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Toolabi, Milad. "Dynamic extended finite element method (XFEM) analysis of discontinuous media." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/44180.
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The extended finite element method (XFEM) is found promising in approximating solutions to locally non-smooth features such as jumps, kinks, high gradients, inclusions, or cracks in solid mechanics problems. The XFEM uses the properties of the partition of unity finite element method (PUFEM) to represent the discontinuities without the corresponding finite element mesh requirements. In the present thesis numerical simulations of statically and dynamically loaded heterogeneous beams, heterogeneous plates and two-dimensional cracked media of isotropic and orthotropic constitutive behaviour are performed using XFEM. The examples are chosen such that they represent strong and weak discontinuities, static and dynamic loading conditions, anisotropy and isotropy and strain-rate dependent and independent behaviours. At first, the Timoshenko beam element is studied by adopting the Hellinger-Reissner (HR) functional with the out-of-plane displacement and through-thickness shear strain as degrees of freedom. Heterogeneous beams are considered and the mixed formulation has been combined with XFEM thus mixed enrichment functions are used. The results from the proposed mixed formulation of XFEM correlate well with analytical solutions and Finite Element Method (FEM) and show higher rates of convergence. Thus the proposed method is shear-locking free and computationally more efficient compared to its conventional counterparts. The study is then extended to a heterogeneous Mindlin-Reissner plate with out-of-plane shear assumed constant through length of the element and with a quadratic distribution through the thickness. In all cases the zero shear on traction-free surfaces at the top and bottom are satisfied. These cases involve weak discontinuity. Then a two-dimensional orthotropic medium with an edge crack is considered and the static and dynamic J-integrals and stress intensity factors (SIF's) are calculated. This is achieved by fully (reproducing elements) or partially (blending elements) enriching the elements in the vicinity of the crack tip or body. The enrichment type is restricted to extrinsic mesh-based topological local enrichment in the current work. A constitutive model for strain-rate dependent moduli and Poisson ratios (viscoelasticity) is formulated. The same problem is studied using the viscoelastic constitutive material model implemented in ABAQUS through an implicit user defined material subroutine (UMAT). The results from XFEM correlate well with those of the finite element method (FEM). It is shown that there is an increase in the value of maximum J-integral when the material exhibits strain rate sensitivity.
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Li, Ziyun. "Haptic Dissection of Deformable Objects using Extended Finite Element Method." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31445.
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Interactive dissection simulation is an important research topic in the virtual reality (VR) community.
There are many efforts on this topic; however, most of them focus on building a realistic simulation system regardless of the cost, and they often require expensive workstations and specialized haptic devices which prevent broader adoption.
We show how to build a realistic dissection simulation at an affordable cost, which opens up applications in elementary education for virtual dissections which are currently not feasible.
In this thesis, we present a fast and robust haptic system for interactive dissection simulations of finite elements based deformable objects which supports two type of haptic interactions: point contacts and cuts.
We design a semi-progressive virtual dissection scheme of deformable objects in a real-time application.
The quality and performance of visual/haptic feedback is demonstrated on a low-end commercial desktop PC with a haptic device.
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McNary, Michael. "Implementation of the extended finite element method (XFEM) in the Abaqus software package." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29665.
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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009.Committee Chair: Cherkaoui, Mohammed; Committee Member: Neu, Richard; Committee Member: van der Sluis, Olaf. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Jung, Yeonhee. "An efficient analysis of resin transfer molding process using extended finite element method." Phd thesis, Saint-Etienne, EMSE, 2013. http://tel.archives-ouvertes.fr/tel-00937556.
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Numerical simulation for Resin Transfer Molding (RTM) manufacturing process is attempted by using the eXtended Finite Element Method (XFEM) combined with the level set method. XFEM allows to obtaining a good numerical precision of the pressure near the resin flow front, where its gradient is discontinuous. The enriched shape functions of XFEM are derived by using the level set values so as to correctly describe the interpolation with the resin flow front. In addition, the level set method is used to transport the resin flow front at each time step during the mold filling. The level set values are calculated by an implicit characteristic Galerkin FEM. The multi-frontal solver of IPSAP is adopted to solve the system. This work is validated by comparing the obtained results with analytic solutions.Moreover, a localization method of XFEM and level set method is proposed to increase the computing efficiency. The computation domain is reduced to the small region near the resin flow front. Therefore, the total computing time is strongly reduced by it. The efficiency test is made with simple channel or radial flow models. Several application examples are analyzed to demonstrate ability of this method. A wind turbine blade is also treated as industrial application. Finally, a Graphic User Interface (GUI) tool is developed so as to make easy the pre/post-processing of the simulation.
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Alizada, Alaskar [Verfasser]. "The eXtended Finite Element Method (XFEM) with Adaptive Mesh Refinement for Fracture Mechanics / Alaskar Alizada." Aachen : Shaker, 2012. http://d-nb.info/1052408818/34.
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Nešpůrek, Lukáš. "STOCHASTIC CRACK PROPAGATION MODELLING USING THE EXTENDED FINITE ELEMENT METHOD." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233900.
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Tato disertační práce vychází z výzkumu v rámci francouzsko-českého programu doktorátu pod dvojím vedením na pracovišti Institut français de mécanique avancée v Clermont-Ferrand a na Ústavu fyziky materiálu AV v Brně. Úvodní výzkumný úkol na brněnském pracovišti se zabýval numerickou analýzou pole napětí v okolí čela trhliny v tenké kovové fólii. Zvláštní pozornost byla zaměřena na vliv speciálního typu singularity v průsečíku čela trhliny s volným povrchem. Těžiště disertační práce spočívá v numerickém modelování a stochastické analýze problémů šíření trhlin se složitou geometrií v dvojrozměrném prostoru. Při analýze těchto problémů se dříve zřídka používaly numerické metody, a to z důvodu vysoké náročnosti na výpočtový čas. V této disertaci je ukázáno, že aplikací moderních metod numerické mechaniky a vhodných technik v analýze spolehlivosti lze tyto problémy řešit s pomocí numerických metod i na PC. Ve spolehlivostní analýze byla využita lineární aproximační metoda FORM. Pro rychlost šíření trhlin se vycházelo z Parisova-Erdoganova vztahu. Pro parametry tohoto vztahu byl použit dvourozměrný statistický model, který postihuje vysokou citlivost na korelaci obou parametrů. Mechanická odezva byla počítána rozšířenou metodou konečných prvků (XFEM), která eliminuje výpočetní náročnost a numerický šum související se změnou sítě v klasické metodě konečných prvků. Prostřednictvím přímé diferenciace bylo odvozeno několik vztahů pro derivace funkce odezvy, čímž se dosáhlo lepší numerické stability a konvergence spolehlivostní analýzy a výrazného zkrácení doby výpočtu. Problém zatížení s proměnou amplitudou byl řešen aplikací transformace zatížení metodou PREFFAS. Využití distribuce výpočtů v síti PC umožnilo další zrychlení analýzy.
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Gigliotti, Luigi. "Assessment of the applicability of XFEM in Abaqus for modeling crack growth in rubber." Thesis, KTH, Hållfasthetslära (Inst.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-103919.
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The eXtended Finite Element Method is a partition of unity based method, particularly suitable for modelling crack propagation phenomena, without knowing a priori the crack path. Its numerical implementation is mostly achieved with stand-alone codes. The implementation of the eXtended Finite Element Method in commercial FEA softwares is still limited, and the most famous one including such capabilities is Abaqus TM. However, due to its relatively recent intro-duction, XFEM technique in Abaqus has been proved to provide trustable results only in few simple benchmark problems involving linear elastic material models.In this work, we present an assessment of the applicability of the eXtendend Finite Element Method in Abaqus, to deal with fracture mechanics problems of rubber-like materials. Results are provided for both Neo-Hookean and Arruda-Boyce material models, under plane strain conditions. In the rst part of this work, a static analysis for the pure Mode-I and for a 45o mixed-Mode load condition, whose objective has been to evaluate the ability of the XFEM technique in Abaqus, to correctly model the stress and displacement elds around a crack tip, has been performed. Outcomes from XFEM analysis with coarse meshes have been compared with the analogous ones obtained with highly re ned standard FEM discretizations. Noteworthy, despite the remarkable level of accuracy in analyzing the displacement eld at the crack tip, concerning the stress eld, the adoption of the XFEM provides no bene ts, if compared to the standard FEM formulation. The only remarkable advantage is the possibility to discretize the model without the mesh con-forming the crack geometry. Furthermore, the dynamic process of crack propagation has been analyzed by means of the XFEM. A 45o mixed-Mode and a 30o mixed-Mode load condition are analyzed. In particular, three fundamental aspects of the crack propagation phenomenon have been investigated, i.e. the instant at which a pre-existing crack starts to propagate within the body under the applied boundary conditions, the crack propagation direction and the predicted crack propagation speeds. According to the obtained results, the most inuent parameters are thought to be the elements size at the crack tip hand the applied displacement ratev. Severe diculties have been faced to attain convergence. Some reasonable motivations of the unsatisfactory convergence behaviour are proposed.
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Fave, Sebastian Philipp. "Investigative Application of the Intrinsic Extended Finite Element Method for the Computational Characterization of Composite Materials." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/50483.
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Computational micromechanics analysis of carbon nanotube-epoxy nanocomposites, containing aligned nanotubes, is performed using the mesh independent intrinsic extended finite element method (IXFEM). The IXFEM employs a localized intrinsic enrichment strategy to treat arbitrary discontinuities defined through the level-set method separate from the problem domain discretization, i.e. the finite element (FE) mesh. A global domain decomposition identifies local subdomains for building distinct partition of unities that appropriately suit the approximation. Specialized inherently enriched shape functions, constructed using the moving least square method, enhance the approximation space in the vicinity of discontinuity interfaces, maintaining accuracy of the solution, while standard FE shape functions are used elsewhere. Comparison of the IXFEM in solving validation problems with strong and weak discontinuities against a standard finite element method (FEM) and analytic solutions validates the enriched intrinsic bases, and shows anticipated trends in the error convergence rates. Applying the IXFEM to model composite materials, through a representative volume element (RVE), the filler agents are defined as individual weak bimaterial interfaces. Though a series of RVE studies, calculating the effective elastic material properties of carbon nanotube-epoxy nanocomposite systems, the benefits in substituting the conventional mesh dependent FEM with the mesh independent IXFEM when completing micromechanics analysis, investigating effects of high filler count or an evolving microstructure, are demonstrated.Master of Science
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Bencheikh, Issam. "Simulation multi-étapes de l’usure des outils de coupe revêtus par une modélisation XFEM/Level-set." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0094/document.
