最新黄永刚单晶塑性有限元umat子程序.docx
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最新黄永刚单晶塑性有限元umat子程序
SUBROUTINEUMAT（stress,statev,ddsdde,sse,spd,scd,
1rpl,ddsddt,drplde,drpldt,
2stran,dstran,time,dtime,temp,dtemp,predef,dpred,cmname,
3ndi,nshr,ntens,nstatv,props,nprops,coords,drot,pnewdt,
4celent,dfgrd0,dfgrd1,noel,npt,layer,kspt,kstep,kinc）
cWRITE（6,*）'
cNOTE:
MODIFICATIONSTO*UMATFORABAQUSVERSION5.3（14APR'94）
c
c
（1）Thelistofvariablesabovedefiningthe*UMATsubroutine,
candthefirst（standard）blockofvariablesdimensionedbelow,
chavevariablenamesaddedcomparedtoearlierABAQUSversions.
c
c
（2）Thestatement:
include'aba_param.inc'mustbeaddedasbelow.
c
c（3）Asofversion5.3,ABAQUSfilesusedoubleprecisiononly.
cThefileaba_param.inchasaline"implicitreal*8"and,since
citisincludedinthemainsubroutine,itwilldefinethevariables
cthereasdoubleprecision.Butothersubroutinesstillneedthe
cdefinition"implicitreal*8"sincetheremaybevariablesthatare
cnotpassedtothemthroughthelistorcommonblock.
c
c（4）Thisiscurrentasofversion5.6ofABAQUS.
c
c（5）NoteaddedbyJ.W.Kysar（4November1997）.ThisUMAThasbeen
cmodifiedtokeeptrackofthecumulativeshearstrainineach
cindividualslipsystem.Thisinformationisneededtocorrectan
cerrorintheimplementationoftheBassaniandWuhardeninglaw.
cAnylineofcodewhichhasbeenaddedormodifiedispreceded
cimmediatelybyalinebeginningCFIXAandsucceededbyaline
cbeginningCFIXB.Anycommentlineaddedormodifiedwillbegin
cwithCFIX.
c
cThehardeninglawbyBassaniandWuwasimplementedincorrectly.
cThislawisafunctionofbothhyperbolicsecantsquaredandhyperbolic
ctangent.However,theargumentsofsechandtanharerelatedtothe*total*
csliponindividualslipsystems.Formerly,theUMATimplementedthis
chardeninglawbyusingthe*current*sliponeachslipsystem.Therein
claytheproblem.TheUMATdidnotrestrictthecurrentsliptobea
cpositivevalue.Sowhenaslipwithanegativesignwasencountered,the
ctermcontainingtanhledtoanegativehardeningrate（sincetanhisan
coddfunction）.
cTheUMAThasbeenfixedbyaddingstatevariablestokeeptrackofthe
c*total*sliponeachslipsystembyintegratinguptheabsolutevalue
cofslipratesforeachindividualslipsystem.These"solutiondependent
cvariables"areavailableforpostprocessing.Theonlyrequiredchange
cintheinputfileisthattheDEPVARcommandmustbechanged.
c
C-----UsesingleprecisiononCrayby
C
（1）deletingthestatement"IMPLICIT*8（A-H,O-Z）";
C
（2）changing"REAL*8FUNCTION"to"FUNCTION";
C（3）changingdoubleprecisionfunctionsDSIGNtoSIGN.
