Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems

Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations conve...

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Authors: Pijaudier-Cabot, Gilles, Bode, L, Huerta, Antonio|||0000-0003-4198-3798
Format: article
Publication Date:1995
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:2117/28021
Online Access:https://hdl.handle.net/2117/28021
https://dx.doi.org/10.1002/nme.1620382406
Access Level:Open access
Keyword:Lagrange equations
non-linear computational mechanics
arbitrary Lagrangian-Eulerian
mesh adaptivity
strain-softening
localization
damage mechanics
wave propagation
Física matemàtica
70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
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network_acronym_str ES
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spelling Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problemsPijaudier-Cabot, GillesBode, LHuerta, Antonio|||0000-0003-4198-3798Lagrange equationsnon-linear computational mechanicsarbitrary Lagrangian-Eulerianmesh adaptivitystrain-softeninglocalizationdamage mechanicswave propagationFísica matemàtica70H Hamiltonian and Lagrangian mechanicsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàticaNon-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the intemallength. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.Peer ReviewedJohn Wiley & Sons19951995-10-0120152015-05-25journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/28021https://dx.doi.org/10.1002/nme.1620382406reponame: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:2117/280212026-05-27T15:37:01Z
dc.title.none.fl_str_mv Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
title Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
spellingShingle Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
Pijaudier-Cabot, Gilles
Lagrange equations
non-linear computational mechanics
arbitrary Lagrangian-Eulerian
mesh adaptivity
strain-softening
localization
damage mechanics
wave propagation
Física matemàtica
70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
title_short Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
title_full Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
title_fullStr Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
title_full_unstemmed Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
title_sort Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
dc.creator.none.fl_str_mv Pijaudier-Cabot, Gilles
Bode, L
Huerta, Antonio|||0000-0003-4198-3798
author Pijaudier-Cabot, Gilles
author_facet Pijaudier-Cabot, Gilles
Bode, L
Huerta, Antonio|||0000-0003-4198-3798
author_role author
author2 Bode, L
Huerta, Antonio|||0000-0003-4198-3798
author2_role author
author
dc.subject.none.fl_str_mv Lagrange equations
non-linear computational mechanics
arbitrary Lagrangian-Eulerian
mesh adaptivity
strain-softening
localization
damage mechanics
wave propagation
Física matemàtica
70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
topic Lagrange equations
non-linear computational mechanics
arbitrary Lagrangian-Eulerian
mesh adaptivity
strain-softening
localization
damage mechanics
wave propagation
Física matemàtica
70H Hamiltonian and Lagrangian mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
description Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the intemallength. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.
publishDate 1995
dc.date.none.fl_str_mv 1995
1995-10-01
2015
2015-05-25
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/2117/28021
https://dx.doi.org/10.1002/nme.1620382406
url https://hdl.handle.net/2117/28021
https://dx.doi.org/10.1002/nme.1620382406
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.publisher.none.fl_str_mv John Wiley & Sons
publisher.none.fl_str_mv John Wiley & Sons
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
_version_ 1869411777539735552
score 15,300724

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