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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/132507
Ver los metadatos del registro completo
id |
SEDICI_69156d01206939d6b3e77fb05b0b8335 |
---|---|
oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/132507 |
network_acronym_str |
SEDICI |
repository_id_str |
1329 |
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 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo 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://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 57-83 |
dc.source.none.fl_str_mv |
reponame:SEDICI (UNLP) instname:Universidad Nacional de La Plata instacron:UNLP |
reponame_str |
SEDICI (UNLP) |
collection |
SEDICI (UNLP) |
instname_str |
Universidad Nacional de La Plata |
instacron_str |
UNLP |
institution |
UNLP |
repository.name.fl_str_mv |
SEDICI (UNLP) - Universidad Nacional de La Plata |
repository.mail.fl_str_mv |
alira@sedici.unlp.edu.ar |
_version_ |
1844616201608626176 |
score |
13.070432 |