1、11.3.1ExtendedDrucker-PragermodelsProducts:ABAQUS/StandardABAQUS/ExplicitTheextendedDrucker-PragermodelsaredefinedbyusingtheTheextendedDrucker-Pragermodels:擴(kuò)展的D-P模式：areusedtomodelfrictionalmaterials,whicharetypicallygranular-likesoilsandrock,andexhibitpressure-dependentyield(thematerialbecomesstrong

2、erasthepressureincreases);可以用來模擬摩擦材料，典型的是粒狀巖土材料及表現(xiàn)壓力相關(guān)屈服材料(由于壓力的增加材料強度增高)；areusedtomodelmaterialsinwhichthecompressiveyieldstrengthisgreaterthanthetensileyieldstrength,suchasthosecommonlyfoundincompositeandpolymericmaterials;可以用來模擬抗壓屈服強度大于抗拉屈服強度的材料，如通常所說的復(fù)合材料；allowamaterialtohardenand/orsoftenisotro

3、pically;容許材料等向硬化和/或軟化generallyallowforvolumechangewithinelasticbehavior:theflowrule,definingtheinelasticstraining,allowssimultaneousinelasticdilation(volumeincrease)andinelasticshearing;Theyieldcriteriaforthisclassofmodelsarebasedontheshapeoftheyieldsurfaceinthemeridionalplane.InABAQUS/Standardtheyi

4、eldsurfacecanhavealinearform,ahyperbolicform,orageneralexponentform;inABAQUS/Explicitonlythelinearformisavailable.ThesesurfacesareillustratedinFigure11.3.1-1.Thestressinvariantsandothertermsineachofthethreerelatedyieldcriteriaaredefinedlaterinthissection.這類材料的屈服準(zhǔn)則基于子午面(pi平面)上的屈服面的形狀。在ABAQUS/Standard

5、中屈服面可以是線性的、雙曲線形的或者是通常的指數(shù)形的；在ABAQUS/Explici中僅采用線形的。圖11.3.1-1解釋了這些面的含義。在本節(jié)后面解釋了在這三個相關(guān)的屈服準(zhǔn)則中的應(yīng)力不變和其它術(shù)語。Figure11.3.1-1Yieldsurfacesinthemeridionalplane.在子午面中的屈服面DRUCKERPRAGERoptiontogetherwiththe*DRUCKERPRAGERHARDENINGoptionand,optionally,the*RATEDEPENDENT,the*DRUCKERPRAGERCREEP,andthe*TRIAXIALTESTDATAo

6、ptions.擴(kuò)展的Drucker-Prager材料模式是由*DRUCKERPRAGER選項連同*DRUCKERPRAGERHARDENING及*RATEDEPENDENT,*DRUCKERPRAGERCREEP,*TRIAXIALTESTDATA定義的。References參考資料*DRUCKERPRAGER*DRUCKERPRAGERHARDENING*RATEDEPENDENT*DRUCKERPRAGERCREEP*TRIAXIALTESTDATA“Materiallibrary:overview,”Section9.1.1“Inelasticbehavior,”Section11.1.

7、1“Rate-dependentyield,Section11.2.3“Rate-dependentplasticity:creepandswelling,Section11.2.4Overview概要通常容許材料的無彈性行為的體積變化：流動法則，定義的無彈性應(yīng)變，容許同時發(fā)生無彈性膨脹(體積增加)和無彈性剪切；canincludecreepinABAQUS/Standardifthematerialexhibitslong-terminelasticdeformations;在ABAQUS/Standard中如果材料表現(xiàn)長期的無彈性變形則可以包含蠕變；canbedefinedtobesens

8、itivetotherateofstraining,asisoftenthecaseinpolymericmaterials;可以定義為對應(yīng)變率靈敏的材料，如在復(fù)合材料中常用到；canbeusedinconjunctionwitheithertheelasticmaterialmodel(“Linearelasticbehavior,”Section10.2.1)or,inABAQUS/Standardifcreepisnotdefined,theporouselasticmaterialmodel(“Elasticbehaviorofporousmaterials,Section10.3.1

9、);and可以用來彈性材料模式或者在如果在ABAQUS/Standard下未定義蠕變的多孔彈性材料模式的協(xié)作；areintendedtosimulatematerialresponseunderessentiallymonotonicloading.可以用來模擬材料在單一荷載作用下的相應(yīng)。Yieldcriteria屈服準(zhǔn)則-t7tan|3-p.Pb)Hyperbolic:Fu討&、一円b閃+q一ptani-cfr-0c)ExponentlormiF=aQr-p-p;=0a)LinesirDrucker-Prager;F=t-ptsinp-=0Thelinearmodel(Figure11.3.

