Inelastic design methods have been used in seismic design for several years and are well accepted in engineering practice. In contrast, an inelastic wind design method is yet to be developed, in part due to the inherent differences between seismic forces and wind forces. Current wind design practice follows a linear method to find a design windspeed for the location where the structure will be built. Once the design windspeed has been determined, the lateral force resisting system is designed such that it will behave elastically. This study was conducted with the hypothesis that by providing ductility at the material level, member level, and system level it may be possible to use a reduced design force for wind (i.e., a design force reduction that is proportional to a wind response modification factor). A three-story office building that uses steel moment frames as the primary lateral force resisting system was examined to test the hypothesis. Various levels of ductility were included based on ductility requirements for material strength, section stability and system stability originally developed for seismic design. Moment frames were designed for a range of design windspeeds and for three levels of ductility. For each design windspeed, a non-ductile (representing the moment frame as it would be designed by current standards), moderately-ductile and highly-ductile moment frame were developed. A finite element model of the building was made to capture inelastic material behavior and large displacements. The finite element model was subjected to wind loads based on wind tunnel tests data, and the static pushover, vibration, and dynamic responses of the building were evaluated. The performance of each moderately-ductile and highly-ductile moment frame was compared to the performance of each non-ductile frame of a higher design windspeed. The results show that for moderately-ductile moment frames, a wind response modification factor equal to 2 provided a collapse capacity that met or exceeded the collapse capacity of the comparative nonductile moment frame. For highly-ductile moment frames, a wind response modification factor equal to 3 met or exceeded the collapse capacity of the comparative non-ductile moment frame. In many instances, the collapse capacity of the moderately-ductile moment frame was similar to the collapse capacity of the highly-ductile moment frame. Thus, the results indicate that the use of a response modification factor for wind may be viable.

[pt] Neste trabalho estudamos o comportamento dinâmico de um gás granular a baixa densidade do ponto de vista hidrodinâmico. Fizemos também uma análise de instabilidade linear das equações de Navier-Stockes para tais sistemas. Finalmente, construímos um modelo de sistema de celulas dinâmicas para simular computacionalmente esses sistema e o aplicamos a um gás granular, a fim de entender um pouco mais sobre seus comportamentos dinâmicos, sob diversas condições de contornos externos. / [en] In this work we study the dynamic behavior of a granular gas at low density from the hydrodynamic point of view. We also perform a linear instability analysis of the Navier- Stockes for such systems. Finally we construct a cell dynamic systems model to simulate computationally these systems and apply it for a granular gas in order to understand a little more about its dynamic behavior, under several boundary conditions.

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.

[pt] No presente trabalho é feito um apanhado de teorias de estruturas unidimensionais que não se utilizam da teoria tridimensional como ponto de partida. São discutidos alguns modelos sob a mesma ótica, ressaltando-se seus pontos comuns e suas diferenças. Posteriormente é desenvolvido um modelo exato para estruturas unidimensionais. São discutidos em profundidade medidas de deformação e esforços internos. É tomado um modelo constitutivo elasto-plástico. A modelagem utilizada não faz restrições quanto ao tamanho das deformações e considera a extensibilidade da estrutura. Através de técnicas numéricas simples, conhecidas como métodos do Tiro, são resolvidos alguns problemas de estruturas unidimensionais modelados pela teoria desenvolvida neste trabalho. Dentro destes casos estuda-se o problema da instabilidade, o efeito do cisalhamento para vigas e o comportamento não linear de materiais (plasticidade). Os resultados são apresentados graficamente. Por fim são indicados novos caminhos que dão continuidade a este trabalho. / [en] A survey of rod’s models which are not based in the three-dimensional theory is presented. One of the models is picked out and discussed in details (kinematics, efforts and balance laws). An elasto-plastic constitutive model is considered. This model takes into account large deformations and the extensibility of the tods. A series of numerical simulations of rod’s problems which utilize the shooting methods are considered. These applications study the non linear behavior of rods, in cases which shear. Geometric instability and plasticity are treated. At the end, suggestions for the continuity of this work are presented.

Im Rahmen der geometrisch und physikalisch nichtlinearen Kontinuumsmechanik werden Beobachterkonzepte und Darstellungsformen tensorieller Größen diskutiert und zum Teil neu eingeführt, die insbesondere die Modellierung und FEM-Implementierung komplizierter Modelle für inelastisches Materialverhalten bei großen Deformationen wirkungsvoll unterstützen. / Observer concepts and several kinds of representations of tensorial quantities are discussed and partly introduced within the framework of geometrically und physically nonlinear continuum mechanics. They are intended to support the modelling of complicated inelastic materials undergoing large deformations.

