Zunehmendes Downsizing und der Trend zum Leichtbau bei Welle-Nabe-Verbindungen erfordern eine exakte Beschreibung des Systemverhaltens. Elastische Simulationen erfordern im Post-processing die Analyse komplexer Zusammenhänge, welche oftmals nur empirisch begründet sind. Elastisch-Plastische Materialmodelle geben die Möglichkeit Stütz- und Setzeffekte von Passfederverbindungen bereits während der Simulation abzubilden. Die vorliegende Arbeit wendet elastisch-plastische Materialmodelle auf Passfederverbindungen an, um auftretende Versagensmechanismen zu beschreiben. / Downsizing and the trend to lightweight design ofshaft-hub-connections need an accurate description of the behaviour of the system. In post-processing, elastic simulations require a complex analysis based on empiric formula. Using elastic-plastic material models enable the possibility to respect support and set effects of feather key connections within the simulation. The current paper applies elastic-plastic material models to feather key connections in order to describe occurring failure mechanisms.

Hyperelasticity is a significant property of rubber, taken advantage of in engineering applications. A common application is the use of seals to prevent fluid transfer (liquid or gas) between solid regions. Volvo CE is often depending on external supplier when developing seals. However, it could be beneficial to be able to do design and analysis in-house. Thus, they want with this master thesis to increase their knowledge about rubber and FEM simulations of seals in ANSYS. The aim with this work is to develop a method and guidelines for analysis and simulation of seals of hyperelastic materials. Components analyzed in this thesis work are two static seals, an O-ring andan in-house modified X-ring design. Selected materials, HNBR and FKM, are commonly used elastomers at Volvo CE. Material tests performed at RISE are for three different load cases:uniaxial tension test, planar tension test and biaxial tension test. Quasi-static analyses are performed in ANSYS. Hyperelastic materials need different constitutive models, hyperelastic material models, to describe their material behavior and these are defined in terms of a strain energy density function.However, the challenge is to determine the material constants in the equation, to characterize the material properties, by processing test data. Research questions answered are ‘’What material tests are needed for hyperelastic materials?’’, ‘’How is the test data converted to work as input to ANSYS and obtain material constants?’’ and ‘’How is an appropriate material model selected for simulation in ANSYS?’’. The study shows the importance of that material test represents the condition the application will experience. It should capture material behavior at the specific frequency, strain amplitude and temperature range for the application. The expected strain range and deformation modes that will play a functional role in the application should be considered in the material testing. Material constants can be determined from test data separately or simultaneously. Test data from at least one deformation mode is required, but one can't accurately predict full deviatoric behavior of hyperelastic material models by using one mode. If data only is used for one deformation mode, simulations in other deformation modes can yield erroneous results. It is therefore recommended to use several deformation modes. For applications with more complex load cases more deformation modes are needed. Generally, recommended tests are uniaxial tension test, planar tension test and biaxial tension test due to homogenous deformation is achieved. It is important to verify the material model before analysis. Using test data from one deformation mode can still provide a good fit. In the cases investigated verifications of the material model Yeoh 3rd order show that the fit obtained by only using uniaxial tension test data and using test data from three tests doesn’t seem to differ. Both uniaxial tension test data and test data from three tests give agood fit when simulating the tests with this material model. The benefit of using test data from three tests is questionable due to costs. It seems that only uniaxial tension test data could have been used as it provided a good fit. Moreover, test data must be processed to work as input to ANSYS. ANSYS requires engineering stress-strain test data for hyperelastic materials besides from the volumetric test, where true stress strain is required. The biaxial tension state which is realized with so called Bulge test thus needs to be converted to engineering stress. Then, test data needs to be adjusted to account for effects such as hysteresis and Mullin’s effect, where choice of curve and a process zero-shift must be done. Hyperelastic material models have different validity