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.

A noção de equilíbrio aplicada ao relevo foi alvo de várias discussões ao longo da edificação do pensamento geomorfológico. Vários autores trataram de ideias a ela relacionada e este se tornou um conceito de grande influência sobre o desenvolvimento da ciência geomorfológica. Apesar das várias nuances associadas ao conceito do ponto de vista geomorfológico, o equilíbrio do relevo admite que haja um comportamento balanceado entre os fluxos de matéria e energia que perpassam por entre os materiais, processos morfogenéticos e formas que constituem o relevo. Baseado na concepção de equilíbrio dinâmico como tentativa de explicar a paisagem da alta bacia do rio Piranga em termos das relações entre formas e processos geomorfológicos o objetivo deste estudo foi o de avaliar se o relevo dessa área planáltica, na região centro-sul de Minas Gerais, área de nascente de uma das grandes bacias hidrográficas da região sudeste do Brasil a do rio Doce apresenta condições morfodinâmicas que permitem caracterizá-lo como em estado de equilíbrio. Para isso foram consideradas análises morfométricas, pedológicas, geoquímicas das águas fluviais e da organização da rede de drenagem numa perspectiva multiescalar contemplando desde a compartimentação regional do relevo até os processos de vertente. Por meio dessas análises verificou-se que as condições dos materiais, processos e formas associados ao relevo, às coberturas pedológicas e à rede de drenagem verificadas no alto rio Piranga reúnem indícios condizentes com uma situação geomorfológica de desequilíbrio morfodinâmico recente e em vigência. Situação desencadeada sobretudo pelo processo de captura fluvial do alto rio Piranga, os resultados morfométricos obtidos são condizentes também com a influência de uma neotectônica regional. O desnivelamento do manto de intemperismo representado sobretudo pela proximidade diferenciada à superfície dos horizontes C de muitos perfis pedológicos, tanto no alto quanto no baixo planalto, é apontado como indicativo de um processo de rejuvenescimento dos solos proporcionado pelas atuais condições morfogenéticas preponderantes às pedogenéticas. A falta de correlação dos gradientes fluviais de canais de 3ª ordem com os declives médios das vertentes demonstra um desajuste entre os processos de vertente e a incisão dos canais. O índice de Hack calculado para estes mesmos canais permite concluir sobre uma franca incisão desses canais nos seus trechos de médio curso. As taxas de desnudação geoquímica anual do relevo, baseadas na carga fluvial dissolvida e variando de 3,46 a 7,91 t/km2.ano, não demonstraram um padrão espacial que se possa associar a um determinado comportamento morfodinâmico relacionado à compartimentação morfológica do alto rio Piranga, por exemplo. A análise do manto de alteração associada a outros fatores em termos da evolução regional do relevo permite indicar com base nessas observações pelos menos duas fases morfogenéticas que estão bem marcadas na paisagem do alto rio Piranga. Uma mais antiga quando se desenvolveram as stone lines provavelmente associada a um soerguimento tectônico proeminente e outra mais recente e atual que se refere ao desequilíbrio geomorfológico em vigência. Por todos estes resultados conclui-se que o desequilíbrio também é uma condição natural nas terras altas da alta bacia do rio Piranga, decorrente de histórias geomorfológicas distintas unificadas a partir da captura do alto rio Piranga. / The concept of equilibrium applied in the study of relief has been central in various discussions over the history of Geomorphology. Several authors thought over ideas involving geomorphological equilibrium, which became an important concept to this science. Despite the slight variations in the core concept, equilibrium condition of relief always takes into account the balance among matter attributes, energy flow, processes and features. Based on the conception that dynamic equilibrium is an theoretical attempt to understand landscape in terms of the relationship between landforms and geomorphological processes, this thesis focused the assessment of the morphodynamical conditions that confirm the state of equilibrium of the relief in upper basin of Piranga River, southeastern Minas Gerais (Brazil). For this purpose were performed morphometric analysis, pedological analysis, geochemical analysis of channel water and drainage network features within a multiscale approach, considering regional relief and hillslope processes. All the analysis demonstrated that this highland has been under geomorphological disequilibrium over the recently time. Such situation has been triggered by a stream capture of upper course of the Piranga River. Results of morphometrical analysis are consonant with the regional neotectonics, which is confirmed by an evident difference in soil thickness, especially for