混凝土或其他脆性材料的塑性破坏.docx
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混凝土或其他脆性材料的塑性破坏.docx
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混凝土或其他脆性材料的塑性破坏
Damagedplasticitymodelforconcreteandotherquasi-brittlematerials
Products:
Abaqus/StandardAbaqus/Explicit
ThissectiondescribestheconcretedamagedplasticitymodelprovidedinAbaqusfortheanalysisofconcreteandotherquasi-brittlematerials.ThemateriallibraryinAbaqusalsoincludesotherconstitutivemodelsforconcretebasedonthesmearedcrackapproach.ThesearethesmearedcrackmodelinAbaqus/Standard,describedin“Aninelasticconstitutivemodelforconcrete,”Section4.5.1,andthebrittlecrackingmodelinAbaqus/Explicit,describedin“Acrackingmodelforconcreteandotherbrittlematerials,”Section4.5.3.
Theconcretedamagedplasticitymodelisprimarilyintendedtoprovideageneralcapabilityfortheanalysisofconcretestructuresundercyclicand/ordynamicloading.Themodelisalsosuitablefortheanalysisofotherquasi-brittlematerials,suchasrock,mortarandceramics;butitisthebehaviorofconcretethatisusedintheremainderofthissectiontomotivatedifferentaspectsoftheconstitutivetheory.Underlowconfiningpressures,concretebehavesinabrittlemanner;themainfailuremechanismsarecrackingintensionandcrushingincompression.Thebrittlebehaviorofconcretedisappearswhentheconfiningpressureissufficientlylargetopreventcrackpropagation.Inthesecircumstancesfailureisdrivenbytheconsolidationandcollapseoftheconcretemicroporousmicrostructure,leadingtoamacroscopicresponsethatresemblesthatofaductilematerialwithworkhardening.
Modelingthebehaviorofconcreteunderlargehydrostaticpressuresisoutofthescopeoftheplastic-damagemodelconsideredhere.Theconstitutivetheoryinthissectionaimstocapturetheeffectsofirreversibledamageassociatedwiththefailuremechanismsthatoccurinconcreteandotherquasi-brittlematerialsunderfairlylowconfiningpressures(lessthanfourorfivetimestheultimatecompressivestressinuniaxialcompressionloading).Theseeffectsmanifestthemselvesinthefollowingmacroscopicproperties:
differentyieldstrengthsintensionandcompression,withtheinitialyieldstressincompressionbeingafactorof10ormorehigherthantheinitialyieldstressintension;
softeningbehaviorintensionasopposedtoinitialhardeningfollowedbysofteningincompression;
differentdegradationoftheelasticstiffnessintensionandcompression;
stiffnessrecoveryeffectsduringcyclicloading;and
ratesensitivity,especiallyanincreaseinthepeakstrengthwithstrainrate.
Theplastic-damagemodelinAbaqusisbasedonthemodelsproposedbyLublineretal.(1989)andbyLeeandFenves(1998).Themodelisdescribedintheremainderofthissection.Anoverviewofthemainingredientsofthemodelisgivenfirst,followedbyamoredetaileddiscussionofthedifferentaspectsoftheconstitutivemodel.
Overview
Themainingredientsoftheinviscidconcretedamagedplasticitymodelaresummarizedbelow.
Strainratedecomposition
Anadditivestrainratedecompositionisassumedfortherate-independentmodel:
whereisthetotalstrainrate,istheelasticpartofthestrainrate,andistheplasticpartofthestrainrate.
Stress-strainrelations
Thestress-strainrelationsaregovernedbyscalardamagedelasticity:
whereistheinitial(undamaged)elasticstiffnessofthematerial;isthedegradedelasticstiffness;anddisthescalarstiffnessdegradationvariable,whichcantakevaluesintherangefromzero(undamagedmaterial)toone(fullydamagedmaterial).Damageassociatedwiththefailuremechanismsoftheconcrete(crackingandcrushing)thereforeresultsinareductionintheelasticstiffness.Withinthecontextofthescalar-damagetheory,thestiffnessdegradationisisotropicandcharacterizedbyasingledegradationvariable,d.Followingtheusualnotionsofcontinuumdamagemechanics,theeffectivestressisdefinedas
TheCauchystressisrelatedtotheeffectivestressthroughthescalardegradationrelation:
Foranygivencross-sectionofthematerial,thefactorrepresentstheratiooftheeffectiveload-carryingarea(i.e.,theoverallareaminusthedamagedarea)totheoverallsectionarea.Intheabsenceofdamage,,theeffectivestressisequivalenttotheCauchystress,.Whendamageoccurs,however,theeffectivestressismorerepresentativethantheCauchystressbecauseitistheeffectivestressareathatisresistingtheexternalloads.Itis,therefore,convenienttoformulatetheplasticityproblemintermsoftheeffectivestress.Asdiscussedlater,theevolutionofthedegradationvariableisgovernedbyasetofhardeningvariables,,andtheeffectivestress;thatis,.
Hardeningvariables
Damagedstatesintensionandcompressionarecharacterizedindependentlybytwohardeningvariables,and,whicharereferredtoasequivalentplasticstrainsintensionandcompression,respectively.Theevolutionofthehardeningvariablesisgivenbyanexpressionoftheform
asdescribedlaterinthissection.
