A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

Naghdabadi, R.; Baghani, Mostafa; Arghavani, J.

doi:10.1016/j.finel.2012.05.001

Cited by 38 publications

(18 citation statements)

References 41 publications

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“…Here, true strain is de ned as the instantaneous elongation per unit length of the specimen and true stress is calculated using Eq. (19). It is observed that the Generalized Mooney-Rivlin model matches quite well with experimental quasistatic uniaxial compression data.…”

Section: Resultssupporting

confidence: 59%

“…Further to that, despite a signi cant amount of research carried out to study the body organs, the preparation of experimental samples and the determination of the material properties of biological tissue is a complex problem due to their nature [17]; therefore, the use of organ-equivalent materials is a usual method. The highly nonlinear and timedependent behavior of polymeric materials has made it desirable to choose these materials over the biological tissue for using the biomaterial areas [18][19][20]. For instance, Tirella et al [21] derived the viscoelastic parameters using the epsilon dot method for soft hydrated biomaterials.…”

Section: Introductionmentioning

confidence: 99%

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Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

2018

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Predicting the nonlinear response of biological tissues is a challenging issue due to strain rate-(short-term) and time-dependent (long-term) nature of its response. While many of the tissue properties have already been extensively examined, some are left unnoticed, such as dependence of the stress-relaxation behavior on the strain levels. In this paper, a hyperviscoelastic constitutive model is derived within the integral form presented by Pipkin and Rogers model to remove this limitation. In the suggested model, the hyperelastic and short-term viscous parts are represented by a suitable strain energy function. The long-term viscous function includes the deformation history, which is expressed through a tensorial-relaxation function and has not been considered elsewhere. The constitutive model involves a number of material parameters. The values of those are identi ed from experimental data for Adiprene-L100 as a tissue-equivalent material. Parameters appearing in constitutive law are estimated by tting the model with the experimental data. It is assumed that the tissue phantom is slightly compressible, isotropic, and homogenous. The obtained results indicate that the presented model can describe the nonlinearity, strain rate-(short-term) and time-dependent (long-term) e ects of materials. The validation of the model is investigated, and very good agreement between the proposed model and the experimental data is shown.

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Section: Resultssupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

2018

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“…The first is based on macro‐model of viscoelastic theory . The second is related to the micromechanical model of phase transformation theory, in which SMPs are composed of activation phase at high temperature and freeze phase at low temperature . The third dealt with frozen volume fraction of solid phase transition theory and classical viscoelastic theory model, with new developed hybrid constitutive equations …”

Section: Constitutive Theorymentioning

confidence: 99%

“…[32][33][34][35][36] The second is related to the micromechanical model of phase transformation theory, in which SMPs are composed of activation phase at high temperature and freeze phase at low temperature. [37][38][39] The third dealt with frozen volume fraction of solid phase transition theory and classical viscoelastic theory model, with new developed hybrid constitutive equations. 40 Thermally induced SMPs have viscoelastic properties and shape memory characteristics.…”

Section: Thermo-mechanical Constitutive Theory Of Smpsmentioning

confidence: 99%

Design and analysis of smart diaphragm based on shape memory polymer

Tao

Liu

Yang

et al. 2018

J of Applied Polymer Sci

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Currently, tank diaphragms are mostly applied in the field of aerospace but one of their limitations have to do with their inability to recycle. In the article, we discussed the modeling of a new kind of reversible diaphragm, so‐called shape memory polymer (SMP) diaphragm. A thermo‐mechanical modeling of SMP is implemented by the finite element method using a constitutive model. A single variable in this model is defined and used to simplify the model compared to other existing models. Evolution of the analysis is conducted by making use of the intermediate difference forms and Jacobian matrix, which is applied to all quantities within the model. The overturning and recovery behaviors of the SMP diaphragm are examined. And, the effect of several parameters, including thickness, height and radius of the diaphragm, as well as temperature on the overturning performance are investigated. This study led to the establishment of an optimized model with the objective function requiring minimum overturning pressure for completing deformation and design variables associated with thickness, height, radius, and temperature. An optimized SMP diaphragm is obtained under the critical pressure constraints. The results contribute to the design and application of novel SMP diaphragms. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46557.

