Este trabalho aborda o estudo de modelos constitutivos a fim de analisar o comportamento mecânico de um biopolímero derivado de óleo de mamona (Ricinus communis). A importância deste trabalho se dá ao fato de: servir como roteiro de ensaio de materiais poliméricos; completar caracterização do material estudado além do regime viscoelástico, bem como aplicação da análise do comportamento do material além do regime viscoelástico linear. A aplicação dos modelos avaliados via Método dos Elementos Finitos (MEF) exigiu o levantamento das propriedades e do comportamento mecânico do biopolímero, bem como a preparação dos ensaios, com as devidas especificações sugeridas pela ASTM (American Society for Testing and Materials) para cada tipo de ensaio. Assim, foram obtidos os corposde- prova (CDP) para a realização dos ensaios mecânicos quase-estáticos de tração, compressão e flexão (monotônicos e cíclicos), bem como, ensaio para análise dinâmicomecânica (Dynamic Mechanical Analysis - DMA) para a obtenção de propriedades associada às parcelas viscosas do material. Com estes foram obtidos parâmetros inerentes a cada tipo de ensaio, permeados com uma cuidadosa revisão bibliográfica sobre as implicações para a realização de cada ensaio. Uma outra etapa foi a verificação de modelos de plastificação baseados na teoria de von Mises, Drucker-Prager e de viscoelasticidade implementados no programa comercial ABAQUS®. Sendo que o objetivo maior foi a comparação dos resultados experimentais obtidos com os modelos em MEF. Os resultados para tração monotônica obtiveram erro de 0,61%, os resultados de compressão monotônica apresentaram erro de 1,5% e as simulações para os carregamentos cíclicos de tração e compressão não foram tão bons quanto os anteriores. Por isso se justifica a criação do modelo fenomenológico utilizando os parâmetros do material que foram identificados. / This work develops the study involving constitutive models with the objective to analyze the mechanical behavior of a biopolymer obtained from the Castor Oil Polyurethane (Ricinus communis). The importance of this work is due to the fact that: serves as a test script for the use of polymer materials; complete the characterization of the material studied beyond the viscoelastic realm, as well as the application of the analysis of the behavior of the material beyond the linear viscoelastic domain. The application of the evaluated models by way of the Finite Element Method (FEM), required the gathering of the properties and mechanical behavior of the biopolymer, as well as the preparation of the tests, with the required specifications suggested by the ASTM (American Society for Testing and Materials) for each type of test. Therefore, there were obtained the body-tests in order to run the mechanical quasi-static traction tests, tensile, compression and flexion (monotonic and cyclical) dynamicmechanical analysis (DMA) in order to obtain the properties associated with the viscous parts of the material. With these the inherent parameters were obtained for each specimen, permeated with a careful biographical revision of the implications for the experimenting of each specimen. Another phase was the verification of laminated models based on the theory by Von Mises, Drucker-Prager and of the viscoelasticity implemented in the commercial program ABAQUS®. The main objective being the comparison of the experimental results obtained with the models in FEM. The results for the monotonic traction obtained a error of 0,61%, the results of monotonic comparison presented an error of 1,5% and the simulations for the cyclical charges of traction and compression were not as good as the former. Therefore it justifies the creation of the phenomenological model utilizing the parameters of the materials that were identified.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

La recherche permanente de solutions d’allègement des structures aéronautiques a conduit au développement de nouveaux alliages comme les Al-Cu-Li et les Al-Mg-Li qui se caractérisent par une densité inférieure aux alliages conventionnels et par des propriétés améliorées. De manière générale, la formabilité de ces alliages, que ce soit à froid ou à chaud est encore assez mal connue. Le projet « Formage avancé des alliages basses densité pour application aéronautique » se propose donc de caractériser précisément la plage de formabilité de ces nouveaux alliages et d’investiguer les voies de mise en œuvre les plus adaptées : procédé d’étirage conventionnel ou procédé de mise en forme pendant une étape de traitement thermique. Ce projet regroupe les entreprises AEROLIA SAS, ACB, AIRBUS Operation SAS et CONSTELLIUM.Ces développements seront destinés au fuselage métallique et plus particulièrement à la structure pointe-avant qui présente une géométrie en double courbure ; ils concernent à la fois les panneaux de fuselage et les profilés. / The ongoing researches to lighten aeronautical structures have led to the development of new materials like Al-Cu-Li and Al-Mg-Li alloys. These alloys exhibit lower density and higher mechanical properties than conventional alloys. However, their ability to be formed either by cold or hot forming process is not well known. The aims of this PhD research works are thus to characterize the formability of these new alloys and to suggest the most appropriate forming sequence to elaborate complex aeronautic parts. Various forming processes will be studied such as cold forming by stretching of sheet metal parts or hot forming by stamping of sheet metal parts after or during different heat treatments. An experimental as well as a numerical approach will be used to develop the forming process of these new alloys to elaborate fuselage panels with more or less complex shapes. These PhD research works are a component of a larger project led by IRT Jules Verne and entitled “Advanced forming of low density alloys for aeronautic applications”. This project includes several firms from aeronautic domain (AEROLIA SAS, ACB, AIRBUS SAS and CONSTELLIUM).

