Reduced order modeling strategies for computational multiscale fracture

Autores
Oliver, J.; Caicedo, M.; Huespe, Alfredo Edmundo; Hernández, J.A.; Roubin, E.
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The paper proposes some new computational strategies for affordably solving multiscale fracture problems through a FE2 approach. To take into account the mechanical effects induced by fracture at the microstructure level the Representative Volume Element (RVE), assumed constituted by an elastic matrix and inclusions, is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths. The RVE response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro-scale level as a continuum stress–strain constitutive equation, which is then used in a conventional framework of a finite element modeling of propagating fracture. For reduced order modeling (ROM) purposes, the RVE boundary value problem is first formulated in displacement fluctuations and used, via the Proper Orthogonal Decomposition (POD), to find a low-dimension space for solving the reduced problem. A domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms of displacement fluctuations. The RVE spatial domain is then decomposed into a regular domain (made of the matrix and the inclusions) and a singular domain (constituted by cohesive bands), the required RVE boundary conditions are rephrased in terms of strains and imposed via Lagrange multipliers in the corresponding variational problem. Specific low-dimensional strain basis is then derived, independently for each domain, via the POD of the corresponding strain snapshots. Next step consists of developing a hyper-reduced model (HPROM). It is based on a second proposed technique, the Reduced Optimal Quadrature (ROQ) which, again unconventionally, is determined through optimization of the numerical integration of the primitive saddle-point problem arising from the RVE problem, rather than its derived variational equations, and substitutes the conventional Gauss quadrature. The ROQ utilizes a very reduced number of, optimally placed, sampling points, the corresponding weights and placements being evaluated through a greedy algorithm. The resulting low-dimensional and reduced-quadrature variational problem translates into very relevant savings on the computational cost and high computational speed-ups. Particular attention is additionally given to numerical tests and performance evaluations of the new hyper-reduced methodology, by “a-priori” and “a-posteriori” error assessments. Moreover, for the purposes of validation of the present techniques, a real structural problem exhibiting propagating fracture at two-scales is modeled on the basis of the strain injection-based multiscale approach previously developed by the authors. The performance of the proposed strategy, in terms of speed-up vs. error, is deeply analyzed and reported.
Fil: Oliver, J.. Universidad Politecnica de Catalunya; España
Fil: Caicedo, M.. Universidad Politecnica de Catalunya; España
Fil: Huespe, Alfredo Edmundo. Universidad Politecnica de Catalunya; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina
Fil: Hernández, J.A.. Universidad Politecnica de Catalunya; España
Fil: Roubin, E.. Université Grenoble; Francia
Materia
COMPUTATIONAL HOMOGENIZATION
HYPER-REDUCED ORDER MODELING (HPROM)
MULTISCALE FRACTURE MODELS
REDUCED OPTIMAL QUADRATURE (ROQ)
REDUCED ORDER MODELING (ROM)
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/20910

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network_name_str CONICET Digital (CONICET)
spelling Reduced order modeling strategies for computational multiscale fractureOliver, J.Caicedo, M.Huespe, Alfredo EdmundoHernández, J.A.Roubin, E.COMPUTATIONAL HOMOGENIZATIONHYPER-REDUCED ORDER MODELING (HPROM)MULTISCALE FRACTURE MODELSREDUCED OPTIMAL QUADRATURE (ROQ)REDUCED ORDER MODELING (ROM)https://purl.org/becyt/ford/2.5https://purl.org/becyt/ford/2The paper proposes some new computational strategies for affordably solving multiscale fracture problems through a FE2 approach. To take into account the mechanical effects induced by fracture at the microstructure level the Representative Volume Element (RVE), assumed constituted by an elastic matrix and inclusions, is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths. The RVE response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro-scale level as a continuum stress–strain constitutive equation, which is then used in a conventional framework of a finite element modeling of propagating fracture. For reduced order modeling (ROM) purposes, the RVE boundary value problem is first formulated in displacement fluctuations and used, via the Proper Orthogonal Decomposition (POD), to find a low-dimension space for solving the reduced problem. A domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms of displacement fluctuations. The RVE spatial domain is then decomposed into a regular domain (made of the matrix and the inclusions) and a singular domain (constituted by cohesive bands), the required RVE boundary conditions are rephrased in terms of strains and imposed via Lagrange multipliers in the corresponding variational problem. Specific low-dimensional strain basis is then derived, independently for each domain, via the POD of the corresponding strain snapshots. Next step consists of developing a hyper-reduced model (HPROM). It is based on a second proposed technique, the Reduced Optimal Quadrature (ROQ) which, again unconventionally, is determined through optimization of the numerical integration of the primitive saddle-point problem arising from the RVE problem, rather than its derived variational equations, and substitutes the conventional Gauss quadrature. The ROQ utilizes a very reduced number of, optimally placed, sampling points, the corresponding weights and placements being evaluated through a greedy algorithm. The resulting low-dimensional and