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.

In the current study we use a multiscale computational methodology to develop an internal state variable model that captures frictional effects during the compaction of particulate materials. Molecular dynamics simulations using EAM potentials were performed to model the contact behavior of spherical nickel nanoparticles. Simulation results for models consisting of various particle sizes and contact angles were compared to quantify the length scale effects of friction. The influence of friction on the microstructure was shown from the nucleation of dislocations near the interface region during sliding. By using an internal state variable theory to couple the microstructural changes due to friction observed at the nanoscale to a macroscopic rate-independent plasticity model, a multiscale friction model that captures the deformation behavior due to dislocations and interparticle friction was developed. The internal state variable friction equation is a function of the volume-per-surface-area parameter and can adequately represent all length scales of importance from the nanoscale to the microscale. The kinematics was modified by including a frictional component in the multiplicative decomposition of the deformation gradient in order to account for the frictional surface effects due to sliding, as well as frictional hardening/softening within the particles. The friction formulation was extended to the macroscale continuum model by determining the rate of change of the friction angle of the powder aggregate based on the evolution of the friction internal state variable. The constitutive model was coupled with the Bammann-Chiesa-Johnson (BCJ) rate-dependent plasticity model to capture the deformation behavior of the particles.

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This thesis presents a simulation model of sliding process of friction, which combines Newtonian particle dynamics and finite element method to study friction mechanisms that bridging micro and macro scales. In the thesis, it first reviews the importance of studying pavement friction that is associated to safety of drivers, society economics and environmental impact. Then, the hybrid numerical methods of Newtonian particle dynamics and finite element method have been introduced, and the rules to bridge these two methods also have been discussed for solid material that assumes the forces and displacements are continuous at the interface of these two methods. The fundamental theories of friction mechanisms are built upon the surface roughness, adhesion and deformation at the contact between two surfaces. At last, the simulation model of sliding process is presented with the hybrid method, and its visualization and result analysis has been given. At the same time, this thesis also includes the procedures of establishing the simulation of the hybrid methods with C++ programming like the program framework, structure and the major pieces of the program. / Master of Science

It is perhaps paradoxical that many material properties arise from the absence of material rather than the presence of it. For example, the strength, stiffness, and toughness of a concrete are related to its pore structure. Furthermore, the volume, size distribution, and interconnectivity of porosity is important for understanding permeability, diffusivity, and capillary action occurring in concrete, which are necessary for predicting service lives in aggressive environments. This research advances the state-of-the-art of multiscale characterization of cement-based materials, and uses this characterization information to model the material behavior under competing durability concerns. In the first part of this research, a novel method is proposed to characterize the entrained air void system. In the second and third parts of this research, microstructural characterization is used in tandem with mechanical models to investigate the behavior of cementitious materials when exposed to rapid rates of loading and to cyclic freezing and thawing. First, a novel analytical technique is presented which reconstructs the 3D entrained air void distribution in hardened concrete using 2D image analysis. This method proposes a new spacing factor, which is believed to be more sensitive to microstructural changes than the current spacing factor commonly utilized in practiced, and specified in ASTM C457, as a measure of concrete's ability to resist to damage under cyclic freeze/thaw loading. This has the potential to improve economy by improving the quality of petrographic assessment and reducing the need for more expensive and time-consuming freeze/thaw tests, while also promoting the durability of concrete. Second, quantitative measurements of the sizes, shapes, and spatial arrangements of flaws which are through to drive failure at strain rates above 100/s were obtained in order to model mortar subjected to high strain-rate loading (i.e., extremes in load rate). A micromechanics model was used to study the ways in which flaw geometry and flaw interaction govern damage. A key finding suggests that dynamic strength may be multimodal, with larger flaws shifting the dynamic strength upwards into the highest strength failure mode. Third, a robust theoretical approach, based upon poroelasticity, is presented to further validate the utility of the novel spacing factor proposed this research. The model is truly multiscale, using in its formulation pore size data ranging from the nanoscale to the micro-scale, entrained air data from the micro-scale to the millimeter scale, and infers a representative volume element on the centimeter scale. The results provide an underlying physical basis for the performance of the novel spacing factor. Furthermore, the framework could be used as a forensic tool, or as a tool to optimize the entrained air void system against freeze/thaw damage.

Modeling the competition between drying and curing processes in polymerizing films is of great importance to many existing and developing materials synthesis processes. These processes involve multiple length and time scales ranging from molecular to macroscopic, and are challenging to fully model in situations where the polymerization is non-ideal, such as sol-gel silica thin film formation. A comprehensive model of sol-gel silica film formation should link macroscopic flow and drying (controlled by process parameters) to film microstructure (which dictates the properties of the films). This dissertation describes a multiscale model in which dynamic Monte Carlo (DMC) polymerization simulations are coupled to a continuum model of drying. Unlike statistical methods, DMC simulations track the entire molecular structure distribution to allow the calculation not only of molecular weight but also of cycle ranks and topological indices related to molecular size and shape. The entire DMC simulation (containing 106 monomers) is treated as a particle of sol whose position and composition are tracked in the continuum mass transport model of drying. The validity of the multiscale model is verified by the good agreement of the conversion evolution of DMC and continuum simulations for ideal polycondensation and first shell substitution effect (FSSE) cases. Because our model allows cyclic and cage-like siloxanes to form, it is better able to predict the silica gelation conversion than other reported kinetic models. By studying the competition between molecular growth and cyclization, and the competition between mass transfer (drying) and reaction (gelation) on the drying process of the sol-gel silica film, we observe that cyclization delays gelation, shrinks the molecular size, increases the likelihood of skin formation, and leads to a molecular structure gradient inside the film. We also find that compared with a model with only 3-membered rings, the molecular structure is more complicated and the structure gradients in the films are larger with 4- membered rings. We expect that our simulation will allow better prediction of the formation of structure gradients in sol-gel derived ceramics and other nonideal multifunctional polycondensation products, and that this will help in developing procedures to reduce coating defects.