for different strain ranges. The selected material model was Yeoh 3rd order, which showed be a good fit for both the materials, HNBR and FKM, in strain range 30 %. The curve fit is based on three tests. The selection was based on the material model with lowest relative error with stability. Material constants were obtained for that material model, and these were used in simulations. Material models tends to be unstable for strains outside the test data. Simulations of seals with fluid pressure were performed for different pressure and stretch of the seal. If the contact pressure is larger than fluid pressure in the seals no leakage will occur. / Hyperelasticitet är en betydande egenskap hos gummi, som används i tekniska tillämpningar. En vanlig tillämpning är tätningar för att förhindra vätskeöverföring (vätska eller gas) mellan fasta områden. Volvo CE är ofta beroende av externa leverantörer vid utveckling av tätningar. De vill därför med detta examensarbete öka sina kunskaper om gummi och FEM-simuleringar av tätningar i ANSYS. Målet med arbetet är att utveckla en metod och riktlinjer för analys och simulering av tätningar av hyperelastiska material. Komponenter som analyseras i detta examensarbete är två statiska tätningar, en O-ring och en intern modifierad X-ringdesign. Utvalda material, HNBR och FKM, är vanliga elastomerer hos Volvo CE. Materialtester som genomförts på RISE är för tre olika belastningsfall: enaxligt dragprov, plant dragprov och biaxialt dragprov. Quasi-statiska analyser genomfördes i ANSYS. Hyperelastiskt material behöver olika konstitutiva modeller, hyperelastsiska materialmodeller, för att beskriva dess materialbeteende och dessa definieras i termer av töjningsenergidensitetsfunktion. Utmaningen är att bestämma materialkonstanterna i ekvationen, för att karakterisera materialegenskaper, genom att processa testdatat. Forskningsfrågor som besvaras är ’’Vilka materialtester är nödvändiga för hyperelastiska material?’’, ’’Hur konverteras testdata för att fungera som indata till ANSYS och erhålla materialkonstanter?’’ och ’’Hur väljs lämplig materialmodell för simulering i ANSYS?’’. Studien visar vikten av att materialtester representerar förhållanden som är representativa för applikationen. Det bör fånga materialbeteendet vid den specifika frekvensen, töjningsamplitud och temperatur för applikationen. Det förväntade töjningsomårdet och deformationslägen som kommer spela en funktionell roll i applikationen bör beaktas i materialtestningen. Materialkonstanter kan beräknas från testdata separat eller simultant. Testdata från minst ett deformationsläge krävs, men man kan inte exakt förutsäga fullständigt devatoriskt beteende hos hyperelastiska materialmodeller genom att använda ett deformationsläge. Om testdata endast används för ett deformationsläge kan simuleringar i andra deformationslägen ge felaktiga resultat. Det är därför rekommenderat att använda flera deformationslägen. Generellt rekommenderade tester är enaxligt dragprov, plant dragprov och biaxialt dragprov då homogen deformation uppnås. Det är viktigt at verifiera materialmodellen innan analys. Att använda testdata från ett deformationsläge kan fortfarande ge en bra passning. I de undersökta fallen visar verifikation av materialmodellen Yeoh 3:e ordningen att passningen som erhållits av enbart enaxligt dragprovtestdata och testdata från tre tester inte skiljer sig åt. Både enaxligt dragprov testdata och testdata från tre tester ger en bra passning när simulerar testerna med den materialmodellen. Fördelarna med att använda testdata från tre tester är ifrågasatt pga. kostnaderna. Det verkar som enbart enaxligt dragprov testdata kunde ha använts då det gav en bra passning. Vidare behövs testdata hanteras för att fungera som indata till ANSYS. ANSYS behöver nominellspänning-töjning testdata för hyperelastiska material förutom för det volymetriska testet, där sannspänning-töjning behövs. Det biaxiala dragprovet som realiserades med s.k. Bulge test måste därför konverteras till nominell spänning. Sedan behöver testdata justeras för att ta hänsyn till effekter som hysteres och Mullins effekt, där val av kurva samt en process ‘’zero-shift’’ måste göras. Hyperelastiska materialmodeller har olika giltighet för olika töjningsområden. Val av materialmodell blev Yeoh 3:e ordningen som visade sig vara en bra passning för båda materialen, HNBR och FKM, i töjningsområden 30%. Kurvanpassningen är baserad på tre tester. Valet baserades på den materialmodell som hade minst relativt fel och som var stabil. Materialkonstanterer hölls för den materialmodellen och dessa användes i simuleringar. Materialmodeller tenderar att vara ostabila för töjningar utanför testdata. Simuleringar av tätningar med flödestryck genomfördes för olika tryck och stretch av tätningen. Om kontakttrycket är större än flödestrycket i tätningen sker inget läckage.

