Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Latin American journal of solids and structures (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252022000400502 |
Resumo: | Abstract The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique. |
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Latin American journal of solids and structures (Online) |
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Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluidsUnified solid-fluid modelKelvin-Voigt visco-hyperelasticityFlory’s decompositionPositional FEMTotal Lagrangian formulationAbstract The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique.Associação Brasileira de Ciências Mecânicas2022-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252022000400502Latin American Journal of Solids and Structures v.19 n.4 2022reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78257010info:eu-repo/semantics/openAccessKishino,Renato TakeoKishino,Vitor HiroshiSanches,Rodolfo André KucheCoda,Humberto Breveseng2022-06-23T00:00:00Zoai:scielo:S1679-78252022000400502Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=1679-7825&lng=pt&nrm=isohttps://old.scielo.br/oai/scielo-oai.phpabcm@abcm.org.br||maralves@usp.br1679-78251679-7817opendoar:2022-06-23T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
title |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
spellingShingle |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids Kishino,Renato Takeo Unified solid-fluid model Kelvin-Voigt visco-hyperelasticity Flory’s decomposition Positional FEM Total Lagrangian formulation |
title_short |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
title_full |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
title_fullStr |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
title_full_unstemmed |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
title_sort |
Large strain Flory’s decomposition for Lagrangian modeling of viscoleastic solids and compressive fluids |
author |
Kishino,Renato Takeo |
author_facet |
Kishino,Renato Takeo Kishino,Vitor Hiroshi Sanches,Rodolfo André Kuche Coda,Humberto Breves |
author_role |
author |
author2 |
Kishino,Vitor Hiroshi Sanches,Rodolfo André Kuche Coda,Humberto Breves |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Kishino,Renato Takeo Kishino,Vitor Hiroshi Sanches,Rodolfo André Kuche Coda,Humberto Breves |
dc.subject.por.fl_str_mv |
Unified solid-fluid model Kelvin-Voigt visco-hyperelasticity Flory’s decomposition Positional FEM Total Lagrangian formulation |
topic |
Unified solid-fluid model Kelvin-Voigt visco-hyperelasticity Flory’s decomposition Positional FEM Total Lagrangian formulation |
description |
Abstract The fundamental difference in the solution of solids and fluids relies on the respective constitutive laws. Based on the Rivlin-Saunders-Düster-Hartmann hyperelastic model and using the Flory’s strain decomposition, we present a new total Lagrangian viscoelastic constitutive model for both Kelvin-Voigt viscoelastic solids and free-surface compressive viscous isothermal fluids. A dissipative viscous virtual work is written as a function of the time rate of isochoric invariants and its relation with the viscous stress is derived. Local time derivatives are solved by backward finite difference, allowing a consistent tangent viscoelastic constitutive tensor. The virtual work principle is used to write the weak equilibrium equation and its position-based finite element counterpart. Dynamic time integration is carried out by the Newmark β method and the Newton-Raphson procedure is used to solve time steps. The formulation is validated against experimental and numerical literature results revealing good precision. Additional examples are shown in order to demonstrate the applicability and future possibilities of the technique. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252022000400502 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252022000400502 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78257010 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
dc.source.none.fl_str_mv |
Latin American Journal of Solids and Structures v.19 n.4 2022 reponame:Latin American journal of solids and structures (Online) instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) instacron:ABCM |
instname_str |
Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
instacron_str |
ABCM |
institution |
ABCM |
reponame_str |
Latin American journal of solids and structures (Online) |
collection |
Latin American journal of solids and structures (Online) |
repository.name.fl_str_mv |
Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
repository.mail.fl_str_mv |
abcm@abcm.org.br||maralves@usp.br |
_version_ |
1754302890989584384 |