Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory

Autores
Lopez Pamies, Oscar; Idiart, Martín Ignacio
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.
Facultad de Ingeniería
Materia
Ingeniería
Matemática
Finite strain
Hamilton–Jacobi equation
Homogenization
Instabilities
Microstructures
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/132507

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network_name_str SEDICI (UNLP)
spelling Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theoryLopez Pamies, OscarIdiart, Martín IgnacioIngenieríaMatemáticaFinite strainHamilton–Jacobi equationHomogenizationInstabilitiesMicrostructuresA new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.Facultad de Ingeniería2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf57-83http://sedici.unlp.edu.ar/handle/10915/132507enginfo:eu-repo/semantics/altIdentifier/issn/0022-0833info:eu-repo/semantics/altIdentifier/issn/1573-2703info:eu-repo/semantics/altIdentifier/doi/10.1007/s10665-009-9359-yinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:32:12Zoai:sedici.unlp.edu.ar:10915/132507Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:32:13.069SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
title Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
spellingShingle Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
Lopez Pamies, Oscar
Ingeniería
Matemática
Finite strain
Hamilton–Jacobi equation
Homogenization
Instabilities
Microstructures
title_short Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
title_full Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
title_fullStr Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
title_full_unstemmed Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
title_sort Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory
dc.creator.none.fl_str_mv Lopez Pamies, Oscar
Idiart, Martín Ignacio
author Lopez Pamies, Oscar
author_facet Lopez Pamies, Oscar
Idiart, Martín Ignacio
author_role author
author2 Idiart, Martín Ignacio
author2_role author
dc.subject.none.fl_str_mv Ingeniería
Matemática
Finite strain
Hamilton–Jacobi equation
Homogenization
Instabilities
Microstructures
topic Ingeniería
Matemática
Finite strain
Hamilton–Jacobi equation
Homogenization
Instabilities
Microstructures
dc.description.none.fl_txt_mv A new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.
Facultad de Ingeniería
description A new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.
publishDate 2010
dc.date.none.fl_str_mv 2010
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info:eu-repo/semantics/publishedVersion
Articulo
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/132507
url http://sedici.unlp.edu.ar/handle/10915/132507
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0022-0833
info:eu-repo/semantics/altIdentifier/issn/1573-2703
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10665-009-9359-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
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