Les lasers femtosecondes sont un outil efficace pour induire des modifications structurelles localisées en volume dans les matériaux diélectriques. Initialement transparents, les diélectriques ne commencent à absorber efficacement l’énergie laser que lorsque l’intensité excède le seuil de claquage optique du matériau. Cette propriété, couplée à une durée d’impulsion femtoseconde plus courte que les temps caractéristiques de relaxation de la matière, permet d’obtenir un dépôt d’énergie précis et localisé dans le volume irradié. Pour modéliser la formation de telles structures, un modèle thermo-élasto-plastique en géométrie 2D planaire, incluant la transition solide-liquide via un modèle de ramollissement, a été implémenté dans un code hydrodynamique lagrangien. Des études de la formation d’une cavité et de l’interaction de multiple cavités ont tout d’abord été réalisées en supposant un dépôt instantané d’énergie laser dans le volume d’une cible de silice fondue. La relaxation de la matière chauffée, portée à l’état de plasma dense, induit alors la propagation d’ondes de choc dans le solide froid environnant. Des déformations permanentes peuvent apparaître dans le matériau si la contrainte, induite par ces ondes, excède la limite élastique. Ces premières études ont notamment permis de comprendre et de décrire les différentes étapes de la formation de micro-structures, fortement corrélées au comportement élasto-plastique du solide environnante. De plus, en utilisant une loi de Weibull, tenant compte de la densité de défauts dans la matière, des probabilités de fractures dans le matériau ont été calculées. Dans un second temps, la structuration de la silice fondue par un faisceau de Bessel a été considérée. Un solveur de Maxwell 3D, couplé à une description fluide de la dynamique électronique, a été utilisé pour modéliser le dépôt d’énergie laser. Les résultats ont permis de comprendre comment s’établit le dépôt d’énergie et rendent compte des effets des différents processus d’ionisation sur les évolutions des profils de densité et d’énergie électronique. Des simulations thermo-élasto-plastiques ont ensuite étaient réalisées en utilisant le dépôt d’énergie calculé. Différents types de déformations induites dans la silice ont pu être mis en évidence en fonction de l’énergie et de la durée de l’impulsion incidente, en accord avec les observations expérimentales. / Femtosecond laser pulses are an efficient tool to induce localized structural modifications in the bulk of dielectrics materials. The dielectrics, initially transparent, start to efficiently absorb the energy when the laser intensity exceeds the optical breakdown threshold of the material. This property, coupled to a femtosecond pulse duration smaller than the caracteristic relaxation times of matter, allows to induce a localized and accurate energy deposition in the irradiated volume. In order to model the formation of such structures, a 2D thermo-elasto-plastic model, including solid-liquid transitions through a softening model, has been implemented in a lagrangian hydrodynamic code. Studies on the formation of a single cavity and several interacting cavities have been firstly performed, assuming an instantaneous energy deposition in the bulk of fused silica. The relaxation of the heated matter, transformed to a warm dense plasma, induces shock waves in the surrounding cold solid. Permanent deformations may appear if the stress, induced by the waves, exceeds the yield strength of the material. This first study allowed to understand and describe the various steps of the micro-structures formation, which are strongly correlated to the elasto-plastic behavior of the surrounding solid. Furthermore, by using a Weibull’s law, accounting for defects density in the material, cracks probabilities have been predicted. Secondly, the structuration of fused silica by a Bessel beam has been considered. For that purpose, a 3D Maxwell solver coupled to a fluid description of the electron dynamics has been used to model the laser energy deposition. Results allow to understand how the energy deposition establishes and show the effects of the different ionization processes on the electron density and energy profiles. Then, thermo-elasto-plastic simulations have been carried out including the calculated energy deposition. Various kinds of induced deformations in fused silica have been obtained depending on the incident pulse energy and duration, which is in agreement with experimental observations.