reduced-quadrature variational problem translates into very relevant savings on the computational cost and high computational speed-ups. Particular attention is additionally given to numerical tests and performance evaluations of the new hyper-reduced methodology, by “a-priori” and “a-posteriori” error assessments. Moreover, for the purposes of validation of the present techniques, a real structural problem exhibiting propagating fracture at two-scales is modeled on the basis of the strain injection-based multiscale approach previously developed by the authors. The performance of the proposed strategy, in terms of speed-up vs. error, is deeply analyzed and reported.Fil: Oliver, J.. Universidad Politecnica de Catalunya; EspañaFil: Caicedo, M.. Universidad Politecnica de Catalunya; EspañaFil: Huespe, Alfredo Edmundo. Universidad Politecnica de Catalunya; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Hernández, J.A.. Universidad Politecnica de Catalunya; EspañaFil: Roubin, E.. Université Grenoble; FranciaElsevier Science2016-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/20910Oliver, J.; Caicedo, M.; Huespe, Alfredo Edmundo; Hernández, J.A.; Roubin, E.; Reduced order modeling strategies for computational multiscale fracture ; Elsevier Science; Computer Methods in Applied Mechanics and Engineering; 313; 10-2016; 560-5950045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2016.09.039info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782516303322info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:01:07Zoai:ri.conicet.gov.ar:11336/20910instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:01:08.192CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Reduced order modeling strategies for computational multiscale fracture
title Reduced order modeling strategies for computational multiscale fracture
spellingShingle Reduced order modeling strategies for computational multiscale fracture
Oliver, J.
COMPUTATIONAL HOMOGENIZATION
HYPER-REDUCED ORDER MODELING (HPROM)
MULTISCALE FRACTURE MODELS
REDUCED OPTIMAL QUADRATURE (ROQ)
REDUCED ORDER MODELING (ROM)
title_short Reduced order modeling strategies for computational multiscale fracture
title_full Reduced order modeling strategies for computational multiscale fracture
title_fullStr Reduced order modeling strategies for computational multiscale fracture
title_full_unstemmed Reduced order modeling strategies for computational multiscale fracture
title_sort Reduced order modeling strategies for computational multiscale fracture
dc.creator.none.fl_str_mv Oliver, J.
Caicedo, M.
Huespe, Alfredo Edmundo
Hernández, J.A.
Roubin, E.
author Oliver, J.
author_facet Oliver, J.
Caicedo, M.
Huespe, Alfredo Edmundo
Hernández, J.A.
Roubin, E.
author_role author
author2 Caicedo, M.
Huespe, Alfredo Edmundo
Hernández, J.A.
Roubin, E.
author2_role author
author
author
author
dc.subject.none.fl_str_mv COMPUTATIONAL HOMOGENIZATION
HYPER-REDUCED ORDER MODELING (HPROM)
MULTISCALE FRACTURE MODELS
REDUCED OPTIMAL QUADRATURE (ROQ)
REDUCED ORDER MODELING (ROM)
topic COMPUTATIONAL HOMOGENIZATION
HYPER-REDUCED ORDER MODELING (HPROM)
MULTISCALE FRACTURE MODELS
REDUCED OPTIMAL QUADRATURE (ROQ)
REDUCED ORDER MODELING (ROM)
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The paper proposes some new computational strategies for affordably solving multiscale fracture problems through a FE2 approach. To take into account the mechanical effects induced by fracture at the microstructure level the Representative Volume Element (RVE), assumed constituted by an elastic matrix and inclusions, is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths. The RVE response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro-scale level as a continuum stress–strain constitutive equation, which is then used in a conventional framework of a finite element modeling of propagating fracture. For reduced order modeling (ROM) purposes, the RVE boundary value problem is first formulated in displacement fluctuations and used, via the Proper Orthogonal Decomposition (POD), to find a low-dimension space for solving the reduced problem. A domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms of displacement fluctuations. The RVE spatial domain is then decomposed into a regular domain (made of the matrix and the inclusions) and a singular domain (constituted by cohesive bands), the required RVE boundary conditions are rephrased in terms of strains and imposed via Lagrange multipliers in the corresponding variational problem. Specific low-dimensional strain basis is then derived, independently for each domain, via the POD of the corresponding strain snapshots. Next step consists of developing a hyper-reduced model (HPROM). It is based on a second proposed technique, the Reduced Optimal Quadrature (ROQ) which, again unconventionally, is determined through optimization of the numerical integration of the primitive saddle-point problem arising from the RVE problem, rather than its derived variational equations, and substitutes the conventional Gauss quadrature. The ROQ utilizes a very reduced number of, optimally placed, sampling points, the corresponding weights and placements being evaluated through a greedy algorithm. The resulting low-dimensional and reduced-quadrature variational problem translates into very relevant savings on the computational cost and high computational speed-ups. Particular attention is additionally given to numerical tests and performance evaluations of the new hyper-reduced methodology, by “a-priori” and “a-posteriori” error assessments. Moreover, for the purposes of validation of the present techniques, a real structural problem exhibiting propagating fracture at two-scales is modeled on the basis of the strain injection-based multiscale approach previously developed by the authors. The performance of the proposed strategy, in terms of speed-up vs. error, is deeply analyzed and reported.
