Cavitation in elastomeric solids: I—A defect-growth theory

Autores
Lopez Pamies, Oscar; Idiart, Martín Ignacio; Nakamura, Toshio
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton–Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.
Fil: Lopez Pamies, Oscar. State University of New York; 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; Argentina
Fil: Nakamura, Toshio. State University of New York; Estados Unidos
Materia
FINITE STRAIN
MICROSTRUCTURES
HOMOGENIZATION METHODS
INSTABILITIES
BIFURCATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/95092

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spelling Cavitation in elastomeric solids: I—A defect-growth theoryLopez Pamies, OscarIdiart, Martín IgnacioNakamura, ToshioFINITE STRAINMICROSTRUCTURESHOMOGENIZATION METHODSINSTABILITIESBIFURCATIONhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton–Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.Fil: Lopez Pamies, Oscar. State University of New York; Estados UnidosFil: Idiart, Martín Ignacio. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nakamura, Toshio. State University of New York; Estados UnidosPergamon-Elsevier Science Ltd2011-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95092Lopez Pamies, Oscar; Idiart, Martín Ignacio; Nakamura, Toshio; Cavitation in elastomeric solids: I—A defect-growth theory; Pergamon-Elsevier Science Ltd; Journal of the Mechanics and Physics of Solids; 59; 8; 8-2011; 1464-14870022-5096CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022509611000858info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmps.2011.04.015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:15:29Zoai:ri.conicet.gov.ar:11336/95092instacron: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 10:15:30.019CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Cavitation in elastomeric solids: I—A defect-growth theory
title Cavitation in elastomeric solids: I—A defect-growth theory
spellingShingle Cavitation in elastomeric solids: I—A defect-growth theory
Lopez Pamies, Oscar
FINITE STRAIN
MICROSTRUCTURES
HOMOGENIZATION METHODS
INSTABILITIES
BIFURCATION
title_short Cavitation in elastomeric solids: I—A defect-growth theory
title_full Cavitation in elastomeric solids: I—A defect-growth theory
title_fullStr Cavitation in elastomeric solids: I—A defect-growth theory
title_full_unstemmed Cavitation in elastomeric solids: I—A defect-growth theory
title_sort Cavitation in elastomeric solids: I—A defect-growth theory
dc.creator.none.fl_str_mv Lopez Pamies, Oscar
Idiart, Martín Ignacio
Nakamura, Toshio
author Lopez Pamies, Oscar
author_facet Lopez Pamies, Oscar
Idiart, Martín Ignacio
Nakamura, Toshio
author_role author
author2 Idiart, Martín Ignacio
Nakamura, Toshio
author2_role author
author
dc.subject.none.fl_str_mv FINITE STRAIN
MICROSTRUCTURES
HOMOGENIZATION METHODS
INSTABILITIES
BIFURCATION
topic FINITE STRAIN
MICROSTRUCTURES
HOMOGENIZATION METHODS
INSTABILITIES
BIFURCATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton–Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.
Fil: Lopez Pamies, Oscar. State University of New York; 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; Argentina
Fil: Nakamura, Toshio. State University of New York; Estados Unidos
description It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton–Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.
publishDate 2011
dc.date.none.fl_str_mv 2011-08
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/11336/95092
Lopez Pamies, Oscar; Idiart, Martín Ignacio; Nakamura, Toshio; Cavitation in elastomeric solids: I—A defect-growth theory; Pergamon-Elsevier Science Ltd; Journal of the Mechanics and Physics of Solids; 59; 8; 8-2011; 1464-1487
0022-5096
CONICET Digital
CONICET
url http://hdl.handle.net/11336/95092
identifier_str_mv Lopez Pamies, Oscar; Idiart, Martín Ignacio; Nakamura, Toshio; Cavitation in elastomeric solids: I—A defect-growth theory; Pergamon-Elsevier Science Ltd; Journal of the Mechanics and Physics of Solids; 59; 8; 8-2011; 1464-1487
0022-5096
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://www.sciencedirect.com/science/article/pii/S0022509611000858
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmps.2011.04.015
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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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