[Truncated abstract] The fracture of brittle materials in uniaxial compression is a complex process with the development of cracks generated from initial defects. The fracture mechanism and pattern of crack growth can be altered considerably by the presence of a free surface. In proximity of a free surface, initially stable cracks that require an increase in the load to maintain the crack growth can become unstable such that the crack growth maintains itself without requiring further increase in the load. This leads to a sudden relief of accumulated energy and, in some cases, to catastrophic failures. In the cases of rock and rock mass fracturing, this mechanism manifests itself as skin rockbursts and borehole breakouts or as various non-catastrophic forms of failure, e.g. spalling. Hence, the study of crack-boundary interaction is important in further understanding of such failures especially for the purpose of applications to resource engineering. Two major factors control the effect of the free boundary: the distance from the crack and the boundary shape. Both these factors as well as the effect of the initial defect and the material structure are investigated in this thesis. Three types of boundary shapes - rectilinear, convex and concave - are considered. Two types of initial defects - a circular pore and inclined shear cracks are investigated in homogeneous casting resin, microheterogeneous cement mixes and specially fabricated granulate material. The preexisting defects are artificially introduced in the physical model by the method of inclusion and are found to successfully replicate the feature of pre-existing defects in terms of load-deformation response to the applied external load. It is observed that the possibility of crack growth and the onset of unstable crack growth are affected by the type of initial defect, inclination of the initial crack, the boundary shape and the location of the initial defect with respect to the boundary. The initial defects are located at either the centre or edge of the sample. The stresses required for the wing crack initiation and the onset of unstable crack growth is highest for the initial cracks inclined at 35° to the compression axis, lowest at 45° and subsequently increases towards 60° for all the boundary shapes and crack locations. In the case of convex boundary, the stress of wing crack initiation and the stress of unstable crack growth are lower than for the case of rectilinear and concave boundary for all the crack inclinations and crack locations. The crack growth from a pre-existing crack in a sample with concave boundary is stable, requiring stress increase for each increment of crack growth. The stress of unstable crack growth for the crack situated at the edge of the boundary is lower than the crack located at the centre of the sample for all the crack inclinations and boundary shapes.

Dans cette thèse, nous étudions principalement les applications semi-conformes et leur influence sur la résolution de certaines équations géométriques importantes comme celle d’un soliton de Ricci et celle d’une application biharmonique. Dans la première partie, nous appliquons un ansatz qui permet de construire des applications semi-conformes à partir d’une équation différentielle en une fonction de deux variables. Nous caractérisons les solutions réelles-analytiques. Parmi les solutions explicites obtenues, nous trouvons le premier exemple d’une application semi-conforme non-harmonique définie entièrement sur R3 à valeurs dans le plan complexe. Dans la deuxième partie, nous étudions les solitons de Ricci. Nous nous intéressons aux solitons de dimension 3, où ils peuvent être décrits, au moins localement, en terme d’une application semi-conforme. Nous développons une nouvelle méthode de construction de ces solitons à partir des transformations biconformes, particulièrement adaptées à l’étude de l’unicité de la structure. Finalement, nous introduisons une nouvelle notion de morphisme harmonique généralisé qui, comme son nom l’indique, contient les morphismes harmoniques comme un cas particulier. Cette classe d’applications a une importance dans la théorie d’applications biharmoniques. Les morphismes harmoniques généralisés ont une caractérisation nette qui permet de donner plusieurs exemples et méthodes de construction d’applications biharmoniques non-harmonique. / In this work, we primarily study semiconformal mappings and their influence in the resolution of important geometric equations, such as those for a Ricci soliton and those for a biharmonic maps. In the first part of this thesis, we exploit an ansatz for the construction of semi-conformal mappings from a differential equation in a function of two variables. We characterize real-analytic solutions.Among the resulting explicit solutions, we find the first known example of an entire semi-conformal mapping into the plane which is not harmonic. In the second part, we study Ricci solitons.We are particularly interested in 3-dimensional Ricci solitons, as they can be described at least locally, in terms of a semi-conformal map. We develop a construction method of solitons from biconformal deformations, particularly adapted to the study of the structure unicity. Finally, we introduce a new notion of generalized harmonic morphism, which, as the name suggests, contain the harmonic morphisms as a special case. These mappings have an elegant characterization which enables the construction of explicit examples, as well as impacting on the theory of biharmonic mappings.

