This work presents a detailed predictive modeling methodology for comprehensive crashworthiness analysis of advanced jet engine forward sections, containing hybrid and composite structures, when subjected to soft impact. Bird strike onto the fan assembly is chosen as the impact event to be studied. The aim is to develop a numerical methodology capable of accurately capturing the full range of multifaceted damage in hybrid and composite structures as they evolve throughout the forward section of a propulsion system. Effective strategies are developed within an explicit finite element framework for modeling a bird, an engine forward section, intra-ply and inter-ply composite damage, and hybrid structural failure. The accuracy of each approach and their numerical modeling considerations are thoroughly investigated. These techniques are then combined to form the full crashworthiness methodology. It is demonstrated that the complete methodology effectively captures progressive hybrid fan blade fracture, leading edge de-bonding, composite casing delamination, and other significant progressive damage effects caused by direct impact and subsequent engine component interactions. The full damage prognosis capabilities demonstrated by this approach encompass aspects which have remained mainly unaddressed in soft impact analysis. A methodology for assessing the complete extent of impact damage for advanced structural engine designs represents a breakthrough that can contribute greatly to the rapid development of these systems in the future. / Master of Science

In this study, a progressive failure analysis is used to investigate leakage in internally pressurized non-circular composite cylinders. This type of approach accounts for the localized loss of stiffness when material failure occurs at some location in a structure by degrading the local material elastic properties by a certain factor. The manner in which this degradation of material properties takes place depends on the failure modes, which are determined by the application of a failure criterion. The finite-element code STAGS, which has the capability to perform progressive failure analysis using different degradation schemes and failure criteria, is utilized to analyze laboratory scale, graphite-epoxy, elliptical cylinders with quasi-isotropic, circumferentially-stiff, and axially-stiff material orthotropies. The results are divided into two parts. The first part shows that leakage, which is assumed to develop if there is material failure in every layer at some axial and circumferential location within the cylinder, does not occur without failure of fibers. Moreover before fibers begin to fail, only matrix tensile failures, or matrix cracking, takes place, and at least one layer in all three cylinders studied remain uncracked, preventing the formation of a leakage path. That determination is corroborated by the use of different degradation schemes and various failure criteria. Among the degradation schemes investigated are the degradation of different engineering properties, the use of various degradation factors, the recursive or non-recursive degradation of the engineering properties, and the degradation of material properties using different computational approaches. The failure criteria used in the analysis include the noninteractive maximum stress criterion and the interactive Hashin and Tsai-Wu criteria. The second part of the results shows that leakage occurs due to a combination of matrix tensile and compressive, fiber tensile and compressive, and inplane shear failure modes in all three cylinders. Leakage develops after a relatively low amount of fiber damage, at about the same pressure for three material orthotropies, and at approximately the same location. / Master of Science

Equivalent, three-dimensional elastic moduli are determined from unit cell models of balanced plain weave, 2D braid, 2D triaxial braid and 4x4 twill textile composite materials consisting of interlaced or intertwined yarns. The yarn paths are modeled with undulation portions, in which one yarn passes over and under one or more yarns, and with straight portions. It is assumed that the centerline of a yarn in the undulation portions is described by the sine function, and that the cross-sectional area of a yarn and the thickness of a yarn, normal to the centerline, are uniform along the centerline. For the balanced plain weave architecture, equations for the fiber volume fraction and the cross-sectional shape of the yarn are derived for large crimp angles. It is shown that the maximum crimp angle is limited to forty-five degrees, and that limits on the ratio of the length of the undulation portion of the path to the width of the unit cell impose constraints on the fiber volume fraction and yarn packing density. For small crimp angles, approximations to the volume fraction and yarn shape equations are obtained. This assumption is used in the derivation of the geometry of the remaining architectures, and subsequent equations are obtained for the corresponding geometric parameters. For each architecture, the yarns are assumed to be transversely isotropic and a stress averaging technique based on an iso-strain assumption is used to determine the effective moduli of the unit cells. Comparisons of the effective moduli are made to other unit cell models in the literature. The micromechanical models are implemented in Fortran programs and user material subroutines for ABAQUS, called UMAT, are created out of these programs. For a balanced plain weave fabric under the small crimp angle approximation, a progressive failure model is developed to predict failure within each yarn and to degrade the material properties of the representative unit cell. Material failure is predicted by discretizing the yarns into slices and applying Tsai-Wu quadratic criterion to the on-axis strains in each slice. A stiffness and strength reduction scheme is then used to account for the change in yarn compliance. At the present time, the UMAT has only been tested as a stand-alone program with Visual Fortran 6.0, and would require further development to be used within ABAQUS on sample structural problems. / Master of Science

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.

