<p align="justify">The conservation of structures of the historical heritage is an increasing concern nowadays for public authorities. The technical design phase of repair operations for these structures is of prime importance. Such operations usually require an estimation of the residual strength and of the potential structural failure modes of structures to optimize the choice of the repairing techniques.</p> <p align="justify">Although rules of thumb and codes are widely used, numerical simulations now start to emerge as valuable tools. Such alternative methods may be useful in this respect only if they are able to account realistically for the possibly complex failure modes of masonry in structural applications.</p> <p align="justify">The mechanical behaviour of masonry is characterized by the properties of its constituents (bricks and mortar joints) and their stacking mode. Structural failure mechanisms are strongly connected to the mesostructure of the material, with strong localization and damage-induced anisotropy.</p> <p align="justify">The currently available numerical tools for this material are mostly based on approaches incorporating only one scale of representation. Mesoscopic models are used in order to study structural details with an explicit representation of the constituents and of their behaviour. The range of applicability of these descriptions is however restricted by computational costs. At the other end of the spectrum, macroscopic descriptions used in structural computations rely on phenomenological constitutive laws representing the collective behaviour of the constituents. As a result, these macroscopic models are difficult to identify and sometimes lead to wrong failure mode predictions.</p> <p align="justify">The purpose of this study is to bridge the gap between mesoscopic and macroscopic representations and to propose a computational methodology for the analysis of plane masonry walls. To overcome the drawbacks of existing approaches, a multi-scale framework is used which allows to include mesoscopic behaviour features in macroscopic descriptions, without the need for an a priori postulated macroscopic constitutive law. First, a mesoscopic constitutive description is defined for the quasi-brittle constituents of the masonry material, the failure of which mainly occurs through stiffness degradation. The mesoscopic description is therefore based on a scalar damage model. Plane stress and generalized plane state assumptions are used at the mesoscopic scale, leading to two-dimensional macroscopic continuum descriptions. Based on periodic homogenization techniques and unit cell computations, it is shown that the identified mesoscopic constitutive setting allows to reproduce the characteristic shape of (anisotropic) failure envelopes observed experimentally. The failure modes corresponding to various macroscopic loading directions are also shown to be correctly captured. The in-plane failure mechanisms are correctly represented by a plane stress description, while the generalized plane state assumption, introducing simplified three-dimensional effects, is shown to be needed to represent out-of-plane failure under biaxial compressive loading. Macroscopic damage-induced anisotropy resulting from the constituents' stacking mode in the material, which is complex to represent properly using macroscopic phenomenological constitutive equations, is here obtained in a natural fashion. The identified mesoscopic description is introduced in a scale transition procedure to infer the macroscopic response of the material. The first-order computational homogenization technique is used for this purpose to extract this response from unit cells. Damage localization eventually appears as a natural outcome of the quasi-brittle nature of the constituents. The onset of macroscopic localization is treated as a material bifurcation phenomenon and is detected from an eigenvalue analysis of the homogenized acoustic tensor obtained from the scale transition procedure together with a limit point criterion. The macroscopic localization orientations obtained with this type of detection are shown to be strongly related to the underlying mesostructural failure modes in the unit cells.</p> <p align="justify">A well-posed macroscopic description is preserved by embedding localization bands at the macroscopic localization onset, with a width directly deduced from the initial periodicity of the mesostructure of the material. This allows to take into account the finite size of the fracturing zone in the macroscopic description. As a result of mesoscopic damage localization in narrow zones of the order of a mortar joint, the material response computationally deduced from unit cells may exhibit a snap-back behaviour. This precludes the use of such a response in the standard strain-driven multi-scale scheme.</p> <p align="justify">Adaptations of the multi-scale framework required to treat the mesostructural response snap-back are proposed. This multi-scale framework is finally applied for a typical confined shear wall problem, which allows to verify its ability to represent complex structural failure modes.</p>

No description available.