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Lors de l'opération d’usinage à grande vitesse, la résistance à l'usure des outils de coupe est améliorée par l’utilisation des revêtements mono ou multicouches sur les faces actives de l’outil. Cependant, le chargement thermomécanique généré à l'interface outil-pièce affecte considérablement les zones de contact. Par cet effet, plusieurs modes d'usure tels que la fissuration, l’abrasion, l’adhésion et le délaminage du revêtement peuvent se manifester. L'étude du comportement des revêtements et de leurs différents modes de dégradation permet de mieux comprendre leur impact sur la durée de vie de l'outil et ainsi optimiser le procédé d'usinage. Dans ce travail de thèse, une approche numérique multi-étapes a été proposée pour prédire l'usure des outils de coupe revêtus. Cette approche est composée par trois principales étapes. La première consiste à effectuer une simulation éléments finis de l’usinage pour une courte durée (jusqu’à la stabilisation du chargement à l’interface outil/pièce). La deuxième étape consiste à récupérer ce chargement et de l’utiliser comme une entrée du modèle XFEM/Level-set. Ce dernier permet d’analyser le comportement des couches de revêtement sans recours à un maillage conforme aux interfaces. Par conséquence, la distorsion du maillage est évitée lorsque le profil d'outil usé est mis à jour, ainsi que le temps de calcul CPU est drastiquement réduit. La dernière étape de cette approche consiste à calculer le taux d’usure et ainsi prédire le déplacement des nœuds de l’outil de coupe affectés par l’usure. Les essais expérimentaux ont permis d’une part d’identifier les paramètres de contact outil/pièce, et d’autre part de valider l’approche proposéeIn high speed machining, wear resistance of the cutting tools is improved by depositing single or multilayered coatings on their surface. However, the thermomechanical loading generated at the tool-workpiece interface greatly affects the contact zones. For this purpose, several wear modes such as cracking, abrasion, adhesion and delamination of the coating can be occurred. The study of the coatings behavior and their different degradation modes lead to better understanding of their impact on the tool life and machining process under optimal conditions. In this PhD thesis work, a multi-step numerical approach has been proposed to predict wear of the coated cutting tools. This approach involves three main steps. The first is to perform a finite element simulation of the orthogonal cutting for a short time (until the loading stabilization at the tool/workpiece interface). The second step is to recover this loading and use it as an input for the XFEM/Level-set model. The latter allow to take into account the coating layers presence without any need of mesh conforming to the interfaces. As a result, the mesh distortion is avoided when the worn tool profile is updated, as well as the CPU calculation time is drastically reduced. The final step of this approach is to convert the wear rate equation into a nodal displacement, thus representing the cutting tool wear. Based on the experimental tests, a procedure for identifying tool/workpiece contact parameters, and for calibrating the wear equation for each coating layer has been proposed. Experimental trials have been also used to validate the proposed approach
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Shibanuma, Kazuki. "Reformulation of XFEM and its application to fatigue crack simulations in steel structures." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120941.
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Jamond, Olivier. "Propagation numérique de zones critiques dans un pneumatique par approches multi-modèles." Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2011. http://www.theses.fr/2011ECAP0020/document.
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Ces travaux se sont attachés au développement, à l’implémentation et à la validation d’une stratégie numérique pour la simulation de l’évolution d’un endommagement localisé susceptible de conduire à l’apparition, puis à la propagation de fissures dans une structure complexe, incompressible. Nous avons abordé cet objectif général en procédant par étapes.Dans un premier temps, nous avons développé une méthodologie numérique innovante pour la propagation de fissures dans le cadre de la mécanique de la rupture fragile. Cette méthodologie a deux caractéristiques importantes : incluant l’enrichissement Heaviside de la méthode XFEM dans le cadre de modélisation Arlequin, cette méthodologie permet de ne pas remailler la structure initiale, au cours de la propagation de la fissure. Attachant un patch Arlequin local en fond de la fissure qui se propage, elle permet d’approcher, avec la précision nécessaire, le comportement local des champs mécaniques. Cette méthodologie a été implémentée et testée numériquement. Dans un deuxième temps, nous avons étendu cette méthodologie pour la prise en compte de l’endommagement par fatigue. Dans l’approche développée, l’initiation et la propagation de fissures sont pilotées par l’évolution du champ d’endommagement. Un modèle heuristique représentatif, fournissant les incréments de propagation d’une fissure à partir des champs d’endommagement et de contraintes au voisinage de sa pointe, est proposé. En utilisant des modèles physiques représentatifs des difficultés liées à la problématique d’initiation et de propagation de fissures, sous l’effet d’un endommagement par fatigue, nous avons montré, à travers des essais numériques, une faisabilité globale de notre approche. Dans un troisième temps, nous nous sommes intéressés à la prise en compte de la contrainte d’incompressibilité dans une modélisation Arlequin. L’intégration de cette contrainte pose pour la formulation Arlequin continue et/ou discrète des questions spécifiques : comment gérer la double contrainte dans la zone de couplage en continu et en discret ?, comment traiter les éléments partiellement incompressibles ? Des réponses sont données et étayées théoriquement et/ou numériquement. Enfin, nous avons proposé un ensemble de procédures pratiques, permettant d’évaluer, de manière générale et performante, une intersection de maillages tridimensionnels. Ces développements, nécessaires à la mise en œuvre opérationnelle du cadre Arlequin dans des codes industriels, sont validés par des résultats de calculs Arlequin 3DRésumé en anglais non disponible
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Santos, Matheus Vilar Mota. "Analysis of delamination of composite laminates through the XFEM based on the Layerwise displacement theory." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/18/18148/tde-03102018-122551/.
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Composite laminates are being more employed as fundamental structures due to its low weight and high stiffness. An example of this innovation is the primary structures of modern aircraft, which are lighter than the material formerly used. To predict the material response as load gradually increases can be quite demanding due to composite\'s complex failure mechanism. Hence superior computational models should be further investigated to precisely predict the mechanical behavior of composite media. This dissertation addresses an extended finite element procedure based on the layerwise displacement theory to simulate purely mode I delamination failure in composite laminates. The present model has the potential to perform structural analyzes in a pre-delaminated structure and also considering progressive failure. The type of element to be employed at the discretion of the model is the rectangular 4-node iso-parametric homogeneous element whose displacement field is approximated based in the layerwise theory. There are four types of degrees of freedom, one displacement in each direction, and one degree of freedom associated to the strong discontinuity. Numerical examples already solved in the bibliography are suggested in this dissertation, which demonstrate the potential of the model developed to accurately simulate pure mode I delamination in case of the investigation here is further elaborated. In addition, one possibility of future development of this dissertation is the modeling of fracture mode I without the need to discretize the cohesive planes as realized in traditional Cohesive Zone Methods.Compósitos laminados estão sendo mais empregados como estruturas fundamentais devido ao seu baixo peso e alta rigidez. Um exemplo dessa inovação são as estruturas primárias das aeronaves modernas, que são mais leves do que as os materiais empregados antigamente. Prever a resposta do material à medida que a carga aumenta gradualmente pode ser difícil devido ao complexo mecanismo de falha dos compósitos. Portanto, modelos computacionais mais refinados devem ser investigados a fim de se prever um comportamento mecânico mais preciso. Esta dissertação aborda um procedimento de elementos finitos estendido baseado na teoria de deslocamento layerwise para simular falhas de delaminação modo I em laminados compósitos. O modelo abordado tem potencial para realizar análises em uma estrutura prédelaminada além de falha progressiva. O tipo de elemento a ser empregado na discrição do modelo é o isoparamétrico, homogêneo de 4 nós, retangular, e o campo de deslocamento é baseado na teoria layerwise. Existem quatro tipos de graus de liberdade, um deslocamento em cada direção, e um grau de liberdade associado à forte. Sugere-se nesse trabalho, exemplos, que são comparados com a bibliografia, e que apontam que o modelo desenvolvido nesta dissertação tem o potencial de simular o fenômeno de delaminação em modo I com acurácia, caso o estudo nessa dissertação seja estendido. Além disso, uma possibilidade de desenvolvimento futuro desse trabalho é a modelagem da fratura modo I sem a necessidade de discretizar os planos coesivos entre as lâminas, como realizado em métodos coesivos tradicionais.
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González, Estrada Octavio Andrés. "Estimación y acotación del error de discretización en el modelado de grietas mediante el método extendido de los elementos finitos." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/7203.
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El Método de los Elementos Finitos (MEF) se ha afianzado durante las últimas décadas como una de las técnicas numéricas más utilizadas para resolver una gran variedad de problemas en diferentes áreas de la ingeniería, como por ejemplo, el análisis estructural, análisis térmicos, de fluidos, procesos de fabricación, etc. Una de las aplicaciones donde el método resulta de mayor interés es en el análisis de problemas propios de la Mecánica de la Fractura, facilitando el estudio y evaluación de la integridad estructural de componentes mecánicos, la fiabilidad, y la detección y control de grietas.
Recientemente, el desarrollo de nuevas técnicas como el Método Extendido de los Elementos Finitos (XFEM) ha permitido aumentar aún más el potencial del MEF. Dichas técnicas mejoran la descripción de problemas con singularidades, con discontinuidades, etc., mediante la adición de funciones especiales que enriquecen el espacio de la aproximación convencional de elementos finitos.
Sin embargo, siempre que se aproxima un problema mediante técnicas numéricas, la solución obtenida presenta discrepancias con respecto al sistema que representa. En las técnicas basadas en la representación discreta del dominio mediante elementos finitos (MEF, XFEM, ...) interesa controlar el denominado error de discretización. En la literatura se pueden encontrar numerosas referencias a técnicas que permiten cuantificar el error en formulaciones convencionales de elementos finitos. No obstante, por ser el XFEM un método relativamente reciente, aún no se han desarrollado suficientemente las técnicas de estimación del error para aproximaciones enriquecidas de elementos finitos.
