Modeling Rubber and Viscoelasticity with Abaqus

ModelingRubberandViscoelasticitywithAbaqusModelingRubberandViscoelasticitywithAbaqusMotivation•Rubbermaterialsarefoundinmanycomponents.•Someoftheseareillustratedonthefollowingslide.•Rubberapplicationsincludetires,gaskets,andbushings,amongothers.•Thevastnumberofapplicationsthatuserubbermaterialsnecessitatesagoodunderstandingofthemodelingtechniquesusedtoanalyzerubbercomponents.1ModelingRubberandViscoelasticitywithAbaqusMotivationTireDecklidGasketMountBootBushingModelingRubberandViscoelasticitywithAbaqusDay1•Lecture1RubberPhysics•Lecture2RubberElasticityModels•Lecture3PhysicalTesting•Lecture4CurveFitting•Lecture5AbaqusUsage•Workshop12ModelingRubberandViscoelasticitywithAbaqusDay2•Lecture6ModelingConsiderationsandUsageTipsinAbaqus•Workshop2•Lecture7ViscoelasticMaterialBehavior•Lecture8TimeDomainViscoelasticity•Lecture9FrequencyDomainViscoelasticity•Lecture10Time-TemperatureCorrespondence•Workshop3•Lecture11ModelingAdvancedBehaviorsModelingRubberandViscoelasticitywithAbaqusAdditionalMaterial•Appendix1FiniteDeformations•Appendix2RubberElasticityModels:MathematicalForms•Appendix3LinearViscoelasticityTheory•Appendix4HarmonicViscoelasticityTheory•Appendix5SuggestedReading3ModelingRubberandViscoelasticitywithAbaqusLegalNoticesTheAbaqusSoftwaredescribedinthisdocumentationisavailableonlyunderlicensefromDassaultSystèmesanditssubsidiaryandmaybeusedorreproducedonlyinaccordancewiththetermsofsuchlicense.Thisdocumentationandthesoftwaredescribedinthisdocumentationaresubjecttochangewithoutpriornotice.DassaultSystèmesanditssubsidiariesshallnotberesponsiblefortheconsequencesofanyerrorsoromissionsthatmayappearinthisdocumentation.NopartofthisdocumentationmaybereproducedordistributedinanyformwithoutpriorwrittenpermissionofDassaultSystèmesoritssubsidiary.©DassaultSystèmes,2009.PrintedintheUnitedStatesofAmericaAbaqus,the3DSlogo,SIMULIAandCATIAaretrademarksorregisteredtrademarksofDassaultSystèmesoritssubsidiariesintheUSand/orothercountries.Othercompany,product,andservicenamesmaybetrademarksorservicemarksoftheirrespectiveowners.Foradditionalinformationconcerningtrademarks,copyrights,andlicenses,seetheLegalNoticesintheAbaqus6.9ReleaseNotesandthenoticesat:•SolidRubber•NetworkStructure•Vulcanization•TemperatureandTimeDependence•Damage•RealStress-StrainResponse•Anisotropy•RubberFoams•CellularStructure•Compressivevs.TensileBehavior7SolidRubberL1.4ModelingRubberandViscoelasticitywithAbaqusSolidRubber:NetworkStructure•Networkofmanyentangledpolymerchains•“E”inthepicturerepresentspointsofentanglement•Longchainsslideacrosseachother;thenetworkactsasaviscousfluid.•Examples:naturalrubberasextracted,latex•Networkhasrandomnessoforientation.•Behaviorisisotropic•Vulcanizationprocess(sulphurandheat)createschemicalbondsbetweenchainsatpointsofentanglement–wecallthesebondscross-links.Changesbehaviortothatofviscoussolid.Cross-linkdensitychangesthemodulus.•Fillerssuchascarbonblackcreateadditionalbondsandmodifythemechanicalbehavior.•Fillersmayalsointroducemicrostructuralchangesthatleadanisotropicresponse.fromEngineeringMaterials2,byAshby&Jones8L1.5ModelingRubberandViscoelasticitywithAbaqusSolidRubber:Vulcanization•Curingorvulcanizationproducesadditionalchemicalbondscalledcross-links;thesebondsstiffentheelastomernetwork.fromEngineeringMaterials2,byAshby&Jones•Cross-linkdensityisfunctionofdegreeofcure,relatedtocuringprocess,curetemperature,andcuringduration.•Beverycarefulthatyourrealcomponentandtestspecimenssharethesamecurehistory,thusthesamestiffness.•Bestsolution:cuttestspecimensfromactualparts.L1.6ModelingRubberandViscoelasticitywithAbaqusSolidRubber:TemperatureDependence•Temperaturedependence•Themobilityoftheselong-chainmoleculesisstronglytemperaturedependent.•Atextremelylowtemperatures(relativetotheglasstransitiontemperature)thechainsareveryimmobileandthematerialbehavesasabrittleorglassysolid–verystiff.•Athighertemperaturesthelong-chainmoleculesaremoremobileandthematerialexhibitswhatwecalla“rubbery”behavior.•Evenintherubberyregime,thelong-chainmobilityisstillquitetemperaturedependentandtheforce-displacementbehavior,stress-strainbehavior,ormodulusbecomessofterasthetemperaturerises.9L1.7ModelingRubberandViscoelasticitywithAbaqusSolidRubber:TimeDependence•Viscoelasticbehavior•Theslidingofentangledlong-chainmoleculesgivesriseto