the depth of horizon C in many soils profiles in both high plateau and low plateau. This setting was associated with a soil rejuvenation provided from recent morphogenetic conditions. In other hand, the lack of correlation between channel gradients and average slope shows an important misfit between earlier hillslope and channel processes. Hack\'s index measured for these channels indicate higher fluvial incision rates at middle river segments compared to the other ones. Annual geochemical denudation rates, based on dissolved load, ranging from 3.46 to 7.91 ton.y- 1.km-2, had not expressed any spatial pattern neither correlation to other data. The analysis of weathering mantle and other geomorphological factors permit the definition of two wellmarked morphogenetic phases for the upper Piranga River landscape: a previous phase, when stone lines are associated with an uplift condition; and the present one with an active disequilibrium. From the results, it was concluded that disequilibrium is a natural condition on both plateaus of Piranga River, due to their specific geomorphological evolution integrated by the stream capture of upper Piranga River.

No description available.

L'utilisation de matériaux isolants à base de granulats végétaux est en plein essor notamment pour la réhabilitation du bâti ancien, améliorant ainsi le confort des habitants. Ces matériaux possèdent des propriétés thermiques, hydriques et acoustiques appréciables. Cependant, leur développement est encore limité par le manque d'information sur l'évolution de leurs performances à long terme. Ainsi, l’objectif de cette étude est d’évaluer l’évolution des propriétés fonctionnelles du béton de chanvre, en identifiant les mécanismes de vieillissement lorsque le matériau est exposé à différents types d'environnements. Pour cela, deux bétons de chanvre formulés avec une même chènevotte et deux liants de nature chimique différente sont retenus. L’approche utilisée dans cette étude est pluridisciplinaire (chimique, physico-chimique, microbiologique, microstructurale, acoustique, thermique et mécanique) et multi échelle. L'étude des propriétés chimiques et microstructurales permet de comprendre les variations des propriétés fonctionnelles. Dans un premier temps, la caractérisation initiale des deux formulations a permis de mettre en évidence l’absence d’influence de la nature du liant sur les propriétés fonctionnelles des isolants, ce qui peut être en partie expliqué par des microstructures similaires. Une faible résistance mécanique des matériaux, liée à l'inhibition de la prise des liants en raison de leurs interactions avec les molécules extraites de la chènevotte, a également été mise en évidence. Dans un second temps, les bétons de chanvre ainsi que la chènevotte brute sont soumis à un vieillissement accéléré en imposant des cycles d’humidification/séchage pendant deux ans. Les modifications des performances des matériaux à différentes échéances sont comparées à celles d'échantillons de référence placés à 50% d’humidité relative et une température constante contrôlée. Dans les conditions de référence, aucune variation de propriétés n'est observée. Pour le vieillissement accéléré, les variations de propriétés mises en évidence sont induites par différents paramètres. Dans le cas de la chènevotte brute, l’action des microorganismes et l’adsorption d’eau entrainent une perte de masse et l'ouverture des porosités à l'origine des variations des propriétés acoustiques et hydriques. Pour le béton de chanvre, aucun développement fongique n’est observé en surface du matériau. En revanche, l’action de microorganismes est bien visible à l’intérieur des granulats végétaux, et des mécanismes supplémentaires sont identifiés : les réactions d'hydratation et de carbonatation au sein du liant ainsi que la minéralisation de la chènevotte entrainent des variations de propriétés thermiques, acoustiques et hydriques en modifiant la microstructure des bétons de chanvre. En conclusion, l’absence de variations des propriétés des bétons de chanvre dans les conditions de référence laisse penser que dans un bâtiment réel, leurs propriétés peuvent être stables dans le temps, les pathologies observées étant alors liées à une mise en œuvre défaillante. Pour aller plus loin, les résultats obtenus lors de ce travail devront être validés par une étude in situ qui permettrait d’estimer la durée de vie de ces matériaux / The use of insulating materials based on plant aggregates is growing quickly, especially for the rehabilitation of old buildings, thus improving the comfort of residents. These materials have significant thermal, hydric and acoustic properties. However, their development is still limited by the lack of information on the evolution of their long-term performances. Thus, the objective of this study is to evaluate the evolution of the functional properties of hemp concretes, by