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“…São produtos de uma extensa linha de estudo que, na segunda metade da década de 90, avaliou-se ser composta por mais de 56000 artigos, 380 livros e 400 anais de congressos [148]. É possível afirmar que o Método dos Elementos Finitos aplicado à análise de estruturas sólidas está em constante evolução, com o desenvolvimento de formulações de elementos mais aperfeiçoadas [79,86,89,105,135,182,197,203,232,246], novos modelos de materiais [14,67,168], propostas de algoritmos numéricos [171,200,251], otimizações [44,53,181], notas de aplicação [3,206], entre outros tópicos.…”

Section: O Método Dos Elementos Finitosunclassified

Um programa de elementos finitos em GPU e orientado a objetos para análise dinâmica não linear de estruturas.

Yamassaki¹

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A Deus, minha mãe, meu irmão e minhas plantas (!) vii AgradecimentosPrimeiramente, agradeço a Deus pela grande ajuda em tornar este trabalho realidade. Em seguida, duas pessoas foram meus grandes mentores e exemplos que ouvi e segui durante todo este tempo: minha mãe, Amélia, e meu irmão, Ricardo. Durante o doutorado, mesmo quando eu me perdia em devaneios sobre a arquitetura do programa ou contava sobre as ideias malucas que tinha, eles sempre ouviam atentamente, sendo as pessoas com quem mais compartilhei as alegrias e tristezas ao longo do processo. Amélia e Ricardo, muito obrigado por tudo! Recebi bastante apoio dos meus colegas no GMSIE, o Grupo de Mecâ-nica dos Sólidos e Impacto em Estruturas. Seguem agradecimentos especiais para Rafael Santiago, Rafael Moura, Roberto Oshiro, Leonardo Mazzariol e Miguel Gonzales, pela paciência e oferecerem boas ideias, além de explicar não-linearidade para um não-engenheiro.Seguem também agradecimentos à Profa. Larissa Driemeier, pelas explicações iniciais em não-linearidade, e ao Prof. Marco Lúcio Bittencourt, pelas valiosas discussões. E, é claro, não podia faltar agradecimentos ao meu orientador, o Prof. Marcílio Alves, que me ofereceu esta grande oportunidade, para um aluno de computação e me apoiou enquanto eu desvendava a área de Engenharia. Por último, agradeço à CAPES pelo financiamento concedido e à Escola Politécnica e à Universidade de São Paulo, pelo oferecimento das instalações onde foi realizado o trabalho.Fui excêntrico ao dedicar este trabalho às minhas plantas. O estresse que sofri por causa da demanda por resultados quase me abalou física e mentalmente. Cultivar plantas foi o que me garantiu dias menos estressantes, se tornando uma verdadeira terapia. Aliás, para esclarecer, alguns nomes dos componentes da arquitetura do programa aqui discutido são nomes de plantas que cultivo. ABSTRACTIt has been recognized that the adoption of graphics processing units (GPU) can significantly boost numerical methods in scientific applications. In order to support such technology, it is necessary to readapt the program, which requires code flexibility. In this work, it is presented the architecture of a finite element (FEM) analysis program for structural analysis with GPU support. Object-oriented design is used to guide development and to build code into a flexible structure. Program scalability is achieved by extensibility of its features, provided by run-time loaded components. In order to demonstrate code robustness, the software is directed to the study of structural dynamics, considering complex non-linear aspects of material (plasticity) and geometry (large displacements). Code accuracy is checked by comparing with known literature problems and with commercial solver packages (ABAQUS). The comparison shows good agreement in the results. The GPU code speedup is analysed against timings of CPU program code, where it is observed performance gain up to 10 times.

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A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

Cited by 38 publications

References 41 publications

Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

Design and analysis of smart diaphragm based on shape memory polymer

Um programa de elementos finitos em GPU e orientado a objetos para análise dinâmica não linear de estruturas.

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