El objetivo de esta Tesis es cuantificar el error de discretización cuando se utilizan aproximaciones enriquecidas del tipo XFEM para representar problemas propios de la Mecánica de la Fractura Elástico Lineal (MFEL), como es el caso del modelado de una grieta.González Estrada, OA. (2010). Estimación y acotación del error de discretización en el modelado de grietas mediante el método extendido de los elementos finitos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/7203
Palancia
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Jan, Yannick. "Modélisation de la propagation de fissure sur des structures minces, soumises à des sollicitations intenses et rapides, par la méthode X-FEM." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI066/document.
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Actuellement, les méthodes classiques (éléments finis, endommagement, critère de rupture) pour analyser la tenue des structures sous des chargements extrêmes sont très dépendantes de la taille de maille du modèle et nécessitent à la fois un savoir-faire spé- cifique dans le domaine et des études de sensibilité au maillage. De nouvelles approches basées sur la méthode des éléments finis étendus permettent de traiter des propagations de fissure sur des structures de petites tailles et volumiques. Cependant, la propagation sur de grandes longueurs avec des modèles volumiques demande une puissance de calcul importante, souvent inaccessible dans le cadre industriel. Cette thèse a pour but de cou- pler des éléments finis de coque avec la méthode des éléments finis étendue (X-FEM). On peut ainsi diminuer la taille des modèles et gagner en temps de calcul. La fissure peut éga- lement évoluer librement dans le maillage. Après avoir fait le choix d’un élément fini de coque simple et de bonne qualité, l’objectif est de modifier cet élément afin de permettre la description d’une fissure au sein même de celui-ci. Ensuite, l’enjeu est d’adapter les critères de propagation qui existent déjà pour des modèles plans ou volumiques pour les matériaux dits "ductiles" afin de les utiliser dans le cadre d’une modélisation coque. Ces critères sont basés sur l’analyse des champs de contrainte et déformation sur un demi- disque aval à la pointe de fissure. Le calcul de la contrainte équivalente extraite de ces champs servant de seuil pour déclencher ou non la propagation est un point clef de ce travail. Cette étude se place dans le cadre de la plasticité généralisée et fait l’hypothèse d’une fissure initialement traversante dans l’épaisseur de la coque. La phase d’amorçage de la fissure n’est pas prise en compte et le défaut initial est supposé préexistant au sein de la structure. En vue de valider le couplage coque/X-FEM et le critère de propagation, des essais de fissuration sur des structures minces sont réalisés et présentés dans ce documentIn shipbuilding industry, classical methods to analyze the behavior of structures under extreme loadings are very dependent on the size of the mesh. Moreover, propagation over long lengths with volumetric models requires huge processing power, often inaccessible within this framework. In order to manage these issues and due to the geometry to be considered, a coupling between shell finite element and the extended finite element method (X-FEM) using an adapted propagation criterion is proposed. The developments are made in the fast explicit dynamic finite element code EUROPLEXUS, CEA Saclay. For shell structures involving significant thickness such as submarines, Mindlin-Reissner theory is needed to enable shear strain. Therefore, locking-free element are used to avoid the numerical issue of shear-locking that appears when the shell becomes too thin. The fracture of Mindlin-Reissner plates based on the X-FEM discrete approximation framework is studied by Dolbow and Belytschko with the MITC4. A four node shell element using the same formulation is here only enriched with a step function along the crack line to take into consideration the discontinuity of the displacement field across the crack. The calculation remains accurate without the asymptotic enrichment functions near the crack-tip, as long as the mesh is refined near the crack tip. The numerical integration issue for elements cut by the crack is solved by a partitioning strategy developed by Elguedj. Since the crack is contained in the shell for which the mid plane's position is entirely known, only one information left is needed to locate it. Therefore, a crack is represented by several line segments on the three-dimensional mesh. Only through thickness cracks are considered so far. As regards to the crack propagation, a local criteria proposed by Haboussa is used based on the calculation of mechanical equivalent quantities in the vicinity of the crack tip. The maximum of the equivalent stress tensor near the crack tip is used to decide if the crack propagates as well as its propagation direction, and the Kaninen equation gives the crack velocity
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Sherif, Ahmed. "Compact High-Order Accurate Scheme for Laminar Incompressible Two-Phase Flows." Electronic Thesis or Diss., Ecole centrale de Nantes, 2023. http://www.theses.fr/2023ECDN0004.
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L'objectif de cette thèse est de développer une méthode précise d'ordre élevé pour résoudre le problème d'écoulementlaminaire incompressible à deux phases. Trois tâches principales sont à accomplir. Premièrement, la méthode doit être stable en énergie, ce qui signifie que la condition sans divergence de l'équation de Navier-Stokes incompressible est satisfaite partout dans le domaine de calcul. Deuxièmement, les discontinuités locales apparaissant dans le champ d'écoulement diphasique doivent être capturées avec précision. Troisièmement, l'interface matérielle entre les deux fluides doit être représentée avec précision à chaque pas de temps. Dans ce travail, une nouvelle méthode Hybridizable Discontinuous Galerkin (HDG) est utilisée pour la discrétisation spatiale. Cette méthode hybride qui appartient à la famille des méthodes DG-FEM satisfait la condition sans divergence en introduisant des variables de trace de vitesse et de pression du même ordre plus une approximation de vitesse et de pression adaptée à l'intérieur des éléments. Deplus, les concepts de FEM eXtended (X-FEM) sont utilisés pour approximer les discontinuités dans le champ d'écoulement en enrichissant l'approximation FEM standard dans les éléments où deux fluides existent. Enfin, l'interface du matériau en mouvement entre les deux fluides est capturée à l'aide de la méthode Level-SetThe objective of this thesis is to develop a high-order accurate method to solve the two-phase incompressible laminar flowproblem. Three main tasks are to be achieved. First, the method has to be energy-stable meaning that the divergence-free condition of the incompressible Navier-Stokes equation is satisfied everywhere in the computational domain. Second, the local discontinuities arising in the two-phase flow field have to be captured accurately. Third, the material interface betweenthe two fluids has to be represented accurately in each time step. In this work, a novel Hybridizable Discontinuous Galerkin (HDG) method is used for the spatial discretization. This hybrid method that belongs to the family of DG-FEM methods satisfies the divergence-free condition by introducing velocity and pressure trace variables of the same order plus a tailoredvelocity and pressure approximation inside the elements. Furthermore, the concepts of eXtended FEM (X-FEM) are used toapproximate discontinuities in the flow field by enriching the standard FEM approximation in elements where two fluids exist. Finally, the moving material interface between the twofluids is captured using the Level-Set method
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Amdouni, Saber. "Numerical analysis of some saddle point formulation with X-FEM type approximation on cracked or fictitious domains." Thesis, Lyon, INSA, 2013. http://www.theses.fr/2013ISAL0007/document.
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Ce mémoire de thèse à été réalisée dans le cadre d'une collaboration scientifique avec "La Manufacture Française des Pneumatiques Michelin". Il porte sur l'analyse mathématique et numérique de la convergence et de la stabilité de formulations mixtes ou hybrides de problèmes d'optimisation sous contrainte avec la méthode des multiplicateurs de Lagrange et dans le cadre de la méthode éléments finis étendus (XFEM). Tout d'abord, nous essayons de démontrer la stabilité de la discrétisation X-FEM pour le problème d'élasticité linéaire incompressible en statique. Le deuxième axe, qui représente le contenu principal de la thèse est dédié à l'étude de certaines méthodes de multiplicateur de Lagrange stabilisées. La particularité de ces méthodes est que la stabilité du multiplicateur est assurée par l'ajout de termes supplémentaires dans la formulation faible. Dans ce contexte, nous commençons par l'étude de la méthode de stabilisation de Barbosa-Hughes appliquée au problème de contact unilatéral sans frottement avec XFEM cut-off. Ensuite, nous construisons une nouvelle méthode basée sur des techniques de projections locales pour stabiliser un problème de Dirichlet dans le cadre de X-FEM et une approche de type domaine fictif. Nous faisons aussi une étude comparative entre la stabilisation avec la technique de projection locale et la stabilisation de Barbosa-Hughes. Enfin, nous appliquons cette nouvelle méthode de stabilisation aux problèmes de contact unilatéral en élastostatique avec frottement de Tresca dans le cadre de X-FEMThis Ph.D. thesis was done in collaboration with "La Manufacture Française des Pneumatiques Michelin". It concerns the mathematical and numerical analysis of convergence and stability of mixed or hybrid formulation of constrained optimization problem with Lagrange multiplier method in the framework of the eXtended Finite Element Method (XFEM). First we try to prove the stability of the X-FEM discretization for incompressible elastostatic problem by ensured a LBB condition. The second axis, which present the main content of the thesis, is dedicated to the use of some stabilized Lagrange multiplier methods. The particularity of these stabilized methods is that the stability of the multiplier is provided by adding supplementary terms in the weak formulation. In this context, we study the Barbosa-Hughes stabilization technique applied to the frictionless unilateral contact problem with XFEM-cut-off. Then we present a new consistent method based on local projections for the stabilization of a Dirichlet condition in the framework of extended finite element method with a fictitious domain approach. Moreover we make comparative study between the local projection stabilization and the Barbosa-Hughes stabilization. Finally we use the local projection stabilization to approximate the two-dimensional linear elastostatics unilateral contact problem with Tresca frictional in the framework of the eXtended Finite Element Method X-FEM
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Gibert, Gaël. "Propagation de fissures en fatigue par une approche X-FEM avec raffinement automatique de maillage." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEI088.
