être une aide à leur conception. Un travail d'investigation expérimentale multi-échelle sur tissus vierge et endommagé est d'abord mis en œuvre afin d'analyser et de caractériser les phénomènes dedégradation qui peuvent y apparaître. Les essais mécaniques de traction résiduelle (avec ou sans cyclage préalable) sont réalisés sur bande (échelle macroscopique) pour déceler une chute de la contrainte à rupture. Les observations par tomographie très haute résolution permettent d'accéder au cœur même des constituants du tissu (échelle mésoscopique). Elles ont révélé la cause principale de la ruine d'un tissu :la rupture des fils de chaîne, avec des informations telles que sa localisation ainsi que l'orientation de la normale à la surface de rupture. Un travail de modélisation multiéchelle est ensuite mené sur le tissu afin de rendrecompte des mécanismes de dégradation observés au préalable. Sous des sollicitationsmacroscopiques représentatives des conditions de service avec lesquellesle tissu considéré est utilisé (traction/flexion), la cellule périodiquedu Volume Elémentaire Représentatif est investiguée. Notammentune analyse très complète de l'état de contraintes (hétérogénéité, gradient, triaxialité, orientation préférentielle) est faite dans les fils de renfort.De cela, des grandeurs jugées pertinentes pour analyser n'importe quel tissu sont identifiées.Ces grandeurs sont en accord avec les observations expérimentales. Elles ontpermis finalement de comprendre et d'expliquer le processus de ruine du tissu.Egalement, avec l'expérience acquise tout au long de ce travail, ces mêmesgrandeurs ont été utilisées en vue d'effectuer le classement de deux types d'architectures tissées. Ceci ouvre la voie pour la troisième thèse qui systématisera et affinera la démarche. / This PhD work is part of global collaboration project with Cobra Europe company.The main motivation is to better understand in order to model the physical degradation mechanisms of woven composite with a well specified design.The present work takes benefit of the results issued from Piezelthesis. It aims at investigating the mechanisms of degradation leading to the failure of woven fabrics but also at introducing relevant parameters dedicated to their design.A multiscale experimental investigation on virgin and degraded samples of fabric is first carried out in order to analyze and characterize the damage phenomena observed within these samples.Tensile tests (with or without pre-cycling) were performed on the composite material (at the macroscopic scale) to detect a decrease in the stress at failure. Tomographic inspections with high resolution allowed for observations inside the constituents of the fabrics (mesoscopic scale)Thus, the main origin of the failure of the fabric was revealed : the warp yarn break with its localisation and information about the orientation of the normal to the fracture surfaces. A multiscale modeling was then performed, motivated by the degradation mechanisms observed previously. Under macroscopic loading representative of in service solicitationapplied to the present woven fabric (tension/bending), the periodic cell of theRepresentative Volume Element was investigated. Namely, a complete analysis of the stress state (heterogeneity, gradient, triaxiality, orientation) is carried out within the reinforcing yarns. It turns out that relevant parameters able to analyze any woven fabric were identified. Their characteristics were in good agreement with the experimental evidences. Furthermore, they allowed for a better understanding of the failure process of the fabric. With the experience acquired during the present work, these parameters were utilized to classify two specific woven architectures.This opens the perspective of a third thesis dedicated to refine and render systematic the present approach.