This work aims at dimensional reduction of nonlinear material models in an asymptotically accurate manner. The three-dimensional(3-D) nonlinear material models considered include isotropic, orthotropic and dielectric compressible hyperelastic material models. Hyperelastic materials have potential applications in space-based inflatable structures, pneumatic membranes, replacements for soft biological tissues, prosthetic devices, compliant robots, high-altitude airships and artificial blood pumps, to name a few. Such structures have special engineering properties like high strength-to-mass ratio, low deflated volume and low inflated density. The majority of these applications imply a thin shell form-factor, rendering the problem geometrically nonlinear as well. Despite their superior engineering properties and potential uses, there are no proper analysis tools available to analyze these structures accurately yet efficiently. The development of a unified analytical model for both material and geometric nonlinearities encounters mathematical difficulties in the theory but its results have considerable scope. Therefore, a novel tool is needed to dimensionally reduce these nonlinear material models. In this thesis, Prof. Berdichevsky’s Variational Asymptotic Method(VAM) has been applied rigorously to alleviate the difficulties faced in modeling thin shell structures(made of such nonlinear materials for the first time in the history of VAM) which inherently exhibit geometric small parameters(such as the ratio of thickness to shortest wavelength of the deformation along the shell reference surface) and physical small parameters(such as moderate strains in certain applications). Saint Venant-Kirchhoff and neo-Hookean 3-D strain energy functions are considered for isotropic hyperelastic material modeling. Further, these two material models are augmented with electromechanical coupling term through Maxwell stress tensor for dielectric hyperelastic material modeling. A polyconvex 3-D strain energy function is used for the orthotropic hyperelastic model. Upon the application of VAM, in each of the above cases, the original 3-D nonlinear electroelastic problem splits into a nonlinear one-dimensional (1-D) through-the-thickness analysis and a nonlinear two-dimensional(2-D) shell analysis. This greatly reduces the computational cost compared to a full 3-D analysis. Through-the-thickness analysis provides a 2-D nonlinear constitutive law for the shell equations and a set of recovery relations that expresses the 3-D field variables (displacements, strains and stresses) through thethicknessintermsof2-D shell variables calculated in the shell analysis (2-D). Analytical expressions (asymptotically accurate) are derived for stiffness, strains, stresses and 3-D warping field for all three material types. Consistent with the three types of 2-D nonlinear constitutive laws,2-D shell theories and corresponding finite element programs have been developed. Validation of present theory is carried out with a few standard test cases for isotropic hyperelastic material model. For two additional test cases, 3-Dfinite element analysis results for isotropic hyperelastic material model are provided as further proofs of the simultaneous accuracy and computational efficiency of the current asymptotically-correct dimensionally-reduced approach. Application of the dimensionally-reduced dielectric hyperelastic material model is demonstrated through the actuation of a clamped membrane subjected to an electric field. Finally, the through-the-thickness and shell analysis procedures are outlined for the orthotropic nonlinear material model.