identifying the aging mechanisms when the material is exposed to different types of environments. For this aim, two hemp concretes formulated with one type of hemp and two binders with different chemical nature are retained. The approach of this study is multidisciplinary (chemical, physico-chemical, microbiological, microstructural, acoustic, thermal and mechanical) and multi-scale. The study of chemical and microstructural properties allows the understanding of the variations of functional properties. Firstly, the initial characterization of the both hemp concretes made it possible to demonstrate the absence of impact of the nature of the binder on the functional properties of the insulators, which can be partly explained by their similar microstructure. A weak mechanical resistance of the materials was also highlighted, related to the inhibition of the setting of the binders because of their interactions with the molecules extracted from the shiv. Secondly, hemp concretes and bulk shiv hemp are subjected to an accelerated aging by imposing cycles of humidification / drying during two years. The modifications of the material performances at different time scales are compared to reference samples stored at 50% of relative humidity and a constant controlled temperature. Under reference conditions, no variation in properties is observed. For accelerated aging, the variations of properties highlighted are induced by several parameters. In the case of bulk shiv, the action of microorganisms and the adsorption of water lead to a loss of mass and to the opening of porosities, leading to variations in acoustic properties. For hemp concretes, no fungal development is observed on the surface of the material. On the other hand, the action of microorganisms is clearly visible inside the plant aggregates, and additional mechanisms are identified: the hydration and carbonation reactions within the binder as well as the mineralization of the vegetal particles cause variations in thermal, acoustic and hydric properties by modifying the microstructure of hemp concretes.In conclusion, the absence of variations in the properties of hemp concretes in the reference conditions suggests that in a real building, their properties can be stable over time, the observed pathologies then being due to a faulty implementation. To go further, the results obtained during this work have to be validated by an in-situ study to be able to estimate the lifetime of these materials

<div>The objective of this dissertation is to develop new methods in the areas of multiscale topology optimization, thermomechanical topology optimization including heat convection, and thermal-fluid topology optimization. The dissertation mainly focuses on developing five innovative topology optimization algorithms with respect to structure and multistructure coupling fluid, thermal and mechanical analysis, in order to solve customary design requirements. Most of algorithms are coded as in-house code in MATLAB.</div><div><br></div><div><div>In Chapter One, a brief introduction of topology optimization, a brief literature review and the objective is presented. Five innovative algorithms are illustrated in Chapter Two</div><div>to Six. From Chapter Two to Four, the methods with respect to multiscale approach are presneted. and Chapter Five and Six aims to contribute further research associated with</div><div>topology optimization considering heat convection. In Chapter Two, a multiphse topology optimization of thermomechanical structures is presented, in which the optimized structure is composed of several phases of prescribed lattice unit cells. Chapter Three presents a</div><div>Multiscale, thermomechanical topology optimization of self-supporting cellular structures. Each lattice unit cell have a optimised porousity and diamond shape that benefit additive</div><div>manufacturing. In Chapter Four, the multiscale approach is extended to topology optimization involved with fluid mechanics problem to design optimized micropillar arrays in</div><div>microfludics devices. The optimised micropillars minimize the energy loss caused by local fluid drag force. In Chapter Five, a novel thermomechanical topology optimization is developed, in order to generate optimized multifunctional lattice heat transfer structure. The algorithm approximate convective heat transfer by design-dependent heat source and natural convection. In Chapter Six, an improved thermal-fluid topology optimization method is created to flexibly handle the changing of thermal-fluid parameters such as external heat source, Reynolds number, Prandtl number and thermal diffusivity. The results show the</div><div>changing of these parameters lead versatile optimized topologies. Finally, the summary and recommendations are presented in Chapter Seven.</div></div><div><br></div>

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.

