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[pt] ANÁLISE EM MICROESCALA DE FRATURAMENTO ÓSSEO UTILIZANDO O MÉTODO DOS ELEMENTOS FINITOS ESTENDIDOS / [en] MICROSCALE ANALYSIS OF BONE FRACTURE USING THE EXTENDED FINITE ELEMENT METHODICARO CAIQUE AZEVEDO ALMEIDA 06 June 2022 (has links)
[pt] Mecânica da fratura pode ser entendida como a área da ciência que
estuda a propagação de fissuras, trincas, fendas e demais falhas a partir
de processos mecânicos que venham afetar negativamente a resistência do
material. Tradicionalmente, os conceitos em que a resistência dos materiais
se baseiam não levam em conta a tenacidade à fratura do material, a qual
pode ser definida como a propriedade que quantifica a resistência à propagação
da trinca. A essência destes estudos pode ser aplicada em qualquer tipo de
material, como por exemplo na área médica ao se estudar o comportamento da
fratura óssea. Esse tipo de fratura geralmente surge através de traumas de alta
energia. O osso, em condições normais, possui a habilidade de suportar cargas
e absorver essa energia. Porém, caso haja um grande nível de energia associado
ao trauma o osso não consegue suportar e acaba sofrendo uma fratura. Este
trabalho tem o objetivo de desenvolver uma análise numérica em microescala de
um fraturamento ósseo utilizando o Método dos Elementos Finitos Estendido
(XFEM), a partir da simulação em 2D do mecanismo de início e propagação
de trincas da ponta de uma fratura inicial em uma unidade do osso compacto
chamada ósteon, que é delimitado pela camada cimentícia, uma zona pobre em
colágeno tipo 1. Dessa forma, foi possível compreender que a camada cimentícia
desempenha um papel de contenção, permitindo maiores deformações antes do
rompimento na propagação da fratura em microescala, além disso, também foi
verificado que ósteons na posição transversal possui a maior rigidez, enquanto
na posição longitudinal tem-se os modelos mais dúcteis, devido a influência do
canal de Haver. / [en] Fracture mechanics can be understood as the area of science that studies
the propagation of fractures, cracks, slits, and other flaws from mechanical
processes that may negatively affect the strength of the material. Traditionally,
the concepts on which the strength of the materials are based do not consider
the toughness to fracture of the material, which can be defined as the property
that quantifies the resistance to crack propagation. The essence of these studies
can be applied to any type of material, such as in the medical field when
studying the behavior of bone fractures. This type of fracture usually arises
through high-energy trauma. Bone, under normal conditions, can support loads
and absorb this energy. However, if there is a high level of energy associated
with the trauma, the bone cannot support it and ends up suffering a fracture.
This paper aims to develop a numerical microscale analysis of a bone fracture
using the Extended Finite Element Method (XFEM). This dissertation studies
two-dimensional simulations of the initiation and propagation mechanisms
of an initial fracture in a compact bone unit called the osteon, which is
bounded by the cement line, a zone that is low in type 1 collagen. In this
way, it was possible to understand that the cement layer plays a role of
containment, allowing greater deformations before rupture in the propagation
of the microscale fracture, in addition, it was also verified that osteons in the
transverse position have the greatest rigidity, while in the longitudinal position
they have the most ductile models were found, due to the influence of the Haver
channel.