La mesure des déformations de la microstructure est importante pour l’étude des propriétés et le contrôle des structures. Nous proposons deux approches nouvelles de caractérisation de déformations nanométriques. Elles utilisent des nanoparticules (NPs) d’or déposées à la surface des matériaux. Dans la première approche, les réseaux de NPs sont déposés par lithographie électronique. Lors d’essais de traction uniaxiale dans un microscope électronique à balayage les images prises à de chargements successifs permettent de suivre le déplacement de NPs qui jouent le rôle de nanojauges. L’analyse des champs cinématiques obtenus à partir des images MEB révèle des phénomènes de plasticité au sein de la microstructure et les hétérogénéités de déformations. La méthode a été appliquée aux aciers inoxydables austénitique et duplex austéno-ferritique. Elle a été couplée à la technique de diffraction des électrons rétrodiffusés. Les mécanismes de déformations locaux ont été mis en évidence. Dans la seconde approche, nous essayons de tirer parti des propriétés optiques de NPs afin de suivre l’évolution de déformations à la surface des matériaux. Les NPs supportent un plasmon localisé de surface dont la résonance est fonction de la taille, de la forme des NPs ou de l’indice optique du milieu environnant. Sa position spectrale dépend aussi de la distance inter-NPs. Notre étude a été limitée à des polymères. Un dispositif permettant de réaliser les mesures d’extinctions au cours de la traction a été développé. Les premiers essais constituent la preuve expérimentale de ce concept / The strain measurement at the microstructure is important for the properties study and structure control. We propose two new approaches of strain characterizations at nanoscale. They are based on the use of gold nanoparticles (NPs) arrays deposited on the surface of materials.In the first approach, arrays of NPs are deposited by the electron beam lithography technique. During in situ tensile test inside a scanning electron microscope, the images of the array are progressively recorded. The treatment of these images gives access to 2D strain tensor components and NPs played the role of nanogauges. The strains at components of the microstructure and the heterogeneities of plastic deformations are evidenced. This method was coupled to the electron backscatter diffraction technique. The local deformation mechanisms can then be highlighted. In the second approach, we try to take advantage of optical properties of gold NPs to track the strain evolutions at the surface of materials. Gold NPs support localized surface plasmon that resonance is function of size and shape of NPs or of the surrounding medium. In addition, plasmon resonance also depends to NPs separation. We therefore sought to determine whether the displacements of NPs during tensile test may be monitored optically. The study was limited to the case of polymers. An experimental set up was developed to carry extinction measurement during a tensile test. These first tests constitute experimental proof of this concept. The spectral variations were analyzed to determine the performance of the optical strain-sensor proposed

L’évolution du champ de localisation des déformations plastiques des métaux ductiles a été suivie par interférométrie de granularité laser (ESPI) au cours d’une sollicitation de traction uniaxiale. Il a été montré que le modèle mathématique utilisé, croisement de deux bandes rectilignes, décrit bien l’évolution du champ de vitesse de déformation depuis la striction diffuse jusqu'à rupture. Les caractéristiques physiques de la localisation, telles que la largeur des bandes, leur orientation et leur vitesse de déformation maximale ont été identifiées quantitativement. Leur évolution a été suivie et analysée sous plusieurs facteurs d’influence, qui sont à la fois microscopiques, tels que la taille de grains et la structure cristalline, et macroscopiques, comme la géométrie de l’éprouvette et la direction de son prélèvement par rapport à la direction de laminage, et la vitesse de traction. Il a été trouvé que les bandes de localisation rétrécissent au cours de la striction et leur orientation évolue également. Ces évolutions, le mode de striction et le moment de transition entre la striction diffuse et localisée sont influencés différemment par ces facteurs / The evolution of the plastic strain localization field of ductile metals was followed by electronic speckle pattern interferometry (ESPI) during a uniaxial tensile test. It was shown that the mathematical model, a system of two crossing straight bands, describes accurately the evolution of the strain rate field from diffuse necking up to rupture. The physical characteristics of the localization, such as the width of the bands, their orientations and maximum strain rates were identified quantitatively. Their evolutions were followed and analyzed from several influencing factors, which are both microscopic, such as grain size and crystal structure, and macroscopic, like the geometry of the specimen and the direction in which the specimen were cut with respect to the rolling direction, and the pulling speed. It has been found that the bands narrow down during the necking process and their orientations were also changing. These evolutions, the necking mode and the transition between the diffuse and localized necking are influenced differently by these factors

PhD by portfolio. Research aim: To investigate if topology optimisation can be used for the development of mechanical structures exposed to large (non-linear) deformations. Research objectives: 1. Analyse and critically evaluate the potential for using state of the art commercially available Finite Element software (and associated topology optimisation algorithms) for topology optimisation of structures exposed to large-deformations. 2. Based on 1 (where feasible) suggest, develop and critically appraise opportunities, methodologies and tools for enhancing the accuracy and precision of current state of the art topology optimisation algorithms for non-linear applications. 3. Based on the outcomes of 1 and 2 define / refine and integrate a topology optimisation algorithm / methodology with enhanced levels of accuracy for structures exposed to large (non-linear) deformations. 4. Critically analyse and assess the outcomes of the tool developed in 3 to competing algorithms and “sound engineering judgement” using case-studies and objectively evaluate the potential for further development/refinement of the proposed algorithm/methodology.