In this thesis we show that the finite element error for the high contrast elliptic interface problem is independent of the contrast in the material coefficient under certain assumptions. The error estimate is proved using a particularly technical proof with construction of a specific function from the finite dimensional space of piecewise linear functions. We review the multiscale finite element method of Chu, Graham and Hou to give clearer insight. We present some generalisations to extend their work on a priori contrast independent local boundary conditions, which are then used to find multiscale basis functions by solving a set of local problems. We make use of their regularity result to prove a new relative error estimate for both the standard finte element method and the multiscale finite element method that is completely coefficient independent. The analytical results we explore in this thesis require a complicated construction. To avoid this we present an adaptive multiscale finite element method as an enhancement to the adaptive local-global method of Durlofsky, Efendiev and Ginting. We show numerically that this adaptive method converges optimally as if the coefficient were smooth even in the presence of singularities as well as in the case of a realisation of a random field. The novel application of this thesis is where the adaptive multiscale finite element method has been applied to the linear elasticity problem arising from the structural optimisation process in mechanical engineering. We show that a much smoother sensitivity profile is achieved along the edges of a structure with the adaptive method and no additional heuristic smoothing techniques are needed. We finally show that the new adaptive method can be efficiently implemented in parallel and the processing time scales well as the number of processors increases. The biggest advantage of the multiscale method is that the basis functions can be repeatedly used for additional problems with the same high contrast material coefficient.

Trabecular bone has a complex and porous microstructure. This study develops approaches to determine the mechanical behaviour of this material at the macroscopic level through the use of homogenisation-based multiscale methods using micro-finite element simulations. In homogenisation-based finite element methods, a simulation involving a representative volume element of the microstructure of the considered material is performed with a specific set of boundary conditions. The macroscopic stresses and strains are retrieved as averaged quantities defined over this domain. Most of the homogenisation-based work on trabecular bone has been performed to study its macroscopic elastic regime, and therefore define its constant macroscopic stiffness tensor. The rod and plate-shaped microstructure of trabecular bone can be precisely identified with advanced scanning tools, such as micro-computed tomography devices. Taking into account the size requirements to achieve a certain independence of boundary conditions for trabecular bone in a homogenisation-based multiscale setting, the resulting stack of images can have around ten million solid voxels after binarisation. Although a completely linear finite element simulation with such a large system may be feasible with commercial packages (with the proper time and memory requirements), it is not possible to perform a nonlinear simulation for such a mesh in a reasonable time frame, and the amount of required memory may not be available. A highly scalable parallel driver program which solves finite strain elastoplastic systems was developed within the framework of the existing parallel code ParaFEM. This code was used throughout this study to evaluate the yield and post-yield properties of trabecular bone. It was run on cutting edge high performance computing platforms (BlueGene/Q at the Hartree Centre, Science and Technology Facilities Council; and ARCHER, UK National Supercomputing Service, at Edinburgh Parallel Computing Centre). Micro-finite element simulations require definition of properties at the microscopic scale and it is unclear how these properties affect the macroscopic response. This study examines the effect of compressive hydrostatic yield at the microscopic scale on the macroscopic behaviour. Two different microscopic yield criteria, one permitting yielding at compressive hydrostatic stresses and the other not, were considered. A large number of load cases were examined. It was found that these two microscopic yield criteria only influence macroscopic yield behaviour in load scenarios which are compression-dominated; for other load cases, macroscopic response is insensitive to the choice of the microscopic yield criterion, provided it has an appropriate strength asymmetry. Also, in compression-dominated load cases, high density bone is much more sensitive as it is more like a continuum, resulting in the microscopic properties being more directly upscaled. Only a few previous studies have employed homogenisation to evaluate the macroscopic yield criterion of trabecular bone. However, they either used a simplified