Microcrackingandcrushingintheconcretearerepresentedbyincreasingvaluesofthehardeningvariables.Thesevariablescontroltheevolutionoftheyieldsurfaceandthedegradationoftheelasticstiffness.Theyarealsointimatelyrelatedtothedissipatedfractureenergyrequiredtogeneratemicro-cracks.
Yieldfunction
Theyieldfunction,,representsasurfaceineffectivestressspace,whichdeterminesthestatesoffailureordamage.Fortheinviscidplastic-damagemodel
Thespecificformoftheyieldfunctionisdescribedlaterinthissection.
Flowrule
PlasticflowisgovernedbyaflowpotentialGaccordingtotheflowrule:
whereisthenonnegativeplasticmultiplier.Theplasticpotentialisdefinedintheeffectivestressspace.Thespecificformoftheflowpotentialfortheconcretedamagedplasticitymodelisdiscussedlaterinthissection.Themodelusesnonassociatedplasticity,thereforerequiringthesolutionofnonsymmetricequations.
Summary
Insummary,theelastic-plasticresponseoftheconcretedamagedplasticitymodelisdescribedintermsoftheeffectivestressandthehardeningvariables:
whereandFobeytheKuhn-Tuckerconditions:
TheCauchystressiscalculatedintermsofthestiffnessdegradationvariable,,andtheeffectivestressas
Theconstitutiverelationsfortheelastic-plasticresponse,Equation4.5.2–1,aredecoupledfromthestiffnessdegradationresponse,Equation4.5.2–2,whichmakesthemodelattractiveforaneffectivenumericalimplementation.Theinviscidmodelsummarizedherecanbeextendedeasilytoaccountforviscoplasticeffectsthroughtheuseofaviscoplasticregularizationbypermittingstressestobeoutsidetheyieldsurface.
Damageandstiffnessdegradation
Theevolutionequationsofthehardeningvariablesandareconvenientlyformulatedbyconsideringuniaxialloadingconditionsfirstandthenextendedtomultiaxialconditions.
Uniaxialconditions
Itisassumedthattheuniaxialstress-straincurvescanbeconvertedintostressversusplasticstraincurvesoftheform
wherethesubscriptstandcrefertotensionandcompression,respectively;andaretheequivalentplasticstrainrates,andaretheequivalentplasticstrains,isthetemperature,andareotherpredefinedfieldvariables.
Underuniaxialloadingconditionstheeffectiveplasticstrainratesaregivenas
Intheremainderofthissectionweadopttheconventionthatisapositivequantityrepresentingthemagnitudeoftheuniaxialcompressionstress;thatis,.
AsshowninFigure4.5.2–1,whentheconcretespecimenisunloadedfromanypointonthestrainsofteningbranchofthestress-straincurves,theunloadingresponseisobservedtobeweakened:
theelasticstiffnessofthematerialappearstobedamaged(ordegraded).Thedegradationoftheelasticstiffnessissignificantlydifferentbetweentensionandcompressiontests;ineithercase,theeffectismorepronouncedastheplasticstrainincreases.Thedegradedresponseofconcreteischaracterizedbytwoindependentuniaxialdamagevariables,and,whichareassumedtobefunctionsoftheplasticstrains,temperature,andfieldvariables:
Figure4.5.2–1Responseofconcretetouniaxialloadingintension(a)andcompression(b).
Theuniaxialdegradationvariablesareincreasingfunctionsoftheequivalentplasticstrains.Theycantakevaluesrangingfromzero,fortheundamagedmaterial,toone,forthefullydamagedmaterial.
Ifistheinitial(undamaged)elasticstiffnessofthematerial,thestress-strainrelationsunderuniaxialtensionandcompressionloadingare,respectively:
Underuniaxialloadingcrackspropagateinadirectiontransversetothestressdirection.Thenucleationandpropagationofcracks,therefore,causesareductionoftheavailableload-carryingarea,whichinturnleadstoanincreaseintheeffectivestress.Theeffectislesspronouncedundercompressiveloadingsincecracksrunparalleltotheloadingdirection;however,afterasignificantamountofcrushing,theeffectiveload-carryingareaisalsosignificantlyreduced.Theeffectiveuniaxialcohesionstresses,and,aregivenas
Theeffectiveuniaxialcohesionstressesdeterminethesizeoftheyield(orfailure)surface.
Uniaxialcyclicconditions
Underuniaxialcyclicloadingconditionsthedegradationmechanismsarequitecomplex,involvingtheopeningandclosingofpreviouslyformedmicro-cracks,aswellastheirinteraction.Experimentally,itisobservedthatthereissomerecoveryoftheelasticstiffnessastheloadchangessignduringauniaxialcyclictest.Thestiffnessrecoveryeffect,alsoknownasthe“unilateraleffect,”isanimportantaspectoftheconcretebehaviorundercyclicloading.Theeffectisusuallymorepronouncedastheloadchangesfromtens
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- 混凝土 其他 脆性 材料 塑性 破坏