La prochaine génération de moteur d'avion civil, LEAP, développé par Snecma (groupe Safran) et General Electric, intègrera de nombreuses innovations matériaux qui contribueront à la réduction de la consommation de carburant, d'émission de polluants et du bruit. Parmi ces innovations, l'utilisation d'aubes de turbine en CMC (Composites à Matrice Céramique) permettra une réduction significative de la masse du moteur. Les travaux présentés concernent à la fois la caractérisation du comportement mécanique de composites tissés 3D-SiC/Si-B-C et le développement d'une approche multi-échelle du comportement élastique adaptée aux structures CMC complexes. Un premier modèle à l'échelle du fil a été développé en prenant en compte la variabilité du matériau (porosité, architecture, usinage, etc...). Le modèle HPZ (Homogénéisation Par Zone) reposant sur la discrétisation du domaine d'homogénéisation permet de faire le lien entre l'échelle mésoscopique et l'échelle de la structure. / Due to their high thermo-mechanical properties and low densities, ceramic matrix composites (CMC) are candidate materials for hot parts in gas-turbine engines. Various applications have been identified for several types of CMC including C/SiC (nozzles), SiC/SiC (compressor blade) and all oxide composites (combustors). This work presented relates to both the characterization of the mechanical behaviour of woven composites 3D-SiC/Si-BC and the development of a multi-scale elastic behaviour suitable for complex CMC structures approach. A first model at the mesoscale has been developed taking into account the variability of the material (porosity, architecture, manufacturing, etc ...). The HPZ model ("Homogenisation par Zone" in French) based on the discretization of the homogenization field allows to link the mesoscopic scale and the scale of the structure.

Adhesion, which includes cell-to-cell and cell-to-extracellular-matrix adhesion, plays an important role in cancer invasion and metastasis. After undergoing morphological changes malignant and invasive tumour cells, i.e., cancer cells, break away from the primary tumour by loss of cell-cell adhesion, degrade their basement membrane and migrate through the extracellular matrix by enhancement of cell-matrix adhesion. These processes require interactions and signalling cross-talks between proteins and cellular components facilitating the cell adhesion. Although such processes are very complex, the necessity to fully understand the mechanism of cell adhesion is crucial for cancer studies, which may contribute to improving cancer treatment strategies. We consider mathematical models in an attempt to understand better the roles of cell adhesion involved in cancer invasion. Using mathematical models and computational simulations, the underlying complex biological processes can be better understood and their properties can be predicted that might not be evident in laboratory experiments. Cancer cell migration and invasion of the extracellular matrix involving adhesive interactions between cells mediated by cadherins and between cell and matrix mediated by integrins, are modelled by employing two types of mathematical models: a continuum approach and an individual-based approach. In the continuum approach, we use Partial Differential Equations in which cell adhesion is treated as non-local and formulated by integral terms. In the individual-based approach, we first develop pathways for cell-cell and cell-matrix adhesion using Ordinary Differential Equations and later incorporate the pathways in a simulation environment for multiscale computational modelling. The computational simulation results from the two different mathematical models show that we can predict invasive behaviour of cancer cells from cell adhesion properties. Invasion occurs if we reduce cell-cell adhesion and increase cell-matrix adhesion and vice versa. Changing the cell adhesion properties can affect the spatio-temporal behaviour of cancer cell invasion. These results may lead to broadening our understanding of cancer cell invasion and in the long term, contributing to methods of patient treatment.