Ce travail concerne l’étude et la modélisation du phénomène de multifissuration transversedes fils dans les CMC tissés. Sa connaissance est fondamentale pour déterminer soneffet sur les champs de contraintes, la progression des endommagements et la durée de viedu matériau.À partir d’observations sur des coupes de CMC, des matériaux virtuels sont développéset des essais virtuels réalisés. Différentes séquences de fissuration transverse sont simuléessur diverses microstructures de CMC. Ces simulations se substituent à des observations expérimentalesimpossibles à réaliser.Un modèle statistique de multifissuration est développé sur la base du principe dumaillon faible appliqué à une distribution ponctuelle de Poisson. Les singularités micostructurellessont représentées par des défauts dans un milieu homogène équivalent (MHE).Les modifications des fonctions de distribution au cours de la multifissuration sont modélisées.Le modèle statistique permet de réaliser un changement d’échelle à la suite duquel lamultifissuration transverse est simulée dans le MHE avec une réduction des temps de calculde l’ordre de 90%. / This work deals with the study and modeling of multiple crakcing of tows in wovenCMCs. Its understanding is fundamental to determine the effect on stress fields, the evolutionof damage and the lifetime of material.From observations on real CMC pieces, virtual materials are developed and multiplecracking virtual testing is achieved. Different scenarii are simulated on various CMC microstructures.These simulations are a substitute for impossible experimental observations.A statistical model for multiple cracking based on the weakest link principle applied to adistribution of Poisson is developed. Micostructural singularities are represented by defectsin a homogeneous medium equivalent (EHM). Modifications of distribution functions duringthe multicracking are modeled.The statistical model realizes a scale changing : transverse multicracking is simulated inthe EHM with a reduction of almost 90% for computational time.

La pose d’une Prothèse Totale de Hanche est l’une des chirurgies orthopédiques les plus pratiquées, et représente un enjeu économique et de santé publique majeur. Ainsi, il est essentiel de comprendre le comportement mécanique de l’os et sa réaction à la suite d’une telle chirurgie. La simulation numérique joue un rôle intéressant dans cette perspective, permettant la reproduction et l’analyse de la réponse osseuse aux stimulus externes. L’os est un matériau complexe présentant une structure hiérarchique et poreuse, et une capacité naturelle d’adaptation structurelle grâce à des cellules spécifiques sensibles aux mouvements de fluide. Basé sur ces caractéristiques, un modèle multi-échelle a été développé au cours de cette thèse dans le but de modéliser la réponse de l’os soumis à des sollicitations mécaniques externes. Le modèle développé repose sur la méthode d’homogénéisation pour les structures périodiques basé sur un développement asymptotique. Il simule l’os cortical comme une structure homogène, composé d’une microstructure périodique, d’une porosité de 5%, saturé de fluide interstitiel qui suit dans ce cas la loi de Darcy. La première application du modèle développé est un cas d’étude, consistant en un volume d’os chargé en compression, permettant la détermination d’une raideur poroélastique équivalente. En considérant principalement deux cas extrêmes de conditions aux limites en fluide, l’analyse de la réponse structurelle correspondante permet d’avoir un aperçu de la contribution du fluide dans le comportement mécanique d’un tel matériau, et en particulier de sa raideur équivalente. Ce paramètre est soit réduit (lorsque le fluide peut sortir de la structure), soit augmenté (lorsque le fluide est confiné dans la structure). Pour valider ce modèle, une étude numérique et expérimentale sont proposées. La validation numérique permet l’estimation de la pertinence du modèle en faisant varier certains paramètres d’entrée comme les propriétés matériaux ou les conditions aux limites. Puis, une validation expérimentale est mise en place. En comparaison, des données issues d’un échantillon d’os trabéculaire de hanche mis en compression sont utilisées. La raideur équivalente de l’échantillon est calculée et comparée à celle obtenue expérimentalement. Les courbes obtenues présentent des résultats similaires et permettent d’attester de la validité du modèle compte tenu des circonstances d’essais. Ainsi, le modèle numérique développé, s’inscrit dans l’objectif de fournir un modèle bio-fidèle de l’os, afin de déterminer les paramètres critiques permettant d’avoir une influence sur le remodelage osseux. En prévision de l’élaboration et de la production de nouvelles générations de prothèses, ce modèle numérique d’os présente à la fois le compromis intéressant de la pertinence scientifique sans requérir des ressources numériques excessives, nécessaires à son application en tant qu’outil de prévision pré-opératoire. / Total Hip Arthroplasty is nowadays one of the most performed orthopedic surgery and is representing a major health and economic issue. Thus, it is essential to provide a better understanding of bone mechanical behavior and its reaction to the implantation of a device such as a hip prosthesis. Numerical simulation plays a key role on this challenge, allowing for the reproduction and analysis of the bone response to the external stimuli. Bone is a complex material showing a hierarchical and porous structure, and natural ability to remodel itself thanks to specific cells, which are sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to simulate the bone response under external mechanical solicitations. The developed model relies on the homogenization technique for periodic structures based on an asymptotic expansion. It simulates cortical bone as a homogeneous structure. It is constituted of a porous microstructure with a 5% saturated with bone fluid, which, in the considered conditions, follows the Darcy’s law. The first application of the developed model is a case study, consisting in the loading of a finite volume of bone, allowing for the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the analysis of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the equivalent stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is confined the structure). To validate the developed model, both numerical and experimental validation are proposed. The numerical validation consists in the estimation of the model accuracy when varying parameters such as material properties or boundary conditions. Then, an experimental validation is set up. As a reference case, a previous work on a cubic trabecular bone sample, extracted from a human hip and put under a compressive load, has been used. Increasing the load applied on the top of the bone specimen, the displacement is extracted, allowing the computation of the equivalent strain-stress curve. The equivalent stiffness of the bone specimen, calculated numerically by the developed numerical tool, is then compared with the one from the experiments. A good agreement between the curves attests the validity of the developed numerical model, accounting for both the solid matrix and fluid contributions. The presented poroelastic numerical, is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling. Towards the design and manufacturing of new generation of prosthesis, this bone model shows both accuracy and ease of computation, which will be required for its application as a preoperative or design tool.

