Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions

This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macrosco...

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Detalles Bibliográficos
Autores: Giusti, Sebastian Miguel, Novotny, Antonio A., De Souza Neto, Eduardo Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/131349
Acceso en línea:http://hdl.handle.net/11336/131349
Access Level:acceso abierto
Palabra clave:MULTI-SCALE MODELLING
SENSITIVITY ANALYSIS
SYNTHESIS OF MICROSTRUCTURES
TOPOLOGICAL DERIVATIVE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/2.3
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repository_id_str
spelling Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusionsGiusti, Sebastian MiguelNovotny, Antonio A.De Souza Neto, Eduardo AlbertoMULTI-SCALE MODELLINGSENSITIVITY ANALYSISSYNTHESIS OF MICROSTRUCTURESTOPOLOGICAL DERIVATIVEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/2.5https://purl.org/becyt/ford/2https://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macroscopic strain and stress tensors are defined as volume averages of their microscopic counterpart fields over a representative volume element (RVE) of material. The proposed formula-a symmetric fourth-order tensor field over the RVE domain-is a topological derivative which measures how the macroscopic elasticity tensor changes when an infinitesimal circular elastic inclusion is introduced within the RVE. In the limits, when the inclusion/matrix phase contrast ratio tends to zero and infinity, the sensitivities to the insertion of a hole and a rigid inclusion, respectively, are rigorously obtained. The derivation relies on the topological asymptotic analysis of the predicted macroscopic elasticity and is presented in detail. The derived fundamental formula is of interest to many areas of applied and computational mechanics. To illustrate its potential applicability, a simple finite element-based example is presented where the topological derivative information is used to automatically generate a bi-material microstructure to meet pre-specified macroscopic properties.Fil: Giusti, Sebastian Miguel. Laboratorio Nacional de Computación Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Novotny, Antonio A.. Laboratorio Nacional de Computación Científica; BrasilFil: De Souza Neto, Eduardo Alberto. Swansea University; Reino UnidoThe Royal Society2010-06-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/131349Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto; Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions; The Royal Society; Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences; 466; 2118; 8-6-2010; 1703-17231364-50211471-2946CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1098/rspa.2009.0499info:eu-repo/semantics/altIdentifier/url/https://royalsocietypublishing.org/doi/10.1098/rspa.2009.0499info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:00:46Zoai:ri.conicet.gov.ar:11336/131349instacron: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:34982024-05-08 14:00:46.698CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
title Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
spellingShingle Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
Giusti, Sebastian Miguel
MULTI-SCALE MODELLING
SENSITIVITY ANALYSIS
SYNTHESIS OF MICROSTRUCTURES
TOPOLOGICAL DERIVATIVE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
title_short Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
title_full Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
title_fullStr Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
title_full_unstemmed Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
title_sort Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
dc.creator.none.fl_str_mv Giusti, Sebastian Miguel
Novotny, Antonio A.
De Souza Neto, Eduardo Alberto
author Giusti, Sebastian Miguel
author_facet Giusti, Sebastian Miguel
Novotny, Antonio A.
De Souza Neto, Eduardo Alberto
author_role author
author2 Novotny, Antonio A.
De Souza Neto, Eduardo Alberto
author2_role author
author
dc.subject.none.fl_str_mv MULTI-SCALE MODELLING
SENSITIVITY ANALYSIS
SYNTHESIS OF MICROSTRUCTURES
TOPOLOGICAL DERIVATIVE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
topic MULTI-SCALE MODELLING
SENSITIVITY ANALYSIS
SYNTHESIS OF MICROSTRUCTURES
TOPOLOGICAL DERIVATIVE
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
description This paper proposes an exact analytical formula for the topological sensitivity of the macroscopic response of elastic microstructures to the insertion of circular inclusions. The macroscopic response is assumed to be predicted by a well-established multi-scale constitutive theory where the macroscopic strain and stress tensors are defined as volume averages of their microscopic counterpart fields over a representative volume element (RVE) of material. The proposed formula-a symmetric fourth-order tensor field over the RVE domain-is a topological derivative which measures how the macroscopic elasticity tensor changes when an infinitesimal circular elastic inclusion is introduced within the RVE. In the limits, when the inclusion/matrix phase contrast ratio tends to zero and infinity, the sensitivities to the insertion of a hole and a rigid inclusion, respectively, are rigorously obtained. The derivation relies on the topological asymptotic analysis of the predicted macroscopic elasticity and is presented in detail. The derived fundamental formula is of interest to many areas of applied and computational mechanics. To illustrate its potential applicability, a simple finite element-based example is presented where the topological derivative information is used to automatically generate a bi-material microstructure to meet pre-specified macroscopic properties.
publishDate 2010
dc.date.none.fl_str_mv 2010-06-08
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/11336/131349
Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto; Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions; The Royal Society; Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences; 466; 2118; 8-6-2010; 1703-1723
1364-5021
1471-2946
CONICET Digital
CONICET
url http://hdl.handle.net/11336/131349
identifier_str_mv Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto; Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions; The Royal Society; Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences; 466; 2118; 8-6-2010; 1703-1723
1364-5021
1471-2946
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1098/rspa.2009.0499
info:eu-repo/semantics/altIdentifier/url/https://royalsocietypublishing.org/doi/10.1098/rspa.2009.0499
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv The Royal Society
publisher.none.fl_str_mv The Royal Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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
_version_ 1799195699833733120
score 15.811543

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