Dans le contexte du « Tout Electrique », les fabricants de l’aéronautique cherchent à augmenter la puissance embarquée tout en limitant la masse de ces dispositifs électriques. Une des solutions envisagées est d’augmenter la densité de flux magnétique des matériaux magnétiques de ces appareils. L’inconvénient de l’emploi de ces matériaux réside dans leurs déformations sous l’effet du champ magnétique. Dans le cas des noyaux magnétiques de transformateurs, ceux-ci sont composés d’un empilement d’une centaine de tôles magnétiques d’épaisseur variant entre 0,2 et 0,5mm. La déformation successive des tôles du transformateur est à l’origine d’un bruit acoustique indésirable. La source principale de ces déformations est la magnétostriction qui provient du réarrangement sous champ magnétique de la structure en domaines du matériau. Dans le cadre de ces travaux de thèse, nous nous intéressons à l’alliage Fe-27%Co produit par la société APERAM Alloys Imphy, commercialement appelé AFK1. Le choix de cet alliage provient du fait qu’il présente une aimantation à saturation la plus élevée de tous les matériaux ferromagnétiques (2,4T). Son emploi permettrait alors un gain certain de densité de puissance. Selon une gamme métallurgique particulière, l’AFK1 présente une basse magnétostriction isotrope, qui s’illustre par une déformation nulle jusqu’à 1,5T puis par une déformation à saturation de l’ordre de 10ppm. L’objectif principal de ces travaux de thèse consiste à déterminer l’origine d’un tel comportement et les mécanismes associés. Les résultats expérimentaux montrent que les conditions de traitements thermiques semblent avoir un effet sur le comportement magnétostrictif. On montre par ailleurs que la magnétostriction est indépendante de l’orientation cristallographique de l’AFK1. Des essais de magnétostriction sous contrainte mécanique ont permis de supposer que l’AFK1 disposait d’une structure en domaines principalement composée de parois à 180°. La mise en place de cette structure a pu être confirmée par microscopie magnéto-optique (effet Kerr). Afin de mieux comprendre l’origine de l’orientation des domaines dans le matériau, l’influence de la géométrie d’échantillon sur le comportement magnétostrictif a également été étudiée au cours de ces travaux de thèse. Une modélisation du comportement faiblement magnétostrictif a finalement été proposée par le biais d’une approche multi-échelle. Le modèle met en évidence la nécessité de considérer une proportion non négligeable de domaines séparés par des parois à 180° pour restituer la basse magnétostriction de l’AFK1. / The main challenge in the aeronautical field concerns the increase of higher power density electrical devices onboard aircrafts. One of the solutions proposed is to increase the magnetic flux density of magnetic materials which compose these devices. The main drawback of this solution leads in the high deformation the materials concerned exhibit under magnetic field. For example, the core of onboard transformers is composed of a stack of about hundred of magnetic steel sheets, with a thickness range between 0.2 and 0.5mm. The deformation of the entire structure leads to an unwanted acoustic noise that originates from the high magnetostriction deformation of the material deriving from the change of magnetic domains configuration under magnetic field. In this thesis work, the magnetostrictive behaviour of the Fe-27$%$Co alloy is studied. This magnetic alloy is produced and marketed by APERAM Alloys Imphy as AFK1. This material leads to a low and isotropic magnetostrictive behaviour after an appropriate metallurgical process. The deformation is null up to 1.5T and the magnetic saturation is reached with a deformation lower than 10ppm. The main goal of this thesis is to understand the origin of the low magnetostrictive behaviour and to model it. The experimental results show that thermal annealing changes significantly the magnetostriction. In addition, we prove that low magnetostriction exhibits no crystallographic orientation dependence. Magnetostriction tests carried out under a mechanical loading show that a microstructure mainly composed magnetic domains separated by 180$^circ$ domain walls can explain the behaviour. The presence of this magnetic configuration was confirmed by magneto optical microscopy observations (Kerr effect) associated with a macroscopic geometry effect and residual magnetic field in the furnaces. A multiscale modeling of the low magnetostriction has been proposed next. This modeling helps us to confirm the requirement of about 80% of grains composed of a bi-domain magnetic structure to simulate low magnetostrictive behaviour in accordance with experiments.