This dissertation addresses new developments in the constitutive modeling and structural analysis pertaining to rate-independent and rate-dependent irrecoverable inelasticity in Shape Memory Alloys (SMAs). A new model for fully recoverable SMA response is derived that accounts for material behaviors not previously addressed. Rate-independent and rate-dependent irrecoverable deformations (plasticity and viscoplasticity) are then considered. The three phenomenological models are based on continuum thermodynamics where the free energy potentials, evolution equations, and hardening functions are properly chosen. The simultaneous transformation-plastic model considers rate-independent irrecoverable strain generation and uses isotropic and kinematic plastic hardening to capture the interactions between irrecoverable plastic strain and recoverable transformation strain. The combination of theory and implementation is unique in its ability to capture the simultaneous evolution of recoverable transformation strains and irrecoverable plastic strains. The simultaneous transformation-viscoplastic model considers rate-dependent irrecoverable strain generation where the theoretical framework is modfii ed such that the evolution of the viscoplastic strain components are given explicitly. The numerical integration of the constitutive equations is formulated such that objectivity is maintained for SMA structures undergoing moderate strains and large displacements. Experimentally validated analysis results are provided for the fully recoverable model, the simultaneous transformation-plastic yield model, and the transformation-viscoplastic creep model.

Made available in DSpace on 2016-12-12T20:25:11Z (GMT). No. of bitstreams: 1 Thiago Andre Carniel.pdf: 5594070 bytes, checksum: 5e24f59f581ec79c2edb07d9afdd502e (MD5) Previous issue date: 2013-07-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents the development of a numerical formulation for the transient analysis of spatial truss structures considering geometrical and material nonlinearities. The equilibrium problem is formulated using the Principle of the Virtual Power in a current Lagrangian description. The displacement and velocity fields are discretized employing the Finite Element Method and the nonlinear equilibrium equations are solved by the full Newton- Raphson procedure. In order to obtain quadratic convergence, the algorithmic tangent matrix expression is developed and presented. Next, the transient problem is formulated and solved using the Newmark integration algorithm. The material model adopted is viscoelastic-viscoplastic coupled to Lemaitre s damage. The viscoelastic behavior is represented by the generalized Kelvin-Voigt rheological model and the viscoplastic contribution is introduced via Perzyna s equation. The evolution laws of the material model are integrated numerically using the implicit Euler scheme, resulting in the corresponding return mapping. The algorithmic tangent modulus for this material model is derived and validated by means of numerical differentiation using the complex variable approach. The constitutive parameters for the model are obtained by minimization of the difference between experimental and numerical curves, aiming at polymeric materials. Since non-uniqueness is expected for the minimization problem, the gradient free Particle Swarm Optimization method (PSO) is adopted for its solution. Finally, the results obtained and some particularities of the proposed model are discussed. / Este trabalho tem por objetivo desenvolver uma formulação numérica para a análise transiente de estruturas treliçadas tridimensionais considerando não linearidade geométrica e material. O problema de equilíbrio é apresentado através do Princípio das Potências Virtuais segundo uma formulação Lagrangeana Corrente. O campo de deslocamentos e velocidades é discretizado através do Método dos Elementos Finitos. As equações não lineares de equilíbrio são resolvidas pelo método de Newton-Raphson, sendo apresentado o desenvolvimento da matriz de rigidez tangente consistente. Posteriormente, o problema transiente é formulado, sendo as equações do movimento solucionadas pelo método de integração implícito de Newmark. O modelo constitutivo