A constitutive model for stress–strain response and mullins effect in filled elastomers
Identifieur interne : 000F10 ( Istex/Corpus ); précédent : 000F09; suivant : 000F11A constitutive model for stress–strain response and mullins effect in filled elastomers
Auteurs : A. K. Mossi Idrissa ; S. Ahzi ; S. Patlazhan ; Y. Rémond ; D. RuchSource :
- Journal of Applied Polymer Science [ 0021-8995 ] ; 2012-09-15.
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Abstract
In this work we propose a new constitutive theory to estimate the stress–strain response and the softening induced by the Mullins effect during the stretching of filled elastomers. In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012
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DOI: 10.1002/app.36596
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In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>A. K. Mossi Idrissa</name><affiliations><json:string>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</json:string></affiliations></json:item><json:item><name>S. Ahzi</name><affiliations><json:string>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</json:string><json:string>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France===</json:string></affiliations></json:item><json:item><name>S. Patlazhan</name><affiliations><json:string>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</json:string><json:string>Semenov Institute of Chemical Physics Russian Academy of Sciences, 4 Kosygin Street, 119991 Moscow, Russia</json:string></affiliations></json:item><json:item><name>Y. 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In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012</abstract><qualityIndicators><score>6.049</score><pdfVersion>1.3</pdfVersion><pdfPageSize>612 x 810 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>978</abstractCharCount><pdfWordCount>4237</pdfWordCount><pdfCharCount>24230</pdfCharCount><pdfPageCount>8</pdfPageCount><abstractWordCount>151</abstractWordCount></qualityIndicators><title>A constitutive model for stress–strain response and mullins effect in filled elastomers</title><refBibs><json:item><host><volume>16</volume><pages><first>275</first></pages><author></author><title>J Rubber Res</title></host></json:item><json:item><host><volume>16</volume><pages><first>257</first></pages><author></author><title>Ann Fac Sci de Toulouse</title></host></json:item><json:item><host><volume>16</volume><pages><first>799</first></pages><author></author><title>Ind Eng Chem</title></host></json:item><json:item><host><volume>16</volume><pages><first>107</first></pages><author></author><title>J Appl Polym Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>271</first></pages><author></author><title>Appl Polym Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>153</first></pages><author></author><title>Comput Methods Appl Mech Eng</title></host></json:item><json:item><host><volume>16</volume><pages><first>87</first></pages><author></author><title>J Mech Phys Solids</title></host></json:item><json:item><host><volume>16</volume><pages><first>213</first></pages><author></author><title>J Mech Phys Solids</title></host></json:item><json:item><host><volume>16</volume><pages><first>323</first></pages><author></author><title>J Mech Phys Solids</title></host></json:item><json:item><host><volume>16</volume><pages><first>2011</first></pages><author></author><title>J Mech Phys Solids</title></host></json:item><json:item><host><volume>16</volume><pages><first>6817</first></pages><author></author><title>Int J Solids Struct</title></host></json:item><json:item><host><volume>16</volume><pages><first>555</first></pages><author></author><title>Rubber Chem Technol</title></host></json:item><json:item><host><volume>16</volume><pages><first>2993</first></pages><author></author><title>J Appl Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>339</first></pages><author></author><title>Rubber Chem Technol</title></host></json:item><json:item><host><volume>16</volume><pages><first>301</first></pages><author></author><title>Continuum Mech Thermodyn</title></host></json:item><json:item><host><volume>16</volume><pages><first>2187</first></pages><author></author><title>J Mech Phys Solids</title></host></json:item><json:item><host><volume>16</volume><pages><first>742</first></pages><author></author><title>Macromol Theor Simul</title></host></json:item><json:item><host><volume>16</volume><pages><first>281</first></pages><author></author><title>Rubber