Dans un contexte de grande concurrence internationale, la simulation numérique du comportement joue un rôle primordial dans le domaine aéronautique, permettant de réduire les délais et les coûts de conception, d'évaluer la pertinence de nouvelles solutions technologiques avant de se lancer dans les investissements qu'elles imposent. Visant la simulation de structures assemblées, ce travail de thèse a consisté a développer une méthode de décomposition de domaine mixte, multiéchelle, s’appuyant sur le solveur LaTIn. Afin de simplifier le traitement discret des quantités d'interface, la méthode proposée utilise un représentant des interefforts qui évolue dans le même espace que les déplacements d’interface (H^1/2). Elle s'appuie sur le produit scalaire associé à ces quantités pour le calcul des travaux d'interface. Délicat à calculer, ce produit scalaire est traité par une approximation validée numériquement. Le calcul de la matrice de masse pleine en découlant est récompensé par un taux de convergence montré indépendant du pas du maillage et de la taille des sous-domaines sur plusieurs cas-tests faisant intervenir notamment du contact. / Mechanical industries' need of liability in numerical simulations leads to evermore fine and complex models taking into account complicated physical behaviours. With the aim of modelling large complex structures, a non-overlapping mixed domain decomposition method based on a LaTIn-type iterative solver is proposed.The method relies on splitting the studied domain into substructures and interfaces which can both bear mechanical behaviors so that perfect cohesion, contact, delamination can be modelled by the interfaces. The associated solver enables to treat at small scales nonlinear phenomena and, as commonly done, scalabilty is ensured by a coarse problem. The method presented uses the Riesz representation theorem to represent interface tractions in H^1/2 in order to discretize them accordingly to the displacements. Independence of convergence and search direction's optimal value from mesh size is evidenced and high precision can be reached in few iterations.Different test-cases assess the method for perfect and contact interfaces.

The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type.

Accurately simulating material systems in a virtual environment requires the synthesis and utilization of all relevant information regarding performance mechanisms for the material occurring over a range of length and time scales. Multiscale modeling is the basis for the Integrated Computational Materials Engineering (ICME) Paradigm and is a powerful tool for accurate material simulations. However, while ICME has experienced adoption among those in the metals community, it has not gained traction in polymer research. This thesis seeks establish a hierarchical multiscale modeling methodology for simulating polymers containing secondary phases. The investigation laid out in the chapters below uses mesoscopic Finite Element Analysis (FEA) as a foundation to build a multiscale modeling methodology for polymer material systems. At the mesoscale a Design of Experiments (DOE) parametric study utilizing FEA of polymers containing defects compared the relative impacts of a selection of parameters on damage growth and coalescence in polymers. Of the parameters considered, the applied stress state proved to be the most crucial parameter affecting damage growth and coalescence. At the macroscale, the significant influence of the applied stress state on damage growth and coalescence in polymers (upscaled from the mesoscale) motivated an expansion of the Bouvard Internal State Variable (ISV) (Bouvard et al. 2013) polymer model stress state sensitivity. Deviatoric stress invariants were utilized to modify the Bouvard ISV model to account for asymmetry in polymer mechanical performance across different stress states (tension, compression, torsion). Lastly, this work implements a hierarchical multiscale modeling methodology to examine parametric effects of heterogeneities on Polymer/Clay Nanocomposite’s (PCNs) mechanical performance under uncertainty. A Virtual Composite Structure Generator (VCSG) built three-dimensional periodic Representative Volume Elements (RVEs) coupled to the Bouvard ISV model and a Cohesive Zone Model (CZM) which featured a Traction-Separation (T-S) rule calibrated to results upscaled from Molecular Dynamics (MD) simulations. A DOE parametric examination utilized the RVEs to determine the relative effects of a selection of parameters on the mechanical performance of PCNs. DOE results determined that nanoclay particle orientation was the most influential parameter affecting PCN elastic modulus while intercalated interlamellar gallery strength had the greatest influence on PCN yield stress