O presente trabalho aborda o estudo do comportamento de túneis em maciços de solo. É dada ênfase na aplicação de análises numéricas com emprego de diferentes modelos constitutivos elasto-plásticos para solos. São apresentadas análises numéricas tridimensionais de um túnel amplamente instrumentado pertencente à Companhia do Metropolitano de São Paulo. As análises são realizadas com auxílio de um programa computacional de elementos finitos. O comportamento do maciço em pontos situados ao redor da escavação é minuciosamente estudado e a capacidade dos modelos em representar adequadamente o comportamento verificado na obra pelas instrumentações é avaliada. Além das análises numéricas o trabalho aborda os principais conceitos relacionados com escavações de túneis em maciços de solo. Conceitos relacionados com a engenharia prática de túneis são apresentados de maneira qualitativa, sem formulações teóricas e matemáticas. Uma revisão bibliográfica com publicações recentes das principais revistas e periódicos que tratam do tema de análise numérica aplicada a túneis é apresentada. O trabalho também apresenta uma revisão dos principais conceitos relacionados com os modelos constitutivos comumente utilizados para análise de problemas de geotecnia. Além do modelo elástico são apresentados os modelos elasto-plásticos de Tresca, von Misses, Drucker-Prager e Mohr-Coulomb. Uma breve introdução aos conceitos básicos de estado crítico, juntamente com as equações do modelo Cam-Clay original e Cam-Clay modificado são apresentadas. Antes da apresentação das equações desses modelos constitutivos, são introduzidos os conceitos básicos relacionados com o comportamento dos materiais elasto-plásticos. Os conceitos de material elástico perfeitamente plástico e de material com endurecimento (ou hardening) e amolecimento (ou softening) são apresentados. Os conceitos de superfície de plastificação e de superfície de potencial plástico também são apresentados. Por fim, são sintetizados os pontos mais relevantes da pesquisa realizada, apontando as limitações do trabalho com sugestões de novos estudos a serem realizados nessa mesma linha de pesquisa. / The present research approaches the study of the behaviour of tunnels in soil. It is given emphasis in the application of numerical analyses using different elasto-plastic constitutive models for soils. Three-dimensional numerical analyses of a widely instrumented tunnel belonging to the Company of the Metropolitan of São Paulo are presented. The analyses are carried through with aid of a computational program of finite elements. The behaviour of the soil mass in points located around the excavation is thoroughly studied and the capacity of the models in adequately representing the field behavior verified by the instrumentations is evaluated. Furthermore, the work approaches the main concepts related to tunneling in soils. Concepts related to practical engineering of tunnels are presented in a qualitative way, without theoretical and mathematical formulations. A literature review of recent publications of the most important periodic magazines and that deal with the subject of numerical analysis applied to tunnels is presented. The work also presents a revision of the main concepts related to the constitutive models normally used for analysis of geotechnical problems. Beyond the elastic model the elasto-plastics models of Tresca, von Misses, Drucker-Prager and Mohr-Coulomb are presented. Brief introductions to the basic concepts of critical state, together with the equations of the (original) Cam-Clay original and (modified) Cam-Clay modified models are presented. Before the presentation of the equations of these constitutive models, the basic concepts of the behaviour of the elasto-plastics materials are introduced. The concepts of perfectly plastic elastic material and material with hardening and softening are presented. The concepts of plastic surface and plastic potencial surface are also presented. Finally, the most relevant points of the research are synthesized, pointing the limitations of the developed work along with suggestions for new studies to be carried through in this line of research.

The analysis presented in this thesis provides a methodology for grouted bolts design, based on empirical and analytical methods. Hence, the main objectives of this thesis are to offer practical means for better characterisation of poor to very poor rock masses, to better predict support pressure, and to develop an elasto-plastic analytical model for design of grouted bolts in tunnels excavated in such rock masses. To improve the applicability of the GSI (Geological Strength Index) in poor to very poor rock masses, using Broken Domain Structure (BSTR), Structure Rating (SR), and Intact Core Recovery (ICR), some modifications have been offered, resulting in the Modified-GSI. Applying rock-load height concept and Modified-GSI, an approach to estimate support pressure has been developed. The main advantage of this approach is its applicability in squeezing ground and anisotropic stress conditions. Numerical modelling was carried out in order to adjust the proposed support pressure equation. Considering convergence reduction approach, an elasto-plastic model based on the latest version of Hoek- Brown failure criterion has been developed for a more effective and practical grouted bolt design. The link between empirical approach and elasto-plastic solution makes it possible to reach more realistic and appropriate bolting pattern design. In this way, the need for the redesign procedure in the convergence reduction approach is eliminated. The results of the proposed elastic-plastic solution have been compared with a numerical model using FLAC2D, and a reasonable agreement was observed. The practical application of the developed methodology is depicted by an analysis of a case study in Turkey.