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Dans cette thèse, une nouvelle approche est présentée, combinant la méthode des éléments finis étendus (X-FEM) et un raffinement adaptatif et automatique de maillage (AMR). La méthode X-FEM, développée durant les deux dernières par une importante communauté, a prouvé son efficacité pour gérer l'évolution de discontinuités dans de nombreux problèmes de mécanique de la rupture. Comme cette méthode permet de décrire la fissure indépendamment du maillage de la structure, un raffinement hiérarchique relativement simple peut être appliqué sur ce dernier pour adapter localement l'échelle de discrétisation à celle des phénomènes physiques mis en jeux. Cela permet d'obtenir une description précise de quantités physiques d'intérêt dans une zone limitée autour du front de fissure et réduire considérablement le coût numérique, particulièrement lorsque le trajet de propagation n'est pas connu a priori. Dans ce travail, on propose une stratégie pour combiner X-FEM et AMR : les relations de compatibilité cinématique et les méthodes de projection nécessaires pour les matériaux dépendant de l'histoire de chargement doivent inclure correctement le modèle d'enrichissement. L'implémentation de cette approche combinant X-FEM et AMR, dans le code éléments finis industriel Cast3M, est présentée en détails. En particulier, une nouvelle méthode de projection spécifique à ce contexte est proposée. Des applications numériques et une étude expérimentale de propagation par fatigue en plasticité confinée ont été réalisées pour démontrer la précision, la robustesse et l'efficacité de cette méthodeTo guarantee the high level of safety of industrial components under fatigue cycles it is essential to be able to predict the initiation and growth of cracks during their entire lifetime. However the numerical cost of a propagation simulation on engineer-sized problems with non-linear behavior may be prohibitive, with the classical techniques. Here, a new approach combining the eXtended Finite Element Method (X-FEM) and automatic Adaptive Mesh Refinement (AMR) is presented taking advantage of both methods. The X-FEM, developed over the past two decades by a large community, have proven its efficiency to handle evolving discontinuities in a variety of fracture analysis. Since this method enables to describe the crack and its propagation independently of the mesh of the structure, a simple hierarchical mesh refinement procedure can be applied. Automatic adaptive re-meshing is a valuable method for elastic-plastic crack propagation analysis since it permits a locally fine mesh and then an accurate description of physical quantities in a limited area around the crack front. This is particularly important when local fracture criteria are concerned. Moreover local refinement saves computational effort, particularly when the propagation path is not a priori known. In the present work, it is shown that both methods combine with minimal effort: the kinematic continuity relations and the field transfer process, needed for history-dependent material, must include in a proper way the enrichment of the model. If this requirement is not fulfilled, numerical error may be introduced. Implementation of this combined X-FEM/AMR approach in the finit elements code Cast3M is presented in detail. In particular, an innovative field transfer strategy is proposed in 2D and 3D. Numerical applications of crack propagation in elastic-plastic media demonstrate accuracy, robustness and efficiency of the technique. Moreover, an experimental study has been conducted on a example propagation with notable impact of confined plasticity. This study provides experimental data to compare with the numerical results obtained with the developed method. This validates our modelization choices. It also is the opportunity to test the developed method robustness on a realistic case of utilization. This study showed the interest of the proposed modelization taking into account plasticity induced crack closure during the fatigue propagation
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Henke, Florian [Verfasser]. "An extended finite element method for turbulent premixed combustion / Florian Henke." München : Verlag Dr. Hut, 2013. http://d-nb.info/1042307482/34.
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BARBOSA, JAIME ANDRES CASTANEDA. "NUMERICAL SIMULATION OF HYDRAULIC FRACTURING BY THE EXTENDED FINITE ELEMENT METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=31482@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Um dos principais objetivos da engenharia de petróleo é desenvolver e aplicar técnicas capazes de aumentar a produtividade de poços de petróleo, incluindo a estimulação do poço por operações de fraturamento hidráulico. Estudos sobre a propagação de fraturas podem ser feitos analiticamente para algumas situações simplificadas envolvendo homogeneidade, isotropia e condições de contorno simples do meio geológico, ou pela aplicação de métodos numéricos, como o método dos elementos finitos, para casos mais complexos. A presente pesquisa apresenta análise numérica de fraturamento hidráulico utilizando o método estendido dos elementos finitos (XFEM), em conjunto com o modelo constitutivo de dano da Zona Coesiva (MZC). No método estendido dos elementos finitos a geometria da fratura se torna independente da malha, permitindo a propagação da fratura através do domínio, dispensando sucessivas gerações de malha necessárias na aplicação do método convencional dos elementos finitos. Os resultados numéricos obtidos foram comparados com soluções analíticas assintóticas no caso limite em que o regime da propagação é dominado pela rigidez da rocha, obtendo uma boa concordância. Adicionalmente, foram investigados os efeitos de diferentes parâmetros do fluido de injeção e as características de propagação da fratura quando a interface entre diferentes camadas geológicas é inclinada, mostrando dependência do ângulo de inclinação, das propriedades do material e das tensões in-situ.
One of the main objectives of petroleum engineering is to develop and apply techniques capable of increasing the productivity of oil wells, including the stimulation of well by hydraulic fracturing operations. Studies on the propagation of fractures can be done analytically for some simplified situations involving homogeneity, isotropy and simple boundary conditions of the geological medium, or by the application of numerical methods, such as the finite element method, for more complex cases. The present research presents a numerical analysis of hydraulic fracturing using the extended finite element method (XFEM), in conjunction with the damage constitutive model of Cohesive Zone (MZC). In the extended finite element method the fracture geometry becomes independent of the mesh, allowing the propagation of the fracture through the domain without successive mesh generations as necessary in the conventional finite element method. The computed numerical results were compared with asymptotic analytical solutions in the limit case in which the propagation regime is dominated by the rigidity of the rock with good compatibility. In addition, this study investigates the effects of different parameters of the injection fluid and the fracture propagation characteristics when the interface between different geological layers is inclined, shows dependency between the angle of inclination with the properties of the material and the in-situ stresses.
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Alpert, David N. "Enriched Space-Time Finite Element Methods for Structural Dynamics Applications." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451.
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Gualandi, Gabriele. "Crack modeling and crack propagation in structures using damage model and extended finite element techniques." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/3931/.
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Jin, Hui, and Hao Wu. "Finite Element Modelling of Fracture in dowel-type timber connections." Thesis, Linnéuniversitetet, Institutionen för maskinteknik (MT), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-34783.
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Dowel-type steel to timber connections are commonly used in timber structure. The load carrying capacity and the stress distribution within the connection area are complicated and the failure behavior of a connection depends on many parameters. The main purpose of this thesis was to verify, using the data obtained from previous experiments, the conventional design method of European Code 5(EC5) (hand calculation) for dowel type joints subjected to pure bending moment and other alternative design methods based on the finite element method (FEM) including the use of the mean stress approach and the extended finite element method (XFEM). Finite element models were created in the software ABAQUS. The models were then used to predict the load bearing capacity and compare this to the experimental results. In addition parametric studies were performed with modifications of material properties and other parameters. The closest prediction in relation to the test results was obtained using XFEM where the predicted capacity was 3.82% larger than the experimental result. An extension of the mean stress method going from a 2D-formulation to a 3D-formulation was verified as well. A general conclusion drawn from this work is that the numerical modelling approaches used should also be suitable for application to complex connections and situations involving other loading situations than pure tension.
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Chirputkar, Shardool U. "Bridging Scale Simulation of Lattice Fracture and Dynamics using Enriched Space-Time Finite Element Method." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1313753940.
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Nagai, Toshiki. "Space-time Extended Finite Element Method with Applications to Fluid-structure Interaction Problems." Thesis, University of Colorado at Boulder, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10844711.
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This thesis presents a space-time extended finite element method (space-time XFEM) based on the Heaviside enrichment for transient problems with moving interfaces, and its applications to the fluid-structure interaction (FSI) analysis. The Heaviside-enriched XFEM is a promising method to discretize partial differential equations with discontinuities in space. However, significant approximation errors are introduced by time stepping schemes when the interface geometry changes in time. The proposed space-time XFEM applies the finite element discretization and the Heaviside enrichment in both space and time with elements forming a space-time slab. A simple space-time scheme is introduced to integrate the weak form of the governing equations. This scheme considers spatial intersection configuration at multiple temporal integration points. Standard spatial integration techniques can be applied for each spatial configuration. Nitsche's method and the face-oriented ghost-penalty method are extended to the proposed space-time XFEM formulation. The stability, accuracy and flexibility of the space-time XFEM for various interface conditions including moving interfaces are demonstrated with structural and fluid problems. Moreover, the space-time XFEM enables analyzing complex FSI problems using moving interfaces, such as FSI with contact. Two FSI methods using moving interfaces (full-Eulerian FSI and Lagrangian-immersed FSI) are studied. The Lagrangian-immersed FSI method is a mixed formulation of Lagrangian and Eulerian descriptions. As solid and fluid meshes are independently defined, the FSI is computed between non-matching interfaces based on Nitsche's method and projection techniques adopted from computational contact mechanics. The stabilized Lagrange multiplier method is used for contact. Numerical examples of FSI and FSI-contact problems provide insight into the characteristics of the combination of the space-time XFEM and the Lagrangian-immersed FSI method. The proposed combination is a promising method which has the versatility for various multi-physics simulations and the applicability such as optimization.
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Behroozinia, Pooya. "Finite Element Analysis of Defects in Cord-Rubber Composites and Hyperelastic Materials." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/87703.
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In recent years, composite materials have been widely used in several applications due to their superior mechanical properties including high strength, high stiffness, and low density. Despite the remarkable advancements in theoretical and computational methods for analyzing composites, investigating the effect of lamina properties and lay-up configurations on the strength of composites still remains an active field of research. Finite Element Method (FEM) and Extended Finite Element Method (XFEM) are powerful tools for solving the boundary value problems. One of the objectives of this work is to employ XFEM as a defect identification tool for predicting the crack initiation and propagation in composites. Another major objective of this study is to investigate the damage development in hyperelastic materials. Two Finite Element models are adopted to study this phenomenon: multiscale modeling of the cord-rubber composites in tires and modeling of intelligent tires for evaluating the feasibility of the proposed defect detection technique.
A new three-dimensional finite element approach based on the multiscale progressive failure analysis is employed to provide the theoretical predictions for damage development in the cord-rubber composites in tires. This new three-dimensional model of the cord-rubber composite is proposed to predict the different types of damage including matrix cracking, delamination, and fiber failure based on the micro-scale analysis. This process is iterative and data is shared between the finite element and multiscale progressive failure analysis. It is shown that the proposed cord-rubber composite model solves the problems corresponding to embedding the rebar elements to the solid elements and also increases the fidelity of numerical analysis of composite parts since the laminate characteristic variables are determined from the microscopic parameters. A tire rolling analysis is then conducted to evaluate the effects of different variables corresponding to the cord-rubber composite on the performance of tires.
