This dissertation proposes a new framework to characterize the nonlinear behavior of anisotropic materials in an on-line manner. The proposed framework applies recursive estimation and a multi-linear model to characterize the nonlinear behavior of anisotropic materials on-line using full-field strains, which are capable of capturing the multi-axial information of anisotropic materials. A stochastic method is developed to characterize the linear behavior of anisotropic materials under the influence of full-field strain measurement noise. This method first derives stochastic equations based on the formulas of energy-based characterization that utilizes the principle of ener-gy conservation, and then recursively estimates elastic constants at every acquisition of measure-ment using a Kalman filter (KF). Since the measurement model is expressed nonlinearly, the KF utilizes a Kalman gain, which is newly derived in this dissertation through variance minimization, to achieve optimal characterization. The aforementioned method, namely stochastic linear characteri-zation in this dissertation, becomes a basis of the multi-linear characterization method. This method utilizes a multi-linear model, which is defined by partitions, to characterize the nonlinear constitu-tive relations. The multi-linear characterization scales up the number of estimates and identifies the coefficients of each linear partition using the previously derived KF. The recursive updates in measurements not only removes uncertainty through sensor measurements, but also enables the on-line capability of the nonlinear characterization of anisotropic materials. A series of numerical and experimental studies were performed to demonstrate the performance of the proposed framework in characterizing the nonlinear behavior of anisotropic materials. The validity and applicability of the proposed framework were confirmed by the comparison with the known values of the characterized constitutive relations. It was found that the proposed framework identified elastic constants that were in good agreement with known values irrespective of the spec-imen geometry. The results of the multi-linear characterization method were well correlated with known nonlinear stress-strain relations and concluded that the proposed framework is capable of characterizing adequate nonlinear behavior on-line. / Ph. D.

En raison de leur porosité élevée, les roches carbonatées forment d'importants réservoirs d'eau et d'hydrocarbures, et conviennent également à d'autres applications telles que le stockage de CO2 ou des déchets nucléaires. Cependant, le compactage localisé dans les roches carbonatées affecte le champ des contraintes et les propriétés hydromécaniques de ces roches, entraînant des déformations inélastiques et des dommages avec des impacts économiques, environnementaux et sociaux potentiels. Des études antérieures sur le terrain et des études expérimentales en laboratoire que dans les roches carbonatées poreuses, contrairement aux grès, une variété de micromécanismes tels que l'effondrement des pores, le broyage des grains, la petre de cimentation, la plasticité des cristaux et la dissolution sous contrainte peuvent entraîner une densification inélastique. En raison de la coexistence de ces multiples processus inélastiques et de leur interactions, le micromécanisme prédominant à l'origine du processus de localisation et de rupture reste mal compris.Cette thèse de doctorat présente une étude expérimentale sur les mécanismes de déformation régissant le comportement mécanique et le mode de rupture des roches carbonatées à haute porosité. A cet effet, le Tuffeau de Maastricht, un calcaire sédimentaire bioclastique présentant jusqu'à 52% de porosité, a été testé à l'état sec. Cette étude s'est concentrée sur la façon dont le chemin des contraintes, la pression de confinement et l'orientation de la stratification influent sur l'apparition et la propagation des bandes de compaction. Trois campagnes expérimentales principales sont menées sur des éprouvettes cylindriques pour étudier la transition fragile-ductile :compression isotrope,compression uniaxiale et compression triaxiale. Une analyse systématique du comportement anisotrope du Tuffeau de Maastricht est effectuée sur des échantillons qui ont été forés perpendiculairement, obliquement 45° et parallèlement au plan de la stratification. La micro-tomographie à rayons X à haute résolution est utilisée pour obtenir des images 3D de l'ensemble de l'échantillon en cours de chargement. Les images acquises sont traitées et des mesures de plein champ ont été utilisées pour élucider les mécanismes d'initiation et de propagation des zones de compactage localisées. Les variations de porosité pendant le chargement sont mesurées macroscopiquement et localement. L'utilisation systématique des rayons X combinée à l'utilisation de l'analyse d'image avancée et de la corrélation