The purpose of this study is to investigate the plastic deformation behavior of a round bar at the roll-gap during the rolling process of a three-roll planetary mill. The analysis is carried out with the aid of a finite element program MARC adopting the large deformation - large strain theory and the updated lagrangian formulation (ULF). A mesh rezoning procedure is also adopted to improve the uncontrollable running error of elements turning inside out. The mesh system of the whole bar billet is created by using three-dimensional brick elements, and the three-dimensional elastic-plastic finite element model in MARC is chosen to perform the simulations of three-roll planetary rolling processes. The simulation examples consist of three groups. Firstly, three different friction coefficients are adopted to investigate the rolling process. Secondly, totally five different offset angles are used during the simulation of the rolling process. Finally, five different profiles of the roller are used to study the simulation of the rolling process. The successfully obtained numerical results, including equivalent von-Mises stress and plastic strain distributions, rolling force, rolling moment, billet speeds at the entrance and exit planes of the roll-gap are useful in designing the pass schedules of the three-roll planetary rolling processes.

Rapid development and stiff competition in material related industries such as the automotive, demand very high precision in end products in very quick time. The transformation of raw material into an intricate-shaped final product involves various intermediate steps like design, material selection, manufacturing processes, etc. In all these steps, an in-depth understanding of material behavior plays an important role. The available traditional methods such as trial-and-error, especially in the case of die design, become highly inefficient in terms of time and money. This, there is a growing interest in simulation of the final product in order to predict different parameters which are important in design and manufacturing. Currently available simulation techniques are based on existing theories of plasticity or large deformation. These theories have been developed over several decades and many theoretical and practical issues have been debated over the years. Though the theories have great utility in understanding and solving some practical problems, there are ranges of applications for which no acceptable models are available. Most of these theories are either materials or process-specific with oversimplified real physical situations using assumptions and empirical relations. Development of field equations from first principles to stimulate elasto-plastic deformation is one such, still a subject of on-going discussion. Materials and composites exhibit hysteresis even at very low stresses, i.e., inelasticity is always present under all types of loading. This observation shows that the representing constitutive relation cannot treat the elastic and plastic deformations separately. The deformation is due to changes in size and shape, and studies with varying strain rates show considerable material sensitivity to the rate of deformation. Therefore, a generalized field equation is developed from first principles in the Eulerian coordinate system using material resistance to changes in size and shape, and their rates. The formulation uses a unified approach representing continuous effect of elastic and plastic strains and strain rates. The field equation involves eight material parameters, viz. bulk modulus, shear modulus, material shear velocity, material bulk viscosity, and four more constants associated with activation points related to deviatoric and volumetric strains and plastic strain rates. The elastic moduli, bulk and shear, are constants, and so also the material viscosities, while plastic stain rates are functions of elastic strain rates. The field equation redces to Cauchy’s equation in the solid limit and Navier-Stokes equation in the fluid limit. Simple experimental measurements are suggested to obtain the numerical values of the material parameters. Uniaxial tension tests are carried out on commercially available mild steel and aluminium alloy at different strain rates to quantify any variations in the values of material parameters during large deformation. Experimental results and the classical understanding of material deformation reveal the constant nature of elastic moduli during large deformation and, from fluids, the viscosities seem to remain constant. Around the yield region, materials experience a sharp increase in absorbed energy which is modeled to represent the plastic strain rates. The variations and contributions from elastic and plastic strains, both volumetric and deviatoric, and the corresponding stresses are observed. The effects of strain rate on plastic stress and energy absorbed are investigated. The model is checked for different materials and loading conditions to ascertain the proposed changes to earlier theories. Available experimental data in the literature are used for this purpose. The analysis shows that, though the overall stress-strain relations of different materials look similar, their internal responses differ. The internal response of a material depends on various microstructural factors, like alloying elements, impurities, etc. The present model is able to capture those internal differences between various materials. Numerical solution of different plasticity problems have to be undertaken to ascertain the applicability, generality, realism, accuracy and feasibility of the model.