Controlling infectious disease spread and preventing disease onset are ongoing challenges, especially in the presence of newly emerging diseases. While vaccines have successfully eradicated smallpox and reduced occurrence of many diseases, there still exists challenges such as fear of vaccination, the cost and difficulty of transporting vaccines, and the ability of attenuated viruses to evolve, leading to instances such as vaccine derived poliovirus. Antibiotic resistance due to mistreatment of antibiotics and quickly evolving bacteria contributes to the difficulty of eradicating diseases such as tuberculosis. Additionally, bacteria and fungi are able to produce an extracellular matrix in biofilms that protects them from antibiotics/antifungals. Mathematical models are an effective way of measuring the success of various control measures, allowing for cost savings and efficient implementation of those measures. While many models exist to investigate the dynamics on a human population scale, it is also beneficial to use models on a microbial scale to further capture the biology behind infectious diseases. In this dissertation, we develop mathematical models at several spatial scales to help improve disease control. At the scale of human populations, we develop differential equation models with quarantine control. We investigate how the distribution of exposed and infectious periods affects the control efficacy and suggest when it is important for models to include realistically narrow distributions. At the microbial scale, we use an agent-based stochastic spatial simulation to model the social interactions between two yeast strains in a biofilm. While cheater strains have been proposed as a control strategy to disrupt the harmful cooperative biofilm, some yeast strains cooperate only with other cooperators via kin recognition. We study under what circumstances kin recognition confers the greatest fitness benefit to a cooperative strain. Finally, we look at a multiscale, two-patch model for the dynamics between wild-type (WT) poliovirus and defective interfering particles (DIPs) as they travel between organs. DIPs are non-viable variants of the WT that lack essential elements needed for reproduction, causing them to steal these elements from the WT. We investigate when DIPs can lower the WT population in the host.

A macroscale Internal State Variable (ISV) constitutive model coupling magnetism effects with thermal, elastic, and damage effects is developed. Previous models for magnetic and mechanical fields included constitutive equations describing their effects on the material system studied independently. Some models explain the mechanisms behind mechanical deformations caused by magnetization changes that are presented in the literature. They mainly focus on the nanoscale level. Other models, describe the behavior of one specific magnet that is mostly a permanent magnet. However permanent magnets are made of rare-earth elements that are subjected to a high supply risk. In attempt to find an alternative to permanent magnets, a mathematical model that captures the physical behavior of magnets is needed, to help develop a tool to create a new permanent magnet. The ISV constitutive model herein describes the macroscale mechanical deformation caused by magnetic fields on ferromagnetic materials, Iron (Fe), Cobalt (Co) and Nickel (Ni) precisely. The ISV model internally coheres the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving histories of internal variables. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term, and the Jacobian that represents the conservation of mass and conservation of momentum. The First and Second Law of Thermodynamics are used to constrain the appropriate constitutive relations through the Clausius-Duhem inequality. The kinetic framework employs a stress-strain relationship with a flow rule that couples the thermal, mechanical, and damage terms. To determine the ISVs needed to mimic the behavior of magnetic materials, we conducted various magnetic experiments on three different specimens made of Iron, Nickel and Cobalt. Experiments captured the mechanical deformation of a rod sample when subjected to a magnetic field using the Michelson Interferometer. To study the magnetic hysteresis of Iron, Nickel, and Cobalt, previous literature data were used. It was shown that the magnetization equation modeled the hysteresis of Iron, Nickel, and Cobalt. The magnetostrictive strain equation shows good agreement for Nickel and Cobalt, but further investigation should be done for Iron.