10、1-1a)providesforapossiblynoncircularyieldsurfaceinthedeviatoricplane(I.-plane)tomatchdifferentyieldvaluesintriaxialtensionandcompression,associatedinelasticflowinthedeviatoricplane,andseparatedilationandfrictionangles.Inputdataparametersdefinetheshapeoftheyieldandflowsurfacesinthemeridionalanddeviat

11、oricplanesaswellasothercharacteristicsofinelasticbehaviorsuchthatarangeofsimpletheoriesisprovidedtheoriginalDrucker-Pragermodelisavailablewithinthismodel.However,thismodelcannotprovideaclosematchtoMohr-Coulombbehavior,asdescribedlaterinthissection.線性模式(Figure11.3.1-1a)提供了一個在偏平面(L平面)里可能的非圓弧屈服面，以符合在三軸

12、拉伸或壓縮的不同的屈服面，偏平面里的無彈性流及各自的膨脹角和摩擦角。輸入數(shù)據(jù)參數(shù)定義子午面和偏平面中屈服面和流動面的形狀及無彈性行為的其它特性，例如提供了一個簡單的理論范圍原始的D-P模式在該模式中仍然是有效的。然而，該模式不能提供一個接近于莫爾庫侖行為的模式，像本節(jié)后面闡述的一樣。ThehyperbolicandgeneralexponentmodelsuseavonMises(circular)sectioninthedeviatoricstressplane.Inthemeridionalplaneahyperbolicflowpotentialisusedforbothmodels,w

13、hich,ingeneral,meansnonassociatedflow.ThesemodelsareavailableonlyinABAQUS/Standard.雙曲線和通用指數(shù)模式為在偏應(yīng)力平面里的vonmis(圓形)截面。在子午面中一個雙曲線流可能用于兩個模型，通常意味著為非關(guān)聯(lián)流。這些模式僅使用于ABAQUS/Standard中。Thechoiceofmodeltobeuseddependslargelyontheanalysistype,thekindofmaterial,theexperimentaldataavailableforcalibrationofthemodelpar

14、ameters,andtherangeofpressurestressvaluesthatthematerialislikelytoexperience.Itiscommontohaveeithertriaxialtestdataatdifferentlevelsofconfiningpressureortestdatathatarealreadycalibratedintermsofacohesionandafrictionangleand,sometimes,atriaxialtensilestrengthvalue.Iftriaxialtestdataareavailable,thema

15、terialparametersmustbecalibratedfirst.Theaccuracywithwhichthelinearmodelcanmatchthesetestdataislimitedbythefactthatitassumeslineardependenceofdeviatoricstressonpressurestress.Althoughthehyperbolicmodelmakesasimilarassumptionathighconfiningpressures,itprovidesanonlinearrelationshipbetweendeviatorican

16、dpressurestressatlowconfiningpressures,whichmayprovideabettermatchofthetriaxialexperimentaldata.Thehyperbolicmodelisusefulforbrittlematerialsforwhichbothtriaxialcompressionandtriaxialtensiondataareavailable,whichisacommonsituationformaterialssuchasrocks.Themostgeneralofthethreeyieldcriteriaistheexpo

17、nentform.Thiscriterionprovidesthemostflexibilityinmatchingtriaxialtestdata.ABAQUSwilldeterminethematerialparametersrequiredforthismodeldirectlyfromthetriaxialtestdata.ABAQUSAleast-squaresfitthatminimizestherelativeerrorinstressisusedforthispurpose.材料模式的選擇很大程度上取決于分析類型、材料類型、可以用于模型參數(shù)判據(jù)的試驗數(shù)據(jù)及材料可能經(jīng)歷的壓應(yīng)力范