d'images numérique fournit une information 3D quantitative du champ de déformation et de son évolution pendant un test.Deux modes de rupture sont identifiés, selon les mesures de porosité et la CIVD: les bandes de cisaillement contractantes développées à basse pression de confinement et les bandes de compaction formées perpendiculairement à la contrainte principale majeure de compression à un confinement plus élevé. Ces bandes se développent à contrante déviatoire presque constante et se propagent dans tout l'échantillon, phase marquée par des chutes épisodiques de la contrainte deviatoire. Les essais de compression triaxiale conduit à des niveux de déformation axiale plus élevée présentent trois phases distinctes: une phase initiale quasi-linéaire, suivie par un plateau de contrainte déviatoire, enfin un durcissement post-plateau. L'observation essentielle de ces expériences est l'existence d'un mécanisme de dégradation del la cimentation entre grains qui transforme l'échantilon cohésif et frottant en un miliu granulaire purement frottant. D'autres expériences réalisées sur du sable obtenu par dégradation artificielle de la roche originelle mettent l'accent sur cette phase de déstructuration qui se produit lors du plateau de la contrainte déviatoire. Les résultats expérimentaux mettent également en évidence la forte influence due à l'anisotropie sur le comportement mécanique du matériau étudié. / Given their high porosity, carbonates form important water and hydrocarbons reservoirs, and they are also suitable for other applications such as CO2 storage and nuclear waste disposal. However, localized compaction in carbonates affects the stress field and the hydromechanical properties of these rocks leading to inelastic deformation and failure with potential economic, environmental and social impacts. Previous field and experimental studies have shown that in porous carbonates, unlike sandstones, a variety of micromechanisms such as pore collapse, grain crushing, debonding, crystal plasticity and pressure solution can potentially lead to inelastic compaction. Due to the coexistence of such multiple inelastic processes and the interplay among them, the dominant micromechanism responsible for failure remains poorly understood.This doctoral thesis presents an experimental investigation into the deformation mechanisms governing the mechanical behavior and failure mode of high porosity carbonate rocks. To this end, Tuffeau de Maastricht, a bioclastic sedimentary limestone exhibiting up to 52% porosity, has been tested under dry conditions. This study focuses on how stress path, confining pressure and bedding orientation affect the onset and propagation of localized compaction. Three main experimental campaigns are conducted on cylindrical specimens of 11.5 mm diameter and 22 mm height to study the brittle-ductile transition: (i) isotropic compression, (ii) uniaxial compression, and (iii) triaxial compression tests at confining pressures ranging from 1 to 5 MPa. A systematic analysis of the anisotropic behavior of Tuffeau de Maastricht is conducted on samples cored perpendicular, oblique 45° and parallel to the bedding plane. High resolution x-ray computed tomography (CT) is used to obtain 3D images of the entire specimen under loading. The acquired images are processed and full-field measurements have been used to elucidate the mechanics of initiation and propagation of localized compaction. Porosity variations during loading are measured macroscopically as well as locally. The porosity measurements are performed over a REV, which is defined with the use of statistical tools. The systematic use of x-ray micro tomography combined with the use of advanced image analysis and Digital Image Correlation (DIC) provides a quantitative 3D information the strain field inside a sample and its evolution during a test.Two failure modes are identified, based on porosity measurements and DIC: compactive shear bands at low confining pressure, and compaction bands (perpendicular to the maximum compressive stress) at higher confinement. These bands develop at essentially constant deviator stress and propagate through the whole sample punctuated by episodic stress drops. Triaxial compression tests at much higher axial strain present three distinct phases: (1) an initial quasi-linear increase of deviator stress, followed by (2) a plateau and (3) a post-plateau hardening. The essential observation from these experiments if the occurrence of a debonding phase which converts the specimen from rock-like to sand-like. A second localization, typical of dense sand, eventually occurs for very axial strain. Additional experiments that are performed on artificially debonded specimens emphasize this destructuration phase during the plateau of deviator stress. The experimental results also highlight the strong anisotropy of the mechanical behavior of the studied material.