Multiscale modeling is an effective tool for integrating different computational methods, creating a way of modeling diverse chemical and physical phenomena. Presented are studies on a variety of chemical problems at different computational scales and also the combination of different computational methods to study a single phenomenon. The methods used encompass density functional theory (DFT), molecular dynamics (MD) simulations and finite element analysis (FEA). The DFT studies were conducted both on the molecular level and using plane-wave methods. The particular topics studied using DFT are the rational catalyst design of complexes for C—H bond activation, oxidation of nickel surfaces and the calculation of interaction properties of carbon dioxide containing systems directed towards carbon dioxide sequestration studies. Second and third row (typically precious metals) transition metal complexes are known to possess certain electronic features that define their structure and reactivity, and which are usually not observed in their first-row (base metal) congeners. Can these electronic features be conferred onto first-row transition metals with the aid of non-innocent and/or very high-field ligands? Using DFT, the impact of these electronic features upon methane C—H bond activation was modeled using the dipyridylazaallyl (smif) supporting ligand for late, first-row transition metal (M) imide, oxo and carbene complexes (M = Fe, Co, Ni, Cu; E = O, NMe, CMe2). To promote a greater understanding of the process and nature of metal passivation, first-principles analysis of partially oxidized Ni(111) and Ni(311) surface and ultra-thin film NiO layers on Ni(111) was performed. A bimodal theoretical strategy that considers the oxidation process using either a fixed GGA functional for the description of all atoms in the system, or a perturbation approach, that perturbs the electronic structure of various Ni atoms in contact with oxygen by application of the GGA+U technique was applied. Binding energy of oxygen to the nickel surfaces, charge states of nickel and oxygen, and the preferred binding mode of oxygen to nickel were studied to gain a better understanding of the formation of oxide layers. Using density functional theory, the thermodynamic properties for developing interaction potentials for molecular dynamics simulations of carbon dioxide systems were calculated. The interactions considered are Ni + H2O, Ni + Ni, Ni + CO2, CO2 + CO2, CO2 + H2O and H2O + H2O. These systems were chosen as the possible interactions that can occur when carbon dioxide is stored in the ocean. Molecular dynamics simulations using the results from the DFT studies were also conducted. Finally, thermal conduction analysis was performed on layered functionally graded materials (FGM) subjected to thermal shock by sudden cooling of the material in order to investigate the results obtained from three different mixing laws: linear, quadratic, and half-order. The functionally graded material considered was a composite of nickel and carbon nanotubes at different compositions varying from two to five layers. The middle layers for the three to five layers are composed of graded (i.e., gradually changing) percentages of nickel and carbon nanotube. The thermal conductivity, specific heat and density for the composites were calculated depending on the percentages of materials in each layer, and assuming different rules of mixture.

Multiscale modeling has become an important tool in material mechanics because material behavior can exhibit varied properties across different length scales. The use of multiscale modeling is essential for accurately capturing these characteristics and predicting material behavior. Mesh-free methods have also been gaining attention in recent years due to their innate ability to handle complex geometries and large deformations. These methods provide greater flexibility and efficiency in modeling complex material behavior, especially for problems involving discontinuities, such as fractures and cracks. Moreover, mesh-free methods can be easily extended to multiple lengths and time scales, making them particularly suitable for multiscale modeling. The thesis focuses on two specific problems of multiscale modeling with mesh-free methods. The first problem is the atomistically informed constitutive model for the study of high-pressure induced densification of silica glass. Molecular Dynamics (MD) simulations are carried out to study the atomistic level responses of fused silica under different pressure and strain-rate levels, Based on the data obtained from the MD simulations, a novel continuum-based multiplicative hyper-elasto-plasticity model that accounts for the anomalous densification behavior is developed and then parameterized using polynomial regression and deep learning techniques. To incorporate dynamic damage evolution, a plasticity-damage variable that controls the shrinkage of the yield surface is introduced and integrated into the elasto-plasticity model. The resulting coupled elasto-plasticity-damage model is reformulated to a non-ordinary state-based peridynamics (NOSB-PD) model for the computational efficiency of impact simulations. The developed peridynamics (PD) model reproduces coarse-scale quantities of interest found in MD simulations and can simulate at a component level. Finally, the proposed atomistically-informed multiplicative hyper-elasto-plasticity-damage model has been validated against limited available experimental results for the simulation of hyper-velocity impact simulation of projectiles on silica glass targets. The second problem addressed in the thesis involves the upscaling approach for multi-porosity media, analyzed using the so-called MultiSPH method, which is a sequential SPH (Smoothed Particle Hydrodynamics) solver across multiple scales. Multi-porosity media is commonly found in natural and industrial materials, and their behavior is not easily captured with traditional numerical methods. The upscaling approach presented in the thesis is demonstrated on a porous medium consisting of three scales, it involves using SPH methods to characterize the behavior of individual pores at the microscopic scale and then using a homogenization technique to upscale to the meso and macroscopic level. The accuracy of the MultiSPH approach is confirmed by comparing the results with analytical solutions for simple microstructures, as well as detailed single-scale SPH simulations and experimental data for more complex microstructures.

