A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall-Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or materials that contain unequal grain size distributions. These deficiencies can be overcome by incorporating both grain size and orientation characteristics into crystal plasticity theory. Homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for high purity α-titanium are recovered through orientation imaging microscopy coupled with the chord length distribution. A comparison between the new method and the traditional viscoplastic Taylor approach is made by evaluating yield surface plots.

No description available.

[pt] Atualmente, o escoamento de fluidos não Newtonianos está presente em diversos processos industriais e também no dia- a-dia de todos. Na presente dissertação, inicialmente, é apresentada uma nova equação constitutiva capaz de modelar fluidos que possuam tanto elasticidade como viscoplasticidade, sendo este novo modelo definido como elasto-viscoplástico. Para a melhor compreensão do modelo, anteriormente, é realizada, uma breve revisão dos fluidos não Newtonianos, com maior ênfase para o modelo viscoplástico SMD e o modelo viscoelástico de Oldroyd-B, que possuem grande influência no novo modelo constitutivo. Em seguida é apresentada uma nova metodologia de adimensionalização levando-se em conta apenas os parâmetros reológicos neste processo, garantindo a independência das equações com relação a vazão. Por fim, é realizada a simulação deste novo modelo em um escoamento com uma expansão e contração abrupta. Nesta simulação, é analisado o comportamento do fluido ao passar por esta cavidade com relação às principais variáveis da equação constitutiva. A simulação foi realizada pelo método dos elementos finitos e os resultados mostram a influência do número de Deborah reológico, da velocidade, do expoente power-law e da razão entre os tempos de retardo e de relaxamento, na perda de carga e no padrão de escoamento. / [en] Currently, the flow of non-Newtonian fluids is present in many industrial processes and also in day-to-day of all. In this dissertation, initially it is exposed a new constitutive equation capable of modeling fluids that present as much elasticity as viscoplasticity, and this new model is called as Elasto-viscoplastic. For better understanding of this model, previously, a brief review of non- Newtonian fluids is done, with a focus on the SMD viscoplastic model and on the Oldroyd-B viscoelastic model, both which have a great influence in this new constitution model.Afterward, a new methodology of non- dimensionalization is presented, taking into account only the rheological parameters in this process and ensuring the independence of equations with respect to flow. Finally, the simulation of this new model is performed in a flow within a abrupt expansioncontraction geometry. In this simulation, it is studied the behavior of the fluid through this cavity with respect to key variables of the constitutive equation. The simulation was carried out by the finite element method and, by the analysis of the results, it is shown the influence of the rheological Deborah, flow speed, the power-law exponent and the ratio of the time of retardation and relaxation on the head loss and the flow pattern.

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

A method is presented for adapting the classical Bishop-Hill model to the requirements of elastic/yield-limited design in metals of arbitrary crystallographic texture. The proposed Hybrid Bishop-Hill (HBH) model, which will be applied to ductile FCC metals, retains the `stress corners' of the polyhedral Bishop-Hill yield surface. However, it replaces the `maximum work criterion' with a criterion that minimizes the Euclidean distance between the applicable local corner stress state and the macroscopic stress state. This compromise leads to a model that is much more accessible to yield-limited design problems. Demonstration of performance for the HBH model is presented for an extensive database for oxygen free electronic (OFE) copper. The study also implements the HBH model to the polycrystalline yield surface via standard finite element analysis (FEA) tools to carry out microstructure-sensitive design. Anisotropic elastic properties are incorporated into the FEA software, as defined by the sample texture. The derived local stress tensor is assessed using the HBH approach to determine a safety factor relating to the distance from the yield surface, and thereby highlighting vulnerable spots in the component and obtaining a quantitative ranking for suitability of the given design. By following standard inverse design techniques, an ideal microstructure (meaning texture in this context) may be arrived at. The design problems considered is a hole-in-plate configuration of sheets loaded in uniaxial tension and simple compliant mechanisms. The further improvement of HBH model is discussed by introducing geometrically necessary dislocation (GND) densities in addition to the crystal orientations procedure in standard microstructure-based method. The correlations between crystal orientations and GND densities are studied. The shape of the yield surface most influenced by the texture of the material, while the volume of the envelope scales in accordance with the GND density. However, correlations between crystal orientation and GND content modify the yield surface shape and size. While correlations between GND density and crystal orientation are not strong for most copper samples, there are sufficient dependencies to demonstrate the benefits of the detailed four-parameter model. The four-parameter approach has potential for improving estimates of elastic-yield limit in all polycrystalline FCC materials.