18、圍。通常具有不同限制壓力水平下的三軸試驗資料或者已經(jīng)按照一個粘聚力和摩擦角校準(zhǔn)了的試驗數(shù)據(jù)，甚至有時候具有一組三軸抗拉強度值。如果三軸試驗數(shù)據(jù)可以利用，那么材料參數(shù)必須首先被校準(zhǔn)。線性材料模式能夠與試驗數(shù)據(jù)相匹配的精度由偏應(yīng)力與壓應(yīng)力的線性相關(guān)程度限制。盡管雙曲線模式假定為在高限制壓力，但是它提供了一個在低限制壓力下偏應(yīng)力和壓應(yīng)力非線性相關(guān)關(guān)系，這一點可以較好的滿足與三軸試驗數(shù)據(jù)相吻合。雙曲線材料模式適用于三軸抗壓強度及三軸抗拉強度均可利用的脆性材料，這是類似巖石材料的共性。三個屈服準(zhǔn)則中最一般的是指數(shù)模式。該準(zhǔn)則在與三軸試驗數(shù)據(jù)相匹配方面最具有適應(yīng)性。將從三軸試驗數(shù)據(jù)中直接得到模型需要的材料

19、參數(shù)。為實現(xiàn)這個目的使用最小二乘法使得應(yīng)力相對誤差最小。Forcaseswheretheexperimentaldataarealreadycalibratedintermsofacohesionandafrictionangle,thelinearmodelcanbeused.IftheseparametersareprovidedforaMohr-Coulombmodel,itisnecessarytoconvertthemtoDrucker-Pragerparameters.Thelinearmodelisintendedprimarilyforapplicationswherethes

20、tressesareforthemostpartcompressive.Iftensilestressesaresignificant,hydrostatictensiondatashouldbeavailable(alongwiththecohesionandfrictionangle)andthehyperbolicmodelshouldbeused.在試驗數(shù)據(jù)已經(jīng)根據(jù)粘聚力和摩擦角校準(zhǔn)了的情況下，可以使用線性模式。如果這些參數(shù)提供給莫爾一庫侖模式，有必要將他們轉(zhuǎn)換為D-P參數(shù)。線性模式主要用于應(yīng)力很多程度上為壓應(yīng)力的情況下。如果拉應(yīng)力為主要的，應(yīng)該使用靜水拉應(yīng)力數(shù)據(jù)(連同粘聚力和摩擦角)

21、并采用雙曲線模式。Calibrationofthesemodelsisdiscussedlaterinthissection.這些模式準(zhǔn)則在本節(jié)的后面進(jìn)行探討。Hardeningandratedependence硬化和率相關(guān)Forgranularmaterialsthesemodelsareoftenusedasafailuresurface,inthesensethatthematerialcanexhibitunlimitedflowwhenthestressreachesyield.Thisbehavioriscalledperfectplasticity.Themodelsareals

22、oprovidedwithisotropichardening.Inthiscaseplasticflowcausestheyieldsurfacetochangesizeuniformlywithrespecttoallstressdirections.Thishardeningmodelisusefulforcasesinvolvinggrossplasticstrainingorinwhichthestrainingateachpointisessentiallyinthesamedirectioninstrainspacethroughouttheanalysis.Althoughth

23、emodelisreferredtoasanisotropichardeningmodel,strainsoftening,orhardeningfollowedbysoftening,canbedefined.對于粒狀材料這些模式常常用作破壞面，在這種意義上當(dāng)材料的應(yīng)力達(dá)到屈服時，材料將表現(xiàn)為無窮流。這種行為稱為理想塑性。模式也提供了等向硬化。在這種情況下塑性流引起屈服面在各個應(yīng)力方向均勻的變化。當(dāng)包含總塑性應(yīng)變或者在整個分析過程中各個點的應(yīng)變在應(yīng)變空間中的同一方向上時，這種硬化是有用的。盡管模式被稱為等向硬化模式，應(yīng)變軟化或者伴隨有軟化的硬化也可以被定義。Asstrainratesincr