proposto é viscoelástico-viscoplástico acoplado com o modelo de dano de Lemaitre. A formulação viscoelástica é representada pelo modelo generalizado de Kelvin-Voigt e a contribuição viscoplástica é dada pela equação de Perzyna. As leis de evolução do modelo material são integradas numericamente através do algoritmo implícito de Euler, resultando no algoritmo de retorno. Para obter a taxa de convergência quadrática do método iterativo de Newton-Raphson durante o equilíbrio estrutural, é apresentado o cálculo analítico do módulo tangente algoritmo consistente, o qual é validado através do método da derivada complexa. Os parâmetros materiais são encontrados através do ajuste entre as curvas experimental e teórica, visando a aplicação para materiais poliméricos. Para o ajuste das curvas utilizou-se o método de Otimização por Nuvem de Partículas Particle Swarm Optimization (PSO). Ao final é realizada uma discussão dos resultados encontrados e comentado as particularidades do modelo proposto.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

Un certain nombre d’écoulements géophysiques, tels que les écoulements de glace ou de lave magmatique, impliquent le mouvement gravitaire à faible nombre de Reynolds d’un fluide viscoplastique à surface libre sur un socle rocheux. Leur modélisation fait apparaître des lois de comportement rhéologique et des descriptions de leurs intéractions avec le socle rocheux qui reposent sur des paramétrisations empiriques. Par ailleurs, l’observation systématique de ce type d’écoulements avec une grande précision est rarement possible ; les données associées à l’observation de ces écoulements, principalement des données de surface (télédétections), peuvent être peu denses, manquantes ou incertaines. Elles sont aussi le plus souvent indirectes : des paramètres inconnus comme le glissement basal ou la rhéologie sont difficilement mesurables in situ.Ce travail de thèse s’attache à la modélisation directe et inverse de ces écoulements géophysiques, particulièrement les écoulements de glace, par des méthodes variationnelles à travers la résolution du problème de Stokes pour les fluides en loi de puissance.La méthode de résolution du problème direct (Stokes non-linéaire) repose sur le principe du minimum de dissipation qui mène à un problème variationnel de type point-selle à quatre champs pour lequel on montre l’existence de solutions. La condition d’incompressibilité et la loi de comportement représentent alors des contraintes associées au problème de minimisation. La recherche des points critiques du lagrangien correspondant est réalisée à l’aide d’un algorithme de type lagrangien augmenté, discrétisé par éléments finis triangles à trois champs. Cet algorithme conduit à un important gain tant en temps de calcul qu’en utilisation mémoire par rapport aux algorithmes classiques.On s’intéresse ensuite à la modélisation numérique inverse de ces fluides à l’aide du modèle adjoint et des deux principaux outils associés : l’analyse de sensibilité et l’assimilation de données. On étudie tout d’abord la modélisation rhéologique de ces fluides à travers les deux paramètres principaux de la loi de comportement : la consistance du fluide et l’exposant rhéologique. Des analyses de sensibilité sur ces paramètres définis localement, permettent de quantifier leurs poids relatifs au sein du modèle d’écoulement, en termes de vitesses de surface. L’identification de ces grandeurs est également réalisée. L’ensemble des résultats est résumé comme une méthodologie vers une “rhéométrie virtuelle” pouvant représenter une aide solide à la mesure rhéologique.Le glissement basal, paramètre majeur dans la dynamique de la glace, est investigué selon la même approche. Les analyses de sensibilité mettent en avant une capacité à voir à travers le caractère “filtré” et non-local de la transmission de la variabilité basale vers la surface, ouvrant des perspectives vers l’utilisation des sensibilités pour la définition de lieux d’intérêt pour l’observation et la mesure. Ce glissement basal, modélisation empirique d’un processus complexe et multiéchelle, est ensuite utilisé pour la comparaison avec une méthode inverse approximative courante en glaciologie (méthode négligeant la dépendance de la viscosité