Joints are critical parts of timber structures, transmitting static and dynamic forces between structural members. The ultimate behavior of a loaded building depends strongly on the structural configuration and the capacity of the joints. The collapse of a whole building or less extensive accidents that may occur is usually starting as a local failure inside or in the vicinity of a joint. Such serious failures have recently occurred in our Nordic countries. Especially the collapse of two large glued laminated timber structures clearly indicates the need of an improved joint design. The trend toward larger and more complex structures even further increases the importance of a safer design of the joints. An aim of this partly experimental and partly numerically based thesis has been to investigate if steel-to-timber dowel joints are affected by moisture-induced stresses. The experimental results showed that the load-bearing capacity of the joints is reduced by such a moisture influence. Most of the decrease in load-bearing capacity observed was found in joints initially exposed to restrained shrinkage deformations caused by the presence of dowel fasteners in the joint area. The load-bearing capacity was, however, also found to decrease in joints exposed to an initial decrease in moisture without any fasteners present in the specimens during storage before loading. An explanation of this unexpected behavior is that moisture gradients cause tensile stresses. It is shown by numerical simulations that the moisture-induced stresses are so large that they may have a considerable influence on the joint behavior. Use of contact-free measurement methods, used in some of the experimental tests, was in many ways found to be superior to traditional measurement techniques, but was also found to be a valuable complement to the numerical analysis performed. From numerical results obtained in combination with results from contact-free measurements several observations of considerable interest were made. For dowel-type joints loaded in tension parallel to the grain a strongly non-uniform strain distribution was found in the joint area. It was further observed that the shear and tensile strains were concentrated close to the fasteners in the joint area. These concentrations will influence the failure mode of the joint. A general observation was that the larger sized joints failed in a brittle manner. Keywords: constraint stresses, contact-free measurement, dowel-type joints, humidity variations, moisture-induced deformations, timber structures

Une déformation isomonodromique d'une sphère épointée est une famille de connexions logarithmiques plates sur cette dernière ayant toutes, à conjugaison globale près, la même représentation de monodromie. Ces objets sont paramétrés par les solutions d'une certaine famille d'équations aux dérivées partielles, les systèmes de Garnier, qui sont équivalents dans le cas de la sphère à quatre trous aux équations de Painlevé VI. L'objet des travaux présentés ici est de construire de nouvelles solutions algébriques des ces systèmes dans le cas de la sphère à cinq trous. Dans une première partie, nous classifions les déformations isomonodromiques algébriques obtenues par restriction aux droites d'une connexion logarithmique plate sur le plan projectif complexe dont le lieu polaire est une courbe quintique. On obtient ainsi deux nouvelles familles de solutions algébriques du système de Garnier associé. Dans une deuxième partie, nous exploitons le fait qu'une déformation isomonodromique algébrique correspond à une orbite finie sous l'action du groupe modulaire sur la variété des caractères de la sphère à cinq trous pour obtenir de nouveaux exemples de telles orbites. Nous employons pour ce faire la convolution intermédiaire sur les représentations de groupes libres développée par Katz Enfin, nous décrivons une généralisation partielle de ce procédé au cas d'un tore complexe à deux trous. / We call isomonodromic deformation any family of logarithmic flat connections over a punctured sphere having the same monodromy representation up to global conjugacy. These objects are parametrised by the solutions of a particular family of partial differential equations called Garnier systems, which are equivalent to the Painlevé VI equations in the four punctured case. The purpose of this thesis is to construct new algebraic solutions of these systems in the five punctured case. First, we give a classification of algebraic isomonodromic deformations obtained by restricting to lines some logarithmic flat connection over the complex projective plane whose singular locus is a quintic curve. We obtain two new families of algebraic solutions of the associated Garnier system. In a second part, we use the fact that any algebraic isomonodromic deformation corresponds to a finite orbit under the mapping class group action on the character variety of the five punctured sphere to obtain new examples of such orbits. We do this by using Katz's middle convolution on representations of free groups. Finally, we give a partial generalisation of this procedure in the case of a twice punctured complex torus.