The overall goal of the present research is to provide a computationally based methodology to realize the projected extraordinary properties of Carbon Nanotube (CNT)- reinforced composites and polymeric nanofibers for engineering applications. The discovery of carbon nanotubes (CNT) and its derivatives has led to considerable study both experimentally and computationally as carbon based materials are ideally suited for molecular level building blocks for nanoscale systems. Research in nanomechanics is currently focused on the utilization of CNTs as reinforcements in polymer matrices as CNTs have a very high modulus and are extremely light weight. The nanometer dimension of a CNT and its interaction with a polymer chain requires a study involving the coupling of the length scales. This length scale coupling requires analysis in the molecular and higher order levels. The atomistic interactions of the nanotube are studied using molecular dynamic simulations. The elastic properties of neat nanotube as well as doped nanotube are estimated first. The stability of the nanotube under various conditions is also dealt with in this dissertation. The changes in the elastic stiffness of a nanotube when it is embedded in a composite system are also considered. This type of a study is very unique as it gives information on the effect of surrounding materials on the core nanotube. Various configurations of nanotubes and nanocomposites are analyzed in this dissertation. Polymeric nanofibers are an important component in tissue engineering; however, these nanofibers are found to have a complex internal structure. A computational strategy is developed for the first time in this work, where a combined multiscale approach for the estimation of the elastic properties of nanofibers was carried out. This was achieved by using information from the molecular simulations, micromechanical analysis, and subsequently the continuum chain model, which was developed for rope systems. The continuum chain model is modified using properties of the constituent materials in the mesoscale. The results are found to show excellent correlation with experimental measurements. Finally, the entire atomistic to mesoscale analysis was coupled into the macroscale by mathematical homogenization techniques. Two-scale mathematical homogenization, called asymptotic expansion homogenization (AEH), was used for the estimation of the overall effective properties of the systems being analyzed. This work is unique for the formulation of spectral/hp based higher-order finite element methods with AEH. Various nanocomposite and nanofibrous structures are analyzed using this formulation. In summary, in this dissertation the mechanical characteristics of nanotube based composite systems and polymeric nanofibrous systems are analyzed by a seamless integration of processes at different scales.

No description available.

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A teoria de elasticidade não-linear é apropriada para a investigação de instabilidades materiais relacionadas ao amolecimento e à formação de bandas de cisalhamento. Estes fenômenos podem surgir em compósitos constituídos de fases que, isoladamente, não apresentam tais fenômenos sob as mesmas condições de carregamento. O objetivo principal desta tese de doutorado é utilizar métodos computacional e de homogeneização na investigação do comportamento de laminados bifásicos compostos de lâminas elásticas não-lineares. Em particular, utilizam-se o método dos elementos finitos (MEF) clássico e os métodos de homogeneização assintótica (MHA) e de segunda ordem tangencial para gerar resultados computacionais e analíticos que possam ser comparados entre si. Com este objetivo em mente, estuda-se primeiramente o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elástico-lineares, homogêneas e isotrópicas. Os bilaminados estão em equilíbrio na ausência de forças de corpo. Gera-se uma sequência de bilaminados com número crescente de lâminas e simulam-se ensaios de tração uniaxial no regime de pequenas deformações utilizando malhas de elementos finitos refinadas. Resultados destas simulações computacionais são comparados a resultados analíticos obtidos de ensaio de tração uniaxial similar de um sólido homogeneizado via MHA. Os resultados computacionais tendem aos resultados analíticos à medida que o número de lâminas na sequência de bilaminados tende ao infinito. Em seguida, investiga-se o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elásticas não-lineares, homogêneas, quase-incompressíveis e isotrópicas submetidos a condições de deformação impostas em seus contornos. Utilizando-se o método de homogeneização de segunda ordem tangencial, determinam-se as propriedades efetivas dos bilaminados. Estas propriedades são utilizadas na condição de Legendre-Hadamard para predizer perda de elipticidade das equações governantes. A violação desta condição está relacionada à formação de bandas de cisalhamento no compósito. Utilizando malha de elementos finitos refinada, simula-se numericamente o problema de equilíbrio de um bilaminado com número elevado de lâminas na ausência de força de corpo e sujeito a deformações impostas no contorno. Os resultados computacionais predizem perda de elipticidade para um nível de deformação próximo ao nível de deformação da perda de elipticidade predita pelo método de homogeneização. Os resultados analíticos e computacionais indicam que a perda de elipticidade é fortemente influenciada pelo contraste de heterogeneidade entre as fases e pelas condições de contorno. / The theory of nonlinear elasticity is suitable for