This thesis is concerned with the accurate numerical simulation of localized deformation that can develop into necking and failure, induced by combined bending and tension in aluminum alloy shell structures. The study is motivated by the need to establish the onset and evolution of such failures in imploding underwater cylindrical aluminum alloy shell structures. However, failure under combined bending and tension is also of concern in sheet metal forming. Such localized zones of deformation are shown to develop under controlled conditions in specially designed crushing experiments of Al-6061-T6 cylindrical shells. In these experiments shells of finite length and radially constrained ends are crushed laterally by rigid punches. The crushing, which is conducted under displacement control, causes the shell to develop bending and stretching stresses that lead to arcs of localized wall thinning to appear near the radially constrained locations. The local wall thinning develops into depressions with a width of the order of the shell wall thickness. As crushing progresses the depressions deepen, increase their span, become neck-like and develop inclined failures. The crushing was terminated when the first of four such depressions ruptured. After unloading, the shell was sliced along the principal plane of crushing and the most deformed cross sections of the necks were measured using an optical microscope. The crushing experiments were simulated numerically using solid FE models. The material was modeled as a finitely deforming elastic-plastic solid that hardens isotropically using three constitutive models: the first is based on the von Mises yield function, the second on the non-quadratic isotropic Hosford yield function and the third on the anisotropic Yld04-3D yield function. The models were calibrated to the same stress-strain response and to data from a set of radial biaxial experiments conducted on the same alloy tubes. The overall structural response was reproduced well by all models. Apparently such global responses smear out local differences introduced by the shape of the yield function adopted. However, differences between the three constitutive models were observed in the evolution of localization in the depressions. For the von Mises yield function, the localized deformation was significantly milder than in the experiments. The isotropic Hosford yield function produced necks that were closer to the experimental ones, while Yld04-3D produced results that were very close to the measurements. Clearly, and in concert with other applications, the adoption of a non-quadratic yield function is necessary for reproduction of localization and other challenging deformation histories in Al alloys. The addition of anisotropy in such models improves further the predictions. The results also demonstrated that accurate simulation of the evolution of the depressions in the presence of normal contact stresses requires the use of solid elements. Localization is clearly a three-dimensional phenomenon and shell elements reproduce most of the structural response well, but not the depressions and their evolution that eventually cause failure. / text

Abstract The thesis is focused on the reconstruction of long-term cosmic ray variability using proxy data. The 11-year solar cycle in production/deposition rates of cosmogenic nuclides ¹⁰Be and ¹⁴C has been modelled for the conditions of grand minima and maxima of solar activity (namely, Maunder Minimum and Grand Modern Maximum). The result shows that contrary to the observed strongly suppressed amplitude of the solar cycle in sunspots during Maunder Minimum relatively to Grand Modern Maximum, the cosmic ray proxies have the comparable amplitudes during the two periods. This phenomenon is caused by the nonlinear relation between solar activity and production of cosmogenic nuclides. In addition to well-established proxies of cosmic rays, nitrate in polar ice has been recently proposed as a new proxy for the long-term variability of galactic cosmic rays. The thesis contains two tests of its applicability for this purpose with TALDICE and EPICA-Dome C ice core data from Central Antarctica. The results support the proposal for the multimillennial time scales. Lunar samples acquired during the Apollo missions are important data for estimating the averaged energy spectra of galactic cosmic rays and solar energetic particles at the Earth’s orbit. The development in modelling of the interaction between energetic particles and matter makes it necessary to revise the earlier results. Because of that, new production rates of ¹⁰Be and ¹⁴C in lunar samples by galactic cosmic rays and solar energetic particles have been computed. New accurate cosmic ray reconstructions from natural archives containing cosmogenic nuclides use sophisticated climatic models requiring yield functions of the nuclides with high altitude resolution. These functions have been computed for ⁷Be, ¹⁰Be, ¹⁴C, ²²Na, and ³⁶Cl in the Earth’s atmosphere. Overall, the major purpose of the studies presented in the thesis is to increase the quality of reconstructions of the long-term cosmic ray variability for better understanding of the solar and heliospheric physics. / Original papers The original publications are not included in the electronic version of the dissertation. Poluianov, S. V., Usoskin, I. G., & Kovaltsov, G. A. (2014). Cosmogenic Isotope Variability During the Maunder Minimum: Normal 11-year Cycles Are Expected. Solar Physics, 289(12), 4701–4709. https://doi.org/10.1007/s11207-014-0587-6 Poluianov, S., Traversi, R., & Usoskin, I. (2014). Cosmogenic production and climate contributions to nitrate record in the TALDICE Antarctic ice core. Journal of Atmospheric and Solar-Terrestrial Physics, 121, 50–58. https://doi.org/10.1016/j.jastp.2014.09.011 Poluianov, S., Artamonov, A., Kovaltsov, G., & Usoskin, I. (2015). Energetic particles in lunar rocks: Production of cosmogenic isotopes. Proceedings of Science, 30-July-2015, art. no. 051 . Traversi, R., Becagli, S., Poluianov, S., Severi, M., Solanki, S. K., Usoskin, I. G., & Udisti, R. (2016). The Laschamp geomagnetic excursion featured in nitrate record from EPICA-Dome C ice core. Scientific Reports, 6(1). https://doi.org/10.1038/srep20235 Poluianov, S. V., Kovaltsov, G. A., Mishev, A. L., & Usoskin, I. G. (2016). Production of cosmogenic isotopes 7Be, 10Be, 14C, 22Na, and 36Cl in the atmosphere: Altitudinal profiles of yield functions. Journal of Geophysical Research: Atmospheres, 121(13), 8125–8136. https://doi.org/10.1002/2016jd025034

