This thesis will be focusing on studies about the hyperelastic material method and how to best implement it in a FEA model. It will look more specific at the Mooney-Rivlin method, but also have a shorter explanation about the different methods. This is due to problems Roxtec has today about simulating rubber takes long time, are instable and unfortunately not completely trustworthy, therefore a deep study about the hyperelastic material method were chosen to try and address these issuers. The Mooney-Rivlin method (which is a part of the hyperelastic material method) is reliant on a few constant to represent the material, how to obtain these constants numerical and later implement these is suggested in this thesis as well. The results is the methodology needed to obtain constants for Mooney-Rivlin and later how to implement these in FEA software. In this thesis the material Roxylon has been studied and given suggestion on these constants as well as an implementation of the given material. / För en bra simulering utav hyperelastiska material, exempelvis för gummi, har detta examensarbete fokuserat på att undersöka hyperelastiska material metoder och hur man kan implementera det i FEA program.

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Low back pain is an ailment that affects a significant portion of the community. However, due to the complexity of the spine, which is a series of interconnected joints, and the loading conditions applied to these joints the causes for back pain are not well understood. Investigations of damage or failure of the spinal structures from a mechanical viewpoint may be viewed as a way of providing valuable information for the causes of back pain. Low back pain is commonly associated with injury to, or degeneration of, the intervertebral discs and involves the presence of tears or lesions in the anular disc material. The aim of the study presented in this thesis was to investigate the biomechanical effect of anular lesions on disc function using a finite element model of the L4/5 lumbar intervertebral disc. The intervertebral disc consists of three main components - the anulus fibrosus, the nucleus pulposus and the cartilaginous endplates. The anulus fibrosus is comprised of collagen fibres embedded in a ground substance while the nucleus is a gelatinous material. The components of the intervertebral disc were represented in the model together with the longitudinal ligaments that are attached to the anterior and posterior surface of the disc. All other bony and ligamentous structures were simulated through the loading and boundary conditions. A high level of both geometric and material accuracy was required to produce a physically realistic finite element model. The geometry of the model was derived from images of cadaveric human discs and published data on the in vivo configuration of the L4/5 disc. Material properties for the components were extracted from the existing literature. The anulus ground substance was represented as a Mooney-Rivlin hyperelastic material, the nucleus pulposus was modelled as a hydrostatic fluid in the healthy disc models and the cartilaginous endplates, collagen fibres and longitudinal ligaments were represented as linear elastic materials. A preliminary model was developed to assess the accuracy of the geometry and material properties of the disc components. It was found that the material parameters defined for the anulus ground substance did not accurately describe the nonlinear shear behaviour of the tissue. Accurate representation this nonlinear behaviour was thought to be important in ensuring the deformations observed in the anulus fibrosus of the finite element model were correct. There was no information found in the literature on the mechanical properties of the anulus ground substance. Experimentation was, therefore, carried out on specimens of sheep anulus fibrosus in order to quantify the mechanical response of the ground substance. Two testing protocols were employed. The first series of tests were undertaken to provide information on the strain required to initiate permanent damage in the ground substance. The second series of tests resulted in the acquisition of data on the mechanical response of the tissue to repeated loading. The results of the experimentation carried out to determine the strain necessary to initiate permanent damage suggested that during daily loading some derangement might be caused in the anulus ground substance. The results for the mechanical response of the tissue were used to determine hyperelastic constants which were incorporated in the finite element model. A second order Polynomial and a third order Ogden strain energy equation were used to define the anulus ground substance. Both these strain energy equations incorporated the nonlinear mechanical response of the tissue during shear loading conditions. Using these geometric data and material properties a finite element model of a representative L4/5 intervertebral disc was developed. When the measured material parameters for the anulus ground substance were implemented in the finite element model, large deformations were observed in the anulus fibrosus and excessive nucleus pressures were found. This suggested that the material parameters defining the anulus ground substance were overly compliant and in turn, implied the possibility that the stiffness of the sheep anulus ground substance was lower than the stiffness of the human tissue. Even so, the mechanical properties of the sheep joints had been shown to be similar to those of the human joint and it was concluded that the results of analyses using these parameters would provide valuable qualitative information on the disc mechanics. To represent the degeneration of the anulus fibrosus, the models included simulations of anular lesions - rim, radial and circumferential lesions. Degeneration of the nucleus may be characterised by a significant reduction in the hydrostatic nucleus pressure and a loss of hydration. This was simulated by removal of the hydrostatic nucleus pressure. Analyses were carried out using rotational loading conditions that were comparable to the ranges of motion observed physiologically. The results of these analyses showed that the removal of the hydrostatic nucleus pressure from an otherwise healthy disc resulted in a significant reduction in the stiffness of the disc. This indicated that when the nucleus pulposus is extremely degenerate, it offers no resistance to the deformation of the anulus and the mechanics of the disc are significantly changed. Specifically, the resistance to rotation offered by the intervertebral disc is reduced, which may affect the stability of the joint. When anular lesions were simulated in the finite element model they caused minimal changes in the peak moments resisted by the disc under rotational loading. This suggested that the removal of the nucleus pressure had a greater effect on the mechanics of the disc than the simulation of anular lesions. The results of the finite element model reproduced trends observed in both the healthy and degenerate intervertebral disc in terms of variations in nucleus pressure with loading conditions, axial displacement of the superior surface and bulge of the peripheral anulus. It was hypothesised that the reduced rotational stiffness of the degenerate disc may result in overload of the surrounding innervated osseoligamentous anatomy which may in turn cause back pain. Similarly back pain may result from the abnormal deformation of the innervated peripheral anulus in the vicinity of anular lesions. Furthermore, it was hypothesised that biochemical changes may result in the degeneration of the nucleus, which in turn may cause excessive strains in the anulus ground substance and lead to the initiation of permanent damage in the form of anular lesions. With further refinement of the components of the model and the methods used to define the anular lesions it was considered that this model would provide a powerful analysis tool for the investigation of the mechanics of intervertebral discs with and without significant degeneration.