C
C-----Subroutines:
C
CROTATION--formingrotationmatrix,i.e.thedirection
Ccosinesofcubiccrystal[100],[010]and[001]
Cdirectionsinglobalsystemattheinitial
Cstate
C
CSLIPSYS--calculatingnumberofslipsystems,unit
Cvectorsinslipdirectionsandunitnormalsto
Cslipplanesinacubiccrystalattheinitial
Cstate
C
CGSLPINIT--calculatinginitialvalueofcurrentstrengths
Catinitialstate
C
CSTRAINRATE--basedoncurrentvaluesofresolvedshear
Cstressesandcurrentstrength,calculating
Cshearstrain-ratesinslipsystems
C
CLATENTHARDEN--formingself-andlatent-hardeningmatrix
C
CITERATION--generatingarraysfortheNewton-Rhapson
Citeration
C
CLUDCMP--LUdecomposition
C
CLUBKSB--linearequationsolverbasedonLU
Cdecompositionmethod（mustcallLUDCMPfirst）
C-----Functionsubprogram:
CF--shearstrain-ratesinslipsystems
C-----Variables:
C
CSTRESS--stresses（INPUT&OUTPUT）
CCauchystressesforfinitedeformation
CSTATEV--solutiondependentstatevariables（INPUT&OUTPUT）
CDDSDDE--Jacobianmatrix（OUTPUT）
C-----Variablespassedinforinformation:
C
CSTRAN--strains
Clogarithmicstrainforfinitedeformation
C（actually,integralofthesymmetricpartofvelocity
Cgradientwithrespecttotime）
CDSTRAN--incrementsofstrains
CCMNAME--namegiveninthe*MATERIALoption
CNDI--numberofdirectstresscomponents
CNSHR--numberofengineeringshearstresscomponents
CNTENS--NDI+NSHR
CNSTATV--numberofsolutiondependentstatevariables（as
Cdefinedinthe*DEPVARoption）
CPROPS--materialconstantsenteredinthe*USERMATERIAL
Coption
CNPROPS--numberofmaterialconstants
C
C-----Thissubroutineprovidestheplasticconstitutiverelationof
CsinglecrystalsforfiniteelementcodeABAQUS.Theplasticslip
CofsinglecrystalobeystheSchmidlaw.Theprogramgivesthe
Cchoiceofsmalldeformationtheoryandtheoryoffiniterotation
Candfinitestrain.
CThestrainincrementiscomposedofelasticpartandplastic
Cpart.Theelasticstrainincrementcorrespondstolattice
Cstretching,theplasticpartisthesumoverallslipsystemsof
Cplasticslip.Theshearstrainincrementforeachslipsystemis
Cassumedafunctionoftheratioofcorrespondingresolvedshear
Cstressovercurrentstrength,andofthetimestep.Theresolved
Cshearstressisthedoubleproductofstresstensorwiththeslip
Cdeformationtensor（Schmidfactor）,andtheincrementofcurrent
Cstrengthisrelatedtoshearstrainincrementsoverallslip
Csystemsthroughself-andlatent-hardeningfunctions.
C-----TheimplicitintegrationmethodproposedbyPeirce,Shihand
CNeedleman（1984）isusedhere.Thesubroutineprovidesanoption
Cofiterationtosolvestressesandsolutiondependentstate
Cvariableswithineachincrement.
C-----ThepresentprogramisforasingleCUBICcrystal.However,
Cthiscodecanbegeneralizedforothercrystals（e.g.HCP,
CTetragonal,Orthotropic,etc.）.OnlysubroutinesROTATIONand
CSLIPSYSneedtobemodifiedtoincludetheeffectofcrystal
Caspectratio.
C
C-----Importantnotice:
C
C
（1）ThenumberofstatevariablesNSTATVmustbelargerthan（or
CFIXequalto）TEN（10）timesthetotalnumberofslipsystemsin
Callsets,NSLPTL,plusFIVE（5）
CFIXNSTATV>=10*NSLPTL+5
CDenotesasaslipdirectionandmasnormaltoaslipplane.
CHere（s,-m）,（-s,m）and（-s,-m）areNOTconsidered
Cindependentof（s,m）.Thenumberofslipsystemsineachset
Ccouldbeeither6,12,24or48foracubiccrystal,e.g.12
Cfor{110}<111>.
C
CUserswhoneedmoreparameterstocharacterizethe
Cconstitutivelawofsinglecrystal,e.g.theframework
CproposedbyZarka,shouldmakeNSTATVlargerthan（orequal
Cto）thenumberofthoseparametersNPARMTplusninetimes
Cthetotalnumberofslipsystems,NSLPTL,plusfive
CFIXNSTATV>=NPARMT+10*NSLPTL+5
C
C
（2）Thetangentstiffnessmatrixingeneralisnotsymmetricif
Clatenthardeningisconsidered.Usersmustdeclare"UNSYMM"
Cintheinputfile,atthe*USERMATERIALcard.
C
PARAMETER（ND=150）
C-----TheparameterNDdeterminesthedimensionsofthearraysin
Cthissubroutine.Thecurrentchoice150isaupperboundfora
Ccubiccrystalwithuptothreesetsofslipsystemsactivated.
CUsersmayreducetheparameterNDtoanynumberaslongaslarger
Cthanorequaltothetotalnumberofslipsystemsinallsets.
