A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity

We propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is complemented by a nodal Jacobian determinan...

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Authors: Scovazzi, Guglielmo, Zorrilla Martínez, Rubén|||0000-0001-8270-7170, Rossi, Riccardo|||0000-0003-0528-7074
Format: article
Publication Date:2023
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/387760
Online Access:https://hdl.handle.net/2117/387760
https://dx.doi.org/10.1016/j.cma.2023.116076
Access Level:Open access
Keyword:Elasticity -- Mathematical models
Variational multiscale method
Stabilized methods
Finite deformation
Nonlinear elasticity
Piece-wise linear interpolation
Nearly incompressible elasticity
Elasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
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oai_identifier_str oai:upcommons.upc.edu:2117/387760
network_acronym_str ES
network_name_str España
repository_id_str
spelling A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticityScovazzi, GuglielmoZorrilla Martínez, Rubén|||0000-0001-8270-7170Rossi, Riccardo|||0000-0003-0528-7074Elasticity -- Mathematical modelsVariational multiscale methodStabilized methodsFinite deformationNonlinear elasticityPiece-wise linear interpolationNearly incompressible elasticityElasticitat -- Mètodes numèricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finitsÀrees temàtiques de la UPC::Enginyeria civil::Materials i estructuresWe propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is complemented by a nodal Jacobian determinant unknown field. This approach is simple to implement in practical applications (e.g., in commercial software), since it only requires information already available when computing the Newton–Raphson tangent matrix associated with irreducible (i.e., displacement-based) finite element formulations. By nature, the proposed method is easily extensible to nonlinear models involving visco-plastic flow. An extensive suite of numerical tests in two and three dimensions is presented, to demonstrate the performance of the method.This research is partly supported by the European High-Performance Computing Joint Undertaking (JU) through the project eFlows4HPC (grant agreement number 955558). The JU receives support from the European Union Horizon 2020 research and innovation program and Spain, Germany, France, Italy, Poland, Switzerland, Norway. This publication is also part of the R&D project PCI2021-121944, financed by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”. The authors also acknowledge financial support from the Spanish Ministry of Economy and Competitiveness , through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2018-000797-S).Peer Reviewed20232023-07-0120232023-05-23journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/387760https://dx.doi.org/10.1016/j.cma.2023.116076reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 955558 Enabling dynamic and Intelligent workflows in the future EuroHPCecosystemAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PCI2021-121944 ENABLING DYNAMIC AND INTELLIGENT WORKFLOWS IN THE FUTURE EUROHPCECOSYSTEMopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3877602026-05-27T15:37:01Z
dc.title.none.fl_str_mv A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
title A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
spellingShingle A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
Scovazzi, Guglielmo
Elasticity -- Mathematical models
Variational multiscale method
Stabilized methods
Finite deformation
Nonlinear elasticity
Piece-wise linear interpolation
Nearly incompressible elasticity
Elasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
title_short A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
title_full A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
title_fullStr A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
title_full_unstemmed A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
title_sort A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity
dc.creator.none.fl_str_mv Scovazzi, Guglielmo
Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
author Scovazzi, Guglielmo
author_facet Scovazzi, Guglielmo
Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
author_role author
author2 Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
author2_role author
author
dc.subject.none.fl_str_mv Elasticity -- Mathematical models
Variational multiscale method
Stabilized methods
Finite deformation
Nonlinear elasticity
Piece-wise linear interpolation
Nearly incompressible elasticity
Elasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
topic Elasticity -- Mathematical models
Variational multiscale method
Stabilized methods
Finite deformation
Nonlinear elasticity
Piece-wise linear interpolation
Nearly incompressible elasticity
Elasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
description We propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is complemented by a nodal Jacobian determinant unknown field. This approach is simple to implement in practical applications (e.g., in commercial software), since it only requires information already available when computing the Newton–Raphson tangent matrix associated with irreducible (i.e., displacement-based) finite element formulations. By nature, the proposed method is easily extensible to nonlinear models involving visco-plastic flow. An extensive suite of numerical tests in two and three dimensions is presented, to demonstrate the performance of the method.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-07-01
2023
2023-05-23
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/387760
https://dx.doi.org/10.1016/j.cma.2023.116076
url https://hdl.handle.net/2117/387760
https://dx.doi.org/10.1016/j.cma.2023.116076
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 955558 Enabling dynamic and Intelligent workflows in the future EuroHPCecosystem
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PCI2021-121944 ENABLING DYNAMIC AND INTELLIGENT WORKFLOWS IN THE FUTURE EUROHPCECOSYSTEM
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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