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[pt] ANÁLISE DE PROPAGAÇÃO DE TRINCAS EM ESTRUTURAS PRÉ-FRATURADAS VIA MÉTODOS DOS ELEMENTOS FINITOS ESTENDIDOS / [en] CRACK PROPAGATION ANALYSIS IN PRE-FRACTURED STRUCTURES VIA EXTENDED FINITE ELEMENT METHODSFELIPE ALVES BACELAR 08 November 2022 (has links)
[pt] Apresenta-se neste trabalho uma revisão bibliográfica sobre o método dos
elementos finitos estendidos (XFEM), que é um método amplamente utilizado para
estudos de mecânica da fratura. Ele pode ser visto como um método eficiente para
esse tipo de problema, tendo em vista que o remalhamento não é necessário durante
o processo de propagação da trinca, e o grande diferencial do método dos elementos
finitos estendidos é a presença das funções Heaviside e assintótica nos elementos
do domínio da trinca. Outro método para resolução de problemas de mecânica da
fratura é o método dos elementos de contorno dual (MECD), que consiste em definir
o domínio da estrutura através de um contorno. Visando o incentivo a futuros
trabalhos nesta linha de pesquisa, foi elaborado um capítulo apontando os principais
detalhes da modelagem de um problema de mecânica da fratura no software
Abaqus. Após isto, foram feitas seis análises em XFEM para dois casos distintos,
resolvidos anteriormente por Portela et al (1993) pelo MECD. Para o primeiro caso
foram feitas duas modelagens de uma chapa quadrada com uma trinca horizontal
localizada na lateral esquerda, o outro conjunto de modelagens foi aplicado a uma
placa em forma de crucifixo com uma trinca na diagonal. Nas análises foi percebido
que há uma variação entre os caminhos da propagação da trinca a depender do
carregamento externo aplicado. Com o objetivo de comparar os dois métodos,
XFEM e MECD, foi analisado os caminhos de propagação obtidos nas simulações,
identificando assim a semelhança entre os resultados. / [en] This work presents a literature review on the extended finite element method
(XFEM), which is a widely used method for fracture mechanics studies. It can be
seen as an efficient method for this type of problem, considering that remeshing is
not necessary during the crack propagation process, and the great differential of the
extended finite element method is the presence of the Heaviside and asymptotic
functions in the crack domain elements. Another method for solving fracture
mechanics problems is the dual boundary element method (DBEM), which consists
of defining the domain of the structure through a boundary. Aiming to encourage
future works in this line of research, a chapter was prepared pointing out the main
details of the modeling of a fracture mechanics problem in the Abaqus software.
After that, six analyzes were performed in XFEM for two different cases, previously
solved by Portela et al (1993) by DBEM. For the first case, two models were made
of a square plate with a horizontal crack located on the left side, the other set of
modeling was applied to a crucifix-shaped plate with a diagonal crack. In the
analyzes it was noticed that there is a variation between the crack propagation paths
depending on the applied external load. In order to compare the two methods,
XFEM and DBEM, the propagation paths obtained in the simulations were
analyzed, thus identifying the similarity between the results.
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[en] ASPECTS OF MODELING FRACTURE PROPAGATION WITH THE EXTENDED FINITE ELEMENT METHOD (XFEM) / [pt] ASPECTOS DA MODELAGEM DA PROPAGAÇÃO DE FRATURAS COM O MÉTODO DOS ELEMENTOS FINITOS ESTENDIDO (XFEM)RENAN MARKS DE OLIVEIRA PEREIRA 05 April 2019 (has links)
[pt] O processo de fraturamento de materiais quase-frágeis requer atenção especial para a predição da direção de propagação de fraturas. A simulação do fraturamento com o método dos elementos finitos (MEF) tem como desvantagem a dependência da trajetória da fratura com respeito à malha adotada. Além disso, há certa dificuldade para os modelos numéricos representarem a fratura em modo misto por conta dos parametros envolvidos. O Método dos Elementos Finitos Estendido (XFEM) é uma técnica que combina o MEF com funções de enriquecimento para representar descontinuidades no campo de deslocamentos. Neste contexto, discutem-se nesta dissertação os critérios para a nucleação e propagação de fraturas e sua implementação no contexto do XFEM. As implementações foram feitas no framework GeMA, um software desenvolvido no Tecgraf / PUC-Rio. Os critérios de propagação de fraturas implementados baseiamse na abordagem das tensões e permitem controlar diferentes geometrias e tamanhos da área de avaliação na ponta da trinca. Um estudo paramétrico é apresentado para modelar uma viga de concreto sob carregamento não proporcional com fratura em modo misto. Foram consideradas diferentes questões como: discretização da malha, zona de avaliação, iniciação e propagação de fraturas e técnicas de controle de solução. Além disso, outros modelos com diferentes condições de contorno foram analisados para validar os critérios em situações complexas. As constatações paramétricas obtidas através do estudo da viga se monstraram válidas para os demais modelos avaliados. As implementações dos critérios de propagação de fraturas no XFEM, demonstraram excelentes concordâncias nas simulações das trajetórias de fraturamento, comparado com os dados experimentais. / [en] The fracture process of quasi-brittle materials requires special attention for the prediction of the direction of fracture propagation. The fracture simulation with the finite element method (FEM) has as its disadvantage the dependence of the fracture trajectory with respect to the mesh adopted. Besides, there is some difficulty for numerical models to represent the fracture in mixed mode because of the parameters involved. The Extended Finite Element Method (XFEM) is a technique which combines the FEM with enrichment functions to represent discontinuities in the displacement field. In this context, this dissertation discusses the criteria for nucleation and propagation of fractures and their implementation in
the context of XFEM. The implementations were made in the GeMA framework, a software developed at Tecgraf / PUC-Rio. The implemented crack growth criteria is based on the stress approach and allows to control different geometries and sizes of the evaluation area in the crack tip. A parametric study is presented for modeling a concrete beam under nonproportional loading with mixed-mode fracture. Different situations were taken into account such as mesh refinement, geometry and size of the evaluation region, crack initiation and propagation and solution control techniques. Also, several models with different loading and boundary conditions were made to validate the criteria under complex situations. The parametric findings obtained through the study of the beam proved to be valid for the other models. The implementations of the fracture propagation criteria in the XFEM demonstrated excellent agreement in the simulations of the fracture trajectories compared to the experimental data.