Carbon dioxide (CO2), as a greenhouse gas, has shown to achieve the highest level in history, causes the global warming issue, leading to a 1.2 ℃ increase of the global average temperature. The consumption of fossil fuels is one of the main reasons that cause CO2 emission. Current industrial production of chemicals accounts for 29% of total fossil fuels consumption, which can be the feedstock or raw materials for carbon source, or act as the fuel to generate heat and power. CO2 conversion technologies, e.g., thermo-catalytic reaction and electrochemical reduction, have drawn researchers' attention, since they have the potential to resolve the feedstock and fuel consumption sectors of chemical production at the same time. CO2 conversion technologies use CO2 as the direct carbon source of chemicals and store the intermittent renewable energies as the energy source, which can ultimately achieve a net-zero CO2 emission and produce value-added chemical products. However, there are challenges for a practical application of CO2 conversion technologies. For instance, electrochemical CO2 reduction reaction (ECO2RR) suffers from the low activity and selectivity, while thermocatalytic CO2 conversion, or the CO2 hydrogenation reaction, usually requires harsh reaction conditions and has a low selectivity. Nonetheless, the improvement of developing new promising catalysts remains limited, due to the lack of insights of the reactions. The complex reaction networks and kinetics lead to an elusive reaction mechanism, and various effects, e.g., solvation, potential, structure, and coverage, hinder our fundamental understanding of catalytic processes. Herein, we report the efforts that we have been put in to gain insights of reaction mechanism of CO2 reduction reactions. Bi has shown to reduce CO2 to formic acid (HCOOH), while we have found that, by constituting a Bi-Cu2S heterostructure catalyst, a better catalytic performance was achieved, due to the structural effect of the interface (Chapter 2). However, it is shown that the CO2 electrochemical reduction mechanism on Bi has changed when switching the electrolyte from water to aprotic media, e.g., ionic liquids, and CO was obtained as the main product instead of HCOOH, showing a shift of reaction pathway due to the electrolyte effect (Chapter 3). However, the fundamental understanding of reaction mechanism requires not only the reaction pathways, but the reaction kinetics under reaction conditions, where the lateral or adsorbate-adsorbate interactions play an important role. In this case, we summarized recent advances of applications of machine learning (ML) algorithms for adsorbate-adsorbate interaction model developments to deal with the realistic reaction kinetics (Chapter 4). The lattice based Kinetic Monte Carlo (KMC) has shown promising performances for considering the lateral interactions of surface reactions. We report the mechanistic and KMC kinetic study of CO2 hydrogenation on Cesium promoted Au(111) surface, to gain insights of alkali metal promoting effects under reaction conditions (Chapter 5). To expand the scope, the integration of CO2 reduction with the C-N bond formation provides a promising strategy to produce more value-added product such as urea. Recent studies show that urea can be produced by reducing CO2 and nitrate (NO3-) from wastewater, which mitigate both global warming and nitrate pollution issue. However, the reaction mechanism remains elusive due to the complicated reaction network. Therefore, we employed the first-principles molecular dynamics to reveal the reaction mechanism of C-N coupling and the effect of different reaction conditions including applied potential and electrolyte (Chapter 6). Although recent advances in the computational catalysis field have significantly push forward the understanding of the chemistry nature of heterogeneous catalysis, the gap between theory and experiment remains far beyond bridged due to the complexity nature of the problem in a wide range of time and length scales, hinders the development and discovery of active catalytic materials. Recent advances of narrowing and bridging the complexity gap between theory and experiment with machine learning have been summarized to emphasize the importance of utilizing machine learning for rational catalyst design (Chapter 7). / Doctor of Philosophy / Global warming issue is a rising topic in recent years which has severe impacts on environments. One of the main reasons is the increase level of greenhouse gases that prevent the release of heat that captured from the sun. Carbon dioxide (CO2) is achieving the highest level in history due to the human activities including the