Le béton est un des matériaux de construction les plus répandus dans le monde. Cependant, dans de nombreux secteurs industriels, il est de plus en plus courant d'étudier les marges de sécurité d'un ouvrage vis à vis de sollicitations. Il devient important de prédire le mode de ruine de l'ouvrage. De nombreux travaux ont déjà été réalisés dans le monde sur ce sujet, conduisant à des modèles opérationnels dans des codes de calcul par éléments finis. Néanmoins, des difficultés subsistent, liées principalement à la fissuration du béton. Ces difficultés se traduisent par des problèmes ouverts concernant la localisation, l'initiation et la propagation des fissures. Le travail de thèse explore deux possibilités d'amélioration des méthodes de simulation numérique de propagation des fissures. La première possibilité d'amélioration concerne l'utilisation de la méthode des éléments finis étendus, XFEM (eXtended Finite Element Method). Une modélisation du comportement mécanique de fissure est introduite et conduit à une description de la propagation de fissure d'un élément à un autre. La deuxième possibilité est basée sur la mécanique de l'endommagement. Dans le cadre de la modélisation de l'endommagement de type standard généralisé, le phénomène de localisation a été étudié numériquement pour des comportements divers : endommagement visqueux ou fragile. Ces comportements sont décrits dans le même esprit que les lois de la visco-élasticité ou de la visco-plasticité ou de la plasticité classiques, à partir d'une interprétation thermodynamique générale. En particulier, les lois à gradient de l'endommagement sont aussi considérées en liaison avec des résultats récents de la littérature. Il est bien connu qu'un modèle à gradient permet d'interpréter les effets d'échelle des structures sous chargement mécanique. Il joue aussi un rôle intéressant dans les effets de localisation de la déformation.

Lors de l'étude du béton armé, la liaison acier béton est un élément "clé" dans le comportement du composite car celle-ci permet le transfert des efforts entre les armatures et le béton. La compréhension du phénomène, ainsi que sa prise en compte dans l'analyse numérique des structures en " béton armé ", ont été le principal objet de ce travail de recherche. Ainsi, on a formulé un modèle de comportement non linéaire thermodynamique de la liaison, écrit en termes de contrainte-déformation, supporté par un élément spécial d'interface 2D d'épaisseur nulle. Ensuite, on a effectué une identification des paramètres ainsi que quelques exemples d'analyse. Finalement, on a montré les bases d'un Elément Fini Enrichi pour le béton armé englobant les trois composants : béton - liaison - acier.

Dowel-type steel to timber connections are commonly used in timber structure. The load carrying capacity and the stress distribution within the connection area are complicated and the failure behavior of a connection depends on many parameters. The main purpose of this thesis was to verify, using the data obtained from previous experiments, the conventional design method of European Code 5(EC5) (hand calculation) for dowel type joints subjected to pure bending moment and other alternative design methods based on the finite element method (FEM) including the use of the mean stress approach and the extended finite element method (XFEM). Finite element models were created in the software ABAQUS. The models were then used to predict the load bearing capacity and compare this to the experimental results. In addition parametric studies were performed with modifications of material properties and other parameters. The closest prediction in relation to the test results was obtained using XFEM where the predicted capacity was 3.82% larger than the experimental result. An extension of the mean stress method going from a 2D-formulation to a 3D-formulation was verified as well. A general conclusion drawn from this work is that the numerical modelling approaches used should also be suitable for application to complex connections and situations involving other loading situations than pure tension.

This work describes the implementation of the eXtended Finite Element Method (XFEM) in the Abaqus software package. A user-defined element was developed containing the analytical functions relating to homogeneous and interface fracture mechanics. The long-term goal of such work is to increase the ability to analyze fractures and other imperfections in multimaterial systems containing large elastic mismatches, such as flexible electronics. A review of XFEM-related literature is presented, as well as an overview of fracture mechanics for both homogeneous and interface systems. The theoretical basis of the XFEM is then covered, including the concepts of Partition of Unity and stress intensity factor evaluation. Finally, numerical results of the implementation are compared to several benchmark cases, along with conclusions and suggestions for future work.