CForexample,if{110}<111>istheonlysetofslipsystem
Cpotentiallyactivated,NDcouldbetakenastwelve（12）.
c
include'aba_param.inc'
c
CHARACTER*8CMNAME
EXTERNALF
dimensionstress（ntens）,statev（nstatv）,
1ddsdde（ntens,ntens）,ddsddt（ntens）,drplde（ntens）,
2stran（ntens）,dstran（ntens）,time
（2）,predef
（1）,dpred
（1）,
3props（nprops）,coords（3）,drot（3,3）,dfgrd0（3,3）,dfgrd1（3,3）
DIMENSIONISPDIR（3）,ISPNOR（3）,NSLIP（3）,
2SLPDIR（3,ND）,SLPNOR（3,ND）,SLPDEF（6,ND）,
3SLPSPN（3,ND）,DSPDIR（3,ND）,DSPNOR（3,ND）,
4DLOCAL（6,6）,D（6,6）,ROTD（6,6）,ROTATE（3,3）,
5FSLIP（ND）,DFDXSP（ND）,DDEMSD（6,ND）,
6H（ND,ND）,DDGDDE（ND,6）,
7DSTRES（6）,DELATS（6）,DSPIN（3）,DVGRAD（3,3）,
8DGAMMA（ND）,DTAUSP（ND）,DGSLIP（ND）,
9WORKST（ND,ND）,INDX（ND）,TERM（3,3）,TRM0（3,3）,ITRM（3）
DIMENSIONFSLIP1（ND）,STRES1（6）,GAMMA1（ND）,TAUSP1（ND）,
2GSLP1（ND）,SPNOR1（3,ND）,SPDIR1（3,ND）,DDSDE1（6,6）,
3DSOLD（6）,DGAMOD（ND）,DTAUOD（ND）,DGSPOD（ND）,
4DSPNRO（3,ND）,DSPDRO（3,ND）,
5DHDGDG（ND,ND）
C-----NSLIP--numberofslipsystemsineachset
C-----SLPDIR--slipdirections（unitvectorsintheinitialstate）
C-----SLPNOR--normalstoslipplanes（unitnormalsintheinitial
Cstate）
C-----SLPDEF--slipdeformationtensors（Schmidfactors）
CSLPDEF（1,i）--SLPDIR（1,i）*SLPNOR（1,i）
CSLPDEF（2,i）--SLPDIR（2,i）*SLPNOR（2,i）
CSLPDEF（3,i）--SLPDIR（3,i）*SLPNOR（3,i）
CSLPDEF（4,i）--SLPDIR（1,i）*SLPNOR（2,i）+
CSLPDIR（2,i）*SLPNOR（1,i）
CSLPDEF（5,i）--SLPDIR（1,i）*SLPNOR（3,i）+
CSLPDIR（3,i）*SLPNOR（1,i）
CSLPDEF（6,i）--SLPDIR（2,i）*SLPNOR（3,i）+
CSLPDIR（3,i）*SLPNOR（2,i）
Cwhereindexicorrespondstotheithslipsystem
C-----SLPSPN--slipspintensors（onlyneededforfiniterotation）
CSLPSPN（1,i）--[SLPDIR（1,i）*SLPNOR（2,i）-
CSLPDIR（2,i）*SLPNOR（1,i）]/2
CSLPSPN（2,i）--[SLPDIR（3,i）*SLPNOR（1,i）-
CSLPDIR（1,i）*SLPNOR（3,i）]/2
CSLPSPN（3,i）--[SLPDIR（2,i）*SLPNOR（3,i）-
CSLPDIR（3,i）*SLPNOR（2,i）]/2
Cwhereindexicorrespondstotheithslipsystem
C-----DSPDIR--incrementsofslipdirections
C-----DSPNOR--incrementsofnormalstoslipplanes
C
C-----DLOCAL--elasticmatrixinlocalcubiccrystalsystem
C-----D--elasticmatrixinglobalsystem
C-----ROTD--rotationmatrixtransformingDLOCALtoD
C
C-----ROTATE--rotationmatrix,directioncosinesof[100],[010]
Cand[001]ofcubiccrystalinglobalsystem
C
C-----FSLIP--shearstrain-ratesinslipsystems
C-----DFDXSP--derivativesofFSLIPw.r.tx=TAUSLP/GSLIP,where
CTAUSLPistheresolvedshearstressandGSLIPi
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