Projeto e construção de uma bancada para ensaios de flambagem em vigas de pequeno porte

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Constitutive framework of a new hyperelastic model for isotropic rubber-like materials for finite element implementation

The strain energy function of hyperelastic material models must fulfill some mathematical conditions to satisfy requirements such as numerical stability and physically plausible mechanical behavior. In the framework of computer simulations with Newton-type methods, numerical stability is assured by the positive definiteness of the tangent operator. The Baker-Ericksen inequalities, on the other hand, are sufficient and necessary conditions in order to guarantee that the material behaves in a physically plausible way, although they are rarely taken into account during parameter identification. The present work proposes a modification in the strain energy function of a previously developed model for isotropic rubber-like materials. The new expression for W allows the satisfaction of both of the aforementioned requirements. The complete constitutive framework for its implementation in a Finite Element code is provided. Representative examples are analyzed and to show the superior performance when compared to well-known models found in the specialized literature both for homogeneous and non-homogeneous cases of deformation

EVALUATION OF THE FATIGUE RESPONSE OF POLYESTER YARNS AFTER THE APPLICATION OF ABRUPT TENSION LOADS

The discovery of oil fields in deeper waters through out the last decades has led the oil industry to the necessity of replacing the mooring systems of offshore platforms from steel to synthetic cables. Consequently, both the industry and the academy started to join forces in order to better understand the mechanical behavior of such materials when subjected to different service conditions. This work aims to assess the change in the fatigue life of polyester (PET) yarns if the material is submitted to an abrupt tension load prior to the application of the fatigue cycling. It was found that the fatigue life of the yarns tested are substantially reduced if the specimen is subjected to this kind of abrupt load in comparison to virgin samples

PRELIMINARY ASSESSMENT OF THE CHANGE IN THE MECHANICAL BEHAVIOR OF SYNTHETIC YARNS SUBMITTED TO CONSECUTIVE STIFFNESS TESTS

Anchoring systems of offshore platforms are designed to work uninterruptedly for 20 to 30 years, and despite the increasing number of studies concerning these systems’ mechanical behavior in working conditions, most of them are conducted in speeding environments, due to the necessity of results in the short term. There are standardized stiffness tests, such as ISO 18692, based on quantities like Dynamic Stiffness and Quasi-static Stiffness, through which one can compare, quantitatively, two different ropes. However, there is a lack of research aiming to assess the change in the mechanical behavior of these ropes after certain number of consecutive loading cycles (or stiffness tests). This study aims to assess, at the yarn level, the change in the quasi-static and dynamic stiffness parameters of two materials when submitted to repeated stiffness tests. Results in terms of qualitative assessment of the mechanical behavior, as well as quantitative changes in the parameters are presented

EVALUATION OF THE FATIGUE RESPONSE OF POLYESTER YARNS AFTER THE APPLICATION OF ABRUPT TENSION LOADS

The discovery of oil fields in deeper waters through out the last decades has led the oil industry to the necessity of replacing the mooring systems of offshore platforms from steel to synthetic cables. Consequently, both the industry and the academy started to join forces in order to better understand the mechanical behavior of such materials when subjected to different service conditions. This work aims to assess the change in the fatigue life of polyester (PET) yarns if the material is submitted to an abrupt tension load prior to the application of the fatigue cycling. It was found that the fatigue life of the yarns tested are substantially reduced if the specimen is subjected to this kind of abrupt load in comparison to virgin samples

Evaluation of residual strength of polymeric yarns subjected to previous impact loads

The discovery of oil fields in deep and ultra-deep waters provided an opportunity to evaluate the use of  synthetic ropes, complementarily or alternatively to traditional steel-based mooring lines in offshore units, mainly because of the former’s lower specific weight. Considering the series of complex dynamic-mechanical mainly axial loads to which these structures may be subjected, originated from different sources, such as wind, water current, tide, etc., there may be cases when at least one of these lines may possibly face an abrupt, shock-like axial load of considerably larger magnitude. The goal of the present study is to evaluate the residual tensile strength of three different synthetic yarns  (polyester, and two grades of high modulus polyethylene) after exposure to such axial impact loads. It was observed that, for the tested materials, polyester is the one with the largest impact resistance to the conditions evaluated herein, mainly because of its comparatively greater energy absorption properties

Dispositivo de acoplamento entre embarcações

Universidade Federal do Rio Grande do SulEngenhariaDepositad

Assessment of a hyperelastic model for incompressible materials: analysis of restrictions, numerical implementation and optimization of the constitutive parameters