La rugosité est une propriété clé des sols qui contrôle de nombreux processus de surface et influence la fonction de diffusion du rayonnement incident, alias sa BRDF (Bidirectional Reflectance Distribution Function). Bien qu’elle dépende fortement de l’échelle spatiale, la rugosité est souvent considérée comme stationnaire dans les modèles photométriques de réflectance de surfaces. En particulier, celui de Hapke l’inclut sous la forme d’un angle de pente moyen, intégré sur toutes les échelles variant de la taille d’un grain du régolithe à celle de la topographie locale. Le sens physique de ce paramètre de rugosité moyenne est largement débattu car l’échelle n’est pas clairement définie. Cette thèse a pour objectifs de comprendre comment la rugosité moyenne peut décrire un phénomène multi-échelle et d’investiguer l’influence des échelles spatiales de rugosité sur la BRDF d’une surface. On teste notamment la capacité du modèle de Hapke à restituer par inversion de la BRDF une rugosité moyenne compatible avec la réalité terrain. La topographie de terrains volcaniques et sédimentaires du Piton de la Fournaise (île de La Réunion) et du rift d’Asal-Ghoubbet (République de Djibouti) a été mesurée par photogrammétrie haute résolution sur une large gamme de résolutions à partir de données multi-instrumentales : images satellite, drone et acquises manuellement. Leur BRDF a été mesurée en parallèle par Pléiades et par un spectro-goniomètre (appelé Chamelon), et simulée numériquement par tracé de rayon sur les MNT réalisés. Une analyse multi-échelle par transformée en ondelettes révèle le comportement multi-modal de la rugosité des surfaces étudiées et permet de montrer que les structures sub-centimétriques dominent à la fois le paramètre de rugosité intégré et la forme de la BRDF. La rugosité estimée par inversion sur les données simulées avec une version simplifiée du modèle de Hapke coïncide avec celle déterminée sur les modèles de surface lorsque les hypothèses du modèle sont respectées et l’albédo connu à priori. L’adéquation n’est pas systématique mais reste bonne dans le cas de terrains à rugosité modérée avec une version complète du modèle de Hapke / Surface roughness is a key property of soils that controls many surface processes and influences the scattering function, or BRDF (Bidirectional Reflectance Distribution Function), of incident radiation. While it is strongly scale-dependent, it is often considered as a stationnary parameter in photometric models. In particular, it is included in the Hapke model as a mean slope angle, integrated over all scales from the grain size to the local topography. Yet its physical meaning is still a question at issue, as the scale at which it occurs is undefined. This thesis aims at understanding how this mean parameter can describe a multiscale phenomenon and to investigate the role of spatial scale on surface BRDF. Finally, we investigate the ability of the Hapke model to retrieve a roughness parameter which is consistent with the ground truth. The topography of volcanic and sedimentary terrains in the Piton de la Fournaise (Réunion Island) and the Asal-Ghoubbet rift (Republic of Djibouti) has been measured using high resolution photogrammetry at a wide range of resolutions thanks to multi-instrumental data : satellite, drone and handheld images. Simultaneously, the BRDF has been numerically simulated, and measured by satellite and a spectrogoniometer (named Chamelon). A multiscale analysis by the means of the wavelet transform reveals the multi-modal behavior of roughness and shows that sub-centimeter surface features dominate both the integrated parameter and the shape of the BRDF. The roughness estimated by inversion of a simplified version of the Hapke model matches the roughness determined over surfaces when the assumptions of the model are verified, with a priori knowledge on surface albedo. The match is not systematic, but remains good for moderately rough terrains using the full Hapke model

An imaging-based computational framework for simulation of airflow in subject specific breathing human lungs is established. The three-dimensional (3D) airways of up to 9 generations and lobes are segmented and reconstructed from computed tomography (CT) images. Beyond the CT-resolved 3D airways, a volume filling method is applied to generate the one-dimensional (1D) conducting airway tree that bridges the central airway with the lung parenchyma. Through 3D-1D airway coupling, a novel image-registration-based boundary condition (BC) is proposed to derive physiologically-consistent regional ventilation for the whole lung and provide flow-rate fractions needed for the 3D airway model via the 1D-tree connectivity and the mass conservation. The in-house parallel finite-element large-eddy simulation (LES) code enables to capture genuinely complex airflow characteristics in a computationally-efficient manner. The 3D-1D coupling framework is multiscale because it can not only predict detailed flows in the 3D central airways at a local level, but also yields subject-specific physiologically-consistent regional ventilation at the whole lung level. The framework has been applied to investigate pulmonary airflow and lung physiology. For example, the study of intra- and inter-subject variability provides insight into the effect of airway geometry on airflow structure. The relations between airflow structure, energy dissipation, and airway resistance under normal breathing condition have also been studied, showing similarity behaviors for inspiratory and expiratory flows. In the study of high-frequency oscillatory ventilation, we have compared counter-flow structures near flow reversal (namely phase change between inspiration and expiration) and quantified associated convective mixing in both idealized and CT-based airway models. Furthermore, the image-registration-derived displacement field is used to deform 3D-1D airway models for breathing lung simulation and estimate diameter changes of 1D airway segments during deformation. In conjunction with an arbitrary Lagrangian Eulerian method, airflow in a breathing lung has been simulated and compared with that of a rigid airway model. The results show that the proposed computational framework is promising in better understanding the human lung physiology and improving the treatment of diseased lung.