Digital Image Correlation (DIC) is a technique which uses images taken before and after deformation to determine displacement and strain data over the surface of the sample. In order to obtain this data for both in-plane as well as out-of-plane direction, multiple views of the sample are required. Typically, this is accomplished using multiple cameras, but it is possible to use diffraction gratings to bend the light coming from the specimen in order to allow a single camera to capture multiple views. This technique is referred to as Diffraction Assisted Image Correlation (DAIC) and has been previously demonstrated at room temperature. This work expands this method for use at high temperatures by incorporating the use of ultraviolet (UV) lights for illumination and filtering out the light in the visible spectrum. This increases the temperature at which useful images can be captured by reducing the glow that specimens produce at elevated temperatures. When not filtered out, this glow saturates the camera sensor making DIC impossible. This new technique is referred to as Ultraviolet Diffraction Assisted Image Correlation (UV-DAIC).

Amorphous polymers under their glass transition temperature (Tg) exhibit large inelastic deformations. Their mechanical behavior is highly dependent upon temperature, strain rate, pressure and loading mode (tension, compression, shear). They also exhibit small strain isotropic hardening, softening and large strain anisotropic rehardening. In addition, while in their glassy state, polymers are far from thermodynamic equilibrium so that their properties may change over time (physical aging). This complex behavior is reflected in the response of composites and affects the onset and propagation of damage therein. Therefore, in order to design polymer composite structures, it is fundamental to develop relevant tools and methodologies which aim at understanding, capturing and predicting the full thermomechanical response of glassy polymers. In this study, the thermomechanical behavior of a thermosetting polymer epoxy is characterized experimentally for temperatures below Tg. The intrinsic behavior of the polymer is obtained using a new methodology based on digital image correlation (DIC) in combination with video-monitored extensometry. In particular, inelastic flow localization patterns are discussed based on the full-field strain measurements and their connection to the stress-strain curves are highlighted. The Boyce-Parks-Argon polymer constitutive model, hereafter called the macromolecular model, has been enhanced to describe the thermomechanical behavior of epoxies. The identification of the material parameters involved in the model is described in a detailed procedure that builds on a limited set of experiments. The model is shown to represent adequately the thermomechanical behavior of the studied epoxy over a wide range of temperatures and strain-rates. Using additional high strain-rate data obtained from collaborators on Kolsky bars, the model capabilities are further discussed. Using finite-element implementations of the constitutive model in both quasi-static and dynamic codes, the processes of plastic flow localization are analyzed in tensile and compression specimens. Such analysis can form the basis of an alternative method for identifying the model parameters through inverse identification. Finally, a preliminary set of experiments were also conducted to investigate the effect of physical aging on the yield behavior and enhance the macromolecular model with the capability of modeling aging effects. Our interpretation of the aging experiments suggests that they are not conclusive and do not permit full determination of model parameters. Specific recommendations are tentatively formulated for conducting aging experiments in the future.