24、ease,manymaterialsshowanincreaseintheiryieldstrength.Thiseffectbecomesimportantinmanypolymerswhenthestrainratesrangebetween0.1and1persecond;itcanbeveryimportantforstrainratesrangingbetween10and100persecond,whicharecharacteristicofhigh-energydynamiceventsormanufacturingprocesses.Theeffectisgenerallyn

25、otasimportantingranularmaterials.Theevolutionoftheyieldsurfacewithplasticdeformationisdescribedintermsoftheequivalentstress,whichcanbechosenaseithertheuniaxialcompressionyieldstress,theuniaxialtensionyieldstress,ortheshear(cohesion)yieldstress:隨著應(yīng)變率的增加，多數(shù)材料的屈服強度也隨之增加。在多數(shù)復(fù)合材料中，當(dāng)應(yīng)變率在每秒鐘從0.1到1范圍變化時這種效應(yīng)

26、是重要的；當(dāng)應(yīng)變率變化在每秒鐘從10到100變化時，這種效應(yīng)將變的異常重要，這是高能動態(tài)事件或者制造夜過程的特性。在粒狀材料中這種效應(yīng)不是那么重要。屈服面隨著塑性變形的發(fā)展是根據(jù)等效應(yīng)變來描述的，這可以被看作為單軸壓縮屈服應(yīng)力，單軸拉伸屈服應(yīng)力或者剪切(粘聚)屈服應(yīng)力。ifhardeningisdefinedbytheuniaxialcompressionyieldstress.(yr:=叭(評.epfi)ifhardeningisdefinedbytheuniaxialtensionyi(4tlstress,a；;or=d(pl.,O.fiiflianhiiigisdefinedby什莊co

27、hesioiL3ifhardeningisdefinedbytheuniaxifilcompressionyieldstress,J昭+s12十#tailj3ifliaideningi各dciinrlbytheuniaxialtensionyieldstress,tr打y/zj+h2ifhardeningis7thecohesion,d.TheisotropichardeningassumedinthismodeltreatsasconstantwithrespecttostressasdepictedinFigure11.3.1-4.Usage:*DRUCKERPRAGER,SHEARCRI

28、TERION=HYPERBOLIC雙曲線屈服準(zhǔn)則是Rankine的最大拉應(yīng)力情形和高約束應(yīng)力下的線性D-P條件的一個連聯(lián)合的產(chǎn)物。表示為：式中-?_-:和川為材料的初始雙曲線抗拉強度必廳為硬化參數(shù)為丁的初始值汎乩站為高約束壓力下的摩擦角，如圖Figure1131-1b.硬化參數(shù)可以通過使用數(shù)據(jù)獲得：dr=J話+7,-牛tanJifhartleningisdefinetlbytheuiiitixialcompressionyitdclstress,(y(.=J氐+庁+tailjSifhardeningisdefinedbythuniaxialtensionyield就ress:;=/彳+護(hù)ifl

29、iardeningisdefinedbythecohesioji.d.本模式中假定為各項同性硬化，為常數(shù)如Figure11.3.1-4用法：*DRUCKERPRAGER,SHEARCRITERION=HYPERBOLICFigure11.3.1-4Hyperbolicmodel:yieldsurfaceandhardeninginthe-：plane.Figure11.3.1-4雙曲線模式：-平面那的屈服面和硬化Generalexponentyieldcriterion通用指數(shù)屈服準(zhǔn)則Thegeneralexponentformprovidesthemostgeneralyieldcriter

30、ionavailableinthisclassofmodels.Theyieldfunctioniswrittenaswhere機(jī)乩fand皿比arematerialparametersthatareindependentofplasticdeformation;and吩尺:isthehardeningparameterthatrepresentsthehydrostatictensionstrengthofthematerialasshowninFigure11.3.1-1(c).吩斥isrelatedtotheinputtestdataasPt=8晉ifhardeningisdefined