Cortical bone tissue - one of the most intriguing materials found in nature - demonstrate some fascinating behaviours that have attracted great attention of many researchers from all over the world. In contrast to engineering materials, bone has its unique characters: it is a material that has both sufficient stiffness and toughness to provide physical support and protection to internal organs and yet adaptively balanced for its weight and functional requirements. Its structure and mechanical properties are of great importance to the physiological functioning of the body. Still, our understanding on the mechanical deformation processes of cortical bone tissue is rather limited. Penetration into a bone tissue is an intrinsic part of many clinical procedures, such as orthopaedic surgery, bone implant and repair operations. The success of bone-cutting surgery depends largely on precision of the operation and the extent of damage it causes to the surrounding tissues. The anisotropic behaviour of cortical bone acts as a distinctive protective mechanism and increases the difficulty during cutting process. A comprehensive understanding of deformation and damage mechanisms during the cutting process is necessary for improving the operational accuracy and postoperative recovery of patients. However, the current literature on experimental results provides limited information about processes in the vicinity of the cutting tool-bone interaction zone; while; numerical models cannot fully describe the material anisotropy and the effect of damage mechanisms of cortical bone tissue. In addition, a conventional finite-element scheme faces numerical challenges due to large deformation and highly localised distortion in the process zone. This PhD project is aimed at bridging the gap in current lack of understanding on cutting-induced deformation and fracture processes in the cortical bone tissue through experimental and numerical approaches. A number of experimental studies were accomplished to characterise the mechanical behaviour of bovine cortical bone tissue and to analyse deformation and damage mechanisms associated with the cutting process II along different bone axes in four anatomic cortices, namely, anterior, posterior, medial and lateral. These experiments included: (1) a Vickers hardness test to provide initial assessments on deformation and damage processes in the cortical bone tissue under a concentrated compressive load; (2) uniaxial tension and compression tests, performed to understand the effect of orientation and local variability of microstructure constituents on the macroscopic material properties of cortical bone; (3) fracture toughness tests, aimed at elucidating the anisotropic character of fracture toughness of cortical bone and its various fracture toughness mechanisms in relation to different orientations; (4) penetration tests, conducted to evaluate and validate mechanisms involved in bone cutting as well as orientation associated anisotropic deformation and damage processes at various different cortex positions. Information obtained in these experimental studies was used to assist the development of advanced finite-element models: (1) the effective homogenised XFEM models developed in conjunction with three-point bending test to represent a macroscopically, anisotropic elasticplastic fracture behaviour of cortical bone tissue; (2) three microstructured XFEM models to further investigate the effect of the randomly distributed microstructural constituents on the local fracture process and the variability of fracture toughness of cortical bone; (3) a novel finite-element modelling approach encompassing both conventional and SPH elements, incorporating anisotropic elastic-plastic material properties and progressive damage criteria to simulate large deformation and damage processes of cortical bone under penetration. The established models can adequately and accurately reflect large deformations and damage processes during the penetration in bone cutting. The results of this study made valuable contributions to our existing understanding of the mechanics of cortical bone tissue and most importantly to the understanding of its mechanical behaviours during the cutting process.

Ces travaux se sont attachés au développement, à l’implémentation et à la validation d’une stratégie numérique pour la simulation de l’évolution d’un endommagement localisé susceptible de conduire à l’apparition, puis à la propagation de fissures dans une structure complexe, incompressible. Nous avons abordé cet objectif général en procédant par étapes.Dans un premier temps, nous avons développé une méthodologie numérique innovante pour la propagation de fissures dans le cadre de la mécanique de la rupture fragile. Cette méthodologie a deux caractéristiques importantes : incluant l’enrichissement Heaviside de la méthode XFEM dans le cadre de modélisation Arlequin, cette méthodologie permet de ne pas remailler la structure initiale, au cours de la propagation de la fissure. Attachant un patch Arlequin local en fond de la fissure qui se propage, elle permet d’approcher, avec la précision nécessaire, le comportement local des champs mécaniques. Cette méthodologie a été implémentée et testée numériquement. Dans un deuxième temps, nous avons étendu cette méthodologie pour la prise en compte de l’endommagement par fatigue. Dans l’approche développée, l’initiation et la propagation de fissures sont pilotées par l’évolution du champ d’endommagement. Un modèle heuristique représentatif, fournissant les incréments de propagation d’une fissure à partir des champs d’endommagement et de contraintes au voisinage de sa pointe, est proposé. En utilisant des modèles physiques représentatifs des difficultés liées à la problématique d’initiation et de propagation de fissures, sous l’effet d’un endommagement par fatigue, nous avons montré, à travers des essais numériques, une faisabilité globale de notre approche. Dans un troisième temps, nous nous sommes intéressés à la prise en compte de la contrainte d’incompressibilité dans une modélisation Arlequin. L’intégration de cette contrainte pose pour la formulation Arlequin continue et/ou discrète des questions spécifiques : comment gérer la double contrainte dans la zone de couplage en continu et en discret ?, comment traiter les éléments partiellement incompressibles ? Des réponses sont données et étayées théoriquement et/ou numériquement. Enfin, nous avons proposé un ensemble de procédures pratiques, permettant d’évaluer, de manière générale et performante, une intersection de maillages tridimensionnels. Ces développements, nécessaires à la mise en œuvre opérationnelle du cadre Arlequin dans des codes industriels, sont validés par des résultats de calculs Arlequin 3D. / Résumé en anglais non disponible.

