141 research outputs found

    Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

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    In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent hardening, dislocation storage and annihilation, mean free path, etc.) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice’s criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional “fitting” parameter, is used to build Ellipticity Limit Diagrams (ELDs).ArcelorMittal Researc

    Estudo numérico e experimental de geomecânica não-linear acoplada a escoamento de fluido em reservatórios

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    Orientador: Philippe Remy Bernard DevlooTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica, Instituto de GeociênciasResumo: A produção de reservatórios pode levar a uma diminuição na pressão do fluido durante a vida útil da produção. O decaimento da pressão dos poros pode alterar a distribuição das tensões in situ e causar um aumento nas tensões efetivas. A deformação associada às tensões efetivas pode levar à compactação do reservatório, perda de permeabilidade e subsidência da terra. Para lidar com tais problemas, é necessário a geomecânica acoplada com escoamento do reservatório. Existem quatro objetivos principais nesta tese: 1) Propor um esquema sequencial aprimorado para desenvolver um simulador acoplado de escoamento e geomecânica não-linear, 2) Implementar modelos elastoplásticos para geomecânica e aplicar modelos de permeabilidade para reservatório, 3) Analisar a permeabilidade dependente de deformação, colapso de poros e compactação aprimorada por cisalhamento em reservatórios, 4) Calibrar os parâmetros de materiais em modelos elastoplásticos. Para apresentar o simulador de geomecânica e escoamento acoplados, propõe-se pela primeira vez um algoritmo sequencial aprimorado e implícito (ESFI), com um esquema de divisão de tensão fixa. O algoritmo sequencial totalmente implícito (SFI) é um método popular para aproximar um sistema acoplado, mas ocasionalmente sofre de convergência lenta ou mesmo falha de convergência. Para melhorar o desempenho do algoritmo SFI, uma nova técnica de aceleração não linear é proposta empregando transformações de Shanks para aprimorar a convergência do loop externo, com um método Quasi-Newton considerando o método Thomas modificado para o loop interno. No algoritmo ESFI, a formulação de fluidos é definida pela lei de Darcy, incluindo modelos de permeabilidade não linear. A deformação da rocha inclui uma parte linear sendo analisada com base na teoria de Biot e uma parte não linear sendo estabelecida através de modelos elastoplásticos. As derivadas temporais são aproximadas por um método implícito de Euler e discretizações espaciais são adotadas usando elementos finitos em duas formulações diferentes. Para analisar a permeabilidade dependente de deformação em reservatórios, usam-se modelos de permeabilidade não-lineares baseados em porosidade, como Costa, Petunin, Nelson e Davies. Para expressar a deformação, são implementados modelos elastoplásticos, por exemplo, Mohr-Coulomb, DiMaggio-Sandler e Cam-Clay modificado. Para indicar o início do colapso dos poros e da compactação aprimorada por cisalhamento e seu impacto na porosidade, permeabilidade e fluxo, são aplicados os modelos de limite de plasticidade e permeabilidade acopladas. Para calibrar os parâmetros de materiais em modelos elastoplásticos, propõe-se uma estratégia que minimiza a diferença entre resultados experimentais e numéricos, aplicando os métodos de otimização iterativa. Para calibrar os parâmetros do modelo de maneira adequada e rápida, foram desenvolvidas equações analíticas para fornecer dados iniciais para cada parâmetroAbstract: Production from hydrocarbon reservoirs can lead to a decrease in the fluid pressure over the lifetime of production. The pore pressure depletion can change the in-situ stresses distribution and cause an increase in effective stresses. Deformation associated with the effective stresses may lead to reservoir compaction, permeability loss and land subsidence. In order to tackle these problems, the coupled geomechanics and reservoir fluid flow is required. There are four main goals in this thesis: 1) To propose an enhanced sequential scheme to develop a coupled nonlinear geomechanics and reservoir simulator, 2) To implement elastoplastic models for geomechanics and apply permeability models for reservoir, 3) To analyze strain-dependent permeability, pore collapse and shear-enhanced compaction in reservoirs, 4) To calibrate the physics-based elastoplastic models. To present coupled geomechanics and reservoir simulator, we propose for the first time an enhanced sequential fully implicit (ESFI) algorithm with a fixed stress split scheme. The sequential fully implicit algorithm (SFI) is a popular method to approximate a coupled system, but it occasionally suffers from slow convergence or even convergence failure. In order to improve the performance of SFI algorithm, a new nonlinear acceleration technique is proposed by employing Shanks transformations to enhance the outer loop convergence, with a Quasi-Newton method considering the modified Thomas method for the internal loop. In this ESFI algorithm, the fluid formulation is defined by Darcy¿s law including nonlinear permeability models. The rock deformation includes a linear part being analyzed based on Biot¿s theory and a nonlinear part being established using elastoplastic models. Temporal derivatives are approximated by an implicit Euler method and spatial discretizations are adopted using finite element in two different formulations: the first one uses a continuous Galerkin for poro-elastoplasticity and Darcy¿s flow; the second one uses a continuous Galerkin for poro-elastoplasticity and a mixed finite element for Darcy¿s flow. To analyze the strain-dependent permeability in reservoirs, we use nonlinear permeability models based on porosity such as, Costa, Petunin, Nelson, and Davies. To express the deformation, we implement elastoplastic models, e.g., Mohr-Coulomb, DiMaggio-Sandler, and modified Cam-Clay. To indicate the onset of pore collapse and shear-enhanced compaction and their impact on porosity, permeability, and flux, we apply the coupled cap plasticity and permeability models. To calibrate the physics-based elastoplastic models, we propose a strategy that minimizes the difference between experimental and numerical results by applying the iterative optimization methods. To calibrate the model parameters properly and fast, we develop analytical equations to provide initial data for each parameterDoutoradoExplotaçãoDoutor em Ciências e Engenharia de Petróleo2014/00090-2FUNCAM