31、bytheuniaxialcompressionyieldstress,rc:=aatb+晉ifhardeningisdefinedbytheuniaxialtensionyieldstresscrt;ifhardciiiijgisdrfinpdbytliccohrwion.Theisotropichardeningassumedinthismodeltreatsandasconstantwithrespecttostress,asdepictedinFigure11.3.1-5.通用指數(shù)模式提供了最為普遍的屈服準(zhǔn)則，屈服函數(shù)表達(dá)為F=aqpp；=07式中:和為獨立與塑性變形的材料參數(shù)，mW)

32、為表現(xiàn)為靜水抗拉強度的材料硬化參數(shù)，如圖Figure11.3.1-1(c)；與輸入試驗數(shù)據(jù)的關(guān)系如下pt寸ifhardeningisdefinedbytheuniaxialcompressionyieldstress,rc:aoth+晉ifhanlenitigisdrfinelbytheuniaxialtensionyieldstrcsfi.(7t;=ifhardeningisdefinedbythecohesion妙該模式假定為等向硬化，和為常數(shù)，如圖Figure11.3.1-5Figure11.3.1-5Generalexponentmodel:yieldsurfaceandhardeni

33、nginthe-plane.Figure11.3.1-5Thematerialparametersandcanbegivendirectly.Alternatively,iftriaxialtestdataatdifferentlevelsofconfiningpressureareavailable,ABAQUS/Standardwilldeterminethematerialparametersfromthetriaxialtestdata.Thisoptionandrelatedusagearediscussedbelow.材料參數(shù)a和b可是直接賦予。另外，如果可以得到不同側(cè)壓條件下的三

34、軸試驗數(shù)據(jù)，ABAQUS/Standard可以從三軸試驗數(shù)據(jù)中的到材料參數(shù)。這個選項和相關(guān)的用法將在下面談到。用法：Usage:*DRUCKERPRAGER,SHEARCRITERION=EXPONENTFORMPlasticflow塑性流:；istheflowpotential,choseninthesemodelsasahyperbolicfunction:G=寸傳廳|o+貳ptan辛where妙他査)isthedilationanglemeasuredinthePplaneathighconfiningpressure;istheinitialyieldstress,takenfromt

35、hehardeningdatagivenwiththeDRUCKERPRAGERHARDENINGoption;andisaparameter,referredtoastheeccentricity,thatdefinestherateatwhichthefunctionapproachestheasymptote(theflowpotentialtendstoastraightlineastheeccentricitytendstozero).Suitabledefaultvaluesareprovidedfor,asdescribedbelow.Thevalueofwilldependon

36、theyieldstressused.系統(tǒng)提供了一個合適的值八的值將取決于使用的屈服應(yīng)力。Thisflowpotential,whichiscontinuousandsmooth,ensuresthattheflowdirectionisalwaysuniquelydefined.ThefunctionapproachesthelinearDrucker-Pragerflowpotentialasymptoticallyathighconfiningpressurestressandintersectsthehydrostaticpressureaxisat90.Afamilyofhyperb

37、olicpotentialsinthemeridionalstressplaneisshowninFigure11.3.1-6.TheflowpotentialisthevonMisescircleinthedeviatoricstressplane(theI-plane).為流勢，在該模型中選擇為雙曲函數(shù).-式中：為高圍壓下的一平面上測得的膨脹角;DRUCKERPRAGER,SHEARCRITERION=EXPONENTFORM|,：I-為初始屈服應(yīng)力，從*DRUCKERPRAGERHARDENING選項中的硬化數(shù)據(jù)得到；為離心率參數(shù)，為描述函數(shù)接近漸近線的速率（當(dāng)離心率趨向零時，流勢趨向一

38、直線）Figure11.3.1-6Familyofhyperbolicflowpotentialsinthe-plane.Forthehyperbolicmodelflowisnonassociatedintheplaneifthedilationangle,andthematerialfrictionangle,aredifferent.Thehyperbolicmodelprovidesassociatedflowintheplaneonlywhen纟心and丨廠I.Adefaultvalueof)isassumediftheflowpotentialisusedwiththehyperb