Tires operate on the principle of safe life and are the only parts of the vehicle which are in contact with the road surface. Establishing a computational method for defect detection in tire structures will help manufacturers to fix and develop more reliable tire designs. A Finite Element model of a tire with a tri-axial accelerometer attached to its inner-liner was developed and the effects of changing the normal load, longitudinal velocity and tire-road contact friction on the acceleration signal were investigated. Additionally, using the model, the acceleration signals obtained from several accelerometers placed in different locations around the inner-liner of the intelligent tire were analyzed and the defected areas were successfully identified. Using the new intelligent tire model, the lengths, locations, and the minimum number of accelerometers in damage detection in tires are determined. Comparing the acceleration signals obtained from the damaged and original tire models results in detecting defects in tire structures.PHD
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Li, Shanhu. "Extended voronoi cell finite element model for damage in brittle matrix composites." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1135317411.
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Gürkan, Ceren. "Extended hybridizable discontinuous Galerkin method." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/664035.
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This thesis proposes a new numerical technique: the eXtended Hybridizable Discontinuous Galerkin (X-HDG) Method, to efficiently solve problems including moving boundaries and interfaces. It aims to outperform available methods and improve the results by inheriting favored properties of Discontinuous Galerkin (HDG) together with an explicit interface definition. X-HDG combines the Hybridizable HDG method with an eXtended Finite Element (X-FEM) philosophy, with a level set description of the interface, to form an hp convergent, high order unfitted numerical method. HDG outperforms other Discontinuous Galerkin (DG) methods for problems involving self-adjoint operators, due to its hybridization and superconvergence properties. The hybridization process drastically reduces the number of degrees of freedom in the discrete problem, similarly to static condensation in the context of high-order Continuous Galerkin (CG). On other hand, HDG is based on a mixed formulation that, differently to CG or other DG methods, is stable even when all variables (primal unknowns and derivatives) are approximated with polynomials of the same degree k. As a result, convergence of order k+1 in the L2 norm is proved not only for the primal unknown, but also for its derivatives. Therefore, a simple element-by-element postprocess of the derivatives leads to a superconvergent approximation of the primal variables, with convergence of order k+2 in the L2 norm. X-HDG inherits these favored properties of HDG in front of CG and DG methods; moreover, thanks to the level set description of interfaces, costly remeshing is avoided when dealing with moving interfaces. This work demonstrates that X-HDG keeps the optimal and superconvergence of HDG with no need of mesh fitting to the interface.
In Chapters 2 and 3, the X-HDG method is derived and implemented to solve the steady-state Laplace equation on a domain where the interface separates a single material from the void and where the interface separates two different materials. The accuracy and the convergence of X-HDG is tested over examples with manufactured solutions and it is shown that X-HDG outperforms the previous proposals by demonstrating high order optimum and super convergence, together with reduced system size thanks to its hybrid nature, without mesh fitting.
In Chapters 4 and 5, the X-HDG method is derived and implemented to solve Stokes interface problem for void and bimaterial interfaces. With X-HDG, high order convergence is demonstrated over unfitted meshes for incompressible flow problems.
X-HDG for moving interfaces is studied in Chapter 6. A transient Laplace problem is considered, where the time dependent term is discretized using the backward Euler method. A collapsing circle example together with two-phase Stefan problem are analyzed in numerical examples section. It is demonstrated that X-HDG offers high-order optimal convergence for time-dependent problems. Moreover, with Stefan problem, using a polynomial degree k, a more accurate approximation of interface position is demonstrated against X-FEM, thanks to k+1 convergent gradient approximation of X-HDG. Yet again, results obtained by previous proposals are improved.Esta tesis propone una nueva técnica numérica: eXtended Hybridizable Discontinuous Galerkin (X-HDG), para resolver eficazmente problemas incluyendo fronteras en movimiento e interfaces. Su objetivo es superar las limitaciones de los métodos disponibles y mejorar los resultados, heredando propiedades del método Hybridizable Discontinuous Galerkin method (HDG), junto con una definición de interfaz explícita. X-HDG combina el método HDG con la filosofía de eXtended Finite Element method (X-FEM), con una descripción level-set de la interfaz, para obtener un método numérico hp convergente de orden superior sin ajuste de la malla a la interfaz o frontera. HDG supera a otros métodos de DG para los problemas implícitos con operadores autoadjuntos, debido a sus propiedades de hibridación y superconvergencia. El proceso de hibridación reduce drásticamente el número de grados de libertad en el problema discreto, similar a la condensación estática en el contexto de Continuous Galerkin (CG) de alto orden. Por otro lado, HDG se basa en una formulación mixta que, a diferencia de CG u otros métodos DG, es estable incluso cuando todas las variables (incógnitas primitivas y derivadas) se aproximan con polinomios del mismo grado k. Como resultado, la convergencia de orden k + 1 en la norma L2 se demuestra no sólo para la incógnita primal sino también para sus derivadas. Por lo tanto, un simple post-proceso elemento-a-elemento de las derivadas conduce a una aproximación superconvergente de las variables primales, con convergencia de orden k+2 en la norma L2. X-HDG hereda estas propiedades. Por otro lado, gracias a la descripción level-set de la interfaz, se evita caro remallado tratando las interfaces móviles. Este trabajo demuestra que X-HDG mantiene la convergencia óptima y la superconvergencia de HDG sin la necesidad de ajustar la malla a la interfaz. En los capítulos 2 y 3, se deduce e implementa el método X-HDG para resolver la ecuación de Laplace estacionaria en un dominio donde la interfaz separa un solo material del vacío y donde la interfaz separa dos materiales diferentes. La precisión y convergencia de X-HDG se prueba con ejemplos de soluciones fabricadas y se demuestra que X-HDG supera las propuestas anteriores mostrando convergencia óptima y superconvergencia de alto orden, junto con una reducción del tamaño del sistema gracias a su naturaleza híbrida, pero sin ajuste de la malla. En los capítulos 4 y 5, el método X-HDG se desarrolla e implementa para resolver el problema de interfaz de Stokes para interfaces vacías y bimateriales. Con X-HDG, de nuevo se muestra una convergencia de alto orden en mallas no adaptadas, para problemas de flujo incompresible. X-HDG para interfaces móviles se discute en el Capítulo 6. Se considera un problema térmico transitorio, donde el término dependiente del tiempo es discretizado usando el método de backward Euler. Un ejemplo de una interfaz circulas que se reduce, junto con el problema de Stefan de dos fases, se discute en la sección de ejemplos numéricos. Se demuestra que X-HDG ofrece un alto grado de convergencia óptima para problemas dependientes del tiempo. Además, con el problema de Stefan, usando un grado polinomial k, se demuestra una aproximación más exacta de la posición de la interfaz contra X-FEM, gracias a la aproximación del gradiente convergente k + 1 de X-HDG. Una vez más, se mejoran los resultados obtenidos por las propuestas anteriores
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Yao, Lan. "Experimental and numerical study of dynamic crack propagation in ice under impact loading." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI043/document.
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Les phénomènes liés au comportement à la rupture de la glace sous impact sont fréquents dans le génie civil, pour les structures offshore, et les processus de dégivrage. Pour réduire les dommages causés par l'impact de la glace et optimiser la conception des structures ou des machines, l'étude sur le comportement à la rupture dynamique de la glace sous impact est nécessaire. Ces travaux de thèse portent donc sur la propagation dynamique des fissures dans la glace sous impact. Une série d'expériences d'impact est réalisée avec un dispositif de barres de Hopkinson. La température est contrôlée par une chambre de refroidissement. Le processus dynamique de la rupture de la glace est enregistré avec une caméra à grande vitesse et ensuite analysé par des méthodes d'analyse d'images. La méthode des éléments finis étendus complète cette analyse pour évaluer la ténacité dynamique. Au premier abord, le comportement dynamique de la glace sous impact est étudié avec des échantillons cylindriques afin d'établir la relation contrainte-déformation dynamique qui sera utilisée dans les simulations numériques plus tard. Nous avons observé de multi-fissuration dans les expériences sur les échantillons cylindriques mais son étude est trop difficile à mener. Pour mieux comprendre la propagation des fissures dans la glace, des échantillons rectangulaires avec une pré-fissure sont employés. En ajustant la vitesse d'impact on aboutit à la rupture des spécimens avec une fissure principale à partir de la pré-fissure. L'histoire de la propagation de fissure et de sa vitesse sont évaluées par analyse d'images basée sur les niveaux de gris et par corrélation d'images. La vitesse de propagation de la fissure principale est identifiée dans la plage de 450 à 610 m/s ce qui confirme les résultats précédents. Elle varie légèrement au cours de la propagation, dans un premier temps elle augmente et se maintient constante ensuite et diminue à la fin. Les paramètres obtenus expérimentalement, tels que la vitesse d'impact et la vitesse de propagation de fissure, sont utilisés pour la simulation avec la méthode des éléments finis étendus. La ténacité d'initiation dynamique et la ténacité dynamique en propagation de fissure sont déterminées lorsque la simulation correspond aux expériences. Les résultats indiquent que la ténacité dynamique en propagation de fissure est linéaire vis à vis de la vitesse de propagation et semble indépendante de la température dans l'intervalle -15 à -1 degrésThe phenomena relating to the fracture behaviour of ice under impact loading are common in civil engineering, for offshore structures, and de-ice processes. To reduce the damage caused by ice impact and to optimize the design of structures or machines, the investigation on the dynamic fracture behaviour of ice under impact loading is needed. This work focuses on the dynamic crack propagation in ice under impact loading. A series of impact experiments is conducted with the Split Hopkinson Pressure Bar. The temperature is controlled by a cooling chamber. The dynamic process of the ice fracture is recorded with a high speed camera and then analysed by image methods. The extended finite element method is complementary to evaluate dynamic fracture toughness at the onset and during the propagation. The dynamic behaviour of ice under impact loading is firstly investigated with cylindrical specimen in order to obtain the dynamic stress-strain relation which will be used in later simulation. We observed multiple cracks in the experiments on the cylindrical specimens but their study is too complicated. To better understand the crack propagation in ice, a rectangular specimen with a pre-crack is employed. By controlling the impact velocity, the specimen fractures with a main crack starting from the pre-crack. The crack propagation history and velocity are evaluated by image analysis based on grey-scale and digital image correlation. The main crack propagation velocity is identified in the range of 450 to 610 m/s which confirms the previous results. It slightly varies during the propagation, first increases and keeps constant and then decreases. The experimentally obtained parameters, such as impact velocity and crack propagation velocity, are used for simulations with the extended finite element method. The dynamic crack initiation toughness and dynamic crack growth toughness are determined when the simulation fits the experiments. The results indicate that the dynamic crack growth toughness is linearly associated with crack propagation velocity and seems temperature independent in the range -15 to -1 degrees
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Lins, Rafael Marques. "A posteriori error estimations for the generalized finite element method and modified versions." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-03092015-083839/.