In vielen industriellen Anwendungen sind Dichtungen im Einsatz. Vergleicht man den Preis mit dem eines Gesamtsystems, in denen Dichtungen verwendet werden, so sind Dichtungen verhältnismäßig günstig. Jedoch führt ein Versagen von Dichtungen meist zu schwerwiegenden Konsequenzen. Dichtungen sind komplexe Subsysteme und ihre Auslegung erfordert umfangreiche Kenntnisse im Bereich Materialmodellierung, Belastung und Versagenskriterien. Die heutige Simulationstechnologie ermöglicht einen parametrischen Workflow für die Berechnung des Verhaltens von Dichtungen mit den auftretenden Effekten wie nichtlinearem Materialverhalten, wechselnden Kontaktbedingungen und Flüssigkeitsunterwanderung bei Druck. Als ein führendes Simulationswerkzeug für diese physikalische Fragestellung wird ANSYS Mechanical für die Auslegung herangezogen. Desweiteren kann das Verständnis für das Produkt erhöht werden, was zu einer Verbesserung der Funktionalität und der Zuverlässigkeit führt. Versuchsdaten können als Spannungs-Dehnungskurven in ANSYS importiert werden, welche das Materialverhalten des hyperelastischen Werkstoffs mit traditionellen Materialmodellen wie Mooney Rivlin, Ogden and Yeoh oder einer neueren Formulierung, der Antwortfunktionsmethode, widerspiegeln. Robuste Kontakttechnologien beschleunigen die Simulation und Entwicklungszeit-Berechnungszeiten und gewährleisten ein genaues Verhalten des Simulationsmodells. Insbesondere bei Dichtungen ist die druckbeaufschlagte Fläche in 2D und 3D Anwendungen von Bedeutung. ANSYS berechnet diese automatisch in Abhängigkeit des aktuellen Kontaktzustandes. Diese benutzerfreundliche Unterstützung führt zu einer höheren Genauigkeit des Simulationsergebnisses, da ein manuelles Schätzen der Druckflächen entfällt. Mit einem parametrischen und durchgängigen Ansatz innerhalb von ANSYS Workbench, beginnend bei der CAD-Geometrie, über die Vernetzung, Material- und Randbedingungsdefinition und Lösung. können eine Reihe von Varianten in kurzer Zeit berechnet werden. Neben einem besseren Verständnis für das Produkt hilft dies dem Ingenieur Änderungen vorzunehmen, was zu exakten und aussagekräftigen Ergebnissen führt. Desweiteren kann der Einfluss von Unsicherheiten berücksichtigt werden, sodass der Berechnungsingenieur fernab von idealen Bedingungen robuste und zuverlässige Dichtungen entwickeln kann.

La simulation de matériaux physico-réalistes est un processus demandant beaucoup de calcul. Les images de synthèse étant destinées aux observateurs humains, nous pouvons utiliser les limitations de notre système visuel pour simplifier le modèle de rendu, en évitant le calcul d’information invisible. Cela s’appelle le réalisme perceptif. Nous nous intéressons à la simulation de peintures d’automobiles, en particulière aux peintures scintillantes à paillettes métalliques. Nous essayons d’améliorer le réalisme perceptif de deux manières : en utilisant de la visualisation stéréoscopique pour apporter de l’information de profondeur additionnelle à partir de la disparité binoculaire ; et en conservant autant d‘information perceptive de la luminance originale que possible. La gamme dynamique illimitée d’une scène réelle est réduite lorsqu’une image est traitée dans des dispositifs à une gamme dynamique plus basse dans la chaîne d’acquisition et de visualisation. Pour assurer un réalisme perceptive, nous proposons une méthodologie reposant sur la caractérisation des dispositifs, l’acquisition d’information radiométrique, et des validations visuo-perceptives. En remplaçant l’œil humain par un appareil photo numérique, en tant qu’intégrateur tristimulaire d’information radiométrique, nous réalisons des comparaisons visuelles entre des échantillons réels et des photographies pour estimer la valeur d’exposition qui maximise le réalisme perceptif dans un environnement d’observation contrôlé. Ces résultats sont ensuite contrastés avec plusieurs méthodes de reproduction tonale, afin d’analyser les effets perceptifs de certains attributs d’image tels que l’exposition, la gamme dynamique, la brillance, et le contraste. Nous proposons également une méthodologie complète pour simuler des scènes réelles qui soient comparables, d’un point vue radiométrique et colorimétrique, aux photographies de la même scène. En assurant des images simulées correctes, cette méthodologie établie les bases face à une future intégration de nos observations dans le moteur de rendu. / The simulation of physico-realistic materials is