In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework. The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales. To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing. To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques.

In this thesis, we develop a temperature-dependent homogenization technique and implement it into the meshfree particle method for nanoscale continuum simulations. As a hierarchical multiscale method, the nanoscale meshfree particle method is employed to model and simulate nanostructured materials and devices. Recently developed multiscale methods can overcome the limitations of both length and time scales that molecular dynamics has. However, multiscale methods have difficulties in investigating temperature-dependent physical phenomena since most homogenization techniques employed in continuum models have an assumption of zero temperature. A new homogenization technique, the temperature-related Cauchy-Born (TCB) rule, is proposed with the consideration of the free energy instead of the potential energy in this thesis. This technique is verified via stress analyses of several crystalline solids. The studies of material stability demonstrate the significance of temperature effects on nanostructured material stability. Since meshfree particle methods have advantages on simulating the problems involving extremely large deformations and moving boundaries, they become attractive options to be used in the hierarchical multiscale modeling to approximate a large number of atoms. In this thesis, a nanoscale meshfree particle method with the implementation of the developed homogenization technique, i.e. the TCB rule, is proposed. It is shown that numerical simulations in nanotechnology can be beneficial from this technique by saving a great amount of computer time. The nanoscale meshfree particle method is employed to investigate the crack propagation in a nanoplate with the development of cohesive zone model and a thermal-mechanical coupling model. In addition, the nanoscale meshfree particle method is simplified to successfully study mechanisms of nanotube-based memory cells.

The present work presents a framework for multiscale modeling of multimaterial flows using surrogate modeling techniques in the particular context of shocks interacting with clusters of particles. The work builds a framework for bridging scales in shock-particle interaction by using ensembles of resolved mesoscale computations of shocked particle laden flows. The information from mesoscale models is “lifted” by constructing metamodels of the closure terms - the thesis analyzes several issues pertaining to surrogate-based multiscale modeling frameworks. First, to create surrogate models, the effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver. After this, closure laws for drag are constructed in the form of surrogate models derived from real-time resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that unlike the DKG method, the MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. In macroscale models for shock-particle interactions, Subgrid Particle Reynolds’ Stress Equivalent (SPARSE) terms arise because of velocity fluctuations due to fluid-particle interaction in the subgrid/meso scales. Mesoscale computations are performed to calculate the SPARSE terms and the kinetic energy of the fluctuations for different values of Mach Number and particle volume fraction. Closure laws for SPARSE terms are constructed using the MBKG method. It is found that the directions normal and parallel to those of shock propagation are the principal directions of the SPARSE tensor. It is also found that the kinetic energy of the fluctuations is independent of the particle volume fraction and is 12-15% of the incoming shock kinetic energy for higher Mach Numbers. Finally, the thesis addresses the cost of performing large ensembles of resolved mesoscale computations for constructing surrogates. Variable fidelity techniques are used to construct an initial surrogate from ensembles of coarse-grid, relative inexpensive computations, while the use of resolved high-fidelity simulations is limited to the correction of initial surrogate. Different variable-fidelity techniques, viz the Space Mapping Method, RBFs and the MBKG methods are evaluated based on their ability to correct the initial surrogate. It is found that the MBKG method uses the least number of resolved mesoscale computations to correct the low-fidelity metamodel. Instead of using 56 high-fidelity computations for obtaining a surrogate, the MBKG method constructs surrogates from only 15 resolved computations, resulting in drastic reduction of computational cost.