Elasto-plastic shock waves in high-velocity compaction of spherical metal particles are the focus of this thesis which consists of four papers (A-D). The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading and adhesion at contacts. Paper A investigates the dynamic compaction of a one-dimensional chain of homogenous particles. The development of the elasto-plastic shock waves, its propagation and influence on the compaction process are examined. Simulations yield information on the contact behavior, velocity of the particle and its deformation during dynamic compaction. Effects of changing loading parameters on the compaction process are also discussed. Paper B addresses the non-homogeneity in a chain having; particles of different sizes and materials, voids between the particles and particles with/without adhesion between them. Simulations show transmission and reflection of elasto-plastic shock wave during compaction process. The particle deformation during incident and reflected shocks and particle velocity fluctuations due to voids between particles are simulated. The effects of adhesion on particles separation during unloading stage are also discussed. Paper C develops a simulation model for a high-velocity compaction process with auxiliary pistons, known as relaxation assists, in a compaction assembly. The simulation results reveals that the relaxation assists offer; smooth compaction during loading stage, prevention of  the particle separation during unloading stage and conversion of  higher kinetic energy of hammer into particles deformation.  Furthermore, the influence of various loading elements on compaction process is investigates. These results support the findings of experimental work. Paper D further extends the one-dimensional case of Paper A and B into two-dimensional assembly of particles while adding friction between particles and between particles and container walls. Three particular cases are investigated including closely packed hexagonal, loosely packed random and a non-homogenous assembly of particles of various sizes and materials. Consistent with the one-dimensional case, primary interest is the linking of particle deformation with the elasto-plastic shock wave propagation. Simulations yield information on particle deformation during shock propagation and change in overall particles compaction with the velocity of the hammer. The force exerted by particles on the container walls and rearrangement of the loosely packed particles during dynamic loading are also investigated. Finally, the effects of presence of friction and adhesion on both overall particles deformation and compaction process are simulated. / QC 20110311

Zr-2.5Nb is currently used for pressure tubes in the CANDU (CANada Deuterium Uranium) reactor. A complete understanding of the deformation mechanism of Zr-2.5Nb is important if we are to accurately predict the in-reactor performance of pressure tubes and guarantee normal operation of the reactors. This thesis is a first step in gaining such an understanding; the deformation mechanism of ZrNb alloys at room temperature has been evaluated through studying the effect of texture and microstructure on deformation. In-situ neutron diffraction was used to monitor the evolution of the lattice strain of individual grain families along both the loading and Poisson’s directions and to track the development of interphase and intergranular strains during deformation. The following experiments were carried out with data interpreted using elasto-plastic modeling techniques: 1) Compression tests of a 100%Zr material at room temperature. 2) Tension and compression tests of hot rolled Zr-2.5Nb plate material. 3) Compression of annealed Zr-2.5Nb. 4) Cyclic loading of the hot rolled Zr-2.5Nb. 5) Compression tests of ZrNb alloys with different Nb and oxygen contents. The experimental results were interpreted using a combination of finite element (FE) and elasto-plastic self-consistent (EPSC) models. The phase properties and phase interactions well represented by the FE model, the EPSC model successfully captured the evolution of intergranular constraint during deformation and provided reasonable estimates of the critical resolved shear stress and hardening parameters of different slip systems under different conditions. The consistency of the material parameters obtained by the EPSC model allows the deformation mechanism at room temperature and the effect of textures and microstructures of ZrNb alloys to be understood. This work provides useful information towards manufacturing of Zr-2.5Nb components and helps in producing ideal microstructures and material properties for pressure tubes. Also it is helpful in guiding the development of new materials for the next generation of nuclear reactors. Furthermore, the large data set obtained from this study can be used in evaluation and improving current and future polycrystalline deformation models. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2008-09-05 13:51:30.42

[pt] O presente trabalho apresenta uma técnica numérica geral para a aproximação da solução do problema de evolução quasi-estático em treliças elasto-plásticas com dano. Uma formulação geral e abstrata é apresentada e uma técnica numérica simples, baseada na técnica de decomposição do operador com um algoritmo sequencial associado, é proposta. Alguns exemplos tratando da análise de falha de treliças metálicas são usados para mostrar a efetividade do método. / [en] This work is corcerned with a general numerical technique for approximating the solution of quase-static evolution problems in damageable elasto-plastic trusses. An abstract and general formulation of the problem is presented and a simple numerical technique based on the operator splitting technique associated with a product formula algorithm is proposed. Some examples concerning the failure analysis of metallic trusses are used to show the effectiveness of the method.