a process that requires a lot of computation. Since the images are meant to be seen by human observers, we can use the limitations of their visual system to simplify the rendering model, avoiding redundant information that will not be seen. This is known as perceptual realism. Focusing on the simulation of automobile paint coatings, with special attention to metallic-flaked coatings with a sparkling appearance, we try to improve perceptual realism in two ways: using stereoscopic visualization, to provide additional depth information from binocular disparity; and preserving as much of the original perceptual luminance information as possible. The unlimited luminance levels, or dynamic range, of a real scene must be reduced as an image is processed by lower-dynamic range media throughout the acquisition and visualization chain. To ensure perceptual accuracy throughout this process, we propose a methodology consisting on device characterization, radiometric acquisition, and visuo-perceptual validations. Replacing the human eye by a DSLR camera, as a trichromatic color integrator of radiometric information, we perform visual comparisons of real samples and photographs to estimate the image exposure that maximizes perceptual accuracy under a controlled observation environment. These results are then contrasted with different tone reproduction methods, in order to analyze the effects on texture perception of specific image attributes like exposure, dynamic range, brightness, and contrast. We also propose a full methodology to produce simulations of a real scene, which are radiometrically and colorimetrically comparable to photographs of the same scene. By ensuring that the simulation produces correct images, this methodology lays the foundations for a future integration of our observations into the rendering engine.

Estruturas aeronáuticas são em sua grande parte fabricadas em material compósito para que sejam atendidas as especificações de projeto. Entre essas estruturas destaca-se a estrutura sanduíche. A utilização desse tipo de estrutura requer estudos extensos em novos materiais, bem como na aplicação dos mesmos. Uma atenção especial para o núcleo dessas estruturas é necessária, pois este material é na verdade uma estrutura celular, como as espumas poliméricas. Esta dissertação busca concatenar a literatura com a prática ao estudar a calibração de modelos de material para descrever o comportamento mecânico de espumas poliméricas, bem como avaliar suas potencialidades e limitações. Estas espumas são estruturas celulares cujos mecanismos de falha consistem em respostas micro e macroscópicas. A identificação e quantificação desses comportamentos podem ser feitas através da investigação de modelos de material micro-mêcanicos ou fenomenológicos (macro-mecânicos) associados a ensaios e análises experimentais tanto do material celular quanto da estrutura na qual este material é utilizado. Cada abordagem, micro ou macro-mecânica, possui vantagens e desvantagens que no presente trabalho são discutidas para o material estudado (espuma polimérica rígida de PVC, poli-cloreto de vinila, com estrutura de células fechada e densidade de 60kg/m³). Uma série de ensaios experimentais com bases em normas é realizada e os dados coletados são comparados com dados obtidos simultaneamente através de uma técnica de correlação de imagens. Todas as informações experimentais são confrontadas e associadas aos mecanismos de falha da espuma polimérica. Finalmente, os dados experimentais são utilizados nas identificações de parâmetros de modelos de material disponíveis em um programa comercial de elementos finitos - ABAQUS. Com os modelos de material calibrados, o presente trabalho investiga a representatividade e as limitações dos mesmos quando aplicados a estruturas aeronáuticas submetidas a cargas localizadas, monotônicas ou não. Observou-se que há uma forte dependência da resposta macroscópica da espuma com sua estrutura celular quando submetida a cargas localizadas e/ou não-monotônicas. Ademais, o uso de modelos de material simplificados, e/ou com hipóteses de implementação, gera resultados duvidosos quando estes modelos são aplicados a materiais celulares com respostas complexas (mecanismos micro-mecânicos, anisotropia, viscosidade, etc.). Todavia, o presente trabalho mostra que uma calibração estratégica relevando as hipóteses de implementação e as limitações do modelo de material, fornece bons resultados macroscópicos