This thesis investigates the appropriateness of a simplified, open-source digital image correlation (DIC) software for use in quasi-static, structural testing utilizing two-dimensional (2D) DIC measurements. DIC is a non-contact optical measurement technique that uses computer vision to track unique attributes on the surface of an object. For structural testing, traditional instrumentation such as displacement sensors and strain gages are impractical for full field measurements due their limited ability to capture large amounts of data. However, over the past decade, DIC has proven a successful method for full-field kinematics measurements, making it an appealing tool for collecting high densities of accurate data. This thesis specifically studies the accuracy and limitations of the DIC software, MODEM, for various test specimens and loading conditions. This research work is part of an experimental program comprised of three phases. The first stage was conducted by another investigator on aluminum coupons tested in pure tension. These results were used to calibrate parameters (speckle pattern density, lighting, and camera settings) used with the DIC software. The second stage included pure compression tests on concrete cubes and concrete cylinders to compare the difference in results between: (i) surface curvature, (ii) camera distance, (iii) surface treatment, and (iv) speckle pattern color. The final stage involved analysis of a tension test of a concrete prism completed at the University of Auckland in an effort to assess how MODEM could be utilized to accurately detect onset and propagation of concrete cracking. Results showed the most accurate DIC strains were within 5% error when compared to traditional instrumentation for aluminum loaded in tension and within 6% error for concrete loaded in compression/tension. This level of accuracy is comparable to existing open source and commercial DIC software utilizing 2D DIC analysis. Therefore, MODEM can be used to provide accurate 2D DIC strain measurements for small and medium scale structural test specimens when using the following parameters: (i) the surface of the specimen is planar, (ii) the camera is placed accordingly so the maximum amount of zoom can be used, (iii) the surface of a test specimen is free of debris or imperfections, and (iv) a high contrast and evenly distributed speckle pattern is used. Computational analysis of the results showed that known material properties can be used to calibrate, or remove errors from, the DIC results when traditional instrumentation is not available. Additionally, results showed MODEM strain contours can be used for initial detection of cracks in concrete loaded in tension while MODEM tracking performance can be used to characterize the centerline and orientation of cracks. The experimental tests provide critical information on how to set up, run, and analyze DIC results when using MODEM. The full field measurements are of value in providing accurate data for structural testing to develop a better understanding of material response and structural performance, since large-scale tests are typically limited by a sparse number of data points when using traditional instrumentation.

Les mesures optiques dimensionnelles sont des techniques en plein essor dont la maîtrise et l'exploitation soulèvent encore de nombreuses questions. Pour une meilleure compréhension d'un système de mesure par stéréo-corrélation d'images, des études de caractérisation et d'évaluation de l'erreur de mesure en corrélation à partir d'images synthétiques et en stéréovision à partir d'images réelles ont été réalisées. Les résultats mettent en avant l'influence de plusieurs paramètres : fenêtre de corrélation, déformation et gradient de déformation. La dernière partie de l'étude est consacrée à l'identification de comportements constitutifs à partir des mesures de champs. Deux méthodes sont mises en œuvre : la méthode des champs virtuel pour l'identification des paramètres élastiques d'un matériau et l'identification paramétrique par recalage éléments finis pour le cas des comportements élasto-plastiques. / The optical dimensional measurements are emergent techniques whose control and exploitation still address many questions. For a better understanding of the stereo-correlation measurement systems, studies are made to characterize and assess the digital image correlation measurement error by the way of synthetic images. The stereovision characterization is made using real images. The results highlight the influence of several parameters : subset size, strain and strain gradient. The last part of this study is devoted to the identification of constitutive behaviour law using full-field measurements. Two identification methods are used : the virtual fields method to determine the elastic parameters of a material and the finite element model updating method to identify the elasto-plastic behaviour law.

Ce travail porte sur l'endommagement des matériaux composites stratifiés utilisés notamment pour la réalisation de pièces structurales minces. La dégradation de ces matériaux induite par la création et le développement de surfaces de décohésion internes est abordée sous deux angles. Une campagne expérimentale a tout d'abord été menée sur des stratifiés en carbone-époxy réalisés par infusion de résine liquide et sollicités en traction uniaxiale. Cette étude propose une analyse originale à l'aide de trois techniques optiques permettant une caractérisation de l'endommagement par mesures de champs : cinématiques (par stéréo-corrélation d'images), thermiques (par thermographie infrarouge) et densimétriques (par tomographie à rayons X). Le second volet du travail concerne la modélisation de la microfissuration dans le contexte d'une anisotropie initiale. A cette fin, une homogénéisation bidimensionnelle de milieux orthotropes fissurés permet la prise en compte de défauts d'orientation arbitraire et des effets unilatéraux (ouverture-fermeture des microfissures) au sein d'une formulation énergétique en déformation. Sur cette base, un modèle de comportement est proposé dans le cadre de la thermodynamique des processus irréversibles avec variables internes. Des simulations numériques permettent de démontrer les capacités prédictives de la formulation, en particulier la représentation du comportement non linéaire de ces matériaux, l'interaction entre les anisotropies initiale et induite et la restitution des propriétés élastiques lors de la fermeture de défauts. / This work deals with the damage of laminated composite materials used in particular for the production of thin structural parts. The degradation of these materials induced by the creation and growth of internal microcracks is considered from two angles. An experimental campaign was first conducted on carbon-epoxy laminates made by liquid resin infusion and loaded in uniaxial tension. This study proposes an original analysis using three advanced optical techniques that allow the damage characterization through full-field measurements : kinematic (with stereo-image correlation), thermal (with infrared thermography) and density (with X-ray tomography). The second part of the work concerns the modeling of microcracking in the context of initial anisotropy. To this end, a two-dimensional homogenization of orthotropic cracked media allows consideration of arbitrary orientation of defects and unilateral effects (opening and closing of microcracks) within a strain energetic formulation. On this basis, a constitutive model is proposed in the framework of thermodynamics of irreversible processes with internal variables. Numerical simulations demonstrate the predictive capabilities of the formulation, in particular the representation of the nonlinear behavior of these materials, the interaction between initial and induced anisotropies and the recovery of elastic properties at the closure of microdefects.

