Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity

This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order inte...

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Autores: Cervera Ruiz, Miguel|||0000-0003-3437-6703, Chiumenti, Michele|||0000-0002-6286-7393, Benedetti, Lorenzo|||0000-0002-6315-5144, Codina, Ramon|||0000-0002-7412-778X
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/27501
Acceso en línea:https://hdl.handle.net/2117/27501
https://dx.doi.org/10.1016/j.cma.2014.11.040
Access Level:acceso abierto
Palabra clave:Plasticity--Mathematical models
Mixed finite elements
Stabilization
Plasticity
Strain softening
Strain localization
Mesh dependence
J2 plasticity
plane-stress
localization
elastoplasticity
discontinuities
formulation
bifurcation
equations
strain
Plasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Física::Física de l’estat sòlid
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
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spelling Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticityCervera Ruiz, Miguel|||0000-0003-3437-6703Chiumenti, Michele|||0000-0002-6286-7393Benedetti, Lorenzo|||0000-0002-6315-5144Codina, Ramon|||0000-0002-7412-778XPlasticity--Mathematical modelsMixed finite elementsStabilizationPlasticityStrain softeningStrain localizationMesh dependenceJ2 plasticityplane-stresslocalizationelastoplasticitydiscontinuitiesformulationbifurcationequationsstrainPlasticitat -- Mètodes numèricsÀrees temàtiques de la UPC::Física::Física de l’estat sòlidÀrees temàtiques de la UPC::Enginyeria civil::Materials i estructuresThis paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) field and (b) it is able to deal with incompressible situations. The first advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the effect of the improved strain and stress fields in problems involving strain softening and localization leading to failure, using low order finite elements with continuous strain and displacement fields (P1P1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.Peer Reviewed20152015-03-0120152015-04-21journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/27501https://dx.doi.org/10.1016/j.cma.2014.11.040reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/275012026-05-27T15:37:01Z
dc.title.none.fl_str_mv Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
title Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
spellingShingle Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
Cervera Ruiz, Miguel|||0000-0003-3437-6703
Plasticity--Mathematical models
Mixed finite elements
Stabilization
Plasticity
Strain softening
Strain localization
Mesh dependence
J2 plasticity
plane-stress
localization
elastoplasticity
discontinuities
formulation
bifurcation
equations
strain
Plasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Física::Física de l’estat sòlid
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
title_short Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
title_full Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
title_fullStr Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
title_full_unstemmed Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
title_sort Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: compressible and incompressible plasticity
dc.creator.none.fl_str_mv Cervera Ruiz, Miguel|||0000-0003-3437-6703
Chiumenti, Michele|||0000-0002-6286-7393
Benedetti, Lorenzo|||0000-0002-6315-5144
Codina, Ramon|||0000-0002-7412-778X
author Cervera Ruiz, Miguel|||0000-0003-3437-6703
author_facet Cervera Ruiz, Miguel|||0000-0003-3437-6703
Chiumenti, Michele|||0000-0002-6286-7393
Benedetti, Lorenzo|||0000-0002-6315-5144
Codina, Ramon|||0000-0002-7412-778X
author_role author
author2 Chiumenti, Michele|||0000-0002-6286-7393
Benedetti, Lorenzo|||0000-0002-6315-5144
Codina, Ramon|||0000-0002-7412-778X
author2_role author
author
author
dc.subject.none.fl_str_mv Plasticity--Mathematical models
Mixed finite elements
Stabilization
Plasticity
Strain softening
Strain localization
Mesh dependence
J2 plasticity
plane-stress
localization
elastoplasticity
discontinuities
formulation
bifurcation
equations
strain
Plasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Física::Física de l’estat sòlid
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
topic Plasticity--Mathematical models
Mixed finite elements
Stabilization
Plasticity
Strain softening
Strain localization
Mesh dependence
J2 plasticity
plane-stress
localization
elastoplasticity
discontinuities
formulation
bifurcation
equations
strain
Plasticitat -- Mètodes numèrics
Àrees temàtiques de la UPC::Física::Física de l’estat sòlid
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
description This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) field and (b) it is able to deal with incompressible situations. The first advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the effect of the improved strain and stress fields in problems involving strain softening and localization leading to failure, using low order finite elements with continuous strain and displacement fields (P1P1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-03-01
2015
2015-04-21
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/2117/27501
https://dx.doi.org/10.1016/j.cma.2014.11.040
url https://hdl.handle.net/2117/27501
https://dx.doi.org/10.1016/j.cma.2014.11.040
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
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
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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