Im Rahmen der geometrisch und physikalisch nichtlinearen Kontinuumsmechanik werden Beobachterkonzepte und Darstellungsformen tensorieller Größen diskutiert und zum Teil neu eingeführt, die insbesondere die Modellierung und FEM-Implementierung komplizierter Modelle für inelastisches Materialverhalten bei großen Deformationen wirkungsvoll unterstützen. / Observer concepts and several kinds of representations of tensorial quantities are discussed and partly introduced within the framework of geometrically und physically nonlinear continuum mechanics. They are intended to support the modelling of complicated inelastic materials undergoing large deformations.

[pt] Neste trabalho estudamos o comportamento dinâmico de um gás granular a baixa densidade do ponto de vista hidrodinâmico. Fazemos também uma análise de instabilidade linear das equações de Navier-Stockes para tais sistemas. Finalmente, construímos um modelo de sistema de Células Dinâmicas para simular computacionalmente esses sistemas e o aplicamos a um gás granular, a fim de entender um pouco mais sobre seus comportamentos dinâmicos, inclusive a formação de aglomerados, sob as mais variadas condições de contorno. / [en] In this work we study the dynamic behavior of a granular gas at low density from the hydrodynamic point of view. We also perform a linear instability analysis of the Navier- Stockesfor for such systems. Finally, we construct a cell dynamic systems model to simulate computationally these systems and apply it for a granular gas in order to understand a little more about its dynamic behavior, enclose formation of clusters, under several boundary conditions.

[pt] Estendemos o formalismo de Fokker-Planck que foi usado previamente para descrever, a partir de primeiros princípios, o comportamento de um gás granular em esfriamento, com potencial de contato Hertziano e força de atrito viscoelástica o qual resulta em um sistema com coeficiente de restituição que depende da velocidade. Nesta tese é estudado, também a partir de primeiros princípios, o caso mais geral, o de um estado estacionário com energia cinética finita e fora do equilíbrio, devido ao acoplamento a um mecanismo externo de alimentação de energia. Estende- se assim a validade do resultado prévio. / [en] We extend the Fokker-Planck formalism used previously to describe the behavior of a cooling granular gas, with a Hertzian contact potential and viscoelastic radial friction, giving a velocity dependent coeficient of restitution. In this thesis, we study the more general case of a steady-state with finite kinetic, energy and far from equilibrium, due to the coupling to an external energy- feeding mechanism, also from first-principles, and extend the validity of the former results.

[pt] Estuda-se a consideração de comportamento inelástico do material na geração de espectros de resposta de projeto. Para tanto, trabalha-se sobre um sistema secundário simplificado acoplado a um pórtico de cinco andares com características dinâmicas ajustadas para modelar um sistema principal real, de uma usina nuclear. Faz-se um estudo paramétrico sobre estes sistemas acoplados onde são variados os parâmetros: fator de escoamento, a intensidade da excitação e o nível de amortecimento. É proposto um fator de dutilidade global formulado em termos de trabalho externo realizado sobre o sistema secundário. São obtidos espectros de dutilidade e de resposta. A análise de tais espectros fornece informações sobre o desempenho do sistema secundário e seus suportes e conclui por fatores de transposição entre os espectros elástico e inelástico. Propõe-se metodologia para obtenção de espectros de resposta elásticos e inelásticos que levam em conta o acoplamento entre os sistemas principal e secundário, o movimento relativo dos suportes e o compromisso probabilístico entre as ordenadas do espectro e a sismicidade da região expressa em termos de uma função densidade de espectro de potência objetivo para a aceleração do terreno. Um exemplo de obtenção de espectros de resposta acoplada de projeto uniformemente provável inelástico é apresentado. / [en] The authors concern includes two main points in the subject of design response spectra generation for secondary systems in nuclear power plant structures: the consideration of inelastic behavior in the secondary systems materials and the production of uniformly probable design response spectra. One works with a previously developed secondary system model attached to primary structure model tuned to the frequency range of a nuclear power plant building. A global ductility factor is formulated relating the plastic to the overall work done by the seismic external forces on the secondary system. This factor together with a particular definition of the yielding factor allows one to determine elastic to inelastic spectrum transpose factors. A methodology is proposed to generate uniformly probable coupled response spectra for multiply supported inelastic secondary systems. The seismic excitation is prescribed by a target power spectrum density function of the ground acceleration and an internal pressure condition is added to the seismic action. Examples illustrate the application of this proposed methodology.

Im Rahmen der geometrisch und physikalisch nichtlinearen Kontinuumsmechanik werden Beobachterkonzepte und Darstellungsformen tensorieller Größen diskutiert und zum Teil neu eingeführt, die insbesondere die Modellierung und FEM-Implementierung komplizierter Modelle für inelastisches Materialverhalten bei großen Deformationen wirkungsvoll unterstützen. / Observer concepts and several kinds of representations of tensorial quantities are discussed and partly introduced within the framework of geometrically und physically nonlinear continuum mechanics. They are intended to support the modelling of complicated inelastic materials undergoing large deformations.