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This thesis investigates two a posteriori error estimators, based on gradient recovery, aiming to fill the gap of the error estimations for the Generalized FEM (GFEM) and, mainly, its modified versions called Corrected XFEM (C-XFEM) and Stable GFEM (SGFEM). In order to reach this purpose, firstly, brief reviews regarding the GFEM and its modified versions are presented, where the main advantages attributed to each numerical method are highlighted. Then, some important concepts related to the error study are presented. Furthermore, some contributions involving a posteriori error estimations for the GFEM are shortly described. Afterwards, the two error estimators hereby proposed are addressed focusing on linear elastic fracture mechanics problems. The first estimator was originally proposed for the C-XFEM and is hereby extended to the SGFEM framework. The second one is based on a splitting of the recovered stress field into two distinct parts: singular and smooth. The singular part is computed with the help of the J integral, whereas the smooth one is calculated from a combination between the Superconvergent Patch Recovery (SPR) and Singular Value Decomposition (SVD) techniques. Finally, various numerical examples are selected to assess the robustness of the error estimators considering different enrichment types, versions of the GFEM, solicitant modes and element types. Relevant aspects such as effectivity indexes, error distribution and convergence rates are used for describing the error estimators. The main contributions of this thesis are: the development of two efficient a posteriori error estimators for the GFEM and its modified versions; a comparison between the GFEM and its modified versions; the identification of the positive features of each error estimator and a detailed study concerning the blending element issues.Esta tese investiga dois estimadores de erro a posteriori, baseados na recuperação do gradiente, visando preencher o hiato das estimativas de erro para o Generalized FEM (GFEM) e, sobretudo, suas versões modificadas denominadas Corrected XFEM (C-XFEM) e Stable GFEM (SGFEM). De modo a alcançar este objetivo, primeiramente, breves revisões a respeito do GFEM e suas versões modificadas são apresentadas, onde as principais vantagens atribuídas a cada método são destacadas. Em seguida, alguns importantes conceitos relacionados ao estudo do erro são apresentados. Além disso, algumas contribuições envolvendo estimativas de erro a posteriori para o GFEM são brevemente descritas. Posteriormente, os dois estimadores de erro propostos neste trabalho são abordados focando em problemas da mecânica da fratura elástico linear. O primeiro estimador foi originalmente proposto para o C-XFEM e por este meio é estendido para o âmbito do SGFEM. O segundo é baseado em uma divisão do campo de tensões recuperadas em duas partes distintas: singular e suave. A parte singular é calculada com o auxílio da integral J, enquanto que a suave é calculada a partir da combinação entre as técnicas Superconvergent Patch Recovery (SPR) e Singular Value Decomposition (SVD). Finalmente, vários exemplos numéricos são selecionados para avaliar a robustez dos estimadores de erro considerando diferentes tipos de enriquecimento, versões do GFEM, modos solicitantes e tipos de elemento. Aspectos relevantes tais como índices de efetividade, distribuição do erro e taxas de convergência são usados para descrever os estimadores de erro. As principais contribuições desta tese são: o desenvolvimento de dois eficientes estimadores de erro a posteriori para o GFEM e suas versões modificadas; uma comparação entre o GFEM e suas versões modificadas; a identificação das características positivas de cada estimador de erro e um estudo detalhado sobre a questão dos elementos de mistura.
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SILVA, PATRICK ANDERSON BAHIA VIEIRA DA. "AN IMPLEMENTATION OF THE EXTENDED FINITE ELEMENT METHOD FOR ANALYSIS OF TWO-DIMENSIONAL FRACTURE PROPAGATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25699@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O Método Estendido dos Elementos Finitos (XFEM) consiste em uma técnica para modelagem explícita de fraturas. Este método carrega toda a estrutura do método dos elementos finitos e baseia-se no Método da Partição da Unidade. O método tem como essência a adição de funções de enriquecimento ao campo dos deslocamentos contínuos, de modo a representar descontinuidades no modelo. O referido método permite a inserção da fratura no modelo de forma independente da malha e apresenta a grande vantagem de não requerer a atualização da mesma à medida que a fratura se propaga. Neste trabalho, foi desenvolvida uma implementação do XFEM para análises bidimensionais de propagação de fraturas com base na Mecânica da Fratura Linear Elástica (MFLE). Essa implementação foi feita para o programa ABAQUS através da sub-rotina UEL. A propagação da fratura ocorre de forma automática em um único processamento. O critério de propagação da fratura adotado baseia-se nos fatores de intensidade de tensão. Estes, por sua vez, tem seus cálculos efetuados com uso da integral de interação na forma de domínio equivalente. Utiliza-se o critério da máxima tensão tangencial para determinação da direção de propagação. O modelo foi aplicado à análise de propagação de fraturas em estruturas com material quase-frágil. Obtiveram-se excelentes resultados na predição da trajetória de propagação da fratura, comprovando a aplicação vantajosa do XFEM na modelagem de fraturas em Modo I e em modo misto de carregamento em estruturas.
The Extended Finite Element Method (XFEM) is a powerful technique for the explicit modeling of fractures. This method has the background of the Finite Element Method and is based on the Partition Unity Method. The essential idea of the method is the addition of enrichment functions to the displacement field approximation for the representation of the discontinuities in the model. The crack geometry is modeled independently of the mesh and remeshing with crack growth is unnecessary. This thesis presents an ABAQUS implementation of XFEM through the UEL subroutine for two-dimensional analysis of fracture propagation following the Linear Elastic Fracture Mechanics theory. Fracture propagation occurs in an automatic procedure. The fracture criterion is based on the stress intensity factors. The domain form of the interaction integral was used for the computation of the stress intensity factors and the maximum circumferential stress criterion was used to determine the fracture propagation direction. The model was applied to the analysis of the propagation of fractures in structures of quasi-brittle material. The implementation shows good results in the prediction of the fracture propagation trajectories and proves the efficiency of the XFEM in Mode I and mixed mode fracture analyzes.
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Melson, Joshua Hiatt. "Fatigue Crack Growth Analysis with Finite Element Methods and a Monte Carlo Simulation." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48432.
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Fatigue crack growth in engineered structures reduces the structures load carrying capacity and will eventually lead to failure. Cycles required to grow a crack from an initial length to the critical length is called the fatigue fracture life. In this thesis, five different methods for analyzing the fatigue fracture life of a center cracked plate were compared to experimental data previously collected by C.M. Hudson in a 1969 NASA report studying the R-ratio effects on crack growth in 7075-T6 aluminum alloy. The Paris, Walker, and Forman fatigue crack growth models were fit the experimental data. The Walker equation best fit the data since it incorporated R-ratio effects and had a similar Root Mean Square Error (RMSE) compared to the other models. There was insufficient data in the unstable region of crack growth to adequately fit the Forman equation.
Analytical models were used as a baseline for all fatigue fracture life comparisons. Life estimates from AFGROW and finite elements with mid-side nodes moved to their quarter point location compared very with the analytical model with errors less than 3%. The Virtual Crack Closure Technique (VCCT) was selected as a method for crack propagation along a predefined path. Stress intensity factors (SIFs) for shorter crack lengths were found to be low, resulting in an overestimated life of about 8%. The eXtended Finite Element Method with Phantom Nodes (XFEM-PN) was used, allowing crack propagation along a solution dependent path, independent of the mesh. Low SIFs throughout growth resulted in life estimates 20% too large. All finite element analyses were performed in Abaqus 6-13.3. An integrated polynomial method was developed for calculating life based on Abaqus' results, leading to coarser meshes with answers closer to the analytical estimate. None of the five methods for estimating life compared well with the experimental data, with analytical errors on life ranging from 10-20%. These errors were attributed to the limited number of crack growth experiments run at each R-ratio, and the large variability typically seen in growth rates.
Monte Carlo simulations were run to estimate the distribution on life. It was shown that material constants in the Walker model must be selected based on their interrelation with a multivariate normal probability density function. Both analytical and XFEM-PN simulations had similar coefficients of variation on life of approximately 3% with similar normal distributions.
It was concluded that Abaqus' XFEM-PN is a reasonable means of estimating fatigue fracture life and its variation, and this method could be extended to other geometries and three-dimensional analyses.Master of Science
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Bhamare, Sagar D. "High Cycle Fatigue Simulation using Extended Space-Time Finite Element Method Coupled with Continuum Damage Mechanics." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1352490187.
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Swindeman, Michael James. "A Regularized Extended Finite Element Method for Modeling the Coupled Cracking and Delamination of Composite Materials." University of Dayton / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1324605778.
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MacFadden, James. "Computational methods for incompressible fluid flows, with reference to interface modelling by an extended finite element method." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42810.
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In this thesis an implicit Semi-Discrete Stabilized eXtended Finite Element formulation has been successfully developed and implemented for laminar Newtonian incompressible fluid flows. In doing so we have contributed to the research into the field of incompressible fluid flows, multiphase flow and fluid-rigid body interaction. The fluid flows are governed by the incompressible viscous Navier-Stokes equations, using a Finite Element formulation to model the fluid behaviour numerically. A Semi-Discrete time integration scheme was implemented, discretizing in space, leaving the system of ordinary differential equations to be integrated in time. Initially the classical Galerkin method is used to formulate the boundary value problem from the governing equations, however stability issues due to incompressibility and dominant advection terms force the implementation of the stabilized formulation, i.e. SUPG/PSPG. This approach gives greater flexibility in choice of velocity/pressure interpolations, such as equal order functions. The time integration schemes (Generalized alpha method and Generalized Midpoint rule) were compared and contrasted, with the Generalized alpha method demonstrating improved convergence. The highly nonlinear form of the governing equations required an implicit iterative solver and the Newton-Raphson procedure was chosen. Several tests were performed throughout the formulation of the boundary value problem to validate the implementation. The result, a robust, efficient and accurate unsteady incompressible Newtonian fluid formulation. extended FEM was introduced by adding terms to the FEM formulation in a Partition of Unity framework. With the addition of complex solution procedures X-FEM was implemented and tested for multiphase and fluid-rigid body interaction, demonstrating the attractive qualities of this method.