Chem Technol</title></host></json:item><json:item><host><volume>16</volume><pages><first>2319</first></pages><author></author><title>J Appl Polym Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>3011</first></pages><author></author><title>J Appl Polym Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>239</first></pages><author></author><title>Rubber Chem Technol</title></host></json:item><json:item><host><volume>16</volume><pages><first>758</first></pages><author></author><title>J Appl Phys</title></host></json:item><json:item><host><volume>16</volume><pages><first>534</first></pages><author></author><title>Rubber Chem Technol</title></host></json:item><json:item><host><volume>16</volume><pages><first>817</first></pages><author></author><title>Comput Mater Sci</title></host></json:item><json:item><host><volume>16</volume><pages><first>195</first></pages><author></author><title>Curr Opin Solid State Mater Sci</title></host></json:item><json:item><host><author></author><title>Vilgis, T. 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K.</forename><surname>Mossi Idrissa</surname></persName><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation></author><author xml:id="author-2"><persName><forename type="first">S.</forename><surname>Ahzi</surname></persName><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France===</affiliation></author><author xml:id="author-3"><persName><forename type="first">S.</forename><surname>Patlazhan</surname></persName><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><affiliation>Semenov Institute of Chemical Physics Russian Academy of Sciences, 4 Kosygin Street, 119991 Moscow, Russia</affiliation></author><author xml:id="author-4"><persName><forename type="first">Y.</forename><surname>Rémond</surname></persName><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation></author><author xml:id="author-5"><persName><forename type="first">D.</forename><surname>Ruch</surname></persName><affiliation>Centre de Recherche Public Henri Tudor, 66 rue de Luxembourg, B.P. 144, L‐4002 Esch‐sur‐Alzette, Luxembourg</affiliation></author></analytic><monogr><title level="j">Journal of Applied Polymer Science</title><title level="j" type="abbrev">J. Appl. Polym. Sci.</title><idno type="pISSN">0021-8995</idno><idno type="eISSN">1097-4628</idno><idno type="DOI">10.1002/(ISSN)1097-4628</idno><imprint><publisher>Wiley Subscription Services, Inc., A Wiley Company</publisher><pubPlace>Hoboken</pubPlace><date type="published" when="2012-09-15"></date><biblScope unit="volume">125</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="4368">4368</biblScope><biblScope unit="page" to="4375">4375</biblScope></imprint></monogr><idno type="istex">57E4D938EF61281BEC4271BCAB89707C2ADB545E</idno><idno type="DOI">10.1002/app.36596</idno><idno type="ArticleID">APP36596</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2012</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>In this work we propose a new constitutive theory to estimate the stress–strain response and the softening induced by the Mullins effect during the stretching of filled elastomers. In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012</p></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><head>keywords</head><item><term>filled elastomers</term></item><item><term>Mullins'</term></item><item><term>effect</term></item><item><term>strain softening</term></item><item><term>Gent model</term></item><item><term>carbon black fillers</term></item><item><term>hard‐to‐soft transformation</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2011-11-30">Received</change><change when="2011-11-30">Registration</change><change when="2012-09-15">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/57E4D938EF61281BEC4271BCAB89707C2ADB545E/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Wiley Subscription Services, Inc., A Wiley Company</publisherName><publisherLoc>Hoboken</publisherLoc></publisherInfo><doi registered="yes">10.1002/(ISSN)1097-4628</doi><issn type="print">0021-8995</issn><issn type="electronic">1097-4628</issn><idGroup><id type="product" value="APP"></id></idGroup><titleGroup><title type="main" xml:lang="en" sort="JOURNAL OF APPLIED POLYMER SCIENCE">Journal of Applied Polymer Science</title><title type="short">J. 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Sci.