Made available in DSpace on 2015-03-04T18:50:57Z (GMT). No. of bitstreams: 1 Phdthesis.pdf: 2066544 bytes, checksum: e0228e0a7b8f6d7fd74050413d2db6d3 (MD5) Previous issue date: 2007-05-25 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / In this work we develop a three-scale mathematical modeling to describe electro-chemical couplings in clays using the asymptotic homogenization procedure of periodic structures. We consider the porous medium composed of kaolinite particles saturated by an electrolyte solution of water-solvent and four ionic solutes monovalents Na+, H+, Cl-, OH-At the nanoscale we develop the model of the electrical double layer wherein the electric potential and local charge distribution are ruled by the Poisson- Boltzmann problem. In addition we incorporate the protonation/deprotonation chemical reaction between the fluid and the particle surface and consequently we quantify the dependence of the surface charge density of the particles with the pH of the electrolyte solution. At the microscale, or pore-scale, the movement of the aqueous solution is governed by the Stokes problem whereas ion transport by the Nernst-Planck equation. The pore-scale governing equations are supplemented by slip boundary condition in the tangential velocity of the fluid and adsorption interface conditions arising from the averaging of the nanoscale model. We then homogenize the microscopic model to the macroscale and derive effective equations with additional closure relations for the macroscopic coefficients. The macroscopic model is discretized by the finite volume method and numerical simulations of electrokinetical remediation of a contaminated soil are performed. The numerical results illustrate the strong dependence of the remediation efficiency on the pH of the aqueous solution. / Neste trabalho desenvolvemos a modelagem matemática e computacional em três escalas (nano-micro-macro) do acoplamento eletroquímico em um meio poroso argiloso adotando técnicas de homogeneização de estruturas periódicas. Consideramos o meio poroso uma caulinita saturada por uma solução eletrolítica composta por um solvente aquoso e quatro solutos iônicos monovalentes Na+, H+, Cl-, OH-. Na escala nanoscópica adotamos a modelagem da dupla camada elétrica onde o potencial elétrico e a densidade de carga são governados pelo problema de Poisson-Boltzmann. Incorporamos ao modelo nanoscópico as reações de protonação/deprotonação entre o fluido e a superfície da partícula argilosa e quantificamos numericamente a dependência da carga superficial com o pH da solução eletrolítica. Na escala microscópica, ou escala do poro, o movimento da solução aquosa é governado pelo problema de Stokes e o transporte dos íons pelas equações de Nernst-Planck. As equações microscópicas são suplementadas por condições de contorno de deslizamento da componente tangencial do campo de velocidade e de adsorção dos íons que representam a média do modelo posto na escala nanoscópica. A partir dos modelos nanoscópico/microscópico desenvolvemos a homogeneização do problema derivando o modelo na escala de Darcy (macroscópica) com os respectivos problemas de fechamento para os coeficientes das equações efetivas postos na célula periódica. Finalmente discretizamos o modelo macroscópico utilizando o método de volumes finitos e realizamos simulações numéricas em regimes permanente e transitório do processo de descontaminação de um solo argiloso por técnicas de eletrocinética. Os resultados ilustram a forte dependência da eletroremediação com o pH da solução.

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.