A viscoelastic viscoplastic constitutive model including mechanical degradation: Uniaxial transient finite element formulation at finite strains and application to space truss structures

Carniel, Thiago André; Muñoz-Rojas, Pablo A.; Vaz, M.

doi:10.1016/j.apm.2014.09.036

Cited by 19 publications

(12 citation statements)

References 15 publications

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“…The development of complex constitutive models for time‐dependent, polymeric truss structures requires a proper parameter identification strategy, as extensively discussed in Carniel et al . A viscoelastic‐viscoplastic approximation fully coupled to a damage model was found appropriate to describe the high density polyethylene (HDPE) used in the simulations.…”

Section: Numerical Examples and Applicationsmentioning

confidence: 99%

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Identification of constitutive parameters – optimization strategies and applications

Vaz

Cardoso

Muñoz-Rojas

et al. 2015

Materialwissenschaft Werkst

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The pursuit to reduce manufacturing costs and increase product quality has led industries to use commercial codes and appropriate material models to simulate a wide range of metal forming operations. This scenario has prompted a healthy discussion on the strategies to obtaining constitutive parameters able to yield accurate numerical predictions. Optimization‐based parameter identification techniques have opened completely new routes to determine material parameters for this class of forming problems. Notwithstanding, the most appropriate optimization strategy (or development of new ones) for the trinomial forming operation – constitutive model – constitutive parameters is still open to debate. This work highlights the important role that optimization strategies play to determine parameters of constitutive models. A brief description of gradient‐based, gradient‐free and hybrid optimization approaches is presented within the framework of parameter identification. Comparative studies and applications to classical and damaged material models are also discussed.

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Section: Numerical Examples and Applicationsmentioning

confidence: 99%

“…HDPE stress-strain curve[37] Bild 3. HDPE Spannungs-Dehnungs-Kurve[37] M. Vaz Jr. et alMat.-wiss. u. Werkstofftech.…”

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Identification of constitutive parameters – optimization strategies and applications

Vaz

Cardoso

Muñoz-Rojas

et al. 2015

Materialwissenschaft Werkst

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“…Aplicando-se o princípio da energia potencial total estacionária (BELYTSCHKO et al, 2013) na Equação (1), pode-se obter a posição de equilíbrio da estrutura a partir da Equação (4). Assim, o equilíbrio da estrutura ocorrerá quando a derivada dessa energia potencial total, em relação aos graus de liberdade, for nula, ou seja, quando a taxa de variação da energia potencial total for nula.…”

Section: -Equacionamento Geral Da Formulação Posicional Não Linearunclassified

“…Carniel; Vaz (2015) apresentam uma formulação do método dos elementos finitos para análise de treliças espaciais com comportamento viscoelástico e viscoplástico incluindo degradação mecânica unidimensional. O modelo reológico generalizado de Kelvin-Voigt é adotado para descrição do comportamento viscoelástico, enquanto o comportamento viscoplástico é considerado a partir da equação de Perzyna e a degradação do material é considerada a partir do modelo de dano de Lemaitre.…”

Section: -Introduçãounclassified

Formulação posicional para descrição do comportamento mecânico de fluência em vigas e estruturas de pórtico

Becho

Barros

Greco

2015

Cieng

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RESUMOEste trabalho trata do desenvolvimento de uma formulação numérica não linear para descrever o comportamento mecânico viscoelástico de estruturas de pórticos e vigas submetidas a estado de tensão constante (fenômeno conhecido como fluência) e discretizadas em elementos finitos de pórtico plano. O desenvolvimento é baseado na formulação posicional não linear do Método dos Elementos Finitos considerando a teoria clássica de Bernoulli-Euler. Essa formulação possibilita a realização de uma análise estrutural não linear física e geométrica. A não linearidade geométrica considerada refere-se à análise do equilíbrio da estrutura na posição deformada utilizando o método de Newton-Raphson. Já a não linearidade física considerada refere-se à adoção de uma relação reológica baseada no modelo de Maxwell generalizado. Três exemplos numéricos são analisados utilizando-se a formulação desenvolvida. Os dois primeiros descrevem e comparam o comportamento de fluência em uma viga com diferentes condições de contorno. O terceiro exemplo descreve o comportamento de fluência em um pórtico formado por dois pilares e uma viga. Além disso, uma calibração simples da formulação é realizada em relação à solicitação axial de uma barra de Plástico Reforçado com Fibra de Vidro. Palavras-chave: Viscoelasticidade, Fluência, Formulação Posicional, Método dos Elementos Finitos, Modelo Reológico. ABSTRACTThe present work aims to develop a nonlinear numerical formulation used to describe the viscoelastic mechanical behavior of framed structures and beams under a constant stress state (known as creep phenomenon) and discretized by plane framed elements. The development is based on the nonlinear positional formulation of the Finite Element Method and it takes into consideration the beam kinematics of Bernoulli-Euler. This approach allows to perform a structural analysis with physical and geometrical nonlinearities. The geometrical nonlinearity involved refers to structural equilibrium in the deformed position obtained by the Newton-Raphson method. The physical nonlinearity is associated with the adoption of a viscoelastic behavior through a suitable rheological relation. This rheological relation is derived from the uniaxial rheological model, based on the generalized Maxwell model. Three numerical examples are analyzed by the developed formulation. The first two examples describe and compare the creep behavior of a beam with different boundary conditions. The third example describes the creep behavior of a framed structure, formed by two columns and one beam. Furthermore, a simple calibration of the formulation is performed considering axial loading experimental results of bar made by Glass Fiber Reinforced Polymers material.

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“…Therefore, a combined viscoelastic-viscoplastic constitutive relationships should be considered. Recently, new models coupling both viscoplastic and viscoelastic effects have been proposed (see, for instance, [3,10,15,16,27,29,33,39,41]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of a dynamic viscoelastic-viscoplastic piezoelectric contact problem

et al. 2017

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In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal compliance contact condition. The variational formulation is written as a nonlinear ordinary differential equation for the stress field, a nonlinear hyperbolic variational equation for the displacement field and a linear variational equation for the electric potential field. An existence and uniqueness result is proved using Gronwall's lemma, adequate auxiliary problems and fixed-point arguments. Then, fully discrete approximations are introduced using an Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some two-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution.

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A viscoelastic viscoplastic constitutive model including mechanical degradation: Uniaxial transient finite element formulation at finite strains and application to space truss structures

Cited by 19 publications

References 15 publications

Identification of constitutive parameters – optimization strategies and applications

Identification of constitutive parameters – optimization strategies and applications

Formulação posicional para descrição do comportamento mecânico de fluência em vigas e estruturas de pórtico

Analysis of a dynamic viscoelastic-viscoplastic piezoelectric contact problem

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