39、olicmodel,sothatassociatedflowisrecoveredwhen:.Forthegeneralexponentmodelflowisalwaysnonassociatedintheplane.Thedefaultflowpotentialeccentricityis1i,whichimpliesthatthematerialhasalmostthesamedilationangleoverawiderangeofconfiningpressurestressvalues.Increasingthevalueofprovidesmorecurvaturetotheflo

40、wpotential,implyingthatthedilationangleincreasesmorerapidlyastheconfiningpressuredecreases.Valuesofthataresignificantlylessthanthedefaultvaluemayleadtoconvergenceproblemsifthematerialissubjectedtolowconfiningpressuresbecauseoftheverytightcurvatureoftheflowpotentiallocallywhereitintersectsthe-axis.Th

41、erelationshipbetweentheflowpotentialandtheincrementalplasticstrainforthehyperbolicandgeneralexponentmodelsisdiscussedindetailin“Modelsforgranularorpolymerbehavior,”Section4.4.2oftheABAQUSTheoryManual：NonassociatedflowNonassociatedflowimpliesthatthematerialstiffnessmatrixisnotsymmetric;therefore,theu

42、nsymmetricmatrixstorageandsolutionschemeshouldbeusedinABAQUS/Standard(see“Procedures:overview,Section6.1.1).Ifthediffereneebetweenandinthehyperbolicmodelisnotlargeandiftheregionofthemodelinwhichinelasticdeformationisoccurringisconfined,itispossiblethatasymmetricapproximationtothematerialstiffnessmat

43、rixwillgiveanacceptablerateofconvergence.Insuchcasestheunsymmetricmatrixschememaynotbeneeded.MatchingexperimentaltriaxialtestdataDataforgeologicalmaterialsaremostcommonlyavailablefromtriaxialtesting.Insuchatestthespecimenisconfinedbyapressurestressthatisheldconstantduringthetest.Theloadingisanadditi

44、onaltensionorcompressionstressappliedinonedirection.Typicalresultsineludestress-straincurvesatdifferentlevelsofconfinement,asshowninFigure11.3.1-7.Tocalibratetheyieldparametersforthisclassofmodels,theuserneedstodecidewhichpointoneachstress-straincurvewillbeusedforcalibration.Forexample,iftheuserwish

45、estocalibratetheinitialyieldsurface,thepointineachstress-straincurvecorrespondingtoinitialdeviationfromelasticbehaviorshouldbeused.Alternatively,iftheuserwishestocalibratetheultimateyieldsurface,thepointineachstress-straincurvecorrespondingtothepeakstressshouldbeused.Figure11.3.1-7Triaxialtestswiths

46、tress-straincurvesfortypicalgeologicalmaterialsatdifferentlevelsofconfinement.*pointschosentodefineshapeandpositionofyieldsurfaceincreasingconfinementOnestressdatapointfromeachstress-straincurveatadifferentlevelofconfinementisplottedinthemeridionalstressplane(planeifthelinearmodelistobeused,or-plane

47、ifthehyperbolicorgeneralexponentmodelwillbeused).Thistechniquecalibratestheshapeandpositionoftheyieldsurface,asshowninFigure11.3.1-8,andisadequatetodefineamodelifitistobeusedasafailuresurface(perfectplasticity).Figure11.3.1-8Yieldsurfaceinmeridionalplane.Themodelsarealsoavailablewithisotropichardeni

48、ng,inwhichcasehardeningdataarerequiredtocompletethecalibration.Inanisotropichardeningmodelplasticflowcausestheyieldsurfacetochangesizeuniformly;inotherwords,onlyoneofthestress-straincurvesdepictedinFigure11.3.1-7canbeusedtorepresenthardening.Thecurvethatrepresentshardeningmostaccuratelyovertherangeo

49、floadingconditionsanticipatedshouldbeselected(usuallythecurvefortheaverageanticipatedvalueofpressurestress).Asstatedearlier,twotypesoftriaxialtestdataarecommonlyavailableforgeologicalmaterials.Inatriaxialcompressiontestthespecimenisconfinedbypressureandanadditionalcompressionstressissuperposedinoned

