abaqus子程序.docx

abaqus子程序.docx

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abaqus子程序

1.1.37 UMATHT

Usersubroutinetodefineamaterial'sthermalbehavior.

Product:

 Abaqus/Standard  

Warning:

  Theuseofthissubroutinegenerallyrequiresconsiderableexpertise.Youarecautionedthattheimplementationofanyrealisticthermalmodelrequiressignificantdevelopmentandtesting.Initialtestingonmodelswithfewelementsunderavarietyofboundaryconditionsisstronglyrecommended.

References

∙“User-definedthermalmaterialbehavior,” Section23.8.2oftheAbaqusAnalysisUser'sManual

∙*USERMATERIAL

∙“Freezingofasquaresolid:

thetwo-dimensionalStefanproblem,” Section1.6.2oftheAbaqusBenchmarksManual

∙“UMATHT,” Section4.1.22oftheAbaqusVerificationManual

Overview

Usersubroutine UMATHT:

∙canbeusedtodefinethethermalconstitutivebehaviorofthematerialaswellasinternalheatgenerationduringheattransferprocesses;

∙willbecalledatallmaterialcalculationpointsofelementsforwhichthematerialdefinitionincludesauser-definedthermalmaterialbehavior;

∙canbeusedwiththeproceduresdiscussedin “Heattransferanalysisprocedures:

overview,” Section6.5.1oftheAbaqusAnalysisUser'sManual;

∙canusesolution-dependentstatevariables;

∙mustdefinetheinternalenergyperunitmassanditsvariationwithrespecttotemperatureandtospatialgradientsoftemperature;

∙mustdefinetheheatfluxvectoranditsvariationwithrespecttotemperatureandtogradientsoftemperature;

∙mustupdatethesolution-dependentstatevariablestotheirvaluesattheendoftheincrement;

∙canbeusedinconjunctionwithusersubroutine USDFLD toredefineanyfieldvariablesbeforetheyarepassedin;and

∙isdescribedfurtherin “User-definedthermalmaterialbehavior,” Section23.8.2oftheAbaqusAnalysisUser'sManual.

Useofsubroutine UMATHT withcoupledtemperature-displacementelements

Usersubroutine UMATHT shouldbeusedonlywithreduced-integrationormodifiedcoupledtemperature-displacementelementsifthemechanicalandthermalfieldsarenotcoupledthroughplasticdissipation.Nosuchrestrictionexistswithfullyintegratedcoupledtemperature-displacementelements.

Usersubroutineinterface

SUBROUTINEUMATHT（U,DUDT,DUDG,FLUX,DFDT,DFDG,

1STATEV,TEMP,DTEMP,DTEMDX,TIME,DTIME,PREDEF,DPRED,

2CMNAME,NTGRD,NSTATV,PROPS,NPROPS,COORDS,PNEWDT,

3NOEL,NPT,LAYER,KSPT,KSTEP,KINC）

C

INCLUDE'ABA_PARAM.INC'

C

CHARACTER*80CMNAME

DIMENSIONDUDG（NTGRD）,FLUX（NTGRD）,DFDT（NTGRD）,

1DFDG（NTGRD,NTGRD）,STATEV（NSTATV）,DTEMDX（NTGRD）,

2TIME

（2）,PREDEF

（1）,DPRED

（1）,PROPS（NPROPS）,COORDS（3）

usercodingtodefineU,DUDT,DUDG,FLUX,DFDT,DFDG,

andpossiblyupdateSTATEV,PNEWDT

RETURN

END

Variablestobedefined

U

Internalthermalenergyperunitmass, U,attheendofincrement.Thisvariableispassedinasthevalueatthestartoftheincrementandmustbeupdatedtoitsvalueattheendoftheincrement.

DUDT

Variationofinternalthermalenergyperunitmasswithrespecttotemperature, 

evaluatedattheendoftheincrement.

DUDG（NTGRD）

Variationofinternalthermalenergyperunitmasswithrespecttothespatialgradientsoftemperature, 

attheendoftheincrement.Thesizeofthisarraydependsonthevalueof NTGRD asdefinedbelow.Thistermistypicallyzeroinclassicalheattransferanalysis.

FLUX（NTGRD）

Heatfluxvector, 

attheendoftheincrement.Thisvariableispassedinwiththevaluesatthebeginningoftheincrementandmustbeupdatedtothevaluesattheendoftheincrement.

DFDT（NTGRD）

Variationoftheheatfluxvectorwithrespecttotemperature, 

evaluatedattheendoftheincrement.

DFDG（NTGRD,NTGRD）

Variationoftheheatfluxvectorwithrespecttothespatialgradientsoftemperature, 

attheendoftheincrement.Thesizeofthisarraydependsonthevalueof NTGRD asdefinedbelow.

Variablesthatcanbeupdated

STATEV（NSTATV）

Anarraycontainingthesolution-dependentstatevariables.

Inanuncoupledheattransferanalysis STATEV ispassedinto UMATHT withthevaluesofthesevariablesatthebeginningoftheincrement.However,anychangesin STATEV madeinusersubroutine USDFLD willbeincludedinthevaluespassedinto UMATHT,since USDFLD iscalledbefore UMATHT.Inaddition,if UMATHT isbeingusedinafullycoupledtemperature-displacementanalysisandusersubroutine CREEP,usersubroutine UEXPAN,usersubroutine UMAT,orusersubroutine UTRS isusedtodefinethemechanicalbehaviorofthematerial,thoseroutinesarecalledbeforethisroutine;therefore,anyupdatingof STATEV donein CREEP, UEXPAN, UMAT,or UTRS willbeincludedinthevaluespassedinto UMATHT.

Inallcases STATEV shouldbepassedbackfrom UMATHT asthevaluesofthestatevariablesattheendofthecurrentincrement.