que são fortemente influenciados pelos mecanismos de falha micro-mecânicos. / Aircraft structures are mostly made of composite material in order to achieve the specifications of a project. Among these structures one highlights the sandwich structure. The usage of this structure requires extensive studies on new materials as well as on the application of these very materials. A special attention for the cores material of these structures is needed because it is in fact a cellular structure, as the polymeric foams. This dissertation seeks to concatenate the literature and practice, studying the calibration of material models to describe the mechanical behavior of polymeric foams, as well as to analyse their potentials and limitations. These foams are cellular structures whose failure mechanisms comprise micro and macro responses. The identification and quantification of these behaviors can be done through micro-mechanical or phenomenological (macro-mechanical) material models along with experimental tests and analyses of both the cellular material and the structure in which this material is used. Each approach, micro or macro, has advantages and disadvantages that in the present work are discussed for the studied material (PVC, poly-vinyl-chloride, rigid closed-cell polymeric foam with a density of 60kg/m³). A series of experimental tests based on standard procedures are carried out and the data collected are compared with data obtained simultaneously through an image correlation technique. All the experimental information are confronted and associated to the failure mechanisms of the polymeric foam. Finally, the experimental data are used for the identification of material models parameters, currently available in the commercial finite elements software - ABAQUS. With the material models calibrated, the present work investigates the representativeness and the limitations of these very models when applied to aircraft structures submitted to monotonic or not localized loads. One has observed that there is a strong dependence of the foams macroscopic response with its cellular structure when it is submitted to localized and/or non-monotonic loads. Moreover, the usage of simplified material models, and/or with some implementation hypotheses, renders doubtful results when these models are applied to cellular materials with complex responses (micro-mechanical mechanisms, anisotropy, viscosity, etc.). Nevertheless, the present work shows that a strategic calibration taking into account the implementation hypotheses and the limitations of the material model, yields good macroscopic results that are strongly influenced by the micro-mechanical failure mechanisms.

Estruturas aeronáuticas são em sua grande parte fabricadas em material compósito para que sejam atendidas as especificações de projeto. Entre essas estruturas destaca-se a estrutura sanduíche. A utilização desse tipo de estrutura requer estudos extensos em novos materiais, bem como na aplicação dos mesmos. Uma atenção especial para o núcleo dessas estruturas é necessária, pois este material é na verdade uma estrutura celular, como as espumas poliméricas. Esta dissertação busca concatenar a literatura com a prática ao estudar a calibração de modelos de material para descrever o comportamento mecânico de espumas poliméricas, bem como avaliar suas potencialidades e limitações. Estas espumas são estruturas celulares cujos mecanismos de falha consistem em respostas micro e macroscópicas. A identificação e quantificação desses comportamentos podem ser feitas através da investigação de modelos de material micro-mêcanicos ou fenomenológicos (macro-mecânicos) associados a ensaios e análises experimentais tanto do material celular quanto da estrutura na qual este material é utilizado. Cada abordagem, micro ou macro-mecânica, possui vantagens e desvantagens que no presente trabalho são discutidas para o material estudado (espuma polimérica rígida de PVC, poli-cloreto de vinila, com estrutura de células fechada e densidade de 60kg/m³). Uma série de ensaios experimentais com bases em normas é realizada e os dados coletados são comparados com dados obtidos simultaneamente através de uma técnica de correlação de imagens. Todas as informações experimentais são confrontadas e associadas aos mecanismos de falha da espuma polimérica. Finalmente, os dados experimentais são utilizados nas identificações de parâmetros de modelos de material disponíveis em um programa