the investigation of material instabilities related to softening and formation of shear bands. These phenomena can arise in composites consisting of phases which, taken separately, do not exhibit such phenomena under the same loading conditions. The main objective of this thesis is to use both computational and homogenization methods in the investigation of the behavior of two-phase laminates composed of nonlinear elastic laminae. In particular, we use the finite element method (FEM) and both the asymptotic homogenization method (AHM) and the tangent second-order homogenization method to generate computational and analytical results that can be compared to each other. With this goal in mind, we study first the effective behavior of bilaminates composed of periodic distributions of linearly elastic, homogeneous, and isotropic laminae. The bilaminates are in equilibrium in the absence of body forces. A sequence of bilaminates with increasing number of laminae is used to numerically simulate uniaxial tensile tests in the small strain regime using refined finite element meshes. Computational results are then compared with analytical results obtained from a similar tensile test of a solid homogenized via MHA. The computational results tend to the analytical result as the number of laminae in the sequence of bilaminates tends to infinity. Next, we investigate the effective behavior of bilaminates composed of periodic distributions of nonlinearly elastic, homogeneous, isotropic, and quasi-incompressible laminae that are subjected to deformation conditions on their boundaries. Using the tangent second-order homogenization method, the effective properties of the bilaminates are determined. These properties are used in the Legendre-Hadamard condition to predict loss of ellipticity of the governing equations. Violation of this condition is related to the formation of shear bands in the composite. Using refined finite element meshes, we simulate numerically the problem of equilibrium of a bilaminate with a high number of laminae in the absence of body force and subjected to deformation conditions on the boundary. The computational results predict loss of ellipticity at a deformation level close to the deformation level for which loss of ellipticity is predicted by the homogenization method. The computational and analytical results indicate that the loss of ellipticity is strongly influenced by both the heterogeneity contrast between the phases and the boundary conditions.

A teoria de elasticidade não-linear é apropriada para a investigação de instabilidades materiais relacionadas ao amolecimento e à formação de bandas de cisalhamento. Estes fenômenos podem surgir em compósitos constituídos de fases que, isoladamente, não apresentam tais fenômenos sob as mesmas condições de carregamento. O objetivo principal desta tese de doutorado é utilizar métodos computacional e de homogeneização na investigação do comportamento de laminados bifásicos compostos de lâminas elásticas não-lineares. Em particular, utilizam-se o método dos elementos finitos (MEF) clássico e os métodos de homogeneização assintótica (MHA) e de segunda ordem tangencial para gerar resultados computacionais e analíticos que possam ser comparados entre si. Com este objetivo em mente, estuda-se primeiramente o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elástico-lineares, homogêneas e isotrópicas. Os bilaminados estão em equilíbrio na ausência de forças de corpo. Gera-se uma sequência de bilaminados com número crescente de lâminas e simulam-se ensaios de tração uniaxial no regime de pequenas deformações utilizando malhas de elementos finitos refinadas. Resultados destas simulações computacionais são comparados a resultados analíticos obtidos de ensaio de tração uniaxial similar de um sólido homogeneizado via MHA. Os resultados computacionais tendem aos resultados analíticos à medida que o número de lâminas na sequência de bilaminados tende ao infinito. Em seguida, investiga-se o comportamento efetivo de bilaminados compostos por distribuições periódicas de lâminas elásticas não-lineares, homogêneas, quase-incompressíveis e isotrópicas submetidos a condições de deformação impostas em seus contornos. Utilizando-se o método de homogeneização de segunda ordem tangencial, determinam-se as propriedades efetivas dos bilaminados. Estas propriedades são utilizadas na condição de Legendre-Hadamard para predizer perda de elipticidade das equações governantes. A violação desta condição está relacionada à formação de bandas de cisalhamento no compósito. Utilizando malha de elementos finitos refinada, simula-se numericamente o problema de equilíbrio de um bilaminado com número elevado de lâminas na ausência de força de corpo e sujeito a deformações impostas no contorno. Os resultados computacionais predizem perda de elipticidade para um nível de deformação próximo ao nível de deformação da perda de elipticidade predita pelo método de homogeneização. Os resultados analíticos e computacionais indicam que a perda de elipticidade é fortemente influenciada pelo contraste de heterogeneidade entre as fases e pelas condições de contorno. / The theory of nonlinear elasticity is suitable for the investigation of material instabilities related to softening and formation of shear bands. These phenomena can arise in composites consisting of phases which, taken separately, do not exhibit such phenomena under the same loading conditions. The main objective of this thesis is to use both computational and homogenization methods in the investigation of the behavior of two-phase laminates composed of nonlinear elastic