VUMAT基本知识汇总.docx
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VUMAT基本知识汇总.docx
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VUMAT基本知识汇总
NBLOCK:
在铜用Vumat吋需要用到的材料点的数量
Ndir:
对称张量中直接应力的数量(sigmal1,sigma22,sigma33)
Nshr:
对称张量中间接应力的数x(sigmal2,sigmal3,sigma23)
Nstafcv:
与材料类型相关朕的用户定义的状态变量的数目
Nficldv:
用户定义的外场变量的个数
Nprops:
用户自定义材料属性的个数
Laimcal:
指示是否在退火过程中被讷用例程的标志。
LanncaI=0,指示在常规力学性能增量,例程被讽用。
Laimcal^l表示,这是退火过程,你应该重新初始化内部状态变量,
stcpTimc:
步骤开始后的数值
totalTimc:
总时间
Dt:
时间增量值
Cmnamc:
用户自定义的材料名称,左对齐。
它是通过字符串传迷的。
一些内部材料模型是以“AEQ_”字符串开头给定的名称。
为了避免冲突,你不应该在
“cmnamc”中使用“ABQ_”作为领先字符串。
c(x)rdMp(nblock,*):
材料点的坐标值。
它是壳单元的中层面材料点,梁和管(pipe)单元的质心。
charLength(nblock):
特征元素长度,是基于几何平均数的•默认值或用户子程序VUCHARLENGTH中定义的用户特征元长度。
props(nprops):
用户使用的材料属性density(nblock):
中层结构的物质点的当前密度
rclSpinlnc(nblock,nshr):
在随转系统中定义的每个物质点处熠加的相对旋转矢量system.Definedas一whereWistheantisymmetricpartofthevelocity
gradient,L,andfl=R-RTStoredin3Das(32,13,21)andin2Das(21)_
tcmp()ld(nblock):
物质点开始增加时的温度。
dcfgradOld(nb]()ck,ndir+2*nshr):
在增量开始时,每个物质点出的变形梯度张量,在3d中形为(Fll,F22,F33,F12,F23,F31,F21,F32,F13),在2d中形为
(Fll,F22,F33,F12,F21)
strctchOld(nblock,ndir+nshr)
Stretchtensor,U,ateachmaterialpointatthebeginningoftheincrementdefinedfromthepolardecompositionofthedeformationgradientbyF=R・U.
ficld()ld(nblock,nficldv):
在增量开始时,每个物质点处用户定义场变量的值strcssOld(nblock,ndir+nshr):
在增量开始时,每个物质点处的应力张量:
stalcOld(nblock,nstatcv):
在增量开始时,每个物质点处的状态变量:
tcmpNcw(nbk)ck):
在增量结束时,每个物质点处的温度
dcfgradNcw(nbk)ck,ndir+2*nshr):
在增量结束吋,每个物质点出的变形梯度张量,在3d中形为(Fll,F22,F33,F12,F23,F31,F21,F32,F13),在2d中形为
(Fll,F22,F33,F12,F21)ficldNcw(nblock,nficldv):
在增量开始时,每个物质点处用户定5L长变量的值
AsasimpleexampleofthecodingofsubroutineVUMAT,considerthegeneralizedplanestraincaseforanelastic/plasticmaterialwithkinematichardening・Thebasicassumptionsanddefinitionsofthemodelareasfollows・
LetObethecurrentvalueofthestress,anddefineStobethedeviatoricpartofthestress・Thecenteroftheyieldsurfaceindeviatoricstressspaceisgivenbythetensor0(,whichhasinitialvaluesofzero.Thestressdifference,£,isthestressmeasuredfromthecenteroftheyieldsurfaceandisgivenby
£=S—a.
ThevonMisesyieldsurfaceisdefinedas
where^Oistheuniaxialequivalentyieldstress・ThevonMisesyieldsurfaceisacylinderindeviatoricstressspacewitharadiusof
Forthekinematichardeningmodel,/?
isaconstant・ThenormaltotheMisesyieldsurfacecanbewrittenas
Wedecomposethestrainrateintoanelasticandplasticpartusinganadditivedecomposition:
Theplasticpartofthestrainrateisgivenbyanormalitycondition
wherethescalarmultiplier'mustbedetermined・Ascalarmeasureofequivalentplasticstrainrateisdefinedby
ThestressrateisassumedtobepurelyduetotheelasticpartofthestrainrateandisexpressedintermsofHooke,slawby
a=Atrace(cf)I+\
whereAand^/^aretheLam^sconstantsforthematerial.