</title></titleGroup></publicationMeta><publicationMeta level="part" position="60"><doi origin="wiley" registered="yes">10.1002/app.v125.6</doi><titleGroup><title type="specialIssueTitle">Contributions from the 4th International Conference on Polymer Behavior (IUPAC), Lodz, Poland, September 19–23, 2010</title></titleGroup><numberingGroup><numbering type="journalVolume" number="125">125</numbering><numbering type="journalIssue">6</numbering></numberingGroup><creators><creator xml:id="sped1" creatorRole="sponsoringEditor"><personName><givenNames>Andrzej</givenNames><familyName>Galeski</familyName></personName></creator></creators><coverDate startDate="2012-09-15">15 September 2012</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="125" status="forIssue"><doi origin="wiley" registered="yes">10.1002/app.36596</doi><idGroup><id type="unit" value="APP36596"></id></idGroup><countGroup><count type="pageTotal" number="8"></count></countGroup><copyright ownership="publisher">Copyright © 2012 Wiley Periodicals, Inc.</copyright><eventGroup><event type="manuscriptReceived" date="2011-11-30"></event><event type="manuscriptAccepted" date="2011-11-30"></event><event type="xmlConverted" agent="Converter:JWSART34_TO_WML3G version:3.1.5 mode:FullText mathml2tex" date="2012-06-01"></event><event type="publishedOnlineEarlyUnpaginated" date="2012-03-01"></event><event type="firstOnline" date="2012-03-01"></event><event type="publishedOnlineFinalForm" date="2012-06-01"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:4.0.1" date="2014-03-24"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.3.4 mode:FullText" date="2015-02-24"></event></eventGroup><numberingGroup><numbering type="pageFirst">4368</numbering><numbering type="pageLast">4375</numbering></numberingGroup><correspondenceTo>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France===</correspondenceTo><linkGroup><link type="toTypesetVersion" href="file:APP.APP36596.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="7"></count><count type="tableTotal" number="0"></count><count type="referenceTotal" number="50"></count><count type="wordTotal" number="5485"></count></countGroup><titleGroup><title type="main" xml:lang="en">A constitutive model for stress–strain response and mullins effect in filled elastomers</title><title type="short" xml:lang="en">Constitutive Model for Stress–Strain Response</title></titleGroup><creators><creator xml:id="au1" creatorRole="author" affiliationRef="#af1"><personName><givenNames>A. K.</givenNames><familyName>Mossi Idrissa</familyName></personName></creator><creator xml:id="au2" creatorRole="author" affiliationRef="#af1" corresponding="yes"><personName><givenNames>S.</givenNames><familyName>Ahzi</familyName></personName><contactDetails><email>ahzi@unistra.fr</email></contactDetails></creator><creator xml:id="au3" creatorRole="author" affiliationRef="#af1 #af2"><personName><givenNames>S.</givenNames><familyName>Patlazhan</familyName></personName></creator><creator xml:id="au4" creatorRole="author" affiliationRef="#af1"><personName><givenNames>Y.</givenNames><familyName>Rémond</familyName></personName></creator><creator xml:id="au5" creatorRole="author" affiliationRef="#af3"><personName><givenNames>D.</givenNames><familyName>Ruch</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="af1" countryCode="FR" type="organization"><unparsedAffiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</unparsedAffiliation></affiliation><affiliation xml:id="af2" countryCode="RU" type="organization"><unparsedAffiliation>Semenov Institute of Chemical Physics Russian Academy of Sciences, 4 Kosygin Street, 119991 Moscow, Russia</unparsedAffiliation></affiliation><affiliation xml:id="af3" countryCode="LU" type="organization"><unparsedAffiliation>Centre de Recherche Public Henri Tudor, 66 rue de Luxembourg, B.P. 144, L‐4002 Esch‐sur‐Alzette, Luxembourg</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">filled elastomers</keyword><keyword xml:id="kwd2">Mullins'</keyword><keyword xml:id="kwd3">effect</keyword><keyword xml:id="kwd4">strain softening</keyword><keyword xml:id="kwd5">Gent model</keyword><keyword xml:id="kwd6">carbon black fillers</keyword><keyword xml:id="kwd7">hard‐to‐soft transformation</keyword></keywordGroup><abstractGroup><abstract type="main" xml:lang="en"><title type="main">Abstract</title><p>In this work we propose a new constitutive theory to estimate the stress–strain response and the softening induced by the Mullins effect during the stretching of filled elastomers. In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A constitutive model for stress–strain response and mullins effect in filled elastomers</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>Constitutive Model for Stress–Strain Response</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A constitutive model for stress–strain response and mullins effect in filled elastomers</title></titleInfo><name type="personal"><namePart type="given">A. K.