laminae. In particular, we use the finite element method (FEM) and both the asymptotic homogenization method (AHM) and the tangent second-order homogenization method to generate computational and analytical results that can be compared to each other. With this goal in mind, we study first the effective behavior of bilaminates composed of periodic distributions of linearly elastic, homogeneous, and isotropic laminae. The bilaminates are in equilibrium in the absence of body forces. A sequence of bilaminates with increasing number of laminae is used to numerically simulate uniaxial tensile tests in the small strain regime using refined finite element meshes. Computational results are then compared with analytical results obtained from a similar tensile test of a solid homogenized via MHA. The computational results tend to the analytical result as the number of laminae in the sequence of bilaminates tends to infinity. Next, we investigate the effective behavior of bilaminates composed of periodic distributions of nonlinearly elastic, homogeneous, isotropic, and quasi-incompressible laminae that are subjected to deformation conditions on their boundaries. Using the tangent second-order homogenization method, the effective properties of the bilaminates are determined. These properties are used in the Legendre-Hadamard condition to predict loss of ellipticity of the governing equations. Violation of this condition is related to the formation of shear bands in the composite. Using refined finite element meshes, we simulate numerically the problem of equilibrium of a bilaminate with a high number of laminae in the absence of body force and subjected to deformation conditions on the boundary. The computational results predict loss of ellipticity at a deformation level close to the deformation level for which loss of ellipticity is predicted by the homogenization method. The computational and analytical results indicate that the loss of ellipticity is strongly influenced by both the heterogeneity contrast between the phases and the boundary conditions.

Ce mémoire aborde les questions relatives à la mise en place de procédures de conception rapide, fiable et automatisée des volumes élémentaires représentatifs (VER) d’un matériau composite à microstructure complexe (matrice/inclusions), et de la détermination de leurs propriétés homogénéisées ou effectives. Nous avons conçu et développé des algorithmes conduisant à des outils efficaces permettant la génération aléatoire de tels matériaux à inclusions sphériques, cylindriques, elliptiques ou toute combinaison de celles-ci. Ces outils sont également capables d’altérer les inclusions : inflation, déflation, arrachements aléatoires, ondulation et de les pelliculer permettant ainsi de générer des VER s’approchant des matériaux composites fabriqués. Un soin particulier a été porté sur la génération de VER périodiques. Les caractéristiques homogénéisées ou propriétés effectives de matériaux constitués de tels VER périodiques peuvent alors être déterminées selon le principe d’homogénéisation périodique, soit par une méthode basée sur un schéma itératif utilisant la FFT (Transformation de Fourier Rapide) via l’équation de Lippmann-Schwinger, soit par une méthode d’éléments finis. Le caractère aléatoire de la génération nous amène à réaliser des études en moyenne à partir d’un ensemble de paramètres morphologiques déterminé : nombre d’inclusions, type et forme, fraction volumique, orientation des inclusions, prise en compte d’une éventuelle altération. Deux études particulières sur la conductivité thermique apparente ont été menées, la première sur les composites à inclusions sphériques pelliculées de façon à déterminer l’influence de l’épaisseur de la pellicule et la seconde sur les composites de type stratifié en polymère et fibre de carbone, cousu par un fil de cuivre pour évaluer l'apport de la couture en cuivre selon la fibre de carbone utilisée. / This thesis focuses on setting up of fast, reliable and automated approaches to design representative volume elements (RVE) of composite materials with complex microstructures (matrix/inclusions) and the evaluation of their effective properties via a homogenization process. We developed algorithms and efficient tools for the random generation of such materials. Inclusions shapes may be spherical, cylindrical, elliptical or any combinations of them. Inflation, deflation, dislocation, undulation and coating are also available to generate RVE. The aim is to approach realistic materials subjected to be damaged during production. Particular attention has been focused on the periodic RVE generation.The homogenized characteristics or effective properties of materials formed from such periodic RVE may then be determined according to the principle of periodic homogenization, by an iterative scheme using FFT (Fast Fourier Transform) via the integral Lippmann-Schwinger or by a finite elements method.The stochastic generation of RVE and the set of morphological parameters studied: number of inclusions, type and shape, volume fraction, orientation of the inclusions lead to achieve an average process. Moreover, a special study has been led to take into account the behavior of altered inclusions. Furthermore, we studied two particular cases on the apparent thermal conductivity of the composite, the first for coated spherical inclusions in order to determine the influence of the layer thickness and the second for laminated polymer and carbon fiber composite sewn by a copper wire, in order to determine the influence of the sewing contribution according to the carbon fiber used.

