Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions
- Autores
- Giusti, Sebastian Miguel; Novotny, Antonio A.; De Souza Neto, Eduardo Alberto
- Año de publicación
- 2010
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Giusti, Sebastian Miguel. Laboratorio Nacional de Computación Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Novotny, Antonio A.. Laboratorio Nacional de Computación Científica; Brasil
Fil: De Souza Neto, Eduardo Alberto. Swansea University; Reino Unido - Materia
-
MULTI-SCALE MODELLING
SENSITIVITY ANALYSIS
SYNTHESIS OF MICROSTRUCTURES
TOPOLOGICAL DERIVATIVE - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/131349
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:09:31Zoai: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:34982025-09-29 10:09:31.414CONICET 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 |
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 |
topic |
MULTI-SCALE MODELLING SENSITIVITY ANALYSIS SYNTHESIS OF MICROSTRUCTURES TOPOLOGICAL DERIVATIVE |
purl_subject.fl_str_mv |
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 |
dc.description.none.fl_txt_mv |
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. Fil: Giusti, Sebastian Miguel. Laboratorio Nacional de Computación Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina Fil: Novotny, Antonio A.. Laboratorio Nacional de Computación Científica; Brasil Fil: De Souza Neto, Eduardo Alberto. Swansea University; Reino Unido |
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 |
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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1844613975389503488 |
score |
13.070432 |