Fil: Oliver, J.. Universidad Politecnica de Catalunya; España
Fil: Caicedo, M.. Universidad Politecnica de Catalunya; España
Fil: Huespe, Alfredo Edmundo. Universidad Politecnica de Catalunya; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina
Fil: Hernández, J.A.. Universidad Politecnica de Catalunya; España
Fil: Roubin, E.. Université Grenoble; Francia
description The paper proposes some new computational strategies for affordably solving multiscale fracture problems through a FE2 approach. To take into account the mechanical effects induced by fracture at the microstructure level the Representative Volume Element (RVE), assumed constituted by an elastic matrix and inclusions, is endowed with a large set of cohesive softening bands providing a good representation of the possible microstructure crack paths. The RVE response is then homogenized in accordance with a model previously developed by the authors and upscaled to the macro-scale level as a continuum stress–strain constitutive equation, which is then used in a conventional framework of a finite element modeling of propagating fracture. For reduced order modeling (ROM) purposes, the RVE boundary value problem is first formulated in displacement fluctuations and used, via the Proper Orthogonal Decomposition (POD), to find a low-dimension space for solving the reduced problem. A domain separation strategy is proposed as a first technique for model order reduction: unconventionally, the low-dimension space is spanned by a basis in terms of fluctuating strains, as primitive kinematic variables, instead of the conventional formulation in terms of displacement fluctuations. The RVE spatial domain is then decomposed into a regular domain (made of the matrix and the inclusions) and a singular domain (constituted by cohesive bands), the required RVE boundary conditions are rephrased in terms of strains and imposed via Lagrange multipliers in the corresponding variational problem. Specific low-dimensional strain basis is then derived, independently for each domain, via the POD of the corresponding strain snapshots. Next step consists of developing a hyper-reduced model (HPROM). It is based on a second proposed technique, the Reduced Optimal Quadrature (ROQ) which, again unconventionally, is determined through optimization of the numerical integration of the primitive saddle-point problem arising from the RVE problem, rather than its derived variational equations, and substitutes the conventional Gauss quadrature. The ROQ utilizes a very reduced number of, optimally placed, sampling points, the corresponding weights and placements being evaluated through a greedy algorithm. The resulting low-dimensional and reduced-quadrature variational problem translates into very relevant savings on the computational cost and high computational speed-ups. Particular attention is additionally given to numerical tests and performance evaluations of the new hyper-reduced methodology, by “a-priori” and “a-posteriori” error assessments. Moreover, for the purposes of validation of the present techniques, a real structural problem exhibiting propagating fracture at two-scales is modeled on the basis of the strain injection-based multiscale approach previously developed by the authors. The performance of the proposed strategy, in terms of speed-up vs. error, is deeply analyzed and reported.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/20910
Oliver, J.; Caicedo, M.; Huespe, Alfredo Edmundo; Hernández, J.A.; Roubin, E.; Reduced order modeling strategies for computational multiscale fracture ; Elsevier Science; Computer Methods in Applied Mechanics and Engineering; 313; 10-2016; 560-595
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20910
identifier_str_mv Oliver, J.; Caicedo, M.; Huespe, Alfredo Edmundo; Hernández, J.A.; Roubin, E.; Reduced order modeling strategies for computational multiscale fracture ; Elsevier Science; Computer Methods in Applied Mechanics and Engineering; 313; 10-2016; 560-595
0045-7825
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2016.09.039
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782516303322
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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