Com o crescente uso de estruturas de membrana tensionada, as relações tensãodeformação do tecido utilizado em sua fabricação devem ser bem entendidas. Deste modo, esta dissertação apresenta um estudo sobre o comportamento mecânico de um tecido arquitetônico PTFE-vidro, ressaltando seu complexo mecanismo de deformação que engloba efeitos de anisotropia, não-linearidade física, troca de ondulações, histerese, remoção do espaçamento entre os fios e variação de temperatura. Diferentes métodos para modelagem do material foram estudados, com ênfase no modelo de material ortótropo representado por um funcional energia de deformação hiperelástico. Além disso, vários protocolos para ensaios de tração em tecidos recobertos foram analisados e uma série de ensaios biaxiais com amostras cruciformes foram realizados no Centro de Pesquisa e Desenvolvimento da Birdair, Inc. Um determinado funcional energia de deformação foi então ajustado aos dados de campo obtidos nestes testes, cujos resultados foram então comparados diretamente aos dados obtidos em campo e a um ajuste direto de uma superfície suave tensão-deformação. A performance do modelo ajustado não se encontra ainda em um patamar de aplicação industrial, entretanto este estudo permite um entendimento global dos mecanismos de deformação do tecido PTFEvidro, fornecendo também uma massa de dados consistentes que podem ser utilizados em situações práticas. / Considering the growing use of tensioned membrane structures, the stress-strain relation of the fabric used on its construction must be well understood. This dissertation presents a study of the mechanical behavior of a PTFE coated fiberglass fabric, emphasizing its complex strain mechanism which is influenced by the material anisotropy, physical non-linearity, crimp interchange, hysteresis, removal of yarn spacing and changes in temperature. Different material models were studied, focusing on an orthotropic material model represented by a hyperelastic strain energy function. Also, different test protocols were reviewed and a series of biaxial tests on cruciform samples were performed at the Birdair, Inc.s Research and Development Center. A strain energy function was adjusted to the collected data and than its results compared to the data itself and to another stress-strain function directly adjusted to the data. The performance of the strain-energy function chosen is not on a level of industrial application; however this study gives a global understanding of the PTFE coated fiberglass strain mechanism and also provides a consistent database that may be used on real situations.

Multi-ribbed serpentine belt is the core of the automotive accessory drive system, which distributes the engine power to other auxiliary systems of the car. Development of a belt life model is of a significant importance to the accessory drive system manufacturers, in order to prevent any premature failures of these belts. However, any numerical analysis on the belt life is heavily dependent on gaining an understanding of stress distribution in the belts under the operational loading conditions. The presented work demonstrates a new systematic approach for determining the hyperelastic material parameters of rubber with specific application in Finite Element Analysis (FEA) of serpentine accessory drive belts. This new approach can be used as a stand-alone tool by manufacturers to determine the stress distribution in the belt under operational conditions; the results of which can be applied to assess the life of accessory drive belts, in a relatively short time.