Pesquisas e projetos envolvendo a complexa interação de maciços rochosos com estruturas de suporte de túneis evoluem constantemente. A adoção de modelos numéricos sofisticados aliada ao desenvolvimento de computadores com capacidade de processamento crescente possibilitam representações mecânicas de processos complexos. Para análises geotécnicas, considerações de resistência, deformabilidade e condutividade hidráulica do maciço são encontradas em códigos computacionais com representações próximas das encontradas nas pesquisas experimentais de vanguarda da área. Por outro lado, estes mesmos códigos atribuem com frequência ao comportamento do concreto reforçado representações simplistas, muitas vezes com base na teoria da elasticidade. Implicações econômicas e de incerteza na avaliação da segurança decorrem desta forma de representação. Esta pesquisa visa a contribuir para análises da interação entre maciço e suporte de uma escavação subterrânea. Para tanto foram elaboradas simulações numéricas considerando técnicas consagradas de avaliação mecânica de uma escavação, aliadas a uma representação do concreto reforçado considerando o marcante efeito de fissuração. Com foco no comportamento do concreto foram desenvolvidas simulações numéricas de distintas estruturas de concreto reforçado selecionadas na literatura e que contam com boa instrumentação e caracterização mecânica adequada de seus materiais. Os resultados obtidos indicam a possibilidade da avaliação concomitante das complexas características do maciço assim como do concreto reforçado. Este fato contribui para a avaliação da segurança de uma escavação subterrânea com possíveis repercussões no custo das obras. / Research and projects involving the intricate interaction between rock mass and tunnel support structures constantly evolve. The adoption of sophisticated numerical models allied to the development of computers with an increasing processing capacity allows mechanical representations of complex processes. For geotechnical analysis, considerations on rock mass strength, deformability and hydraulic conductivity are found in computational codes with representations close to those found in vanguard experimental research of this subject. However, these same codes often attribute simplistic representations to reinforced concrete behavior, frequently based on elasticity theory. Economic and uncertainty implications in safety evaluation result from this sort of representation. This research aims to contribute to analysis of interaction between rock mass and support of an underground excavation. Thus, numerical simulations were elaborated considering established techniques of mechanical evaluation of excavations, allied to a reinforced concrete representation taking into account the prominent effect of cracking. Focused on the concrete behavior, there were developed numerical simulations of distinct reinforced concrete structures selected in literature and that rely on fair instrumentation and adequate mechanical characterization of the involved materials. The results indicate the possibility of concomitant evaluation of the rock mass complex character and the reinforced concrete. This fact contributes to safety evaluation of an underground excavation with potential repercussions on project cost.

A rather complete picture of automatic plastic-hinge analysis onto steel frames under static loads is made in the present thesis. One/two/three-linear behaviours of mild steel are considered. The frames are submitted to fixed or repeated load. The geometric nonlinearity is taken into account. The beam-to-column joints of structures could be rigid or semi-rigid. The compact or slender cross-sections are examined. The investigation is carried out using direct or step-by-step methods. Both analysis and optimization methodologies are applied. From the fundamental theory to the computer program aspect are presented. Various benchmarks in open literatures are tested demonstrating the efficiency of the implementation.

No description available.