The
evolutionlawforCXisgivenas
a=
:
纭hq、
whereHistheslopeoftheuniaxialyieldstressversusplasticstraincurve・
Duringactiveplasticloadingthestressmustremainontheyieldsurface,sothat
\Q:
Q=1“
Theequivalentplasticstrainrateisrelatedto"by
Thekinematichardeningconstitutivemodelisintegratedinarateformasfollows・Atrialelasticstressiscomputedas
G盅*=^oid+Atrace(Ae)I+2“△氐
wherethesubscriptsoldandnewrefertothebeginningandendoftheincrement,respective!
y.Ifthetrialstressdoesnotexceedtheyield
stress,thenewstressissetequaltothetrialstress・Iftheyieldstressisexceeded,plasticityoccursintheincrement・Wethenwritetheincrementalanalogsoftherateequationsas
W=甬鬻-=毗-2口4Q、
2
anew=aold—可H
where
A7=7Ai.
Fromthedefinitionofthenormaltotheyieldsurfaceattheendoftheincrement,Q,
Thiscanbeexpandedusingtheincrementalequationsas
aoid++¥|(70Q=s伫倍一Aj2^Q..
TakingthetensorproductofthisequationwithQ,usingtheyieldconditionattheendoftheincrement,andsolvingfor“7:
△丁=2p(l+H/3“)
Thevalueforisusedintheincrementalequationstodetermine
^ncwyand「仁etr・
subroutinevumat(
CReadonly一
1nblock,ndir,nshr,nstatev,nfieldv,nprops,1anneal
2stepTime,totalTime,dt,cmname,coordMp,charLength,
3
props,density,straininc,relSpinlnc,
C
include'vaba_param・inc'
C
CJ2MisesPlasticitywithkinematichardeningforplane
Cstraincase・
CElasticpredictor,radialcorrectoralgorithm.
CThestatevariablesarestoredas:
stress
stress
stress
CAllarraysdimensionedby(*)arenotusedinthisalgorithmdimensionprops(nprops),density(nblock),
1coordMp(nblock,*),
2charLength(*),straininc(nblock,ndir+nshr),
3relSpinlnc(*),%eiiy)01d(*),
4stretchOld(*),defgrad01d(*),
5fieldOla11.'
6stateOld(nblock,nstatev),enerlnternOld(nblock),
7enerlnelasOld(nblock),tempNew(*),
8stretchNew(*),defgradNew(*),fieldNew(*),
9stressNew(nblock,ndir+nshr),stateNew(nblock,nstatev),
1enerlnternNew(nblock),enerlnelasNew(nblock)
C
character*80cmname
C
parameter(zero=0.,one=1・,two=2.、three=3.,
1third=one/three,half=・5,twoThirds=two/three,
2threeHalfs二1・5)
props
(1)
xnu
props
(2)
yield=props(3)
hard=props(4)
c
twomu=e/(one+xnu)thremu=threeHalfs*twomusixmu=three*twomu
*(e-twomu)/(sixmu-two*e)(twomu*(one+hard/thremu))
do100i=1,nblock
Ctheyieldstressandfacyldwillbezero.
dsmag=dsmag+(one-facyld)
c
CCalculatedincrementingamma(thisexplicitlyincludesthe
Ctimestep)
diff=dsmag一radius
dgamma=facyld*term*diff
c
CUpdateequivalentplasticstrain
deqps=coni*dgamma
stateNew(i,5)=state01d(i,5)+deqps
c
CDividedgammabydsmagsothatthedeviatoricstressesare
Cexplicitlyconvertedtotensorsofunitmagnitudeinthe
Cfollowingcalculations
dgamma=dgamma/dsmag
C
*
*
*
*
dsl
ds2
ds3
s4
CUpdatethespecificinternalenergy一stressPower=half*(
1(stress01d(i,l)+stressNew(i,1))*strainlnc(i,1)
1+(stress01d(i,2)+stressNew(i,2))*strainlnc(i,2)
1+(stress01d(i,3)+stressNew(i,3))*strainlnc(i,3)
1+two*(stress01d(i,4)+stressNew(i,4))*strainlnc(i,4))
c
enerlnternNew(i)=enerlnternOld(i)
1+stressPower/density(i)
C
CUpdatethedissipatedinelasticspecificenergy一plasticWorklnc=dgamma*half*(
1(stress01d(i,1)+stressNew(i,1))*dsl
1+(stress01d(i,2)+stressNew(i,2))*ds2
1+(stress01d(i,3)+stressNew(i,3))*ds3
1+two*(stress01d(i,4)+stressNew(i,4))*s4)
enerlnelasNew(i)=enerlnelasOld(i)
1+plasticWorklnc/density(i)
100continue
c
return
end
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