A three-dimensional finite element model is constructed to predict the failure of a hybrid and thick laminate containing bolted joints. The results of the simulation are compared with test results. The simulation comprises two main challenging steps. Firstly, for a realistic model, a 3D model is established with geometric nonlinearities and contact is takeninto account. The laminated composite model is constructed by 3D layered elements. The effect of different number of elements through the thickness is investigated. The failure prediction is the second part of the simulation study. Solutions with and without progressive failure approach are obtained and the effect of progressive failure analysis for an optimum simulation of failure is discussed. The most appropriate failure criteria to predict the failure of a thick composite structure is also investigated by considering various failure criteria. By comparing the test results with the ones found from the finite element analyses, the validity of the developed model and the chosen failure criteria are discussed.

This thesis presents a finite element method based comparative study of linear and geometrically non-linear progressive failure analysis of thin walled composite aerospace structures, which are typically subjected to combined in-plane and out-of-plane loadings. Different ply and constituent based failure criteria and material property degradation schemes have been included in a PCL code to be executed in MSC Nastran. As case studies, progressive failure analyses of sample composite laminates with cut-outs under combined loading are executed to study the effect of geometric non-linearity on the first ply failure and progression of failure. Ply and constituent based failure criteria and different material property degradation schemes are also compared in terms of predicting the first ply failure and failure progression. For mode independent failure criteria, a method is proposed for the determination of separate material property degradation factors for fiber and matrix failures which are assumed to occur simultaneously. The results of the present study show that under combined out-of-plane and in-plane loading, linear analysis can significantly underestimate or overestimate the failure progression compared to geometrically non-linear analysis even at low levels of out-of-plane loading.

The objective of this thesis is to investigate the progressive failure behavior of laminated fiber reinforced composite shell structures under different loading conditions. The laminates are assumed to be orthotropic and the first order shear deformation theory is applied. Three-node layered flat-shell elements are used in the analysis. To verify the numerical results obtained, experimental and analytical results found in literature are compared with the outputs of the study, and the comparison is found to have shown good agreement with the previous work. Rectangular graphite/epoxy composite laminates under transverse loading are analyzed through several boundary conditions and stacking sequences. Maximum stress criteria, Hashin&rsquo / s criteria and Tsai Wu criteria are employed to detect the failure and progressive failure methodology is be implemented according to instantaneous degradation approach. First ply failure, final failure loads, corresponding deformations and failure patterns are presented and compared.