consumption of fossil fuels. Therefore, CO2 conversion technologies are needed to tackle reduce the CO2 level in the atmosphere and the emission of CO2 in industries. CO2 conversion technologies, e.g., thermo-catalytic reaction and electrochemical reduction, have drawn researchers' attention, since they have the potential to resolve the feedstock and fuel consumption sectors of chemical production at the same time. However, the complexity of the CO2 conversion processes hinders the development of new technologies. Since the nature of these technologies are heterogeneous catalytic reactions, all reactions are happening at the interface between catalysts and reactants/products, which calls for the understanding of interfacial mechanisms of CO2 reduction reactions. For this type of high degree of freedom problem where many phases including solid-solid, solid-liquid, and solid-gas phases exist, multiscale simulations turn out to be a proper approach since the wide time and length scale that can be covered. Herein, we employed different multiscale modeling methods to tackle various CO2 reduction problems. For electrochemical reduction of CO2, we designed a novel Bi-Cu2S hetero-structured catalyst, which has abundant interfacial sites between Bi and Cu2S, demonstrating the improved catalytic performance of ECO2RR toward formate production. At the same time, it has been found that in non-aqueous solution, the reaction pathway has been switched, where CO is obtained as the final product instead of formate. This effect has been investigated using constant potential calculation method to probe the reaction under reaction condition. For thermo-catalytic reactions, we studied the CO2 hydrogenation on Cesium promoted Au(111) surface using quantum mechanics and kinetic Monte Carlo (KMC) calculations, to gain insights of alkali metal promoting effects under reaction conditions. To expand the scope, the integration of CO2 electroreduction with C-N coupling is a promising strategy for global warming and pollution control, which utilizes the nitrate (NO3-) from wastewater and CO2 to produce high value-added product such as urea. The fundamental investigation of reaction mechanism of C-N coupling has been studied using first principles molecular dynamics.

In the current study, mechanoporation-related neuronal injury as a result of mechanical loading has been studied using a multiscale approach. Injurious mechanical loads to the head induce strains in the brain tissue at the macroscale. As each length scale has its own unique morphology and heterogeneities, the strains have been scaled down from the macroscale brain tissue to the nanoscale neuronal components that result in mechanoporation of the neuronal membrane, while relevant neuronal membrane mechanoporation-related damage criteria have been scaled up to the macroscale. To achieve this, first, damage evolution equations has been developed and calibrated to molecular dynamics simulations of a representative neuronal membrane at the nanoscale. These damage evolution equations are strain rate and strain state dependent. The resulting damage evolution model has been combined with Nernst-Planck diffusion equations to analytically compare to intracellular ion concentration disruption through mechanical loading of in vitro neuron cell culture and found to agree well. Then, these damage evolution equations have been scaled up to the microscale for dynamic simulations of 3-dimensional reconstructed neurons of similar mechanical loads. It was found that the neuronal orientation significantly affects average damage accumulation on the neuron, while the morphology of neurons, for a given neuron type, had little effect on the average damage accumulation. At the mesoscale, finite element simulations of geometrical complexities of sulci and gyri, and the structural complexities of the gray and white matter and CSF on stress localization were studied. It was found that the brain convolutions, sulci, and gyri, along with the effects of impedance mismatch between the cerebrospinal fluid (CSF) and brain tissue localized shear stresses, at the depths of the sulcus end (near field effects) and in-between sulci (far field effects), that correlated well with the regions of tau protein accumulation that is observed in chronic traumatic encephalopathy (CTE). Further, sulcus length and orientation, with respect to impending stress waves, had a significant impact on the magnitude of stress localization in the brain tissue. Lastly, gray-white matter differentiation, pia matter, and brain-CSF interface interaction properties had minimal impact of the shear stress localization trends observed in these simulations.