A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model

In this work, we describe a finite element formulation for the approximation of solid mechanics problems using a damage model under finite strain conditions. The balance equations are written in a total Lagrangian framework, employing the deviatoric component of the second Piola–Kirchhoff stress ten...

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Autores: Castañar Pérez, Inocencio|||0000-0003-4139-9380, Codina, Ramon|||0000-0002-7412-778X, Baiges Aznar, Joan|||0000-0002-3940-5887
Formato: artículo
Fecha de publicación:2026
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:dnet:upcommonspor::f7d25a5f5b44d1a0dae8632fd07a5e77
Acesso em linha:https://hdl.handle.net/2117/460752
https://dx.doi.org/10.1016/j.cma.2026.118868
Access Level:acceso abierto
Palavra-chave:Mixed three-field formulation
Finite strain
Continuum damage mechanics
Stress accuracy
Stabilization
Àrees temàtiques de la UPC::Enginyeria dels materials::Assaig de materials
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spelling A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage modelCastañar Pérez, Inocencio|||0000-0003-4139-9380Codina, Ramon|||0000-0002-7412-778XBaiges Aznar, Joan|||0000-0002-3940-5887Mixed three-field formulationFinite strainContinuum damage mechanicsStress accuracyStabilizationÀrees temàtiques de la UPC::Enginyeria dels materials::Assaig de materialsIn this work, we describe a finite element formulation for the approximation of solid mechanics problems using a damage model under finite strain conditions. The balance equations are written in a total Lagrangian framework, employing the deviatoric component of the second Piola–Kirchhoff stress tensor, the displacement, and the pressure as primary variables. Introducing the pressure as a variable enables the treatment of incompressible materials, while incorporating the stress improves the stress approximation, which is crucial when nonlinear material laws depending on stress (or strain) are considered. In particular, we adopt the damage model proposed by Comellas et al. (International Journal for Numerical Methods in Engineering, Vol. 105, pp. 781–800, 2016), which generalizes previous isotropic damage models from infinitesimal strains to finite ones. This damage model is combined with a hyperelastic formulation for the reversible component of the deformation. The three-field formulation we consider was first introduced and analyzed for the Stokes problem by Codina (SIAM Journal on Numerical Analysis, Vol. 47, pp. 699–718, 2009). The interest of interpolating stress as an independent variable was highlighted in the work of Cervera et al. (Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2559–2570, 2010), and has since been successfully applied to numerous problems involving both linear and nonlinear constitutive behavior under the small strain assumption. More recently, Codina et al. (International Journal for Numerical Methods in Engineering, Vol. 125, e7540, 2024), extended the three-field formulation to geometrically nonlinear problems. The purpose of the present work is to combine these approaches, addressing problems that involve both nonlinear constitutive laws and geometrical nonlinearity with a mixed, three-field approach.Peer ReviewedElsevier20262026-06-1520262026-04-20journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/460752https://dx.doi.org/10.1016/j.cma.2026.118868reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen 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:dnet:upcommonspor::f7d25a5f5b44d1a0dae8632fd07a5e772026-05-27T15:37:01Z
dc.title.none.fl_str_mv A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
title A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
spellingShingle A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
Castañar Pérez, Inocencio|||0000-0003-4139-9380
Mixed three-field formulation
Finite strain
Continuum damage mechanics
Stress accuracy
Stabilization
Àrees temàtiques de la UPC::Enginyeria dels materials::Assaig de materials
title_short A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
title_full A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
title_fullStr A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
title_full_unstemmed A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
title_sort A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model
dc.creator.none.fl_str_mv Castañar Pérez, Inocencio|||0000-0003-4139-9380
Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author Castañar Pérez, Inocencio|||0000-0003-4139-9380
author_facet Castañar Pérez, Inocencio|||0000-0003-4139-9380
Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author_role author
author2 Codina, Ramon|||0000-0002-7412-778X
Baiges Aznar, Joan|||0000-0002-3940-5887
author2_role author
author
dc.subject.none.fl_str_mv Mixed three-field formulation
Finite strain
Continuum damage mechanics
Stress accuracy
Stabilization
Àrees temàtiques de la UPC::Enginyeria dels materials::Assaig de materials
topic Mixed three-field formulation
Finite strain
Continuum damage mechanics
Stress accuracy
Stabilization
Àrees temàtiques de la UPC::Enginyeria dels materials::Assaig de materials
description In this work, we describe a finite element formulation for the approximation of solid mechanics problems using a damage model under finite strain conditions. The balance equations are written in a total Lagrangian framework, employing the deviatoric component of the second Piola–Kirchhoff stress tensor, the displacement, and the pressure as primary variables. Introducing the pressure as a variable enables the treatment of incompressible materials, while incorporating the stress improves the stress approximation, which is crucial when nonlinear material laws depending on stress (or strain) are considered. In particular, we adopt the damage model proposed by Comellas et al. (International Journal for Numerical Methods in Engineering, Vol. 105, pp. 781–800, 2016), which generalizes previous isotropic damage models from infinitesimal strains to finite ones. This damage model is combined with a hyperelastic formulation for the reversible component of the deformation. The three-field formulation we consider was first introduced and analyzed for the Stokes problem by Codina (SIAM Journal on Numerical Analysis, Vol. 47, pp. 699–718, 2009). The interest of interpolating stress as an independent variable was highlighted in the work of Cervera et al. (Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2559–2570, 2010), and has since been successfully applied to numerous problems involving both linear and nonlinear constitutive behavior under the small strain assumption. More recently, Codina et al. (International Journal for Numerical Methods in Engineering, Vol. 125, e7540, 2024), extended the three-field formulation to geometrically nonlinear problems. The purpose of the present work is to combine these approaches, addressing problems that involve both nonlinear constitutive laws and geometrical nonlinearity with a mixed, three-field approach.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-06-15
2026
2026-04-20
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/460752
https://dx.doi.org/10.1016/j.cma.2026.118868
url https://hdl.handle.net/2117/460752
https://dx.doi.org/10.1016/j.cma.2026.118868
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
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.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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