O presente trabalho aborda o estudo do comportamento de túneis em maciços de solo. É dada ênfase na aplicação de análises numéricas com emprego de diferentes modelos constitutivos elasto-plásticos para solos. São apresentadas análises numéricas tridimensionais de um túnel amplamente instrumentado pertencente à Companhia do Metropolitano de São Paulo. As análises são realizadas com auxílio de um programa computacional de elementos finitos. O comportamento do maciço em pontos situados ao redor da escavação é minuciosamente estudado e a capacidade dos modelos em representar adequadamente o comportamento verificado na obra pelas instrumentações é avaliada. Além das análises numéricas o trabalho aborda os principais conceitos relacionados com escavações de túneis em maciços de solo. Conceitos relacionados com a engenharia prática de túneis são apresentados de maneira qualitativa, sem formulações teóricas e matemáticas. Uma revisão bibliográfica com publicações recentes das principais revistas e periódicos que tratam do tema de análise numérica aplicada a túneis é apresentada. O trabalho também apresenta uma revisão dos principais conceitos relacionados com os modelos constitutivos comumente utilizados para análise de problemas de geotecnia. Além do modelo elástico são apresentados os modelos elasto-plásticos de Tresca, von Misses, Drucker-Prager e Mohr-Coulomb. Uma breve introdução aos conceitos básicos de estado crítico, juntamente com as equações do modelo Cam-Clay original e Cam-Clay modificado são apresentadas. Antes da apresentação das equações desses modelos constitutivos, são introduzidos os conceitos básicos relacionados com o comportamento dos materiais elasto-plásticos. Os conceitos de material elástico perfeitamente plástico e de material com endurecimento (ou hardening) e amolecimento (ou softening) são apresentados. Os conceitos de superfície de plastificação e de superfície de potencial plástico também são apresentados. Por fim, são sintetizados os pontos mais relevantes da pesquisa realizada, apontando as limitações do trabalho com sugestões de novos estudos a serem realizados nessa mesma linha de pesquisa. / The present research approaches the study of the behaviour of tunnels in soil. It is given emphasis in the application of numerical analyses using different elasto-plastic constitutive models for soils. Three-dimensional numerical analyses of a widely instrumented tunnel belonging to the Company of the Metropolitan of São Paulo are presented. The analyses are carried through with aid of a computational program of finite elements. The behaviour of the soil mass in points located around the excavation is thoroughly studied and the capacity of the models in adequately representing the field behavior verified by the instrumentations is evaluated. Furthermore, the work approaches the main concepts related to tunneling in soils. Concepts related to practical engineering of tunnels are presented in a qualitative way, without theoretical and mathematical formulations. A literature review of recent publications of the most important periodic magazines and that deal with the subject of numerical analysis applied to tunnels is presented. The work also presents a revision of the main concepts related to the constitutive models normally used for analysis of geotechnical problems. Beyond the elastic model the elasto-plastics models of Tresca, von Misses, Drucker-Prager and Mohr-Coulomb are presented. Brief introductions to the basic concepts of critical state, together with the equations of the (original) Cam-Clay original and (modified) Cam-Clay modified models are presented. Before the presentation of the equations of these constitutive models, the basic concepts of the behaviour of the elasto-plastics materials are introduced. The concepts of perfectly plastic elastic material and material with hardening and softening are presented. The concepts of plastic surface and plastic potencial surface are also presented. Finally, the most relevant points of the research are synthesized, pointing the limitations of the developed work along with suggestions for new studies to be carried through in this line of research.

The increasing demand for more sustainable construction has led to the development of new structural systems that include wood as building material. Cross laminated timber (CLT) has been identified as a potential system to address this need and to provide alternative options in the range of low- to medium-rise construction. The appeal in using CLT as a shearwall is driven by the combination of the rigid panels and small dimension fasteners, which allows for significant energy dissipation in the structure. However, there is currently no reliable analytical model to accurately predict the behaviour of multi-segment CLT shearwalls. The current study aims to develop an analytical model capable of predicting the elastic and plastic phases associated with the behaviour of multi-panel CLT shearwalls. The model describes the wall behaviour as a function of the connectors’ properties in terms of stiffness, strength and ductility. This dependency means that the only input required in the model is the behavioural parameters of the connections. The proposed model contains six cases with a total of 36 different failure mechanisms. Two final wall behaviours were developed, and it was found that behaviour (i.e. single wall) could be achieved if the yielding in the hold-down occurred prior to yielding in the panel joints. Inversely, the other behaviour (i.e. coupled panels) was achieved if the yielding in the vertical joint occur prior to yielding in the hold-down. The analytical model was validated using a numerical model, and the results of the comparison showed very close match between the two models. The study proposed simplified design provisions with the aim to optimize the walls ductility (CP behaviour) or strength and stiffness (SW behaviour).