Cette thèse concerne la modélisation du comportement mécanique de poudres ductiles au cours de leur mise en forme par le procédé de compression à froid. L’approche utilisée consiste à modéliser la poudre par un échantillon numérique de 50 particules sphériques distribuées aléatoirement. Chaque particule est maillée en éléments finis avec un comportement élasto-plastique et interagit par contact avec ses voisines. Sous l’effet du chargement, les particules se déforment et subissent de grandes transformations.La méthode développée consiste à imposer aux frontières de l'échantillon numérique des conditions aux limites en déplacement ou en force afin de simuler une réponse continue équivalente en termes de contrainte-déformation pour plusieurs chemins de chargement depuis les faibles valeurs de densité relative jusqu'aux fortes valeurs. Outre le fait que la méthode permet d’appliquer par la simulation des chemins de chargement inaccessibles aux techniques expérimentales, elle fournit de nombreuses indications sur la phénoménologie du comportement aux frontières de l'échantillon en relation avec la morphologie des particules déformées plastiquement et l’évolution des surfaces de contact inter-particules.Cette réponse obtenue sera étudiée au moyen des notions de l'élasto-plasticité classique, à savoir la surface de charge et la loi d'écoulement. L'accent est mis sur l’analyse de l’écoulement plastique et l'existence du potentiel plastique. Les résultats montrent que la direction d’écoulement est approximativement unique pour les états de contrainte éloignés du point de chargement. En revanche, la direction d’écoulement cesse d’être unique à proximité de point de chargement, ce qui révèle le caractère anisotrope de l’écrouissage. Ce comportement, propre aux poudres ductiles, est intimement lié à la déformation des grains. La dégradation anisotrope des propriétés mécaniques résultant du mécanisme de dilatance est également étudiée. / This thesis is concerned with the modelling of the mechanical behaviour of ductile powders during cold compaction process. A numerical method was implemented, in which a powder sample was assimilated to an assembly of 50 meshed particles in a cubic box which was submitted to compressive loadings simulated by means of the finite element method. Each particle was meshed and assigned an elastic-plastic constitutive behaviour. Particles interacted through mechanical, frictional contact and underwent large transformation during loading.The method developped in the thesis consisted in imposing boundary conditions as displacements or forces on the bounding walls of the numerical sample. The mechanical response of the sample was averaged to obtain the equivalent response of a continuum in terms of stress and strain. Various loading paths, including loading paths that are technically not attainable by experimental means, were applied up to different values of relative densities, from low (60%) to high values (98%). Much information on the phenomenological behaviour of the numerical sample could be obtained, in relation with the morphology of deformed particles and the evolution of contact surfaces.The results were interpreted based on the concepts of classical elasto-plasticity, i.e., yield surface and flow rule. The main focus of the study was the analysis of incremental plastic flow and the existence of a plastic potential. Results showed that the flow rule postulate, based in the plastic potential, could be considered as valid for stress states relatively far from the loading point. In the vicinity of the loading point, the direction of the plastic strain increment vector ceases to be unique. This behaviour, which is an original feature of ductile powders mechanical behaviour, was attributed to the anisotropic strain-hardening processes at stake, related to the anisotropic formation of contact surfaces between particles. The drop in mechanical properties related to dilatancy was also studied.

Escoamentos sem inércia de fluido elasto-viscoplástico, dentro de uma cavidade, são numericamente analisados. As soluções visam compreender a influência dos efeitos viscosos e elásticos na topologia de superfícies de escoamento. Assumindo-se que o colapso da microestrutura do material é instantâneo, o modelo mecânico é constituído pelas equações governantes de massa e momentum para fluidos incompressíveis, associado a uma equação hiperbólica para o tensor tensão extra, baseado na equação do modelo Oldroyd-B (Nassar et al, 2011). A principal característica do modelo é considerar a viscosidade e o tempo de relaxação como função da taxa de deformação, permitindo a pseudoplasticidade de viscosidade e restringindo os efeitos elásticos para as regiões não deformadas do material. As simulações numéricas são realizadas através do método de Galerkin mínimos quadrados a três campos: tensor tensão extra, pressão e velocidade. Os resultados mostram que as superfícies de escoamento do material são fortemente influenciadas pela ação combinada entre os efeitos elásticos e viscosos, estando em conformidade com a recente visualização experimental dos fluxos elasto-viscoplásticos. / Elasto viscoplastic uid ows without inertia, within a cavity, are numerically analyzed. The solutions aim to understand the in uence of viscous and elastic e ects on the topology of yield surfaces. Assuming that the collapse of the material microstructure is instantaneous, the mechanical model consists of the governing equations of mass and momentum for incompressible uids, associated with a hyperbolic equation for the extra stress tensor, based on the equation of the Oldroyd-B model (Nassar et al, 2011). The main feature of model is to consider the viscosity and the relaxation time as a function of shear rate, allowing the shear-thinning of viscosity and restricting elastic e ects for regions not deformed material. Numerical simulations are performed by the method of Galerkin Least Squares to three elds: extra stress tensor, pressure and velocity. The results show that the yield surfaces of material are strongly in uenced by the combined action between the elastic and viscous e ects, complying with the recent experimental visualization of elasto-viscoplastic ows.