In this work the compression behavior of masonry was investigated. After a detailed review of code approaches and different research works, a new formula was suggested to describe the compression strength of masonry, based on the mechanical and geometrical properties of its components, when deformation properties of units are larger than the ones of mortar. Later on, a new model, Extended Drucker-Prager Cap Yielding Function, is suggested to describe the three axial compression stress state of mortar in masonry in case deformation properties of mortar are larger than the ones of mortar, and to describe the three axial compression stress state of brick in the other case. This includes defining its parameters based on test diagrams of the mortar material, implementing the model in the numerical software ANSYS, and the numerical results are evaluated for simple cube example. The controlling equations of creep based on the visco-elastic creep theory are presented in the general case of three axial creep under three axial loading conditions. The special case of three axial creep under axial loading is also presented. The “transversal creep” relevant for the compression strength of masonry was discussed and numerical examples have been added to show the effect of changed time-dependent Poisson’s ratio. In another chapter, many examples are presented showing the application of the suggested material models and discontinuous numerical method named eXtended finite element method. Conclusions and recommendations are given in the last chapter.

En esta tesis se aborda primeramente el estudio de las grietas tridimensionales partiendo de las premisas de la MFEL y considerando la importancia de los términos de segundo orden del desarrollo de Williams para la correcta descripción del campo de tensiones en problemas tridimensionales. El estudio de las grietas tridimensionales se realiza mediante una extensión de los resultados bidimensionales en los que se suponen conceptos que en un estado tridimensional no pueden ser admitidos directamente. En la tesis se hace un análisis del efecto de la triaxialidad sobre estos resultados, poniéndose de manifiesto que no basta con aceptar los términos singulares, sino que al menos se deben incluir los términos constantes del desarrollo de Williams. El segundo punto lo constituye una introducción al XFEM para grietas tridimensionales, incluyendo algunos de los avances desarrollados en los últimos años. A continuación se aborda el cálculo de los FIT en grietas genéricas tridimensionales con curvatura. Para ello se proponen mejoras en la formulación de las integrales de dominio y se realizan verificaciones numéricas y estudios de convergencia. El cálculo de los FIT en grietas que presentan curvatura es el objetivo principal de la tesis. La formulación de la integral de interacción ha sido modificada para mejorar su eficacia. Además se ha introducido el efecto de la curvatura en los gradientes, para lo cual se han usado conceptos de geometría diferencial aprovechando la formulación mediante la LS. Esta propuesta mejora apreciablemente los resultados obtenidos mediante las integrales de dominio. El último punto es el estudio y propuesta de un enriquecimiento para mejorar la descripción del estado existente en las cercanías de la singularidad de esquina ---o de borde libre---. Además de una revisión bibliográfica del problema de esta singularidad, se ha introducido parte del efecto local de esta singularidad en la formulación de XFEM mediante una propuesta de enriq / González Albuixech, VF. (2012). Estudio de las singularidades de frente de grieta y de esquina en grietas tridimensionales mediante el método de los elementos finitos extendido [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19116 / Palancia

El Método de los Elementos Finitos (MEF) se ha afianzado durante las últimas décadas como una de las técnicas numéricas más utilizadas para resolver una gran variedad de problemas en diferentes áreas de la ingeniería, como por ejemplo, el análisis estructural, análisis térmicos, de fluidos, procesos de fabricación, etc. Una de las aplicaciones donde el método resulta de mayor interés es en el análisis de problemas propios de la Mecánica de la Fractura, facilitando el estudio y evaluación de la integridad estructural de componentes mecánicos, la fiabilidad, y la detección y control de grietas. Recientemente, el desarrollo de nuevas técnicas como el Método Extendido de los Elementos Finitos (XFEM) ha permitido aumentar aún más el potencial del MEF. Dichas técnicas mejoran la descripción de problemas con singularidades, con discontinuidades, etc., mediante la adición de funciones especiales que enriquecen el espacio de la aproximación convencional de elementos finitos. Sin embargo, siempre que se aproxima un problema mediante técnicas numéricas, la solución obtenida presenta discrepancias con respecto al sistema que representa. En las técnicas basadas en la representación discreta del dominio mediante elementos finitos (MEF, XFEM, ...) interesa controlar el denominado error de discretización. En la literatura se pueden encontrar numerosas referencias a técnicas que permiten cuantificar el error en formulaciones convencionales de elementos finitos. No obstante, por ser el XFEM un método relativamente reciente, aún no se han desarrollado suficientemente las técnicas de estimación del error para aproximaciones enriquecidas de elementos finitos. El objetivo de esta Tesis es cuantificar el error de discretización cuando se utilizan aproximaciones enriquecidas del tipo XFEM para representar problemas propios de la Mecánica de la Fractura Elástico Lineal (MFEL), como es el caso del modelado de una grieta. / González Estrada, OA. (2010). Estimación y acotación del error de discretización en el modelado de grietas mediante el método extendido de los elementos finitos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/7203 / Palancia