50、irection.Thus,theprincipalstressesareallnegative,with_-(Figure11.3.1-9a).Intheprecedinginequality,andarethemaximum,intermediate,andminimumprincipalstresses,respectively.Figure11.3.1-9a)Triaxialcompressionandb)tension.Thevaluesofthestressinvariantsarep=_扌（細(xì)+也）.andsothatThetriaxialcompressionresultsca

51、n,thus,beplottedinthemeridionalplaneshowninFigure11.3.1-8.LinearDrucker-PragermodelFittingthebeststraightlinethroughthetriaxialcompressionresultsprovidesand-forthelinearDrucker-Pragermodel.Triaxialtensiondataarealsoneededtodefine/.inthelinearDrucker-Pragermodel.Undertriaxialtensionthespecimenisagain

52、confinedbypressure,afterwhichthepressureinonedirectionisreduced.Inthiscasetheprincipalstressesare=(Figure11319b).Thestressinvariantsarenow+2如.andsothatThus,人canbefoundbyplottingthesetestresultsas：versus.andagainfittingthebeststraightline.Thetriaxialcompressionandtensionlinesmustinterceptthe-axisatth

53、esamepoint,andtheratioofvaluesof、：fortriaxialtensionandcompressionatthesamevalueof.thengives(Figure11.3.1-10).Figure11.3.1-10Linearmodel:fittingtriaxialcompressionandtensiondata.HyperbolicmodelFittingthebeststraightlinethroughthetriaxialcompressionresultsathighconfiningpressuresprovidesandforthehype

54、rbolicmodel.Thisfitisperformedinthesamemannerasthatusedtoobtainand-forthelinearDrucker-Pragermodel.Inaddition,hydrostatictensiondataarerequiredtocompletethecalibrationofthehyperbolicmodelsothattheinitialhydrostatictensionstrength,canbedefined.GeneralexponentmodelGiventriaxialdatainthemeridionalplane

55、,ABAQUS/Standardprovidesacapabilitytodeterminethematerialparameters,and.-requiredfortheexponentmodel.Theparametersaredeterminedonthebasisofabestfit”ofthetriaxialtestdataatdifferentlevelsofconfiningstress.Aleast-squaresfitwhichminimizestherelativeerrorinstressisusedtoobtainthebestfit”valuesfor，八,and.

56、Thecapabilityallowsallthreeparameterstobecalibratedor,ifsomeoftheparametersareknown,onlytheremainingparameterstobecalibrated.Thisabilityisusefulifonlyafewdatapointsareavailable,inwhichcasetheusermaywishtofitthebeststraightlineC)throughthedatapoints(effectivelyreducingthemodeltoalinearDrucker-Pragerm

57、odel).Partialcalibrationcanalsobeusefulinacasewhentriaxialtestdataatlowconfinementareunreliableorunavailable,asisoftenthecaseforcohesionlessmaterials.Inthiscaseabetterfitmaybeobtainedifthevalueof.isspecifiedandonlyandarecalibrated.Thedatamustbeprovidedintermsoftheprincipalstresses:：=:.and,whereisthe

58、confiningstressandisthestressintheloadingdirection.TheABAQUSsignconventionmustbefollowedsuchthattensilestressesarepositiveandcompressivestressesarenegative.Onepairofstressesmustbeenteredfromeachtriaxialtest.Asmanydatapointsasdesiredcanbeenteredfromtriaxialtestsatdifferentlevelsofconfiningstress.Usag

59、e:Usebothofthefollowingparameters:*DRUCKERPRAGER,SHEARCRITERION=EXPONENTFORM,TESTDATA*TRIAXIALTESTDATAIftheexponentmodelisusedasafailuresurface(perfectplasticity),theDrucker-Pragerhardeningoptioncanbeomitted.Thehydrostatictensionstrength,.,obtainedfromthecalibrationwillthenbeusedasthefailurestress.H

60、owever,iftheDrucker-Pragerhardeningoptionisusedtogetherwiththetriaxialtestdataoption,thevalueof.obtainedfromthecalibrationwillbeignored.InthiscaseABAQUS/Standardwillinterpolatedirectlyfromthehardeningdata.MatchingMohr-CoulombparameterstotheDrucker-PragermodelSometimesexperimentaldataarenotdirectlyav