Les fractures du fémur proximal de la personne âgée sont généralement fixées par des dispositifs d’ostéosynthèse. Pour les fractures particulières dites inter-trochantériennes, il est possible de fixer la fracture de manière intra-médullaire (à l’intérieur de l’os) ou de manière extra-médullaire (en dehors de l’os). Pour chaque type de traitement, les hôpitaux sont équipés des deux systèmes de fixation. Les différences de morphologie des individus impliquent l’existence de multiples références d’implants et donc de surcoûts en termes d’équipement. Dans ce travail de thèse, un implant original adaptable à la plupart des morphologies a été développé. Cet implant permettra non seulement d’offrir aux chirurgiens une souplesse au cours des interventions chirurgicales mais aussi de réduire de manière significative les stocks d’implants dans les hôpitaux. Le comportement mécanique de l’implant est étudié dans différents cas de fractures par deux approches complémentaires, une méthode numérique par Éléments Finis et une approche expérimentale mettant en oeuvre des techniques de stéréo-corrélation à partir d’images de caméras rapides. Les résultats des calculs numériques sont confrontés à ceux issus d’essais réalisés sur des fémurs synthétiques, puis cadavériques en laboratoire d’anatomie. Les comparaisons avec des implants existants montrent que ce nouveau concept d’implant permet une fixation plus stable des fragments osseux et une bonne compression du foyer de fracture. / Proximal femoral fractures in the elderly are generally fixed with osteosynthetic devices. For specific fractures called intertrochanteric, it is possible to fix the fracture in an intramedullary way (inside the bone) or in an extramedullary way (outside the bone). For each type of treatment, hospitals are equipped with the two fixing systems. The differences in physical characteristics between individuals imply the existence of multiple references implants and therefore additional costs in terms of equipment. In this thesis work,an original implant adaptable to most people has been developed. This implant will provide surgeons greater flexibility during surgery but also significantly reduce stocks implants in hospitals. The mechanical behavior of the implant is studied in different cases of fractures by two complementary approaches,a finite element analysis and an experimental study employing stereo-image correlation technique from images of high speed cameras. The results of the numerical calculation are compared with those derived from tests on synthetic femurs, then cadaver in anatomy laboratory. Comparisons with existing implants show that this new implant concept allows for a more stable fixation of bone fragments and a good compression of the fracture.