à la vitesse, i.e. la non-linéarité). Le modèle adjoint, obtenu par différentiation automatique et évalué par accumulation retour, permet de définir cette approximation comme un cas limite de la méthode inverse complète. Ce formalisme mène à une généralisation du processus d’évaluation numérique de l’état adjoint, ajustable en précision et en temps de calcul en fonction de la qualité des données et du niveau de détail souhaité dans la reconstruction.L’ensemble de ces travaux est associé au développement du logiciel DassFlow-Ice de simulation directe et inverse de fluides viscoplastiques à surface libre. Ce logiciel prospectif bidimensionnel, diffusé dans la communauté glaciologique, a donné lieu au développement d’une version tridimensionnelle. / Several geophysical flows, such as ice flows or lava flows, are described by a gravity-driven low Reynolds number movement of a free surface viscoplastic fluid over a bedrock. Their modeling involves constitutive laws, typically describing their rheological behavior or interactions with their bedrock, that lean on empirical parameterizations. Otherwise, the thorough observation of this type of flows is rarely possible; data associated to the observation of these flows, mainly remote-sensed surface data, can be sparse, missing or uncertain. They are also generally indirect : unknown parameters such as the basal slipperiness or the rheology are difficult to measure on the field.This PhD work focuses on the direct and inverse modeling of these geophysical flows described by the power-law Stokes model, specifically dedicated to ice flows, using variational methods.The solution of the direct problem (Stokes non-linear) is based on the principle of minimal dissipation that leads to a variational four-field saddle-point problem for which we ensure the existence of a solution. In this context, the incompressibility condition and the constitutive rheological law represent constraints associated to the minimization problem. The critical points of the corresponding Lagrangian are determined using an augmented Lagrangian type algorithm discretized using three- field finite elements. This algorithm provides an important time and memory saving compared to classical algorithms.We then focus on the inverse numerical modeling of these fluids using the adjoint model through two main associated tools : sensitivity analysis and data assimilation. We first study the rheological modeling through the two principal input parameters (fluid consistency and rheological exponent). Sensitivity analyses with respect to these locally defined parameters allow to quantify their relative weights within the flow model, in terms of surface velocities. Identification of these parameters is also performed. The results are synthetized as a methodology towards “virtual rheometry” that could help and support rheological measurements.The basal slipperiness, major parameter in ice dynamics, is investigated using the same approach. Sensitivity analyses demonstrate an ability to see beyond the ”filtered” and non-local transmission of the basal variability to the surface. Consequently these sensitivities can be used to help defining areas of interest for observation and measurement. This basal slipperiness, empirical modeling of a multiscale complex process, is then used to carry on a comparison with a so called “self-adjoint” method, common in glaciology (neglecting the dependency of the viscosity on the velocity, i.e. the non-linearity). The adjoint model, obtained by automatic differentiation and evaluated by reverse accumulation, leads to define this approximation as a limit case of the complete inverse method. This formalism allows to generalize the process of the numerical evaluation of the adjoint state into an incomplete adjoint method, adjustable in time and accuracy depending on the quality of the data and the level of detail required in the identification.All this work is associated to the development of DassFlow-Ice software dedicated to the direct and inverse numerical simulation of free-surface viscoplastic fluids. This bidimensional prospective software, distributed within the glaciological com- munity, serves as a model for the current development of the tridimensional version.

