The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids

[EN] We revisit the well-known three-field formulation introduced by Simo and Taylor, [5]. However, while in [5] a semi-discretization is used to eliminate the additional primary unknowns before the problem is linearized in terms of the not yet discretized displacement field, we introduce hybrid/mix...

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Detalles Bibliográficos
Autores: Schneider, Patrick, Schönherr, Josef, Mittelstedt, Christian
Tipo de recurso: capítulo de libro
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/186461
Acceso en línea:https://riunet.upv.es/handle/10251/186461
Access Level:acceso abierto
Palabra clave:Hybrid finite element
Mixed formulation
Finite deformation
Hyperelasticity
Rubber-like material
Quasi-incompressible material
Discontinuous finite element
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spelling The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solidsSchneider, PatrickSchönherr, JosefMittelstedt, ChristianHybrid finite elementMixed formulationFinite deformationHyperelasticityRubber-like materialQuasi-incompressible materialDiscontinuous finite element[EN] We revisit the well-known three-field formulation introduced by Simo and Taylor, [5]. However, while in [5] a semi-discretization is used to eliminate the additional primary unknowns before the problem is linearized in terms of the not yet discretized displacement field, we introduce hybrid/mixed elements based directly on the consistent linearization of the threefield formulation on the continuum-level. In the latter case, static condensation is used to eliminate the additional unknowns on the element-level after the linearization of the continuum formulation in order to derive discontinuous hybrid-elements. A family of Simo-Taylor-Pister (STP) elements, as well as a family of elements based on the continuum-level linearization (CL3F), designed to coincide in terms of the interpolation schemes, the number of assembled degrees of freedom and the number of integration points with the Abaqus hybrid-elements (C3D8H,C3D20H,C3D10H) are compared to those elements by benchmark tests. Material parameters were obtained by least-square fitting to experimental data of an industrial NR/IR-blend (natural rubber / isoprene rubber) used for damping applications. All tested elements are free of volumetric locking. The STP-elements show severe stability issues. In general the maximum stable step-width of the Abaqus hybrid-elements is higher in comparison to the STP-elements. However, the CL3F-elements outperform the Abaqus elements in general without the usage of numerical stabilization. Especially in combination with strongly nonlinear compression models, the advantage of the CL3F-elements is huge – here the stable step-width is up to 22 times larger. Details can be found in a contribution which is currently under review, [7].Editorial Universitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20222022-05-11book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://riunet.upv.es/handle/10251/186461reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1864612026-06-13T07:49:27Z
dc.title.none.fl_str_mv The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
title The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
spellingShingle The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
Schneider, Patrick
Hybrid finite element
Mixed formulation
Finite deformation
Hyperelasticity
Rubber-like material
Quasi-incompressible material
Discontinuous finite element
title_short The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
title_full The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
title_fullStr The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
title_full_unstemmed The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
title_sort The effect of a consistent linearization on the numerical stability of hydrid-elements for quasi-incompressible hyperelastic solids
dc.creator.none.fl_str_mv Schneider, Patrick
Schönherr, Josef
Mittelstedt, Christian
author Schneider, Patrick
author_facet Schneider, Patrick
Schönherr, Josef
Mittelstedt, Christian
author_role author
author2 Schönherr, Josef
Mittelstedt, Christian
author2_role author
author
dc.contributor.none.fl_str_mv Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Hybrid finite element
Mixed formulation
Finite deformation
Hyperelasticity
Rubber-like material
Quasi-incompressible material
Discontinuous finite element
topic Hybrid finite element
Mixed formulation
Finite deformation
Hyperelasticity
Rubber-like material
Quasi-incompressible material
Discontinuous finite element
description [EN] We revisit the well-known three-field formulation introduced by Simo and Taylor, [5]. However, while in [5] a semi-discretization is used to eliminate the additional primary unknowns before the problem is linearized in terms of the not yet discretized displacement field, we introduce hybrid/mixed elements based directly on the consistent linearization of the threefield formulation on the continuum-level. In the latter case, static condensation is used to eliminate the additional unknowns on the element-level after the linearization of the continuum formulation in order to derive discontinuous hybrid-elements. A family of Simo-Taylor-Pister (STP) elements, as well as a family of elements based on the continuum-level linearization (CL3F), designed to coincide in terms of the interpolation schemes, the number of assembled degrees of freedom and the number of integration points with the Abaqus hybrid-elements (C3D8H,C3D20H,C3D10H) are compared to those elements by benchmark tests. Material parameters were obtained by least-square fitting to experimental data of an industrial NR/IR-blend (natural rubber / isoprene rubber) used for damping applications. All tested elements are free of volumetric locking. The STP-elements show severe stability issues. In general the maximum stable step-width of the Abaqus hybrid-elements is higher in comparison to the STP-elements. However, the CL3F-elements outperform the Abaqus elements in general without the usage of numerical stabilization. Especially in combination with strongly nonlinear compression models, the advantage of the CL3F-elements is huge – here the stable step-width is up to 22 times larger. Details can be found in a contribution which is currently under review, [7].
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-05-11
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/186461
url https://riunet.upv.es/handle/10251/186461
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editorial Universitat Politècnica de València
publisher.none.fl_str_mv Editorial Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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