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Extension de l'approche X-FEM en dynamique rapide pour la propagation tridimensionnelle de fissure dans des matériaux ductiles / Extension of XFEM approach in dynamic for 3D crack propagation in ductile materialPelée de Saint Maurice, Romains 25 February 2014 (has links)
Le développement actuel de l’industrie vise à prévoir l’intégrité des structures dans le temps ou dans le cas de sollicitation extrême. Les risques liés à la propagation des fissures dans le cas de chocs ou d’impacts sont encore difficiles à prévoir. Les codes de calcul dans ce domaine regroupent plusieurs méthodes de simulation au sein d’un même code de calcul. Afin de présenter les différentes méthodes numériques mises en oeuvre, ce mémoire a été découpé en trois parties distinctes. Dans la première partie, nous présentons la bibliographie, puis notre apport aux méthodes de simulation numérique en l’appliquant au cas de la propagation de fissure dynamique et enfin les résultats obtenus à partir des méthodes proposées. Nous comparons ces simulations à des résultats expérimentaux ou à des simulations 2D trouvés dans la littérature. À travers la bibliographie, nous présenterons la théorie de la mécanique de la rupture pour arriver à un critère de propagation de fissure adapté à la dynamique transitoire. Ce critère a déjà été utilisé pour la fissuration dynamique en 2 dimensions. Nous décrirons la méthode des éléments finis étendus utilisée jusqu’ici principalement en quasi-statique. Nous donnerons les avantages mais aussi les limites de mise en oeuvre de cette méthode, notamment à travers le choix des enrichissements et de l’intégration des éléments coupés par la fissure. La méthode des level-sets est ensuite présentée : elle permet de décrire et faire évoluer la fissure indépendamment de la structure. On met en évidence le besoin de robustesse pour faire évoluer la fissure en dynamique explicite. La seconde partie est consacrée au développement et à l’extension de la méthode en 3D. Après avoir rappelé le critère de propagation en 3D fragile et avec plasticité, on cherche à proposer des schémas d’intégration spatiale plus économiques. Une nouvelle stratégie de propagation des level-sets basé sur la géométrie est proposée pour la dynamique explicite 3D. Enfin dans la troisième partie, nous appliquerons les méthodes à des cas de propagation de fissure bidimensionnelle puis tridimensionnelle. Nous simulerons dans un premier temps des cas 2D en mode I puis en mode mixte, afin de vérifier que l’on arrive à résultats proches des cas déjà simulés en 2D. Pour terminer par des simulations de propagation tridimensionnelle de fissure avec arrêt et redémarrage de la fissure. Tous ces développements on été implémentés dans le code de calcul de dynamique explicite EUROPLEXUS, co-propriété du CEA et de la Commission Européenne. / The current development of the industry focus on structural integrity over time or in the case of extremes stresses. Risks related to the cracks propagation in the event of shocks or impacts are still difficult to predict. Computing codes in this area groups several methods of simulation within the same computer software. To present the various numerical methods used, this thesis was divided into three distinct parts. In the first part we present the literature. Then, in second part, our contribution to the numerical simulation methods are presented by applying it to the case of dynamic crack propagation. Finally the results obtained from the proposed methods are described. We compare these simulations with experimental results or 2D simulations found in the literature. Through the first part, we present the theory of fracture mechanics to reach a criterion of crack propagation adapted to the transient dynamics. This criterion has been used for dynamic cracks in two dimensions. We describe the extended finite element method mainly used for quasi-static problems. We give the advantages but also the limits of this method: the choice of enrichment and the integration method are particularly important. The level-sets method is then presented: it allows to describe and develop the crack regardless of the structure. It highlights the need of robustness due to explicit dynamics scheme. The second part is devoted to the development and extension of the method in 3D. After reminding the propagation criterion in 3D, we try to offer more economic patterns of spatial integration. A new strategy of level-sets propagation based on geometrical approach is proposed for the explicit dynamic and applied in 3D. In the third part, we apply the methods to the case of two-dimensional crack propagation and three-dimensional. We initially simulate 2D mode I then mixed mode, to ensure that we arrive at results close to earlier 2D simulations. To finish, we present three-dimensional simulations of crack propagation with stopping and restarting crack. All these developments have been implemented in the computing software EUROPLEXUS , co-owned by the CEA and the European Commission.