De nombreuses applications industrielles mettent en jeu des fluides complexes qui possèdent souvent un seuil d'écoulement leur permettant de résister à des efforts finis sans s'écouler. Par ailleurs, ces fluides peuvent glisser aux parois lorsque les conditions interfaciales sont favorables. Toutes ces propriétés influencent leurs écoulements autour d'obstacles. Cette thèse se propose de comprendre ces écoulements dans le domaine où les vitesses d'écoulement sont telles que les effets inertiels peuvent être négligés devant les effets visqueux eux-mêmes faibles par rapport aux effets plastiques. Elle analyse l'influence de la vitesse et du glissement sur la force de traînée et les champs cinématiques générés par l'écoulement très lent et en régime permanent d'un fluide à seuil autour d'obstacles aux surfaces adhérentes ou glissantes. Les géométries considérées sont le disque, la sphère, le cône et la plaque plane. Le fluide utilisé a un comportement élasto-viscoplastique pouvant être décrit par les modèles de Herschel-Bulkley et de Hooke. Ce comportement a été caractérisé en volume et en présence de glissement par des mesures rhéométriques. Le nombre adimensionnel clé de l'étude est le nombre d'Oldroyd, ratio entre les effets plastiques et les effets visqueux, compris ici entre 10 et 200. Les mesures de forces de traînée ont montré qu'indépendamment de l'obstacle et des conditions interfaciales, le coefficient de traînée diminue avec le nombre d'Oldroyd et tend vers une valeur asymptotique. Cette valeur montre qu'au-delà d'un certain nombre d'Oldroyd, ce coefficient n'est plus gouverné par la vitesse mais dépend uniquement du seuil et de la surface caractéristique de l'obstacle. Elle permet de calculer un critère de stabilité pour lequel l'objet est maintenu en suspension. Les champs cinématiques déterminés par PIV ont permis de caractériser la forme et l'étendue des zones rigides et cisaillées. Les mesures de forces de traînée et de champs cinématiques ont permis de quantifier la contribution des contraintes normales et tangentielles dans la force de traînée totale. La présence de glissement aux parois de l'obstacle diminue significativement le coefficient de traînée et modifie la morphologie de l'écoulement en réduisant l'étendue des zones cisaillées. Une simulation numérique a été menée dans le cas de la plaque plane avec un modèle élasto-viscoplastique et un code à éléments finis avec points d'intégration Lagrangiens. / Many industrial processes include numerous complex fluids often presenting a yield stress. Those fluids can also slip when interfacial conditions are favorable. All these properties affect their flows around obstacles. This thesis aims to understand such flows in a domain where the flow velocities are so low that inertia effects can be neglected compared to viscous effects which are substantially low compared to plastic effects. It analyzes the influence of the velocity and the slip on the drag force and the kinematic fields of the creeping flow of a yield stress fluid around obstacles either with adhesive or slippery wall. The flow is analyzed in steady regime. The considered geometries are the disc, the sphere, the cone and the flat plate. The fluid used has an elasto-viscoplastic behavior which is modelled by the Herschel-Bulkley and Hooke models. This behavior has been characterized by rheometrical tests performed with adherence and slip conditions. The main non-dimensional number is the Oldroyd number, i.e. the ratio between plastic and viscous effects, which ranges from 10 to 200. The drag forces measurements have shown that regardless of the obstacle and the interfacial conditions, the drag coefficient decreases with the Oldroyd number before tending towards to an asymptotical value. This asymptotical value highlights that for high Oldroyd numbers the drag coefficient is no longer governed by the velocity but depends only on the yield stress and the characteristic section of the obstacle. A stability criterion for which the obstacle is held in suspension has been calculated from it. The kinematic fields determined by PIV have enabled to characterize the shape and the extent of the sheared and static regions. The drag forces and the kinematic fields measurements have enabled to quantify the contribution of the normal and tangential stresses in the total drag force. The wall slip significantly reduces the drag coefficient and also reduces the extent of the sheared zones. A numerical simulation has been performed with an elasto-viscoplastic model by means of a code using finite elements method with Lagrangian integration points in the case of an adhesive flat plane.

Esta dissertação investiga numericamente a influência dos efeitos viscosos e elásticos em escoamentos de materiais viscoplásticos no interior de uma cavidade dirigida. O modelo mecânico empregado é constituído pelas equações de conservação de massa e pelo princípio da quantidade de movimento linear, para fluidos incompressíveis, acoplado à equação constitutiva. Esta equação modifica o modelo viscoelástico de Oldroyd-B de modo a acomodar que os tempos de relaxação e retardo do material, bem como sua viscosidade viscoplástica, dependam das mudanças de sua microestrutura. A aproximação numérica do modelo emprega o método multi-campos de Galerkin mínimos-quadrados em termos do tensor de tensão extra, do vetor velocidade e do campo de pressão. Os resultados objetivam a determinção do tamanho e localização das regiões aparentemente não-escoadas do material, bem como sua deformação elástica, intensidade de tensão, e a sua vorticidade no interior da cavidade. Os resultados claramente indicam que o padrão do escoamento é fortemente influenciado pela variação dos efeitos elásticos (variação do tempo de relaxação adimensional, θ0 * ), viscosos (variação do índice de power-law, n) e cinemáticos (variação da velocidade adimensional, U* , do escoamento) no interior da cavidade. / This dissertation investigated numerically the influence of viscous and elastic effects on flows of viscoplastic materials within a lid-driven cavity. The mechanical model used is made up of mass and momentum balance equations, coupled with the constitutive equation. This equation modifies the viscoelastic Oldroyd-B model to accommodate both relaxation and retardation times, and viscosity function, dependent on the microstructure changes. Numerical approximations of the model make use a three-field Galerkin least squares method in terms of the extra stress tensor, velocity vector and pressure field. Computations focus on the determination of the size and position of apparently unyielded regions as well as the elastic deformation, stress intensity, and the vorticity within of the cavity. Results clearly indicate that the flow pattern is strongly influenced by the elastic (variation of the dimensionless relaxation time, θ0 * ), viscous (variation of the power-law index, n) and kinematic (variation of the dimensionless flow velocity, U* ) effects within the cavity.

