Exact results for weakly nonlinear composites and implications for homogenization methods

Autores
Furer, Joshua; Idiart, Martín Ignacio; Ponte Castañeda, Pedro
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m = 1 + δ, such that |δ| ¿ 1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.
Fil: Furer, Joshua. University of Pennsylvania; Estados Unidos
Fil: Idiart, Martín Ignacio. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Ponte Castañeda, Pedro. University of Pennsylvania; Estados Unidos
Materia
COMPOSITE MATERIALS
EFFECTIVE CONDUCTIVITY
EXACT SOLUTION
HETEROGENEOUS MATERIALS
HOMOGENIZATION
NONLINEAR
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/138835
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Exact results for weakly nonlinear composites and implications for homogenization methodsFurer, JoshuaIdiart, Martín IgnacioPonte Castañeda, PedroCOMPOSITE MATERIALSEFFECTIVE CONDUCTIVITYEXACT SOLUTIONHETEROGENEOUS MATERIALSHOMOGENIZATIONNONLINEARhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m = 1 + δ, such that |δ| ¿ 1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.Fil: Furer, Joshua. University of Pennsylvania; Estados UnidosFil: Idiart, Martín Ignacio. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Ponte Castañeda, Pedro. University of Pennsylvania; Estados UnidosElsevier France-Editions Scientifiques Medicales Elsevier2020-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/138835Furer, Joshua; Idiart, Martín Ignacio; Ponte Castañeda, Pedro; Exact results for weakly nonlinear composites and implications for homogenization methods; Elsevier France-Editions Scientifiques Medicales Elsevier; Comptes Rendus Mecanique; 348; 10-11; 11-2020; 893-9091631-0721CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://comptes-rendus.academie-sciences.fr/mecanique/item/CRMECA_2020__348_10-11_893_0/info:eu-repo/semantics/altIdentifier/doi/10.5802/crmeca.66info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:02:38Zoai:ri.conicet.gov.ar:11336/138835instacron: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:34982025-10-22 12:02:39.245CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Exact results for weakly nonlinear composites and implications for homogenization methods
title Exact results for weakly nonlinear composites and implications for homogenization methods
spellingShingle Exact results for weakly nonlinear composites and implications for homogenization methods
Furer, Joshua
COMPOSITE MATERIALS
EFFECTIVE CONDUCTIVITY
EXACT SOLUTION
HETEROGENEOUS MATERIALS
HOMOGENIZATION
NONLINEAR
title_short Exact results for weakly nonlinear composites and implications for homogenization methods
title_full Exact results for weakly nonlinear composites and implications for homogenization methods
title_fullStr Exact results for weakly nonlinear composites and implications for homogenization methods
title_full_unstemmed Exact results for weakly nonlinear composites and implications for homogenization methods
title_sort Exact results for weakly nonlinear composites and implications for homogenization methods
dc.creator.none.fl_str_mv Furer, Joshua
Idiart, Martín Ignacio
Ponte Castañeda, Pedro
author Furer, Joshua
author_facet Furer, Joshua
Idiart, Martín Ignacio
Ponte Castañeda, Pedro
author_role author
author2 Idiart, Martín Ignacio
Ponte Castañeda, Pedro
author2_role author
author
dc.subject.none.fl_str_mv COMPOSITE MATERIALS
EFFECTIVE CONDUCTIVITY
EXACT SOLUTION
HETEROGENEOUS MATERIALS
HOMOGENIZATION
NONLINEAR
topic COMPOSITE MATERIALS
EFFECTIVE CONDUCTIVITY
EXACT SOLUTION
HETEROGENEOUS MATERIALS
HOMOGENIZATION
NONLINEAR
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m = 1 + δ, such that |δ| ¿ 1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.
Fil: Furer, Joshua. University of Pennsylvania; Estados Unidos
Fil: Idiart, Martín Ignacio. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Ponte Castañeda, Pedro. University of Pennsylvania; Estados Unidos
description Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m = 1 + δ, such that |δ| ¿ 1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.
publishDate 2020
dc.date.none.fl_str_mv 2020-11
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/11336/138835
Furer, Joshua; Idiart, Martín Ignacio; Ponte Castañeda, Pedro; Exact results for weakly nonlinear composites and implications for homogenization methods; Elsevier France-Editions Scientifiques Medicales Elsevier; Comptes Rendus Mecanique; 348; 10-11; 11-2020; 893-909
1631-0721
CONICET Digital
CONICET
url http://hdl.handle.net/11336/138835
identifier_str_mv Furer, Joshua; Idiart, Martín Ignacio; Ponte Castañeda, Pedro; Exact results for weakly nonlinear composites and implications for homogenization methods; Elsevier France-Editions Scientifiques Medicales Elsevier; Comptes Rendus Mecanique; 348; 10-11; 11-2020; 893-909
1631-0721
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://comptes-rendus.academie-sciences.fr/mecanique/item/CRMECA_2020__348_10-11_893_0/
info:eu-repo/semantics/altIdentifier/doi/10.5802/crmeca.66
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier France-Editions Scientifiques Medicales Elsevier
publisher.none.fl_str_mv Elsevier France-Editions Scientifiques Medicales Elsevier
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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score 12.982451

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