comercial de elementos finitos - ABAQUS. Com os modelos de material calibrados, o presente trabalho investiga a representatividade e as limitações dos mesmos quando aplicados a estruturas aeronáuticas submetidas a cargas localizadas, monotônicas ou não. Observou-se que há uma forte dependência da resposta macroscópica da espuma com sua estrutura celular quando submetida a cargas localizadas e/ou não-monotônicas. Ademais, o uso de modelos de material simplificados, e/ou com hipóteses de implementação, gera resultados duvidosos quando estes modelos são aplicados a materiais celulares com respostas complexas (mecanismos micro-mecânicos, anisotropia, viscosidade, etc.). Todavia, o presente trabalho mostra que uma calibração estratégica relevando as hipóteses de implementação e as limitações do modelo de material, fornece bons resultados macroscópicos que são fortemente influenciados pelos mecanismos de falha micro-mecânicos. / Aircraft structures are mostly made of composite material in order to achieve the specifications of a project. Among these structures one highlights the sandwich structure. The usage of this structure requires extensive studies on new materials as well as on the application of these very materials. A special attention for the cores material of these structures is needed because it is in fact a cellular structure, as the polymeric foams. This dissertation seeks to concatenate the literature and practice, studying the calibration of material models to describe the mechanical behavior of polymeric foams, as well as to analyse their potentials and limitations. These foams are cellular structures whose failure mechanisms comprise micro and macro responses. The identification and quantification of these behaviors can be done through micro-mechanical or phenomenological (macro-mechanical) material models along with experimental tests and analyses of both the cellular material and the structure in which this material is used. Each approach, micro or macro, has advantages and disadvantages that in the present work are discussed for the studied material (PVC, poly-vinyl-chloride, rigid closed-cell polymeric foam with a density of 60kg/m³). A series of experimental tests based on standard procedures are carried out and the data collected are compared with data obtained simultaneously through an image correlation technique. All the experimental information are confronted and associated to the failure mechanisms of the polymeric foam. Finally, the experimental data are used for the identification of material models parameters, currently available in the commercial finite elements software - ABAQUS. With the material models calibrated, the present work investigates the representativeness and the limitations of these very models when applied to aircraft structures submitted to monotonic or not localized loads. One has observed that there is a strong dependence of the foams macroscopic response with its cellular structure when it is submitted to localized and/or non-monotonic loads. Moreover, the usage of simplified material models, and/or with some implementation hypotheses, renders doubtful results when these models are applied to cellular materials with complex responses (micro-mechanical mechanisms, anisotropy, viscosity, etc.). Nevertheless, the present work shows that a strategic calibration taking into account the implementation hypotheses and the limitations of the material model, yields good macroscopic results that are strongly influenced by the micro-mechanical failure mechanisms.

The aim of the Diploma Thesis is to discuss the creation of material models for the forming technology in quasi-static and dynamic loading conditions and to practically propose a methodology of modeling the mechanical behavior of the selected material for dynamic load conditions using the Split Hopkinson Tensile Bar Test. The presented work contains an overview and analysis of individual experimental methods with the influence of the strain rate in terms of the extent of their suitability, the analysis of the plastic deformation mechanism, an overview of the mathematical mechanical behavior models for the materials used for technological practice and the evaluation of the mechanical behavior of stainless steel according to ČSN 41 7348 in terms of flat formability incl. evaluation of microstructure, fractographic analysis and evaluation of results from ferromagnetism measurement of steel after dynamic loading.