    Differential-Algebraic Equations

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    Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

    Schnelle Löser für Partielle Differentialgleichungen

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    This workshop was well attended by 52 participants with broad geographic representation from 11 countries and 3 continents. It was a nice blend of researchers with various backgrounds

    On the formulation of closest-point projection algorithms in elastoplasticity. Part I: The variational structure.

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    Report UCB/SEMM 2000-01 - Dept. of Civil Engineering - University of California at Berkeley, USAWe present in this paper the characterization of the variational structure behind the discrete equa- tions defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite strain multiplicative plasticity. Primal variational prin- ciples in terms of the stresses and stress-like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented La- grangian extensions are also presented allowing a complete regularization of the problem in the constrained rate-independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work.Preprin

    Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model

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    In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent hardening, dislocation storage and annihilation, mean free path, etc.) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice’s criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional “fitting” parameter, is used to build Ellipticity Limit Diagrams (ELDs).ArcelorMittal Researc

    Modélisation et simulation du couplage changement de phases-mécanique par la méthode des champs de phases

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    A general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws (i.g. elastoviscoplasticity) into a standard phase field model. A finite element formulation of a coupled phase field/diffusion/mechanical problem for alloys is proposed within the general framework of continuum thermodynamics. This formulation is based on the concept of generalized stresses as proposed by Gurtin, where an additional balance equation for generalized stresses, called microforces, associated with the order parameter and its first gradient, is postulated. The formulation is used to simulate the complex morphological evolutions of the heterogeneous microstructures and to describe the diffuse interface between two phases in the presence of the stresses induced by phase transformation. Using the principles of the thermodynamics of irreversible processes, the balance and constitutive equations are clearly separated in the formulation. Also, boundary and initial conditions for the displacement, concentration and order parameter and their dual quantities are clearly stated within the formulation. The theory is shown to be well-suited for a finite element formulation of the initial boundary value problems on nite size specimens with arbitrary geometries and for very general non-periodic or periodic boundary conditions. In the diffuse interface region where both phases coexist, mixture rules taken from homogenization theory are introduced into the formulation. The consequences of the choice of a specific interface behaviour is investigated, with regard to the mechanical effect on phase equilibria (equilibrium compositions and volume fractions of the coexisting phases), as well as on the transformation kinetics. The set of coupled evolution equations, which are the local static equilibrium, the balance of generalized stresses and the balance of mass, is solved using a finite element method for the space discretization and a finite difference method for the temporal discretization. To validate the numerical finite element implementation and to illustrate the ability of the proposed model to handle precipitation together with mechanical contribution effect, some elementary initial boundary value problem in coupled diusion-elasto-plasticity on finite size specimens has been solved and validated against corresponding sharp interface analytical solutions.Nous proposons un cadre générique, permettant l'incorporation des différentes lois de comportement de mécanique linéaires ou non-linéaires (i.e. elastoviscoplastique) dans les approches des champs de phases utilisées pour la modélisation et la simulation de la mobilité d'interfaces diffuses. Dans ce cadre, une formulation par éléments finis des modèles couplés champ de phases-élastoplasticité pour les alliages binaires est développée dans le formalisme général de la thermodynamique des milieux continus. Cette formulation est basée sur la théorie d'équilibre des microforces, proposée par Gurtin, où une équation supplémentaire, fonction du paramètre d'ordre et de son gradient, est introduite. La formulation est employée pour simuler les évolutions morphologiques complexes des microstructures hétérogènes et décrire l'interface diffuse entre deux phases en présence des contraintes induites par transformation de phase. En utilisant les principes de la thermodynamique des processus irréversibles, les lois de comportement et les équations d'évolution sont clairement exposées et séparées dans la formulation de sorte que des modèles non-linéaires et fortement couplés puissent être implantés plus facilement dans un code par éléments finis. Cette formulation peut être appliquée aux corps finis périodiques et non périodiques, aux microstructures hétérogènes. Les conditions initiales et les conditions aux limites en paramètre d'ordre et en concentration ainsi que leurs quantités duales sont clairement énoncées. Des techniques d'homogénéisation ont été utilisées pour décrire le comportement dans les interfaces diffuses. Les conséquences de ces choix de modélisation ont été déterminées en ce qui concerne les effets des contraintes mécaniques sur les équilibres de phases et la cinétique de transformation. L'ensemble des équations d'évolution couplées, à savoir l'équation d'équilibre statique local, l'équation de champ de phases et l'équation de conservation de la masse, est résolu en utilisant la méthode des éléments finis pour la discrétisation spatiale et un schéma implicite des différences finies pour la discrétisation temporelle. Afin d'illustrer l'intérêt de l'approche proposée, des calculs par éléments finis ont été effectués sur des situations élémentaires telles que le calcul des concentrations d'équilibre des phases en présence de contraintes et la croissance de précipités dans une matrice élastique ou élasto-plastique, situations pour lesquelles des solutions analytiques pour des interfaces parfaites sont disponibles