The primary objective of this work is to propose a state-of-the-art physics based multiscale modeling framework for simulating material phase change problems. Both ice melting and copper crystallization problems are selected to demonstrate this multiscale modeling and simulation. The computational methods employed in this thesis include: classical molecular dynamics, finite element method, phase-field method, and multiscale (nano/micro coupling) methods. Classical molecular dynamics (MD) is a well-known method to study material behaviors at atomic level. Due to the limit of MD, it is not realistic to provide a complete molecular model for simulations at large length and time scales. Continuum methods, including finite element methods, should be employed in this case. In this thesis, MD is employed to study phase change problems at the nanoscale. In order to study material phase change problems at the microscale, a thermal wave method one-way coupling with the MD and a phase-field method one-way coupling with MD are proposed. The thermal wave method is more accurate than classical thermal diffusion for the study of heat transfer problems especially in crystal based structures. The second model is based on the well-known phase-field method. It is modified to respond to the thermal propagation in the crystal matrix by the thermal wave method, as well as modified to respond to temperature gradients and heat fluxes by employing the Dual-Phase-Lag method. Both methods are coupled with MD to obtain realistic results. It should be noted that MD simulations can be conducted to obtain material/thermal properties for microscopic and/or macroscopic simulations for the purpose of hierarchical/sequential multiscale modeling. These material parameters include thermal conductivity, specific heat, latent heat, and relaxation time. Other type of interfacial parameters that occur during the phase change process, such as nucleus shape, interfacial energy, interfacial thickness, etc., are also obtained by MD simulation since these have so far been too difficult to measure experimentally. I consider two common phase change phenomena, ice melting and copper crystallization, in this thesis. For the case of ice melting, MD is first employed to study its phase change process and obtain thermal properties of ice and water. Several potential models are used. I conduct simulations of both bulk ice and ice/water contacting cases. It is found that various potential models result in similar melting phenomena, especially melting speed. Size effects are also studied and it is found that the melting time is longer for larger bulk ice segments but that the average melting speed is size dependent. There is no size effect for the melting speed at ice/water interface at the nanoscale if the same temperature gradient is applied. The melting speed of ice should depend on the temperature gradient. To study ice melting at the microscale, the thermal wave model is employed with parameters obtained from MD simulations. It is found that ice melting speed is scale, for both length scale and time scale, dependent. For the case of copper crystallization, an EAM potential is first employed to conduct MD simulations for studying the copper crystallization process at the nanoscale. I obtain thermal properties and interfacial parameters, including thermal diffusion coefficient, latent heat, relaxation time, interfacial thickness, interfacial energy and the anisotropy coefficients, and nucleus shape etc. A central symmetry parameter is used to identify an atom in solid state or liquid state. And then an initial nucleus shape is obtained and used as the input for microscale simulation, in which the phase-field method is used to study copper crystallization at the microscale.

Complex industrial processes are represented by data that are well known to be multiscaled due to the variety of events that occur in a process at different time and frequency localizations. Wavelet based multiscale analysis approaches provide an excellent means to examine these events. However, the scope of the existing wavelet based methods in the fields of statistical applications, such as process monitoring and defect identification are still limited. Recent literature contains several wavelet decomposition based multiscale process monitoring approaches including many real life process monitoring applications, such as tool-life monitoring, bearing defect monitoring, and monitoring of ultra-precision processes such as chemical mechanical planarization (CMP) in wafer fabrication. However, all of the above mentioned wavelet based methodologies are offline and depend on the visual observations of the wavelet coefficients and details. The offline analysis paradigm was imposed by the high computation needs of the multiscale analysis, whereas the visual observation based approach was necessitated by the lack of statistical means to identify undesirable events. One of the most recent multiscale application, that deals with detecting delamination in CMP, addressed the need for online analysis by developing a moving window based approach to reduce computation time. This research presents 1) development of a fully online multiscale analysis approach where the speed of wavelet based analysis of the data matches the rate of data generation, 2) development of a statistical tool based on Sequential Probability Ratio Test (SPRT) to detect events of interest, and 3) development of an approach to display the analysis results through real time graphs for ease of process supervisory decision making. The developed methodologies are programmed using MATLAB 6.5 and implemented on several data sets obtained from metal and oxide CMP of wafer fabrication. The results and analysis are presented.