Multi-ribbed serpentine belt is the core of the automotive accessory drive system, which distributes the engine power to other auxiliary systems of the car. Development of a belt life model is of a significant importance to the accessory drive system manufacturers, in order to prevent any premature failures of these belts. However, any numerical analysis on the belt life is heavily dependent on gaining an understanding of stress distribution in the belts under the operational loading conditions. The presented work demonstrates a new systematic approach for determining the hyperelastic material parameters of rubber with specific application in Finite Element Analysis (FEA) of serpentine accessory drive belts. This new approach can be used as a stand-alone tool by manufacturers to determine the stress distribution in the belt under operational conditions; the results of which can be applied to assess the life of accessory drive belts, in a relatively short time.

Com o crescente uso de estruturas de membrana tensionada, as relações tensãodeformação do tecido utilizado em sua fabricação devem ser bem entendidas. Deste modo, esta dissertação apresenta um estudo sobre o comportamento mecânico de um tecido arquitetônico PTFE-vidro, ressaltando seu complexo mecanismo de deformação que engloba efeitos de anisotropia, não-linearidade física, troca de ondulações, histerese, remoção do espaçamento entre os fios e variação de temperatura. Diferentes métodos para modelagem do material foram estudados, com ênfase no modelo de material ortótropo representado por um funcional energia de deformação hiperelástico. Além disso, vários protocolos para ensaios de tração em tecidos recobertos foram analisados e uma série de ensaios biaxiais com amostras cruciformes foram realizados no Centro de Pesquisa e Desenvolvimento da Birdair, Inc. Um determinado funcional energia de deformação foi então ajustado aos dados de campo obtidos nestes testes, cujos resultados foram então comparados diretamente aos dados obtidos em campo e a um ajuste direto de uma superfície suave tensão-deformação. A performance do modelo ajustado não se encontra ainda em um patamar de aplicação industrial, entretanto este estudo permite um entendimento global dos mecanismos de deformação do tecido PTFEvidro, fornecendo também uma massa de dados consistentes que podem ser utilizados em situações práticas. / Considering the growing use of tensioned membrane structures, the stress-strain relation of the fabric used on its construction must be well understood. This dissertation presents a study of the mechanical behavior of a PTFE coated fiberglass fabric, emphasizing its complex strain mechanism which is influenced by the material anisotropy, physical non-linearity, crimp interchange, hysteresis, removal of yarn spacing and changes in temperature. Different material models were studied, focusing on an orthotropic material model represented by a hyperelastic strain energy function. Also, different test protocols were reviewed and a series of biaxial tests on cruciform samples were performed at the Birdair, Inc.s Research and Development Center. A strain energy function was adjusted to the collected data and than its results compared to the data itself and to another stress-strain function directly adjusted to the data. The performance of the strain-energy function chosen is not on a level of industrial application; however this study gives a global understanding of the PTFE coated fiberglass strain mechanism and also provides a consistent database that may be used on real situations.