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Materiais compÃsitos vÃm sendo extensamente estudados, pois seu uso permite a obtenÃÃo de estruturas leves e resistentes, com bom isolamento tÃrmico e boa resistÃncia a fadiga. CompÃsitos laminados, foco do presente trabalho, sÃo compostos pelo empilhamento de um conjunto de lÃminas, cada uma composta de fibras unidirecionais imersas em uma matriz polimÃrica. Cascas laminadas sÃo utilizadas em muitas situaÃÃes prÃticas de interesse, como fuselagens de aeronaves, estruturas marÃtimas, dentre outras. Devido ao elevado nÃmero de variÃveis envolvidas no projeto de cascas laminadas, mÃtodos de otimizaÃÃo devem ser utilizados em seu projeto. Na anÃlise estrutural de tais cascas, devido ao seu complexo comportamento mecÃnico, mÃtodos numÃricos, como o MÃtodo dos Elementos Finitos (MEF), sÃo utilizados. De modo a determinar a capacidade Ãltima de carga em cascas laminadas, à necessÃrio considerar tanto a presenÃa de grandes deslocamentos (nÃo-linearidade geomÃtrica) quanto o comportamento nÃo- linear do material (nÃo-linearidade fÃsica). No presente trabalho, a nÃo-linearidade geomÃtrica foi introduzida utilizando a formulaÃÃo Lagrangiana Total aplicada a um elemento de casca abatida baseado na Teoria de Marguerre. O elemento foi implementado em um programa de cÃdigo-aberto e vÃrios exemplos com resposta analÃtica e numÃrica presentes na literatura foram tratados. Os resultados obtidos indicaram que o elemento à muito eficiente no tratamento de cascas com pequenas curvaturas iniciais sujeitas a deslocamentos moderadamente grandes. Jà a nÃo-linearidade fÃsica foi considerada por meio de modelos de falha progressiva, com a diminuiÃÃo instantÃnea das propriedades mecÃnicas das lÃminas que falham ao longo da anÃlise. TrÃs mÃtodos de falha progressiva distintos foram formulados e implementados em conjunto com a formulaÃÃo de anÃlise pelo MEF. Os resultados se mostraram promissores, com a correta obtenÃÃo das cargas de falha em laminados tanto submetidos a esforÃos axiais como de flexÃo, mostrando concordÃncia tanto com resultados numÃricos da literatura quanto com resultados experimentais. O desempenho mecÃnico da estrutura foi entÃo utilizado em um modelo de otimizaÃÃo com o objetivo de encontrar um esquema de laminaÃÃo Ãtimo. Neste trabalho, propÃe-se um Algoritmo GenÃtico com um esquema hÃbrido de computaÃÃo paralela para a otimizaÃÃo de laminados. Tal algoritmo utiliza uma configuraÃÃo em ilhas e pode ser executado tanto em clusters quanto em computadores pessoais. AlÃm disso, o algoritmo possui operadores especÃficos para a troca, adiÃÃo e eliminaÃÃo de camadas em laminados. As metodologias implementadas foram combinadas na otimizaÃÃo de placas e cascas laminadas tanto utilizando anÃlise linear quanto nÃo-linear. Nos exemplos lineares, o algoritmo foi verificado e os ganhos em eficiÃncia e tempo de execuÃÃo devidos à paralelizaÃÃo do algoritmo foram estudados. Mostrou-se que o algoritmo paralelo nÃo à somente mais rÃpido que o sequencial, mas tambÃm produz melhores resultados. Jà nos exemplos nÃo-lineares, foram obtidos projetos significativamente mais eficientes que aqueles obtidos utilizando anÃlise linear. / Composite materials are being extensively studied, as their use allows the design of structures that are lighter and stronger than their metal counterparts and feature good thermal insulation and fatigue resistance. Fiber Reinforced Composites (FRC), the focus of the present work, consist in stacking multiple laminae, each one consisting of unidirectional fibers embedded in a polymeric matrix. Laminated shells are used in many industrial applications, such as modern aircraft fuselages and wing systems, offshore structures, among others. Due to the many variables involved in the design of such structures, such as the number of layers (plies) and the mate- rial, thickness and fiber orientation of each layer, the traditional trial-and-error design procedure becomes arduous, which leads to the use of optimization techniques. In the structural analysis of laminated shells, numerical methods are commonly used, particularly the Finite Element Method (FEM), which is capable of modeling complex geometries, loads and boundary conditions. In order to determine the final load-carrying capacity of such shells, it is necessary to take into account not only the presence of large displacements (geometric non-linearity) but also its failure behavior (material non-linearity). In the present work, the geometric non-linearity was introduced by using the Total Lagrangian approach in a shallow shell finite element based on Marguerreâs Shell Theory. The element was implemented in an academic finite element software and multiple benchmark numerical examples were treated. The obtained results showed that the element is efficient when dealing with shells with small initial curvatures and moderately large displacements and rotations. The material non-linearity was considered by using progressive failure models, with the instantaneous degradation of the mechanical properties of layers that fail during the analysis. Three distinct progressive failure methods were formulated and implemented and the numerical examples yielded promissing results, with the correct determination of the ultimate failure load of laminates subjected to in-plane and bending loads, which were in good agreement with experimental and numerical results from the literature. The structural performance evaluated through the analysis procedure was then used in an optimization model in order to find the optimum stacking sequence for a given applied load. Here, a novel Genetic Algorithm with a hybrid computational parallelization scheme was proposed. The algorithm is based on the island model and can be executed in both clusters and personal computers alike. The algorithm was implemented and combined with the analysis procedures in the optimization of laminated shells considering both linear and non-linear analysis. In the linear examples, the algorithm was verified and the efficiency and execution time gains due to the parallel implementation were measured. The results show that the parallel algorithm not only runs faster than a sequential one, but also provides better results. In the non-linear examples, significant lighter and more efficient designs were obtained due to the consideration of the two types of non-linearities.