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Thermal and mechanical properties of gypsum boards and their influences on fire resistance of gypsum board based systemsRahmanian, Ima January 2011 (has links)
Gypsum board assemblies are now widely used in buildings, as fire resistant walls or ceilings, to provide passive fire protection. The fire resistance of such systems is fundamentally due to the desirable thermal properties of gypsum. Yet there is wide variability in reported values of thermal properties of gypsum at high temperatures and a lack of understanding of its integrity in fire. To evaluate the fire protection performance of gypsum board assemblies, it is essential to quantify its thermal properties and obtain information on its mechanical properties at high temperatures. Gypsum boards shrink and crack at high temperatures, and this leads to collapse of parts of the gypsum boards in fire. Fall-off of gypsum in fire affects the fire resistance of the assembly considerably, and cannot be overlooked when evaluating the fire resistance of gypsum board assemblies. The current research proposes a model to define the temperature-dependent thermal properties of gypsum boards at high temperatures. Thermal conductivity of gypsum is considered as the most influential parameter in conduction of heat through gypsum, and a hybrid numerical-experimental method is presented for extracting thermal conductivity of various gypsum board products at elevated temperatures. This method incorporates a validated one-dimensional Finite Difference heat conduction program and high temperature test results on small samples of gypsum boards. Moreover, high temperature mechanical tests have been performed on different gypsum board products; thermal shrinkage, strength and stress-strain relationships of gypsum products at elevated temperatures are extracted for use in numerical mechanical analysis. To simulate the structural performance of gypsum boards in fire, a two-dimensional Finite Element model has been developed in ABAQUS. This model successfully predicts the complete opening of a through-thickness crack in gypsum, and is validated against medium-scale fire tests designed and conducted as part of this research. Gypsum fall-off in fire is a complex phenomenon; however, it is believed that delaying the formation of through-thickness cracking will delay falling off of gypsum in fire, and hence improve the fire resistance of gypsum board assemblies. Finally, a study has been performed on the effects of various detailing parameters in gypsum board wall assemblies, and recommendations are offered for improving the fire resistance of such systems.
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Numerical method to investigate and assess the capacity of a damaged concrete structure : Using image analysis and advanced concrete modelingBenosmane, Zakariya January 2022 (has links)
Concrete has for decades been one of the main materials used to construct important structuressuch as dams and bridges. However, after years of service, the concrete structuresstart deteriorating and signs of damages start showing on the structure. The inspectionof such structures is compulsory to assess their state and plan repairing operations ifnecessary. The main inspection method has for long been field inspection, however, thismethod presents several problems, namely, the complexity to access some parts of thestructures and the subjectivity of the decisions. These difficulties make the operationtime-consuming and prone to error, thus a need for a new methodology that would benumerical and more automated.One of the damages that affect the carrying capacity the most in concrete structuresare surface-cracks. In this work, the focus is brought on this type of damage and a solutionfor the inspection methodology is presented and applied to a case study.The methodology first consists in using the photogrammetry technology, which allows theproduction of a 3D point cloud model of the structure by taking multiple pictures of it usingUAVs to facilitate access to its complex parts. From this point cloud, surface-openingcracks could be visualized and an orthoimage featuring the damages can be produced.Then, an image-based crack detection program will be used on the orthoimage to extractthe crack. From this, a program is developed to find the coordinates of the crack in thestructure and to process the model of the crack. Then a program is made to importthe crack model to a finite element software, and from there the extended finite elementmethod (XFEM) combined with the concrete damaged plasticity (CDP) method will beused to assess the carrying capacity of the structure and to study the evolution of itscrack pattern.The methodology was tested in a case study. In this case study, a steel-reinforced concretebeam was damaged and all of the methodology steps were applied. An adaptationto some steps was needed due to challenges raised by the test set-up.A three-point bending experience was carried out on the beam while recording the forceand displacement data and the crack pattern evolution. Numerically, this experience wasreproduced and relevant results were extracted and compared to the experimental ones.Differences in the carrying capacity were observed and multiple numerical analyses werecarried out to test the taken assumptions and detect the source of error. On the otherhand, for the crack pattern, satisfying results were achieved. Moreover, the degree of thedetailing in the crack model and its effect on the results is discussed.Globally, it can be concluded that the methodology can effectively in a numericalsemi-automated way capture the surface cracks in concrete structures and import theirmodel to a finite element software to apply analyses to assess the capacity of the damagedstructure and study the evolution of the cracks.This methodology could be further developed in the future by including more technologiessuch as lasergrammetry to make it go from a 2D surface-based damage analysis to a 3Danalysis. Moreover, criteria specialized for inspection and repairing purposes could becreated and implemented in the methodology.
