Nonlinear constitutive laws in viscoelasticity.pdf

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1、MathematicsandMechanicsofSolidshttp://mms.sagepub.com/NonlinearConstitutiveLawsinViscoelasticityC.S.Drapaca,S.SivaloganathanandG.TentiMathematicsandMechanicsofSolids200712:475DOI:10.1177/1081286506062450Theonlineversionofthisarticlecanbefoundat:http://mms.sagepub.com/content/12/5/475Publishedby:http

2、://www.sagepublications.comAdditionalservicesandinformationforMathematicsandMechanicsofSolidscanbefoundat:EmailAlerts:http://mms.sagepub.com/cgi/alertsSubscriptions:http://mms.sagepub.com/subscriptionsReprints:http://www.sagepub.com/journalsReprints.navPermissions:http://www.sagepub.com/journalsPerm

3、issions.navCitations:http://mms.sagepub.com/content/12/5/475.refs.htmlDownloadedfrommms.sagepub.comatUNIVERSITYOFMICHIGANonJune7,2011NonlinearConstitutiveLawsinViscoelasticityC.S.DRAPACAS.SIVALOGANATHANG.TENTIDepartmentofAppliedMathematics,UniversityofWaterloo,Waterloo,ON,CanadaN2L3G1(Received22Octo

4、ber20041accepted8November2005)Abstract:Thetheoryofviscoelasticityappearstoplayacentralroleinthedescriptionofmaterialswhichexhibittimedependentstress–strainbehavior.Variousmaterialslikepolymers,somesoftbiologicaltissues,andvariousfoodshavebeenalreadysuccessfullymodeledasnonlinearviscoelasticmaterials

5、.Theliteratureintheseapplicationareasisrepletewithdifferent,seeminglyunconnectednonlinearviscoelasticmodels.Theaimofthepresentpaperistoreviewtheclassicalnonlinearviscoelasticmodelsandprovideaunifyingframeworkusingthecontinuummechanicsformalism.KeyWords:nonlinearviscoelasticity,continuummechanics,mat

6、hematicalmodeling1.INTRODUCTIONThetheoryofviscoelasticityappearstobecrucialindescribingmaterialswhichexhibittimedependentstress–strainbehavior.Bearinginmindtheimportanceofknowingthemostac-curatestress–strainrelationforagivenmaterial,inordertopredictitsmechanicalresponseindifferentcircumstances,muchw

7、orkhasbeenfocused(inthefieldofcontinuummechan-ics)onthedevelopmentofappropriateconstitutiveequations.Theaimofthispaperistoreviewtheclassicalnonlinearviscoelasticmodelsandprovideaunifyingframework(usin