    Finite Strain Elastoplasticity: Consistent Eulerian and Lagrangian Approaches

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    Infinitesimal strain approximation and its additive decomposition into elastic and plastic parts used in phenomenological plasticity models are incapable of predicting the hardening behavior of materials for large strain loading paths. Experimentally observed second-order effect in finite torsional loading of cylindrical bars, known as the Swift effect, as well as deformations involving significant amount of rotations are examples for which infinitesimal models fail to predict the material response accurately. Several different Eulerian and Lagrangian formulations for finite strain elastoplasticity have been proposed based on different decompositions of deformation and their corresponding flow rules. However, issues such as spurious shear oscillation in finite simple shear and elastic dissipation in closed-path loadings as well as elastic ratchetting under cyclic loading have been identified with the classical formulations for finite strain analysis. A unified framework of Eulerian rate-type constitutive models for large strain elastoplasticity is developed here which assigns no preference to the choice of objective corotational rates. A general additive decomposition of arbitrary corotational rate of the Eulerian strain tensor is proposed. Integrability of the model for the elastic part of the deformation is investigated and it is shown that the proposed unified model is consistent with the notion of hyperelasticity for its elastic part. Based on this, the stress power is physically separable into its reversible and irreversible parts using the proposed constitutive model irrespective of the objective rate used in the model. As a result, all of the issues of finite strain elastoplasticity are resolved using the proposed Eulerian rate model for arbitrary corotational rate of stress. A modified multiplicative decomposition of the right stretch tensor is proposed and used to set up a new Lagrangian framework for finite strain elastoplasticity. Decomposition of the deformation is solely defined by the multiplicative decomposition of the total right stretch tensor into its elastic and plastic parts. The flow rule and evolution of the plastic internal variables are based on the Hencky measure of the plastic right stretch tensor instead of the strain rate tensor. As a result, the issue of mismatch between the elastic and plastic parts of the deformation which mostly exists in the classical multiplicative models does not exist in the proposed Lagrangian model. The problem of back stress oscillation observed in the classical Lagrangian models is also resolved using the proposed Lagrangian model and results are identical to those of the proposed unified Eulerian rate model for finite strain elastoplasticity. In the context of nonlinear elasticity, no preference for either Lagrangian or Eulerian formulations exists since the two formulations can be related through proper transformations and are equivalent form of each other in different backgrounds. However, classical Eulerian and Lagrangian models of elastoplasticity do not provide such an equivalency under the same loading path. This is due to different definitions used for the elastic and plastic parts of the deformation and different flow rules used in the classical Eulerian and Lagrangian models. In this research it is shown that both the proposed Lagrangian and unified Eulerian rate models are equivalent and results obtained from both models are identical for the same finite strain loading path. Such an equivalency verifies that the proposed Eulerian and Lagrangian models are unified and transformable to each other. The unified Eulerian and Lagrangian models are extended to mixed nonlinear hardening material behavior. Predicted results for the second-order effect (the well-known Swift effect) are in good agreement with experimental data for fixed-end finite torsional loading of SUS 304 stainless steel tubes. The proposed models are therefore good candidates to be implemented in the displacement-based formulation of the finite element method for the Lagrangian and Eulerian frameworks of finite strain elastoplasticity
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