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[pt] O presente trabalho tem por objetivo desenvolver um otimizador eficiente de grande escala, que permita a aplicabilidade prática da Análise Limite Numérica pelo MEF, para resolver problemas reais da Engenharia Geotécnica. Para isto, foi desenvolvido um otimizador para o programa GEOLIMA (GEOtechnical LIMit Analysis) (Carrión, 2004) baseado no algoritmo de Pontos Interiores, computacionalmente mais eficiente que os otimizadores comerciais existentes. Pelo fato das propriedades do solo serem de natureza aleatória, a possibilidade de aplicar Análise de Confiabilidade com a Análise Limite pelo método FORM em problemas geotécnicos é pesquisada também. Sendo a grande vantagem do método FORM a possibilidade de se aplicar para funções de falha quaisquer e variáveis com distribuição quaisquer. Inicialmente, são apresentados os fundamentos da teoria de Análise Limite e sua formulação numérica pelo MEF (Método dos Elementos Finitos). A seguir, é investigada a possibilidade de se usar otimizadores comerciais para resolver o problema matemático resultante da aplicação de Análise Limite com o MEF e são descritos os fundamentos teóricos do otimizador implementado baseado no algoritmo de Pontos Interiores. Um resumo dos fundamentos teóricos da Análise de Confiabilidade é apresentado. É descrito o processo de cálculo pelo método FORM e dois exemplos de aplicação são realizados. Finalmente, análises de diferentes problemas resolvidos com o otimizador implementado são apresentados indicando o grande potencial da Análise Limite Numérica, na solução de problemas reais da Engenharia Geotécnica. / [en] This work has, as its main objective, the development of an efficient and large scale optimizer, that allows the practical application of Numerical Limit Analysis (NLA) with Finite Element Method (FEM) to solve real problems in Geotechnical Engineering. For that purpose, an optimizer was developed for GEOLIMA (GEOtechnical LIMit Analysis) program (Carrión, 2004), based on Interior Points algorithm, computationally more efficient than the existing commercial optimizers. Due to the fact that soils have random properties, the possibility to apply Reliability Analysis with Limit Analysis using the FORM method was also investigated. Initially, Limit Analysis theory was presented together with its numerical formulation using the FEM. In sequence, the use of commercial optimizers was investigated in order to solve the resulting mathematical problem. Subsequently, the theorical foundations of the developed optimizer, based on the Interior Points algorithm were described. A summary of Reliability Analysis was also presented together with a description of computational procedures using FORM and two examples were developed. Finally, analyses of different problems solved with developed optimizer were presented. The obtained results demonstrated the great potential of Numerical Limit Analysis (NLA), in the solution of real problems in Geotechnical Engineering.

Les alliages d'aluminium ont été largement utilisés dans l'industrie automobile et maritimes en raison des avantages d'une faible densité, d'une bonne résistance à la corrosion. Les travaux présentés dans ce mémoire de thèse s’intéressent à la mise en forme à chaud de tôles minces en alliage d’aluminium AA5383. L'objectif principal est de réduire le temps de formage sans sacrifier l'intégrité de la pièce. Tout d'abord, le comportement à la déformation à chaud de l'alliage AA5383 est caractérisé expérimentalement. Une campagne expérimentale comprenant d’essais de traction uniaxiale, de traction entaillées, de cisaillement et de gonflement libre est réalisée pour couvrir une plage importante de températures (623~723 K) et de vitesses de déformation (10-4~10-1 s-1). Ensuite, les modèles de matériau, tels qu'une règle de flux composite avec le critère de plasticité BBC2003 et le critère de dommage Mohr Coulomb Modifié, sont développés et mis en œuvre dans ABAQUS à l'aide du sous-programme utilisateur. Enfin, les simulations numériques des processus de formation de gaz sont effectuées et comparées aux résultats expérimentaux correspondants. / Aluminum alloys have been extensively used in the automotive and marine industry due to the advantages of low density, high strength to weight ratio and good corrosion resistance. Major challenge of their application lies in the ability to form deep-drawing shapes. Superplastic Forming is widely used to produce this type of parts. However, high forming cycle time due to the low forming strain rate limits their wide application. The present dissertation focuses on hot forming strategies to produce deep drawing parts from AA5383 aluminum thin sheets. The main objective is to reduce the forming time without sacrificing the part integrity. Firstly, the hot deformation behavior of the AA5383 alloy is experimentally characterized. An experimental campaign, including uniaxial tension, notched tension, shear and free bulging tests, is performed to cover an important range of temperatures (623~723 K) and strain rates (10-4~10-1 s-1). Then, the material models, such as a composite flow rule with the BBC2003 anisotropic yield criterion and the modified Mohr-Coulomb damage criterion, are developed and implemented in ABAQUS by using user subroutine. Finally, the numerical simulations of the gas forming processes are performed and compared with the corresponding experimental results.