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[en] AN IMPLEMENTATION OF THE EXTENDED FINITE ELEMENT METHOD FOR ANALYSIS OF TWO-DIMENSIONAL FRACTURE PROPAGATION / [pt] UMA IMPLEMENTAÇÃO DO MÉTODO ESTENDIDO DOS ELEMENTOS FINITOS PARA ANÁLISE DE PROPAGAÇÃO DE FRATURAS BIDIMENSIONAISPATRICK ANDERSON BAHIA VIEIRA DA SILVA 29 January 2016 (has links)
[pt] 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. / [en] 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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[en] NUMERICAL SIMULATION OF HYDRAULIC FRACTURING BY THE EXTENDED FINITE ELEMENT METHOD / [pt] SIMULAÇÃO NUMÉRICA DO FRATURAMENTO HIDRÁULICO PELO MÉTODO ESTENDIDO DOS ELEMENTOS FINITOSJAIME ANDRES CASTANEDA BARBOSA 19 September 2017 (has links)
[pt] 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. / [en] 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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STOCHASTIC CRACK PROPAGATION MODELLING USING THE EXTENDED FINITE ELEMENT METHOD / STOCHASTICKÉ MODELOVÁNÍ ŠÍŘENÍ TRHLIN S VYUŽITÍM ROZŠÍŘENÉ METODY KONEČNÝCH PRVKŮNešpůrek, Lukáš January 2010 (has links)
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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Contribution à la simulation numérique des structures en béton armé : utilisation de fonctions de niveau pour la modélisation de la fissuration et des renforts / Contribution to the numerical simulation of reinforced concrete structures : use of level set functions to model cracking and rebarsLé, Benoît 15 November 2016 (has links)
La prédiction de l’état de fissuration est un enjeu crucial pour l’analyse des structures en béton armé, qui nécessite le recours à la modélisation et à la simulation numérique. Le calcul par éléments finis des structures en béton armé pose au moins deux problèmes majeurs :d’une part il existe peu de modèles permettant de traiter à la fois l’initiation, la propagation et l’ouverture des fissures, d’autre part le diamètre généralement faible des armatures métalliques par rapport aux dimensions des structures étudiées nécessite des maillages particulièrement fins. On propose donc des solutions à ces deux problématiques basées sur l’utilisation de fonctions de niveau (level set). L’endommagement et la fissuration du béton sont modélisés à l’aide de l’approche TLS (Thick Level Set). Cette méthode,développée en tant que méthode de régularisation des modèles d’endommagement locaux, utilise une level set afin d’introduire une longueur caractéristique. Cela permet de rendre aisée la localisation de la position des fissures, et donc d’enrichir le champ de déplacement parla méthode des éléments finis étendus (X-FEM) afin de modéliser l’ouverture des macro-fissures. Concernant la modélisation des armatures, une nouvelle approche multidimensionnelle est proposée. Une représentation volumique des armatures par la méthode X-FEM est utilisée dans les zones d’intérêt afin d’obtenir des résultats précis tout en simplifiant la procédure de maillage, tandis qu’une représentation linéique est utilisée dans le reste de la structure afin de réduire le nombre de degrés de liberté du calcul. La méthode de transition développée ici permet d’assurer la cohérence des résultats obtenus / Prediction of cracking is a key point for the analysis ofreinforced concrete structures, which requires the use of Modeling and numerical simulation. The analysis of reinforced concrete structures using the finite element method raises two issues: on one hand, few models areable to deal with the initiation, the propagation and the opening of cracks, on the other hand the diameter of thereinforcements which is usually small compared to the dimensions of the structures necessitates very fine meshes. Some solutions to these two problematics areproposed, based on the use of level set functions.Damage and cracking of concrete are modeled using theThick Level Set (TLS) approach. This method,developped as a mean to regularize local damagemodels, uses a level set to introduce a characteristic length. It makes the location of the cracks easy, whichallows to enrich the displacement field with the eXtendedFinite Element Method (X-FEM) in order to model the macro-cracks opening. Concerning the modeling of thereinforcements, a new multidimensionnal approach isproposed. A volumic representation of the reinforcements with the X-FEM method is used in the zones of interest to get accurate results while simplifying the meshing process, whereas a lineic representation isused elsewhere to decrease the number of degrees of freedom. The developed transition method insures the consistency of the results.
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