In the literature, there are various material models proposed so as to model the constitutive behavior of hyperelastic materials for example, St. Venant-Kirchho_ model, Mooney-Rivlin model etc. The stability of such material models under various states of deformation is of important concern, and generally stability analysis is conducted in homogeneous states of deformation. Within hyperelasticity, instabilities can be broadly classified as geometrical and material types. Geometrical instabilities such as buckling, symmetric bifurcation etc. are of physical origin, and lead to multiple solutions at critical stretch. Material instability is a aw in the material model and leads to unphysical solutions at the onset. It is required that the constitutive model should be materially stable i.e., should not give unphysical results, and be able to predict correctly the onset of geometrical instabilities. Certain constitutive restrictions proposed in the literature are inadequate to characterize such instabilities. In the work, we propose stability criteria which will characterize geometrical as well as material instabilities. A new elasticity tensor is defined, which is found to characterize material instability adequately. In order to investigate the validity of proposed stability criteria, three important constitutive models of hyperelasticity viz., St. Venant-Kirchho_, compressible Mooney-Rivlin and compressible Ogden models are investigated for stability.

The diploma thesis deals with the assessment of the prediction of brain aneurysm rupture based on its geometrical and material properties. In the first part of the thesis there is a~detailed research study of cardiovascular systems with a focus on the cerebral artery and aneurysm occurring on their bifurcates. The second part of the thesis is focused on the creation of two models of arterial cerebral bifurcation with the presence of aneurysm and on obtaining their geometry in unloaded state. Emphasis is placed on the most realistic constitutive model of the artery wall material based on real data from uniaxial tensile tests and on a suitably chosen blood pressure load. This blood pressure may be step-changed, for example, in bungee jumping. In the work, a calculation of the increase in blood pressure during the step-change is performed, which is subsequently used in calculations of tension in the wall of the cerebral aneurysm. In conclusion, the risk of rupture is evaluated in two model idealized brain aneurysms and a discussion of the credibility of the results is given.

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.

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O câncer de mama é um problema de saúde pública e possui a maior incidência e mortalidade na população feminina em todo o mundo. A detecção precoce do câncer de mama é essencial para redução da morbidade e mortalidade associadas a esta doença. Alguns dos métodos usados para detecção dos tumores mamários são a ultrassonografia, a imagem por ressonância magnética (MRI), a tomografia por emissão de pósitrons (PET), a tomossíntese e a mamografia, recomendada como técnica de rastreamento. Cada um dos métodos apresenta vantagens e desvantagens, como provocar desconforto ao paciente durante a realização dos exames, possíveis reações ao agente de contraste, emissão de radiação, dependência do operador para análise dos resultados, dificuldade de detecção em tecidos densos, falta de acessibilidade para pessoas com deficiência ou baixa mobilidade, alto custo e produção de rejeitos radioativos. O objetivo principal deste trabalho é aplicar os métodos de impedância eletromecânica e térmica na detecção de inclusões para que possam ser futuramente usados como técnicas alternativas às já existentes na identificação de tumores mamários. A aplicação do método da impedância eletromecânica que utiliza transdutores piezelétricos, atuando simultaneamente como sensor e atuador, acoplados à estrutura analisada permite o monitoramento das mudanças da massa, rigidez e/ou amortecimento e a consequente detecção da inclusão. O mesmo procedimento é aplicado no método da impedância térmica que, por sua vez, consiste na razão entre a variação da resposta da temperatura superficial da estrutura em função da aplicação de um fluxo de calor externo. A detecção das inclusões torna-se possível devido a definições de métricas de dano que são parâmetros estatísticos capazes de representar numericamente a diferença entre duas medições antes e após o dano. A metodologia proposta é validada experimentalmente através da aplicação em materiais hiperplásticos de geometria simples e complexa. Amostras de silicone e modelos de aplicação médica são analisadas. Os métodos de impedância propostos apontaram, preliminarmente, para uma maior sensibilidade da técnica a inclusões menores, de 10 mm de diâmetro para os testes realizados. Além disso, observou-se que o aquecimento externo imposto aos modelos e a presença de geração de calor nas inclusões auxiliou na detecção. Um teste qualitativo foi realizado in vivo para a análise do potencial de uso da impedância eletromecânica em aplicações clínicas. Este trabalho apresenta contribuições importantes, não só no campo da engenharia biomecânica, mas também na análise do comportamento estrutural, ampliando as aplicações de técnicas de dano em materiais hiperelásticos, assim como, propondo o uso da impedância térmica como um novo parâmetro para identificação de inclusões ou falhas estruturais em ensaios não destrutivos. / Breast cancer is a public health problem and has the highest incidence and mortality in the female population worldwide. Early detection of breast cancer is essential for reducing the morbidity and mortality associated with this disease. Some of the methods used to detect breast tumors are ultrasonography, magnetic resonance imaging (MRI), positron emission tomography (PET), tomosynthesis and mammography, which is recommended as a screening technique. Each method has its advantages and disadvantages, such as discomfort to the patient during the exams, possible reactions to the contrast agent, radiation emission, operator dependence for the analysis of results, difficulty for detection in dense tissues, lack of accessibility for people with disabilities or low mobility, high cost and radioactive waste production. The main objective of this work is to apply the electromechanical and thermal impedance methods in the detection of inclusions, in order to be used, in the future, as alternative techniques to those already existent for the identification of breast tumors. The application of the electromechanical impedance method using piezoelectric transducers, acting simultaneously as a sensor and actuator, coupled to the analyzed structure allows the monitoring of mass, rigidity and/or damping variations, and consequent detection of the inclusion. The same procedure is applied in the thermal impedance method, which consists of the ratio between the gradient of the surface temperature response of the structure as a function of the application of an external heat flow. The detection of inclusions is possible due to the damage metrics that are statistical parameters capable of numerically representing the difference between two measurements before and after the damage. The proposed methodology is validated experimentally through the application in hyperplastic materials of simple and complex geometry. Silicone samples and medical application models are analyzed. The proposed impedance methods preliminarily presented a higher sensitivity of the technique to smaller inclusions of 10 mm in diameter for the tests performed. In addition, it was observed that the external heating imposed on the models and the presence of heat generation in the inclusions aided in the detection. A qualitative test was performed in vivo to analyze the potential of the use of electromechanical impedance in clinical applications. This work presents important contributions not only in the field of biomechanical engineering, but also in the analysis of structural behavior, expanding the applications of damage techniques in hyperelastic materials, as well as proposing the use of thermal impedance as a new parameter for identification of inclusions or structural failures in nondestructive testing. / Tese (Doutorado)

This thesis is focused on stress in brain aneurysms. It consists of three parts. First part is aimed for gaining information about the topic from scientific resources. Next part consists of analyses of geometry of cerebral aneurysms on the computed wall stress. Analyses are performed on four basic geometrical models and results are being discussed. The risky areas in each investigated shape have been identified as well as the comparisons of stress between those shapes have been performed and the most dangerous shape among investigated shapes has been determined. Third part investigates the influence of surrounding tissue on the brain aneurysm. Conclusion of this thesis is that brain gray tissue has positive yet negligible effect on the computed wall stress.

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.