Nous analysons les propriétés dynamiques de milieux architecturés périodiques et de réseaux fibreux aléatoires en petites et grandes déformations, à partie de méthodes d’homogénéisation afin de calculer leurs propriétés statiques et dynamiques. Des modèles effectifs de type micropolaire et du second gradient sont élaborés afin de prendre en compte l’impact de la microstructure sur le comportement effectif. L’influence des degrés de liberté en rotation additionnels et des gradients d’ordre supérieur du déplacement sur les relations de dispersion sont analysés pour des comportements élastique et viscoélastique du matériau constitutif. Les milieux continus généralisés ainsi construits conduisent à des effets dispersifs, en accord avec les observations. Dans la seconde partie du travail, nous analysons l’influence des grandes déformations sur la propagation des ondes élastiques dans des milieux architecturés périodiques. Des méthodes théoriques assortis de schémas numériques sont développés afin de prédire l’influence des déformations finies générées au sein des structures sur l’évolution de leur diagramme de bande. Un schéma incrémental d’évolution de la fréquence et de la vitesse de phase du milieu continu homogénéisé est établi, à partir d’une méthode de perturbation établie pour des structures 1D, 2D et 3D, en considérant plus particulièrement des structures auxétiques. Ce schéma montre un effet important de l’état de déformation appliquée et de la densité effective sur l’évolution de la fréquence et de la vitesse de phase des ondes. Une méthode de perturbation spécifique aux structures périodiques nonlinéaires est développée afin de généraliser le théorème de Bloch pour couvrir les non linéarités tant géométriques que matérielles. Des modèles hyperélastiques du premier et du second gradient de différentes structures sont identifiés par des tests virtuels reposant sur une méthode d’homogénéisation dédiée, qui permettent de formuler des équations d’onde spécifiques – équations de Burgers et de Boussinesq – dont les propriétés dispersives sont analysées / Micropolar and second gradient effective continua are constructed as two different strategies to account for microstructural effects. The influence of additional degrees of freedom or higher order displacement gradients on the dispersion relations is analyzed in both situations of elastic and viscoelastic behaviors of the material. Generalized effective continua lead to dispersive waves, as observed in experiments. In the second part of the thesis, we analyze the influence of large deformations on the propagation of acoustic waves in repetitive network materials. Both theoretical and numerical methods are developed in order to assess the influence of finite strains developing within the networks on the evolution of their band diagrams. An incremental scheme for the update of frequency and phase velocity of the computed homogenized medium is developed based on a perturbation method for 1D, 2D and 3D structures, considering with a special emphasis auxetic networks. This scheme shows an important effect of the applied finite deformation on the frequency and phase velocity of the propagating waves. A perturbation method for nonlinear periodic structures is developed to extend Bloch’s theorem to cover both geometrical and material nonlinearities. Hyperelastic first and second order gradient constitutive models of different network materials are identified based on dedicated homogenization methods, from which specific wave equations are formulated - Burgers and Boussinesq equations - the dispersion properties of which are analyzed