microscopic yield surface or examined only a small number of load cases. A thorough multiaxial evaluation of the macroscopic yield surface was performed by applying a wide range of loading scenarios (160 load cases) on trabecular bone samples. Closed-form yield surfaces with different symmetries (isotropy, orthotropy and full anisotropy) were fitted to the numerically obtained macroscopic yield points in strain space, and the fitting errors were evaluated in detail for different subsets of load cases. Although orthotropy and full anisotropy showed the smallest fitting errors, they were not significantly superior to the isotropic fit. Thus, isotropy in strain space presents itself as the most suitable option due to the simplicity of its implementation. The study showed that fitting errors do depend on the chosen set of load cases and that shear load cases are extremely important as it was found that even for these highly aligned samples, trabecular bone presents some degree of shear asymmetry, i.e. different strength in clockwise and counter-clockwise shear directions. There have been no previous attempts to evaluate the post-yield behaviour of trabecular bone through homogenisation-based studies on detailed micro-finite element trabecular bone meshes. A damage and plasticity constitutive law for the microscale based on existing data in the literature was considered. A homogenisation-based multiscale approach was used to evaluate the hardening and stiffness reduction at the macroscale when uniaxial load scenarios are applied to trabecular bone samples, for a small range of plastic strain Euclidean norms. Results show that damage progression at the macroscale for trabecular bone is not isotropic, which is contrary to what has been assumed previously, and that both the evolution of the yield surface and damage are different for tension, compression and shear. Nonetheless, they can be correlated with plastic strain Euclidean norms by using linear relationships. It was also observed that macroscopic damage in a specific load case affects differently the on-axis orthotropic stiffness and the off-axis orthotropic stiffness components. The findings of this study will permit the use of a more rigorous definition of the post-elastic macroscopic behaviour of trabecular bone in finite element settings.

Collagen is the most abundant protein in the animal kingdom and, together with elastin, forms extensive fibrous networks that constitute the primary structure of the mammalian extracellular matrix, respectively endowing it with the tensile and elastic properties that fulfil its principal role as the passive framework of the body. The fibrous proteins are distinctly hierarchically organised from the molecular scale upwards; for example, the nanoscale tropocollagen monomer assembles in arrays that form the micrometer scale microfibrils and fibrils, and thence into collections of millimetre scale collagen fibres, that in-turn, constitute functional tissues such as skin, tendon and bone. Much is known about the structure at each of these individual scales – collagen being the most extensively researched – and the macromechanics of the fibres are well established. However, far less is known about the micromechanics of these proteins, in particular how the monomers influence the functional mechanics of the macroscopic fibres. In this thesis, I explore the multiscale mechanics of collagen and elastin fibres over a range of hydrations – with fibres in direct contact with aqueous solution, and progressively dehydrated in humidity-controlled environments. I use quasi-static tensile testing to probe the macroscopic mechanical response (Young’s modulus and stress relaxation) of the fibres, and employ Brillouin and Raman microscopy to assess the longitudinal modulus in the GHz range and corresponding molecular properties of the proteins. Brillouin microscopy is an emerging technique in the biomedical field. It enables the all-optical, contact-free and non-destructive testing of tissue micromechanics through detection of frequency shifted light scattered off thermally excited acoustic waves or “phonons” in the GHz range. As one of the first studies of Brillouin light scattering in these fibres, it sets the basis for further investigation of tissue biomechanics. In particular, I provide the full description of the protein fibre micromechanics by performing angular measurements using a so-called platelet-like configuration with sample mounted onto a reflective substrate at 45° angle to the excitation beam. I derive the high-frequency longitudinal modulus, and discuss the results in comparison to the Young’s modulus, in terms of the different frequency and spatial scale of the measurements. I obtained a full description of elasticity using Brillouin spectroscopy applied to dried fibres; however, obtaining the same description in hydrated fibres is a challenge, as the Brillouin spectrum is dominated by water. An assessment of the mechanical differences between type-I and type-II collagens is also given here. Water is known to be a primary determinant of tissue biomechanics, and I identified