Dans cette thèse, nous présentons et étudions une nouvelle formulation du problème de contact frottant entre deux corps élastiques se basant sur la méthode de Nitsche. Dans cette méthode les conditions de contact sont imposées faiblement, grâce à un terme additionnel consistant et stabilisé par un paramètre gamma. En premier lieu, nous introduisons, l’étude effectuée en petites déformations pour une version non biaisée de la méthode. La non-distinction entre une surface maître et une surface esclave permettera à la méthode d’être plus générique et applicable directement au problème d’auto-contact. Le cadre restrictif des petites déformations nous permet d’obtenir des résultats théoriques sur la stabilité et la convergence de la méthode. Ces résultats sont complétés par une validation numérique. Ensuite, nous introduisons l’extension de la méthode de Nitsche au cadre des grandes déformations qui est d’avantage pertinent pour les applications industrielles et les situations d’auto-contact. La méthode de Nitsche est formulée pour un matériau hyper-élastique avec frottement de Coulomb et se décline en deux versions : biaisée ou non. La formulation est généralisée à travers un paramètre theta pour couvrir toute une famille de méthodes. Chaque variante particulière a des propriétés différentes du point de vue théorique et numérique, en termes de précision et de robustesse. La méthode est testée et validée à travers plusieurs cas tests académiques et industriels. Nous effectuons aussi une étude de l’influence de l’intégration numérique sur la précision et la convergence de la méthode. Cette étude couvre une comparaison entre plusieurs schémas d’intégration proposés dans la littérature pour d’autres méthodes intégrales. / In this thesis, we present and study a new formulation of frictional contact between two elastic bodies based on Nitsche’s method. This method aims to treat the interface conditions in a weak sense, thanks to a consistent additional term stabilized with the parameter gamma. At first, we introduce the study carried out in the small strain framwork for an unbiased version of the ethod. The non-distinction between a master surface and a slave one will allow the method to be more generic and directly applicable to the self-contact problem. The restrictive framework of small strain allowed us to obtain theoretical results on the consistency and convergence of the method. Then, we present the extension of the Nitsche method to the large strain case more relevant for industrial applications and situations of self-contact. This Nitsche’s method is formulated for an hyper-elastic material and declines in the two versions: biased and unbiased. We describe a class of methods through a generalisation parameter theta . Particular variants have different properties from a numerical point of view, in terms of accuracy and robustness. To prove the accuracy of the method for large deformations, we provide several academic and industrial tests. We also study the influence of numerical quadrature on the accuarcy and convergence of the method. This study covers a comparison of several integration rules proposed in the literature for other integral methods.

Une méthode complètement Eulérienne reposant sur un modèle 1-fluide est présentée afinde résoudre les problèmes d’interaction fluide-structure élastique. L’interface entre le fluideet la structure élastique est représentée par une fonction level-set, transportée par le champde vitesse du fluide et résolue par un schéma d’ordre élevé WENO 5. Les déformationsélastiques sont calculées sur la grille eulérienne à l’aide des caractéristiques rétrogrades.Nous utilisons différents modèles d’hyperélasticité, afin de générer puis d’intégrer les forcesélastiques comme terme source des équations de Navier Stokes. Le couplage vitesse/pressionest résolu par une méthode de correction de pression et les équations sont discrétisées parla méthode des volumes finis sur la grille eulérienne. La principale difficulté réside dansles grands déplacements de fluide autour du solide, source d’instabilités numériques. Afind’éviter ces problèmes, nous effectuons périodiquement une redistanciation de la level-setet une extrapolation linéaire des caractéristiques rétrogrades. Dans un premier temps,nous effectuons la vérification et la validation de notre approche à l’aide de plusieurs castests comme celui proposé par Turek. Ensuite, nous appliquons notre méthode à l’étudedu phénomène d’atténuation des vagues par des structures élastiques. Il s’agit d’une desvoies possibles pour réduire l’impact des fortes houles sur notre littoral. De plus dans lalittérature et à notre connaissance, seules des structures élastiques rigides ou élastiquesmais monodimensionnelles ont été utilisées pour réaliser ces études. Nous proposons deplacer des structures élastiques sur les fonds marins et analysons leur capacité d’absorptionde l’énergie produite par les vagues. / A fully Eulerian method is developed to solve the problem of fluid-elastic structure interactionsbased on a 1-fluid method. The interface between the fluid and the elastic structureis captured by a level set function, advected by the fluid velocity and solved with a WENO5 scheme. The elastic deformations are computed in an Eulerian framework thanks to thebackward characteristics. We use the Neo Hookean or Mooney Rivlin hyperelastic modelsand the elastic forces are incorporated as a source term in the incompressible Navier-Stokesequations. The velocity/pressure coupling is solved with a pressure-correction methodand the equations are discretized by finite volume schemes on a Cartesian grid. The maindifficulty resides in that large deformations in the fluid cause numerical instabilities. Inorder to avoid these problems, we use a re-initialization process for the level set and linearextrapolation of the backward characteristics. First, we verify and validate our approachon several test cases, including the benchmark of FSI proposed by Turek. Next, we applythis method to study the wave damping phenomenon which is a mean to reduce thewaves impact on the coastline. So far, to our knowledge, only simulations with rigid orone dimensional elastic structure has been studied in the literature. We propose to placeelastic structures on the seabed and we analyse their capacity to absorb the wave energy