Este trabalho aborda o estudo de modelos constitutivos a fim de analisar o comportamento mecânico de um biopolímero derivado de óleo de mamona (Ricinus communis). A importância deste trabalho se dá ao fato de: servir como roteiro de ensaio de materiais poliméricos; completar caracterização do material estudado além do regime viscoelástico, bem como aplicação da análise do comportamento do material além do regime viscoelástico linear. A aplicação dos modelos avaliados via Método dos Elementos Finitos (MEF) exigiu o levantamento das propriedades e do comportamento mecânico do biopolímero, bem como a preparação dos ensaios, com as devidas especificações sugeridas pela ASTM (American Society for Testing and Materials) para cada tipo de ensaio. Assim, foram obtidos os corposde- prova (CDP) para a realização dos ensaios mecânicos quase-estáticos de tração, compressão e flexão (monotônicos e cíclicos), bem como, ensaio para análise dinâmicomecânica (Dynamic Mechanical Analysis - DMA) para a obtenção de propriedades associada às parcelas viscosas do material. Com estes foram obtidos parâmetros inerentes a cada tipo de ensaio, permeados com uma cuidadosa revisão bibliográfica sobre as implicações para a realização de cada ensaio. Uma outra etapa foi a verificação de modelos de plastificação baseados na teoria de von Mises, Drucker-Prager e de viscoelasticidade implementados no programa comercial ABAQUS®. Sendo que o objetivo maior foi a comparação dos resultados experimentais obtidos com os modelos em MEF. Os resultados para tração monotônica obtiveram erro de 0,61%, os resultados de compressão monotônica apresentaram erro de 1,5% e as simulações para os carregamentos cíclicos de tração e compressão não foram tão bons quanto os anteriores. Por isso se justifica a criação do modelo fenomenológico utilizando os parâmetros do material que foram identificados. / This work develops the study involving constitutive models with the objective to analyze the mechanical behavior of a biopolymer obtained from the Castor Oil Polyurethane (Ricinus communis). The importance of this work is due to the fact that: serves as a test script for the use of polymer materials; complete the characterization of the material studied beyond the viscoelastic realm, as well as the application of the analysis of the behavior of the material beyond the linear viscoelastic domain. The application of the evaluated models by way of the Finite Element Method (FEM), required the gathering of the properties and mechanical behavior of the biopolymer, as well as the preparation of the tests, with the required specifications suggested by the ASTM (American Society for Testing and Materials) for each type of test. Therefore, there were obtained the body-tests in order to run the mechanical quasi-static traction tests, tensile, compression and flexion (monotonic and cyclical) dynamicmechanical analysis (DMA) in order to obtain the properties associated with the viscous parts of the material. With these the inherent parameters were obtained for each specimen, permeated with a careful biographical revision of the implications for the experimenting of each specimen. Another phase was the verification of laminated models based on the theory by Von Mises, Drucker-Prager and of the viscoelasticity implemented in the commercial program ABAQUS®. The main objective being the comparison of the experimental results obtained with the models in FEM. The results for the monotonic traction obtained a error of 0,61%, the results of monotonic comparison presented an error of 1,5% and the simulations for the cyclical charges of traction and compression were not as good as the former. Therefore it justifies the creation of the phenomenological model utilizing the parameters of the materials that were identified.