La connaissance du comportement mécanique à l’échelle du micron est déterminante pour arriver à prédire la dégradation des matériaux. Dans le cas des polycristaux, les lois de plasticité cristalline sont généralement utilisées pour décrire le comportement d’un grain. Ces lois possèdent de nombreux paramètres qui doivent être ajustés à l’état métallurgique et mécanique du matériau.Le travail rapporté ici explore une manière originale d’identifier ces paramètres à partir du comportement observé expérimentalement à l’échelle microscopique, sans recourir à un maillage éléments finis. Cette observation est réalisée en couplant (i) une évaluation du champ de contrainte locale par les techniques de microdiffraction Laue et d’EBSD à haute résolution angulaire et (ii) la mesure du champ de déformation total par corrélation d’images numériques.Afin de garantir la fiabilité des résultats, la justesse des mesures par microdiffraction Laue (Laue-DIC) et HR-EBSD est évaluée, pour la première fois, dans un matériau plastifié à moins de 0,5% de déformation. Les champs de déformation et de contrainte sont ensuite déterminés simultanément en surface d’une éprouvette monocristalline, sollicitée in-situ en flexion quatre points. Le comportement local est ainsi mesuré puis utilisé pour identifier deux paramètres d’une loi de plasticité cristalline, dans un acier austénitique monocristallin de type 316L. / The prediction of damage occurring in metallic materials is dependent on the knowledge of the mechanical behavior at a micron scale. Crystal plasticity laws are often used to describe the behavior of a single grain in polycrystals. Such laws include many parameters which should be tuned according to the metallurgical and mechanical state of the material.An original way to identify theses parameters is presented in this work. The local constitutive behavior is measured at the local scale. It is used to adjust the parameters’ value on a single point calculation without the need for a finite element mesh. To observe the local behavior two types of full filed measurements are carried out: (i) stress measurements using diffraction-based Laue microdiffraction and high angular resolution EBSD – HR-EBSD – and (ii) strain measurements by digital image correlation.To ensure trustworthy results, the accuracy of Laue microdiffraction (Laue-DIC) and HR-EBSD measurements are determined for the first time in a plastically deformed material. Then, stress and strain fields are monitored at the surface of a single crystal bent in-situ in the low deformation regime (0.5%). The local behavior is determined and used to identify two parameters of a crystal plasticity law, in a 316L stainless steel single crystal.

La caractérisation des propriétés matérielles basée sur le dialogue essai-calcul requiert des précautions quant à la prise en compte des grandeurs physiques mises en jeu, aussi bien mesurées que calculées. Les mesures de champs cinématiques délivrent des informations qui permettent de rendre compte du comportement local du matériau et constituent une entrée riche pour ce type de dialogue axé sur la confrontation modèle - mesure. L’objet de ce travail est de discuter l’identification de propriétés élastiques homogènes ou hétérogènes, basée sur l’exploitation de mesures de champs, qui soulève la problématique de la prise en compte de mesures perturbées et d’hypothèses fortes de modélisation. Le but de cette étude est de discuter deux manières différentes pour aborder le problème. La première consiste à traiter les mesures en amont de l’étape d’identification, afin de filtrer les perturbations de mesures, et est basée sur l’outil d’approximation diffuse. La seconde consiste à développer une méthode d’identification inverse à partir d’essais quasi-statiques cherchant à tenir compte du caractère incertain des mesures, dès sa formulation, en utilisant l’ensemble des informations théoriques et expérimentales disponibles, en particulier en l’absence d’informations sur les conditions aux limites. Cette méthode est basée sur les principes de l’erreur en relation de comportement modifiée, amenant à résoudre des problèmes éléments finis non standards, et a conduit à mettre en œuvre des méthodes de résolution adaptées. L’étude a permis de souligner la robustesse de la méthode face aux incertitudes de mesure, notamment en comparaison avec le recalage par éléments finis. / The identification of material properties based on the confrontation between the experimental data and their numerical counterpart needs to pay special attention to their reliability and then to take some precautions. Especially, when dealing with full-field measurements which provide rich kinematic information enabling new possibilities for the characterization of material constitutive parameters. The aim of this work is to discuss the identification of the elastic parameters, for either homogeneous or heterogeneous materials, leading to the more general problem of the taking into account of noisy experimental data and strong model hypotheses. Two different approaches are addressed in this study. The first one consists in the processing of the experimental data upstream of the identification stage, by filtering them through a diffuse approximation algorithm. The second approach focuses on the development of an inverse identification strategy from static tests. This method takes into account the uncertainty of the measurements from the beginning of the formulation and is based on the modified constitutive relation error principles. It involves the resolution of non standard finite element problems using specific resolution methods. The study pointed out the robustness of the proposed method towards measurement errors, in particular when compared to the finite element model updating method.