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Dinh, Anh thi. "Finite Element Methods for nonlinear interface problems. Application to a biofilm growth model." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCD083.
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Un biofilm est un ensemble de micro-organismes tels que les bactéries, les champignons ou encore les algues qui vivent en communauté. Les biofilms ont la capacité d’être présents en tout lieu. Ils sont observés dans les milieux aqueux ou humides. Ils peuvent se développer sur n’importe quel type de surface naturelle ou artificielle,qu’elle soit minérale (roche, interfaces air-liquide...) ou organique (peau, tube digestif,racines et feuilles des plantes), industrielle (canalisations, coques des navires) ou médicale comme les prothèses et les cathéters. Cette ubiquité est à l’origine de nombreuses infections bactériennes. Les infections nosocomiales contractées dans les hôpitaux sont un exemple majeur. Certaines de ces infections pouvant être mortelles.Le traitement médical des biofilms est souvent inefficace pour lutter contre ce type d’infection. Il est donc important de comprendre les mécanismes de croissance d’un biofilm. Telle est la motivation de la présente thèse. Afin de réaliser des simulations numériques d’un modèle décrivant la croissance d’un biofilm, nous combinons différentes méthodes de calcul basées sur la méthode Nitsche-Extended Finite Element Method (NXFEM) ainsi que sur la méthode des lignes de niveau. Ces méthodes nous permettent d’étudier des modèles complexes dans lesquels l’interface entre le biofilm et son environnement est capable de se déformer tout en dépendant du temps. Ceci permet de considérer une discrétisation à l’aide d’un maillage ne coïncidant pas avec l’interface biofilm/environnement.Nous présentons également une technique de découplage d’un système d’équations aux dérivées partielles semi-linéaires et la fac¸on dont nous appliquons la méthode NXFEM pour résoudre un tel problème. Ce système est en relation avec le modèle de croissance du biofilm qui est traité dans cette thèse. Pour l’implémentation, une boite à outils NXFEM, développée en Matlab, a été entièrement conçue pour résoudre un tel problème. Nous donnons dans ce document les détails des algorithmes et techniques numériques utilisés afin que chacun puisse utiliser cette boite à outils pour ses propres projetsA biofilm is a collective of living, reproducing microorganisms, such as bacteria, that stick together as a colony or community. They appear everywhere in human life and have impacts on our environment. Biofilm modeling, together with laboratory experiments,has risen toproduce quantitative tools for scientists to better understand the biofilm’s growth. This thesis is motivated to research on this subject.A combination of computational methods which are based on Nitsche-Extended Finite Element Method (NXFEM), Level Set Method and some other stabilized techniques is used to solve and simulate a biofilm growth model. These methods allow us to work with a complex scheme in which the interface between the biofilm and its environment may change with time and on an unfitted mesh. We also present a technique of decoupling a system of semilinear differential equations and how we apply the NXFEM method to solve such a problem. This system has a relation to a model of biofilm’s growth which will be examined carefully in the work.For the implementations, NXFEM toolbox which is a Matlab based toolbox is built for solving such a problem. We also give the details of all algorithms and numerical techniques so that everyone can use this toolbox for their own projects
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Dumstorff, Peter. "Modellierung und numerische Simulation von Rissfortschritt in spröden und quasi-spröden Materialien auf Basis der extended finite element method." Aachen Shaker, 2005. http://d-nb.info/994959834/04.
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Rempler, Hans-Uwe [Verfasser], and Wolfgang [Akademischer Betreuer] Ehlers. "Damage in multi-phasic materials computed with the extended finite-element method / Hans-Uwe Rempler. Betreuer: Wolfgang Ehlers." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2012. http://d-nb.info/1028801238/34.
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Pham, Hung Tien [Verfasser], Ingo [Akademischer Betreuer] Sass, and Wolfram [Akademischer Betreuer] Rühaak. "Extended fully coupled analysis of consolidation using the finite element method / Hung Tien Pham ; Ingo Sass, Wolfram Rühaak." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2020. http://d-nb.info/1207999903/34.
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Jox, Stefan. "3D-hygromechanische Modellierung von Rissbildung in Verbindung mit Feuchtetransport in Betonstrukturen auf Basis der extended finit element method." Aachen Shaker, 2008. http://d-nb.info/995684421/04.
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Bach, Dang Phong. "Development of a finite element strategy for the modeling of nano-reinforced materials." Thesis, Compiègne, 2020. http://bibliotheque.utc.fr/EXPLOITATION/doc/IFD/2020COMP2550.
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La modélisation des matériaux nano-renforcés nécessite de prendre en compte l’effet de taille induit par les phénomènes locaux à l’interface entre la nanoinclusion et la matrice. Cet effet de taille est interprété par une augmentation du rapport interface/volume et peut être pris en compte en introduisant une élasticité surfacique à l’interface. Alors que de nombreux travaux ont été développés du point de vue analytique, peu de contributions ont trait à la description numérique et à la mise en œuvre de cette élasticité surfacique dans la méthode des éléments finis (FEM). Nos études visent à développer des outils numériques efficaces basés sur la FEM pour la modélisation de nanocomposites. Dans un premier temps, nous évaluons les deux stratégies numériques existantes, à savoir l’approche XFEM et l’approche des éléments d’interface, dans la reproduction de l’effet de taille dans le processus d’homogénéisation. Deuxièmement, sur la base d’un test de performance des trois types de formulations d’E-FEM dans le cas de discontinuités faibles, nous proposons une formulation améliorée de SKON permettant d’intégrer l’effet d’une interface cohérente. Enfin, la modélisation numérique du comportement non linéaire des nanocomposites est étudiée. Lors de la première étape, une loi élastoplastique de type von Mises avec durcissement linéaire isotrope est considérée pour le volume, tandis que l’interface est considérée comme élastique linéaireThe modelization of nano-reinforced material requires to take into account the size effect caused by the local phenomena at the interface between the nano-inclusion and the matrix. This size effect is interpreted through an increase in the ratio interface/volume and can be taken into account by introducing a surface elasticity at the interface. Whereas a lot of works have been developed from the analytical point of view, few contributions are related to numerical description and implementation of such surface elasticity in Finite Element Method (FEM). Our studies aim to develop efficient numerical tools based on FEM for the modeling of nanocomposites. Firstly, we evaluate the two existent numerical strategies namely the XFEM approach and the Interface element approach in reproducing the size effect in the homogenization process. Secondly, based on a performance test on the three types of formulations of E-FEM for the case of weak discontinuity, we propose an enhanced SKON formulation allowing to incorporate the effect of a coherent interface. Finally, the numerical modeling on the nonlinear behavior of nanocomposites is investigated. In the first step, a von Mises type elastoplastic law with linear isotropic hardening is considered for the bulk while the interface is considered as linear elastic
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Zangmeister, Tobias [Verfasser], and Ralf [Akademischer Betreuer] Müller. "On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials / Tobias Zangmeister. Betreuer: Ralf Müller." Kaiserslautern : Technische Universität Kaiserslautern, 2015. http://d-nb.info/1064868894/34.
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Jox, Stefan [Verfasser]. "3D hygromechanische Modellierung von Rissbildung in Verbindung mit Feuchtetransport in Betonstrukturen auf Basis der Extended Finite Element Method / Stefan Jox." Aachen : Shaker, 2009. http://d-nb.info/1159832781/34.
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Müller, Sebastian. "Modellierung des schädigungsbehafteten inelastischen Materialverhaltens von Faser-Kunststoff-Verbunden." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-161374.
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Die Arbeit beschreibt eine Modellierung des Materialverhaltens von Faser-Kunststoff-Verbunden unter Berücksichtigung der lokalen Materialstruktur, den konstitutiven Eigenschaften der Verbundbestandteile sowie charakteristischer Schädigungsphönomene. Die Diskretisierung eines repräsentativen Ausschnitts der Materialstruktur erfolgt unter Verwendung der erweiterten Finiten-Elemente-Methode (XFEM). Sie ermöglicht die effiziente Modellierung des Steifigkeitssprunges an den inneren Materialgrenzen und deren Versagen. Der Verlauf der Elementgrenzen muss dabei nicht an die Materialstruktur angepasst werden. Für die Beschreibung der Dehnratenabhängigkeit der polymeren Matrix wird ein Modell der nichtlinearen fraktionalen Viskoelastizität angewendet. Die Kombination mit einem nichtlokalen Kontinuumsschädigungsmodell ermöglicht weiterhin die Modellierung einer verzerrungsgesteuerten Schädigung des Matrixwerkstoffs. Die Parametrisierung, Validierung des Gesamtmodells erfolgt anhand ausgewählter experimenteller Untersuchungen an einem unidirektional verstärkten Glasfaser-Polypropylen-VerbundThe thesis addresses the modelling of the material behavior of fibre reinforced polymers. It systematically includes the influence of the local material structure, the mechanical behaviour of the consituents and characteristic damage phenomena. The diskretisation of a representative volume element of the material structure is based on the extended finite element method (XFEM). It allows for an efficient modelling of the stiffness jump at internal material boundaries as well as their damage. With the XFEM, the element boundaries are no longer required to coincide with the material structure. The approximation of the strain rate dependence of the polymeric matrix is based on a nonlinear, fractional viscoelasticity approach. Its combination with a nonlocal strain driven continuum damage modell allows for the modelling of damage effects. The parametrisation and validation of the overall approach is based on a comparison with experimental results for a unidirectional reinforced glass-fibre-polypropylene composite
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Dumstorff, Peter [Verfasser]. "Modellierung und numerische Simulation von Rissfortschritt in spröden und quasi-spröden Materialien auf Basis der Extended Finite Element Method / Peter Dumstorff." Aachen : Shaker, 2009. http://d-nb.info/1156518784/34.