Ce travail de thèse est consacré à l’étude des écoulements thermogravitaires et thermocapillaires induits par chauffage laser dans des couches liquides. Le chauffage d’un système à deux liquides donne naissance à deux effets thermiques. Le premier est dû à la variation de la masse volumique avec la température et le second à la variation de la tension interfaciale avec la température. Nous avons dans un premier temps étudié ces deux contributions séparément. En confrontant expériences, théorie et simulations numériques nous avons démontré que la morphologie des écoulements thermogravitaires dépend de l’épaisseur de la couche liquide ainsi que de la largeur du champ de température. Ensuite nous nous sommes intéressés à l’étude théorique et numérique de l’effet thermocapillaire. Cette étude a révélé qu’il est possible d’étudier les écoulements à partir des déformations d’interface induites par ces mêmes écoulements. Nous avons montré qu’il existe deux régimes de déformations en fonction du rapport de hauteurs et du signe de la variation de la tension interfaciale avec la température. Enfin, nous nous sommes intéressés à la compétition entre ces deux mécanismes. L’analyse des déformations d’interface et la comparaison avec un modèle à une dimension a montré qu’en fonction du rapport de hauteurs des couches liquides nous avons une transition d’un régime d’écoulements thermocapillaires vers une régime d’écoulements thermogravitaires. De plus, nous avons montré expérimentalement et numériquement qu’il est possible d’induire une instabilité d’origine thermogravitaire conduisant à la formation d’un pont liquide. / This thesis work is dedicated to thermocapillary and thermogravitary flows induced bylaser-heating in liquid layers. The laser-heating of a two fluids system induces two thermaleffects. The first effect come from the variation of the density with temperature andthe second one is due to the variation of the interfacial tension with the temperature.In a first part, we study separately these two mechanism. With a comparison betweenexperiments, theory and numerical simulations we demonstrated that the morphology ofthe flows depends on the thickness of the layer and the width of the temperature field.Then, we studied numerically and theoretically the thermocapillary effect. That revealedit is possible to understand the flows from the interface deformations. We highligth theseare two deformation regimes depending the thickness ratio and the sign of the interfacialtension gradient. Finally, we studied the competition between the two mechanism and theexperiments revealed a transition between two flow regimes. The comparison of these resultsand a theoritical model showed there is a transition from a thermocapillary regime to athermogravitary regime. In addition, we showed the possibility to induce an instibility bythermogravitary effect which can lead to the formation of a liquid bridge.

Orientador: Marco Lúcio Bittencourt / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-22T09:29:00Z (GMT). No. of bitstreams: 1 Suzuki_JorgeLuis_M.pdf: 2667128 bytes, checksum: 86588ab0b8799da0e2c3f0242102caea (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta uma implementação em ambiente C++ da teoria do Dano em Meio Contínuo para hiperelasticidade sob regime compressível e quasi-incompressível. Para o caso quasi-incompressível, uma formulação mista (u=p) é tratada com um procedimento de projeção local da pressão hidrostática. O dano é um escalar que dependente da máxima deformação atingida. Para a validação dos métodos implementados, são realizados estudos de convergência através da imposição de soluções analíticas, variando a ordem de interpolação e o número de elementos. Também é analisado o comportamento da tensão através de ciclos de carregamento, para a observação da perda de rigidez progressiva sob os efeitos de dano. A formulação implementada contorna o problema de travamento de malha, sendo que de maneira geral, solução é melhor aproximada com o aumento do grau polinomial combinado com o aumento do número de elementos / Abstract: The objective of this work is the application of the high-order hpFEM to the analysis of hyperelastic materials coupled to isotropic damage. A mixed (u=p) formulation with a pressure projection procedure is used in conjunction with the hpFEM to overcome the volumetric locking. The isotropic damage model introduces a scalar variable that evolves coupled with the maximum attained strain. It is based on the equivalent stress concept, by applying a reduction factor over the stress tensor. A cyclic loading test was performed to reproduce the Mullins effect. Convergence analyses were made for a compressible and a quasi-incompressible material imposing analytical solutions. Both materials presented a spectral convergence rate for the p refinement using smooth solutions. In the case of quasi-incompressibility, the material showed locking-free characteristics, but the approximation errors were higher compared to the compressible case / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

The content of this master´s thesis is a geodetic measuring of movements and deformations of skeleton and underwork of „Gagarin“ railway bridge during the seventh period and processing of the data got. This was done by comparison of the movements according to the fifth and sixth period. The work includes also the calibration of appliance used. The results involve figures of the movements with their graphic interpretation and calibration sheets of the appliance.