Different rock formations may appear within the same mass, or even within the same formation there may exist layers of different materials, creating interfaces between layers (an interface may be defined, in more general terms, as a frictional contact that separates two similar or dissimilar materials). Currently, there is no well-established experimental work that investigates the influence of frictional interfaces, interface orientation and flaw geometries on crack behavior (i.e. initiation, propagation and coalescence) in brittle specimens under compressive loading. A series of experiments on homogeneous gypsum specimens, used as a rock-model material, containing two pre-existing open flaws and a frictional interface has been performed under uniaxial compression. The experiments investigate how cracks interact with interfaces and how different variables (i.e. flaw geometry, interface inclination angle and interface roughness) affect crack behavior in homogeneous materials separated by an interface. The specimens are 203.2mm high, 101.6mm wide, and 25.4mm thick. The two flaws, with 0.1mm aperture and 12.7mm length (2a), are created through the thickness of the specimen. The spacing (S) between flaws, continuity (C), and inclination angle, measured from the horizontal, (β) define the geometry of the flaws. Three flaw geometries are tested: S=0, C= -2a= -12.7mm, β= 30° (i.e. a left-stepping geometry); S= 2a= 12.7 mm, C=a=6.35 mm, β= 30° (i.e. an overlapping geometry) and S= 3a= 19.05mm, C=0, β= 30° (i.e. a right-stepping geometry). Smooth and rough unbonded interfaces are created by casting the specimen in two parts. The first half of the specimen is cast against a PVC block with an inclined face (i.e. 90°, 80° or 70°) with respect to the vertical axis of the specimen. The second half is then cast against the first one. Sandpaper may be attached to the PVC block to provide different roughness to the interface; a debonding agent applied to the interface ensures a cohesionless contact. In the experiments, digital image correlation (DIC) is used to monitor crack propagation on the specimen surface. The experiments indicate that the interface itself is an important contributor to new cracks and its presence in the specimens reduce crack initiation stress. Furthermore, the increase in roughness and inclination of the interface (i.e. from horizontal to 70° from the vertical) causes crack initiation stress to decrease. It was also observed that the angle between the incident crack plane and the interface affects whether an incident crack will penetrate an interface or be arrested: Tensile cracks that meet the interface at 30° to 60° angle get arrested, while those at or above 70° cross the interface with an offset of 0 – 1.2 mm. While shear cracks that meet the interface at 20° to 63° angles get arrested at the interface, while those at or above 70° cross the interface with an offset in the range of 0 – 1.76 mm. Another relevant finding is the fact that changes in interface roughness or inclination angle did not affect the angles at which cracks initiate or reinitiate at the interface.<div>A numerical study was conducted using the Extended Finite Element Method (XFEM) capability in ABAQUS, to further investigate the fracture behavior observed in the experiments and, more specifically, the influence of the different types of interfaces. An extensive investigation of the stress fields around the tips of the flaws and of the new cracks, as well as along the interface in the specimens, was conducted to determine the relationship between stresses and crack initiation and propagation (i.e. type and direction of cracks). The stress-based approach yields predictions of tensile and shear cracks location and initiation direction that are in good agreement with experimental results. The numerical investigation indicated that rougher horizontal interfaces induced slightly higher tensile stresses around the interior and exterior flaw tips than smoother interfaces, which may explain why tensile cracks at these locations initiated earlier in specimens with a rough interface. Moreover, inclined interfaces induced higher tensile stresses around the interior and exterior flaw tips than horizontal interfaces, which may justify that, in the experiments, inclined interfaces promoted crack initiation earlier than horizontal interfaces.</div>