Apesar do crescente número de publicações estudando as diferentes propriedades e o comportamento peculiar inerente dos materiais hiperelásticos submetidos a deformações, as quais muitas vezes propõem modelos matemáticos para caracterizá-los, muito pouco esforço é observado no sentido de conferir a este modelo matemático propriedades básicas como garantia de unicidade das soluções, estabilidade numérica ou mesmo comportamento físico condizente com a realidade. Este trabalho apresenta uma revisão das diferentes restrições matemáticas que devem ser impostas às equações da função energia de deformação dos modelos hiperelásticos para garantir-lhes estas propriedades básicas desejadas aplicadas à família de modelos de Hoss- Marczak [Hoss, 2009]. Como resultado, obtém um conjunto de desigualdades que devem ser satisfeitas pelas constantes constitutivas destes modelos. Posteriormente estes mesmos modelos são implementados em um programa comercial de elementos finitos e casos de deformações homogêneas e não-homogêneas são simulados para comparar os seus resultados com aqueles obtidos utilizando-se modelos consagrados pela literatura. Por fim, este trabalho apresenta uma metodologia de otimização multi-critério das constantes hiperelásticas baseada na minimização do erro entre dados teóricos e experimentais não somente de um ensaio, como usualmente é feito, e sim da soma dos erros de dois ou mais ensaios. As curvas dos ajustes teóricos assim obtidas são confrontadas com as experimentais e, através da comparação direta entre os coeficientes de correlação não-linear das curvas, concluise que a metodologia proposta fornece resultados superiores a outras metodologias.In spite of the increasing in the number of publications proposing hyperelastic models to better characterize different types of rubber-like materials, the number of them concerned with aspects related to unicity of solution, numerical stability or plausibility of the physical behavior is much smaller. This work presents a literature review of the various types of mathematical restrictions that should be verified in strain energy density functions for hyperelastic constitutive models. These restrictions are verified for the HMI constitutive models [Hoss, 2009]. As a result, a set of inequalities that must be respected by the constitutive parameters of those models is obtained. In order to further assess the performance of the HMI models, their strain energy functions are implemented in a commercial finite element software. Different cases of homogeneous and non-homogeneous deformations are analyzed and the results are compared to those obtained when using some classical constitutive models. Finally, a multi-objective optimization procedure is implemented to obtain the best possible set of constitutive parameters for a general hyperelastic model. The method allows one to fit the chosen model to more than one set of experimental data. Theoretical predictions obtained using the proposed method are compared with experimental curves through non-linear fitting coefficients. The results show that the methodology generates better predictions than those obtained by adjusting the parameters against a single set of experimental data or combining multiple single-objective fittings

Numerical implementation of finite viscoelasticity via higher order runge-kutta integrators and consistent interpolation between temporal and spatial discretizations

Em problemas de viscoelasticidade computacional, a discretização espacial para a solução global das equações de equilíbrio é acoplada à discretização temporal para a solução de um problema de valor inicial local do fluxo viscoelástico. É demonstrado que este acoplamento espacial-temporal (ou global-local) éconsistente se o tensor de deformação total, agindo como elemento acoplador, tem uma aproximação de ordem p ao longo do tempo igual à ordem de convergência do método de integração de Runge-Kutta (RK). Para a interpolação da deformação foram utilizados polinômios baseados em soluções obtidas nos tempos tn+1, tn, . . ., tn+2−p, p ≥ 2, fornecendo dados consistentes de deformação nos estágios do RK. Em uma situação onde tal regra para a interpolação da deformação não é satisfeita, a integração no tempo apresentará, consequentemente, redução de ordem, baixa precisão e, por conseguinte, eficiência inferior. Em termos gerais, o propósito é generalizar esta condição de consistência proposta pela literatura, formalizando-a matematicamente e o demonstrando através da utilização de métodos de Runge-Kutta diagonalmente implícitos (DIRK) até ordem p = 4, aplicados a modelos viscoelásticos não-lineares sujeitos a deformações finitas. Através de exemplos numéricos, os algoritmos de integração temporal adaptados apresentaram ordem de convergência nominal e, portanto, comprovam a validade da formalização do conceito de interpolação consistente da deformação. Comparado com o método de integração de Euler implícito, é demonstrado que os métodos DIRK aqui aplicados apresentam um ganho considerável em eficiência, comprovado através dos fatores de aceleração atingidos.In computational viscoelasticity, spatial discretization for the solution of the weak form of the balance of linear momentum is coupled to the temporal discretization for solving a local initial value problem (IVP) of the viscoelastic flow. It is shown that this spatial- temporal (or global-local) coupling is consistent if the total strain tensor, acting as the coupling agent, exhibits the same approximation of order p in time as the convergence order of the Runge-Kutta (RK) integration algorithm. To this end we construct interpolation polynomials based on data at tn+1, tn, . . ., tn+2−p, p ≥ 2, which provide consistent strain data at the RK stages. If this novel rule for strain interpolation is not satisfied, time integration shows order reduction, poor accuracy and therefore less efficiency. Generally, the objective is to propose a generalization of this consistency idea proposed in the literature, formalizing it mathematically and testing it using diagonally implicit Runge-Kutta methods (DIRK) up to order p = 4 applied to a nonlinear viscoelasticity model subjected to finite strain. In a set of numerical examples, the adapted time integrators obtain full convergence order and thus approve the novel concept of consistency. Substantially high speed-up factors confirm the improvement in the efficiency compared with Backward Euler algorithm