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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/95092
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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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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1844614091413389312 |
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13.070432 |