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Videla, Marió Javier Andrés. "Fracture modelling directly from computer-aided design (CAD) by the extended isogeometric finite element method (X-IGA FEM) with trimmed nurbs." Tesis, Universidad de Chile, 2017. http://repositorio.uchile.cl/handle/2250/146434.
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Ingeniero Civil MecánicoTanto los software de Diseño Asistido por Computadora (CAD) como las herramientas de análisis por medio del Método de Elementos Finitos (FEM) han tenido un enorme impacto en la actividad ingenieril en las últimas décadas. Aun así, tienen la desventaja de que las geometrías CAD no son directamente compatibles con las geometrías utilizas en FEM, lo cual resulta en la necesidad de re-mallar la geometría varias veces durante un ciclo de soluciones FEM. Para solucionar esto, IGA ha sido propuesto como una metodología capaz de generar un vínculo directo entre el diseño mediante CAD y el análisis FEM. La principal idea dentro de IGA es sustituir las funciones de forma utilizadas en FEM por las funciones de base que utiliza el software CAD, conocidas como NURBS. Por otro lado, los problemas de mecánica de fractura presentan dificultades extras para los métodos numéricos debido a las irregularidades que presenta la geometría de la grieta y el campo de esfuerzos singular que se origina alrededor de la punta de la grieta. Para solucionar esto, una nueva generación de métodos numéricos ha sido desarrollada, la cual incluye el renombrado XFEM. La misma idea del XFEM ha sido formulada dentro del contexto de IGA, conocido como Análisis Isogeométrico Extendido (XIGA) y ha sido aplicado exitosamente en grietas rectas y curvas en problemas de elasticidad 2-D. Sin embargo, los trabajos publicados en este tema se han limitado a problemas simples. El objetivo de este trabajo es aplicar el XIGA en problemas de mecánica de fractura con grietas en geometrías complejas dadas por curvas CAD. El trabajo consiste en implementar la metodología de enriquecimiento del XFEM dentro de un código IGA para solucionar problemas de mecánica de fractura 2D. La primera simulación consiste en el problema de una placa infinita con una grieta recta. Esta es resuelta utilizando enriquecimiento Heaviside y Heaviside con punta de grieta. La segunda simulación consiste en emplear NURBS cuadráticos y cúbicos para resolver el problema de un agujero circular con una grieta. En ambas simulaciones se calculan las normas de error $L^{2}$, $H^{1}$ y energética, y el factor de intensidad de esfuerzos (SIF) $K_{I}$ para evaluar los resultados. Ambos problemas exhiben convergencia sub-óptima al momento de refinar la malla y el $K_{I}$ está en concordancia con la solución analítica. ---- Both the CAD software and FEM software have a huge impact on engineering nowadays. Even though both are powerful tools for design and analysis, the main drawback is that CAD geometries and Finite Element models do not completely match, which results in the necessity to re-parametrize the geometry many times during the solution cycle in FEM. Isogeometric Analysis (IGA) was proposed to fulfill this gap and create the direct link between the CAD design and FEM analysis. The main idea of IGA is to substitute the shape functions used in FEM by the shape functions used in the CAD software. Nevertheless, fracture mechanics problems present difficulty for any numerical method due to the irregularity in the crack domain and the singularity of the stress field in the vicinity of the crack tip. To overcome this difficulty, a new generation of numerical methods has been developed, which includes the so-called Extended Finite Element Method (XFEM). The same idea was implemented within the IGA (XIGA) and applied successfully for straight and curved cracks in two-dimensional elasticity. However, the published work is limited to simple crack configurations. The objective of this work is to investigate the applicability and efficiency of the XIGA for cracks of complex geometries given by CAD curves. The work consists in implementing the enrichment method of the XFEM into the in-house IGA code and in verifying the approach on a number of benchmark problems. Heaviside and Heaviside $+$ crack tip enrichment has been implemented for a benchmark problem of an edge crack and the results are shown to be in excellent agreement with the analytic solution. The comparison of the results is done in $L^{2}$, $H^{1}$ and Energy norm of the error, which exhibit the sub-optimal convergence rates, when the mesh size tends to zero. Quadratic and Cubic NURBS were employed to solve the benchmark problem of an edge crack in a circular hole and the results are shown to be in agreement with the analytic solution, despite the complicity of the geometry. The stress intensity factor (SIF) $K_{I}$ is computed and in both benchmark problems it is in agreement with their theoretical value.
Este trabajo ha sido parcialmente financiado por el proyecto FONDECYT 11130259
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Woodward, Huw. "On the application of the method of difference potentials to linear elastic fracture mechanics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/on-the-application-of-the-method-of-difference-potentials-to-linear-elastic-fracture-mechanics(fec9a25c-0e37-4e53-ac35-ba85233c7dae).html.
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The Method of Difference Potentials (DPM) has proven an efficient tool for the solution of boundary value problems (BVPs) in various fields of research including acoustics and fluid mechanics. The method converts the solution of problems of complex geometry to the multiple solutions of a simple, well defined auxiliary problem, on which efficient solvers can be used, and which also avoids the numerical computation of stiffness matrices. So far, most problems solved by the method have been considered for regular domains. Here the method is considered for the solution of Linear Elastic Fracture Mechanics (LEFM) problems. These problems contain a crack which introduces irregularities into the solution space in the form of a discontinuity across the crack boundary and a strain singularity at the crack tip. The relative ease with which the DPM can solve problems of complex geometry makes it particularly attractive for LEFM problems due to the often complex geometries of cracks and the possibility of multiple cracks. The DPM is developed here for the solution of crack problems with the aim of demonstrating the method's potential within this field. As part of this development, for the first time the DPM is combined with the Finite Element Method (FEM). In particular the Extended Finite Element Method (XFEM) is used in order to deal with the irregularities at the crack. Using a geometrical enrichment scheme for the XFEM, near-optimal convergence rates are achieved. The computation time is then significantly reduced by introducing a system of basis functions along the physical boundary of the problem. Applying the DPM with the XFEM, the discontinuity and singularity are dealt with entirely within the XFEM space, therefore avoiding the need to approximate the singularity along the physical crack boundary. With the intention of further reducing the computation time, a Fast Fourier Transform (FFT) algorithm is provided for the solution of the enriched auxiliary problem. The algorithm utilises the regular grid of the auxiliary problem to provide a potentially fast solution method. The above research was applied using Matlab. A Matlab script was written formulating the DPM and XFEM along with various interpolation functions required for the utilisation of the system of boundary basis functions. These included local spline functions and Lagrange polynomials. The FFT algorithm was also applied within Matlab. A Python script was also written for the application of a simple DPM algorithm within Code_Aster, EDF's open source finite element code for thermo-mechanical analyses. These developments are documented in two academic journal papers submitted during the course of the PhD and included in the appendix of this thesis. The Python script for the application of the method within Code_Aster is also included in the appendix.
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Gutiérrez, Aqueveque Rodrigo Hernán [Verfasser], and L. [Akademischer Betreuer] Stempniewski. "Two-dimensional modelling of fracture in reinforced concrete structures applying the extended finite element method / Rodrigo Hernán Gutiérrez Aqueveque ; Betreuer: L. Stempniewski." Karlsruhe : KIT-Bibliothek, 2020. http://d-nb.info/1220359041/34.
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Sutula, Danas. "Energy minimising multi-crack growth in linear-elastic materials using the extended finite element method with application to Smart-Cut™ silicon wafer splitting." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/95561/.
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We investigate multiple crack evolution under quasi-static conditions in an isotropic linear-elastic solid based on the principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith’s theory of cracks. The technique, which has been implemented within the extended finite element method, enables minimisation of the total energy of the mechanical system with respect to the crack extension directions. This is achieved by finding the orientations of the discrete crack-tip extensions that yield vanishing rotational energy release rates about their roots. In addition, the proposed energy minimisation technique can be used to resolve competing crack growth problems. Comparisons of the fracture paths obtained by the maximum tension (hoop-stress) criterion and the energy minimisation approach via a multitude of numerical case studies show that both criteria converge to virtually the same fracture solutions albeit from opposite directions. In other words, it is found that the converged fracture path lies in between those obtained by each criterion on coarser numerical discretisations. Upon further investigation of the energy minimisation approach within the discrete framework, a modified crack growth direction criterion is proposed that assumes the average direction of the directions obtained by the maximum hoop stress and the minimum energy criteria. The numerical results show significant improvements in accuracy (especially on coarse discretisations) and convergence rates of the fracture paths. The XFEM implementation is subsequently applied to model an industry relevant problem of silicon wafer cutting based on the physical process of Smart-CutTM technology where wafer splitting is the result of the coalescence of multiple pressure-driven micro-crack growth within a narrow layer of the prevailing micro-crack distribution. A parametric study is carried out to assess the influence of some of the Smart-CutTM process parameters on the post-split fracture surface roughness. The parameters that have been investigated, include: mean depth of micro-crack distribution, distribution of micro-cracks about the mean depth, damage (isotropic) in the region of micro-crack distribution, and the influence of the depth of the buried-oxide layer (a layer of reduced stiffness) beneath the micro-crack distribution. Numerical results agree acceptably well with experimental observations.
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Zhang, Chao Verfasser], Timon [Akademischer Betreuer] [Rabczuk, Carsten [Gutachter] Könke, and Pedro [Gutachter] Areias. "Crack Identification using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials / Chao Zhang ; Gutachter: Carsten Koenke, Pedro Areias ; Betreuer: Timon Rabczuk." Weimar : Institut für Strukturmechanik, 2019. http://d-nb.info/1176197266/34.
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Zhang, Chao [Verfasser], Timon [Akademischer Betreuer] Rabczuk, Carsten [Gutachter] Könke, and Pedro [Gutachter] Areias. "Crack Identification using Dynamic Extended Finite Element Method and Thermal Conductivity Engineering for Nanomaterials / Chao Zhang ; Gutachter: Carsten Koenke, Pedro Areias ; Betreuer: Timon Rabczuk." Weimar : Institut für Strukturmechanik, 2019. http://d-nb.info/1176197266/34.
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