[pt] Neste trabalho um estudo de estruturas pneumáticas considerando acoplamento pressão–volume e modelos constitutivos plásticos e viscoplásticos são desenvolvidos. Estruturas pneumáticas são estruturas de membrana sobre as quais atuam pressão de gases estabilizadas por tensões de tração. Essas estruturas são mais leves que estruturas convencionais resultando em soluções mais econômicas. Elas possuem ainda algumas características que contribuem para um desenvolvimento sustentável, como a utilização de luz natural e ventilação e a possibilidade de reutilização. Quando as estruturas pneumáticas são submetidas a cargas externas, essas estruturas apresentam variação da pressão internal e do volume. Este acoplamento é um dos objetos de estudo do presente trabalho. Soluções analíticas são desenvolvidas para descrever este acoplamento. Em programas convencionais de elementos finitos esse acoplamento não é considerado. Uma formulação para o acoplamento pressão–volume para câmaras fechadas é incluído no modelo de elementos finitos com grandes deformações. A variedade de modelos de material implementados tem a finalidade de abranger o comportamento de muitos tipos de materiais de membrana usados em estruturas pneumáticas. Na literatura o estudo dos materiais de membrana para estruturas pneumáticas tem foco na análise experimental. Modelos para material de membrana são incorporados no modelo de elementos finitos para pequenas e grandes deformações. Os modelos constitutivos considerados neste trabalho são hiperelástico, elastoplástico e elastoviscoplástico. A ocorrência de grandes deformações é incluída. Um novo material baseado em superfícies NURBS é proposto e validado com base em resultados experimentais e modelos clássicos de materiais. Neste trabalho ênfase é dada ao material ETFE (Etileno tetrafluoretileno), o qual é amplamente usado em estruturas pneumáticas. Os modelos desenvolvidos aqui, como o acoplamento pressão–volume e os modelos de materiais são implementados em elementos finitos no programa usado na cadeira de estática das construções da TUM (Technische Universitat Munchen), chamado CARAT++ (Computer Aided Research Analysis Tool). / [en] In this work a study of pneumatic structures considering pressure–volume coupling under plastic and viscoplastic material behavior is developed. Pneumatic structures are membrane structures acted on by air or gases stabilized by tension. These structures are lighter than conventional structures resulting in economic structural solutions. They present also some characteristics that contribute to the sustainable development, such as the utilization of natural lighting and ventilation and its possibility of reuse. When pneumatic structures are subjected to external loads these structures present both internal pressure and volume variation. This coupling is one of the objects of the present work. Analytical solutions are developed to describe this coupling. In conventional finite element systems this coupling is not considered. A formulation for pressure–volume coupling by closed chambers is included in the framework of a finite element large strain model. The variety of material models implemented has the purpose to cover the behavior of the many kinds of membrane materials used in pneumatic structures. In the literature the study of the membrane materials for pneumatic structures focuses on experimental analysis. Membrane material models are incorporated in the finite element model for small and large strains. The constitutivematerial models considered in this work are hyperelastic, elastoplastic and elastoviscoplastic. The onset of large strains is enclosed. A new material model based on NURBS surfaces is proposed an validated on hand of experimental results and classic material models. In this work emphasis is given to the material ETFE (Ethylene tetrafluoroethylene), which is widely used in pneumatic structures. The models developed here, such as the pressure-volume coupling and the material models, are implemented in finite elements on the program used in the Static Chair at TUM (Technische Universitat Munchen), which is called CARAT++ (Computer Aided Research Analysis Tool).

Im vorliegenden Beitrag werden die prognostizierten Verformungen gemäß der Materialmodelle des fib Model Code 2010 sowie der DIN EN 1992-1-1:2011 realen Messdaten gegenübergestellt, die über einen Zeitraum von mehr als 12 Jahren an einer großen Talbrücke erfasst wurden. Die numerischen Berechnungen zeigen, dass sich die Stoffgesetze deutlich in ihrer Höhe und dem zeitlichen Verlauf der prognostizierten viskosen Betonverformungen unterscheiden. Die höchste Übereinstimmung mit den Messdaten wiesen die Stoffgesetze des EC 2 auf.