</namePart><namePart type="family">Mossi Idrissa</namePart><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Ahzi</namePart><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France===</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Patlazhan</namePart><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><affiliation>Semenov Institute of Chemical Physics Russian Academy of Sciences, 4 Kosygin Street, 119991 Moscow, Russia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Y.</namePart><namePart type="family">Rémond</namePart><affiliation>Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, 2 Rue Boussingault, 67000 Strasbourg, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Ruch</namePart><affiliation>Centre de Recherche Public Henri Tudor, 66 rue de Luxembourg, B.P. 144, L‐4002 Esch‐sur‐Alzette, Luxembourg</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>Wiley Subscription Services, Inc., A Wiley Company</publisher><place><placeTerm type="text">Hoboken</placeTerm></place><dateIssued encoding="w3cdtf">2012-09-15</dateIssued><dateCaptured encoding="w3cdtf">2011-11-30</dateCaptured><dateValid encoding="w3cdtf">2011-11-30</dateValid><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="figures">7</extent><extent unit="references">50</extent><extent unit="words">5485</extent></physicalDescription><abstract lang="en">In this work we propose a new constitutive theory to estimate the stress–strain response and the softening induced by the Mullins effect during the stretching of filled elastomers. In this study, we used the Mullins and Tobin concept where the filled elastomers are treated as composites with hard‐domains and soft‐domains and the softening is due to the hard domain transformation into soft domain during stretching. Gent strain energy is assumed to represent the behavior of the unfilled elastomers. This strain energy representation is then reformulated in order to consider fillers effect in the case of filled elastomers. The proposed approach takes into account the effect of the type of carbon‐black filler and of its volume fraction on the mechanical response and microstructure evolution during stretching. The predicted results are compared to Mullins and Tobin experimental data, and good agreements are obtained. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012</abstract><subject lang="en"><genre>keywords</genre><topic>filled elastomers</topic><topic>Mullins'</topic><topic>effect</topic><topic>strain softening</topic><topic>Gent model</topic><topic>carbon black fillers</topic><topic>hard‐to‐soft transformation</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Applied Polymer Science</title></titleInfo><titleInfo type="abbreviated"><title>J. Appl. Polym. Sci.</title></titleInfo><name type="personal"><namePart type="given">Andrzej</namePart><namePart type="family">Galeski</namePart></name><genre type="journal">journal</genre><identifier type="ISSN">0021-8995</identifier><identifier type="eISSN">1097-4628</identifier><identifier type="DOI">10.1002/(ISSN)1097-4628</identifier><identifier type="PublisherID">APP</identifier><part><date>2012</date><detail type="title"><title>Contributions from the 4th International Conference on Polymer Behavior (IUPAC), Lodz, Poland, September 19–23, 2010</title></detail><detail type="volume"><caption>vol.</caption><number>125</number></detail><detail type="issue"><caption>no.</caption><number>6</number></detail><extent unit="pages"><start>4368</start><end>4375</end><total>8</total></extent></part></relatedItem><identifier type="istex">57E4D938EF61281BEC4271BCAB89707C2ADB545E</identifier><identifier type="DOI">10.1002/app.36596</identifier><identifier type="ArticleID">APP36596</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2012 Wiley Periodicals, Inc.</accessCondition><recordInfo><recordContentSource>WILEY</recordContentSource><recordOrigin>Wiley Subscription Services, Inc., A Wiley Company</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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