for the first time, the critical hydration ranges between 100 and 85% relative humidity (RH) for collagen, and around 85% RH for elastin, at which point each macroscopic fibre switched from viscoelastic to plastic-like behaviour. Dehydration below these critical points was shown to severely diminish collagen fibrillar sliding, and completely rob elastin of its ability to reversibly deform under strain. The Young’s modulus increased markedly below these hydrations, and I observed a parallel increase in the longitudinal modulus at high frequencies in each protein, indicating a concomitant increase in stiffness at the two scales. The major difference observed between the two fibrous proteins is that, in the case of elastin, I observe a two-fold increase in the longitudinal modulus as the hydration is decreased from 100 to 21% RH, whilst the Young’s modulus increases by two orders of magnitude. This discrepancy was not observed in collagen, which confirmed that the protein maintained its long-range order in the form of the triple helix at all hydrations employed in this work, whilst the elastin ultrastructure experiences a liquid-to-solid state change at a critical hydration. I demonstrate through the analysis of the low-wavenumber region (< 500 cm-1) of the Raman spectrum, that the increase in molecular stiffness of both proteins, is reflected in an increase in torsional rigidity of the peptide backbone upon dehydration. Moreover in collagen, I observe a reduction in the number of inter-protein water bridges, which I propose causes a collapse of the lateral spacing between monomers and an increase in direct backbone-backbone hydrogen bonding, that further stiffens the fibre. Small strain induced reorientations of the amide III and C–C stretching modes in dehydrated collagen fibres suggest that macroscopic stresses may be transferred to the triple helix, otherwise left unperturbed in the hydrated state. I postulate that this is a result of the degraded intra- and interfibrillar sliding mechanism below the critical hydration. Hence in its dehydrated state, the collagen whole-fibre mechanics are similar to those at the molecular scale. The role of proteoglycans and glycosaminoglycans and their potential connection to hydration, is also discussed. In agreement with previous work, I found no Raman spectral changes as a result of stretching hydrated elastin fibres, indicating that even large strains e.g. 80%, have no significant effect on the structural scale probed by Raman microscopy, nor in the air-dried state where the brittle fibres break at low strains. I suggest this may imply a limited sensitivity of Raman bands to these changes, possibly an indication of elastin’s dynamic ultrastructure, or that stress is dissipated at a higher level of the fibre structure. On the macroscopic scale, it is the poroelastic nature of elastin which controls the stress relaxation under strain, and the elastic recovery is mediated by an interplay of hydrophobic interactions and hydration forces.

Angiogenesis is the process by which new blood vessels develop from existing vessels. Angiogenesis is important in a number of conditions such as embryogenesis, wound healing and cancer. It has been modelled phenomenologically at the macroscale, using the well-known 'snail-trail' approach in which trailing endothelial cells follow the paths of other, leading endothelial cells. In this thesis, we systematically determine the collective behaviour of endothelial cells from their behaviour at the cell-level during corneal angiogenesis. We formulate an agent-based model, based on the snail-trail process, to describe the behaviour of individual cells. We incorporate cell motility through biased random walks, and include processes which produce (branching) and annihilate (anastomosis) cells to represent sprout and loop formation. We use the transition probabilities associated with the discrete model and a mean-field approximation to systematically derive a system of non-linear partial differential equations (PDEs) of population behaviour that impose physically realistic density restrictions, and are structurally different from existing snail-trail models. We use this framework to evaluate the validity of a classical snail-trail model and elucidate implicit assumptions. We then extend our framework to explicitly account for cell volume. This generates non-linear PDE models which vary in complexity depending on the extent of volume exclusion incorporated on the microscale. By comparing discrete and continuum models, we assess the extent to which continuum models, including the classical snail-trail model, account for single and multi-species exclusion processes. We also distinguish macroscale exclusion effects introduced by each cell species. Finally, we compare the predictive power of different continuum models. In summary, we develop a microscale to macroscale framework for angiogenesis based on the snail-trail process, which provides a systematic way of deriving population behaviour from individual cell behaviour and can be extended to account for more realistic and/or detailed cell interactions.