PNEWDT

Ratioofsuggestednewtimeincrementtothetimeincrementbeingused（DTIME,seebelow）.ThisvariableallowsyoutoprovideinputtotheautomatictimeincrementationalgorithmsinAbaqus/Standard（ifautomatictimeincrementationischosen）.

PNEWDT issettoalargevaluebeforeeachcallto UMATHT.

If PNEWDT isredefinedtobelessthan1.0,Abaqus/Standardmustabandonthetimeincrementandattemptitagainwithasmallertimeincrement.ThesuggestednewtimeincrementprovidedtotheautomatictimeintegrationalgorithmsisPNEWDT × DTIME,wherethe PNEWDT usedistheminimumvalueforallcallstousersubroutinesthatallowredefinitionof PNEWDT forthisiteration.

If PNEWDT isgivenavaluethatisgreaterthan1.0forallcallstousersubroutinesforthisiterationandtheincrementconvergesinthisiteration,Abaqus/Standardmayincreasethetimeincrement.Thesuggestednewtimeincrementprovidedtotheautomatictimeintegrationalgorithmsis PNEWDT × DTIME,wherethe PNEWDT usedistheminimumvalueforallcallstousersubroutinesforthisiteration.

Ifautomatictimeincrementationisnotselectedintheanalysisprocedure,valuesof PNEWDT thataregreaterthan1.0willbeignoredandvaluesof PNEWDT thatarelessthan1.0willcausethejobtoterminate.

Variablespassedinforinformation

TEMP

Temperatureatthestartoftheincrement.

DTEMP

Incrementoftemperature.

DTEMDX（NTGRD）

Currentvaluesofthespatialgradientsoftemperature, 

TIME

（1）

Valueofsteptimeatthebeginningofthecurrentincrement.

TIME

（2）

Valueoftotaltimeatthebeginningofthecurrentincrement.

DTIME

Timeincrement.

PREDEF

Arrayofinterpolatedvaluesofpredefinedfieldvariablesatthispointatthestartoftheincrement,basedonthevaluesreadinatthenodes.

DPRED

Arrayofincrementsofpredefinedfieldvariables.

CMNAME

User-definedmaterialname,leftjustified.

NTGRD

Numberofspatialgradientsoftemperature.

NSTATV

Numberofsolution-dependentstatevariablesassociatedwiththismaterialtype（definedasdescribedin “Allocatingspace”in“Usersubroutines:

overview,” Section15.1.1oftheAbaqusAnalysisUser'sManual）.

PROPS（NPROPS）

User-specifiedarrayofmaterialconstantsassociatedwiththisusermaterial.

NPROPS

User-definednumberofmaterialconstantsassociatedwiththisusermaterial.

COORDS

Anarraycontainingthecoordinatesofthispoint.Thesearethecurrentcoordinatesinafullycoupledtemperature-displacementanalysisifgeometricnonlinearityisaccountedforduringthestep（see “Procedures:

overview,” Section6.1.1oftheAbaqusAnalysisUser'sManual）;otherwise,thearraycontainstheoriginalcoordinatesofthepoint.

NOEL:

Elementnumber.

NPT:

Integrationpointnumber.

LAYER:

Layernumber（forcompositeshellsandlayeredsolids）.

KSPT:

Sectionpointnumberwithinthecurrentlayer.

KSTEP:

Stepnumber.

KINC:

Incrementnumber.

Example:

 Usingmorethanoneuser-definedthermalmaterialmodel

Tousemorethanoneuser-definedthermalmaterialmodel,thevariable CMNAME canbetestedfordifferentmaterialnamesinsideusersubroutine UMATHT,asillustratedbelow:

IF（CMNAME（1:

4）.EQ.'MAT1'）THEN

CALLUMATHT_MAT1（argument_list）

ELSEIF（CMNAME（1:

4）.EQ.'MAT2'）THEN

CALLUMATHT_MAT2（argument_list）

ENDIF

UMATHT_MAT1 and UMATHT_MAT2 aretheactualusermaterialsubroutinescontainingtheconstitutivematerialmodelsforeachmaterial MAT1 and MAT2,respectively.Subroutine UMATHT merelyactsasadirectoryhere.Theargumentlistcanbethesameasthatusedinsubroutine UMATHT.

Example:

 Uncoupledheattransfer

Asasimpleexampleofthecodingofusersubroutine UMATHT,consideruncoupledheattransferanalysisinamaterial.Theequationsforthiscasearedevelopedhere,andthecorresponding UMATHT isgiven.Thisproblemcanalsobesolvedbyspecifyingthermalconductivity,specificheat,density,andinternalheatgenerationdirectly.

First,theequationsforanuncoupledheattransferanalysisareoutlined.

Thebasicenergybalanceis

where V isthevolumeofsolidmaterialwithsurfacearea S, 

 isthedensityofthematerial, 

 isthematerialtimerateoftheinternalthermalenergy, q istheheatfluxperunitareaofthebodyflowingintothebody,and r istheheatsuppliedexternallyintothebodyperunitvolume.

Aheatfluxvector 

 isdefinedsuchthat

where 

 istheunitoutwardnormaltothesurface S.Introducingtheaboverelationintotheenergybalanceequationandusingthedivergencetheorem,thefollowingrelationisobtained:

Thecorrespondingweakformisgivenby

where

isthetemperaturegradientand 

 isanarbitraryvariationalfieldsatisfyingtheessentialboundaryconditions.

Introducingthebackwarddifferenceintegrationalgorithm:

theweakformoftheenergybalanceequationbecomes

ThisnonlinearsystemissolvedusingNewton'smethod.

Intheaboveequationsthethermalconstitutivebehaviorofthematerialisgivenby

And

where 

 arestatev