Hi all, I am a new ABAQUS VUMAT user. Recently I try to define the matreial behavior in stamping of sheet metal through the VUMAT. there are several questions about VUMAT.
（1）accoring to the ABAQUS user manual，for plane stress problem，stressnew(nblock,ndir+nshr), where ndir=3,nshr=1, but in fact,there are 5 stress commponents: sigma_{11},sigma_{22},sigma_{12},sigma_{23},sigma_{31}. how to match stressnew(*,i)(i=1,2,3,4) with the stress commponents: sigma_{11},sigma_{22},sigma_{12},sigma_{23},sigma_{31}?
in my view, the direct commponents：tressnew(*,1)=sigma_{11},stressnew(*,2)=sigma_{22},stressnew(*,3)=sigma_{33} and the indirect commponent：stressnew(*,4)=sigma_{12}. However,how about sigma_{23}and sigma_{31}?。
how to update the sigma_{23}and sigma_{31}?
Is it right to use the transverse shear stiffness update thesigma_{23}and sigma_{31} ? for example K*（epsilon_{23},epsilon_{31}） where K means the transverse shear stiffness？
（2）the following is a simple example of the coding of subroutine VUMAT in ABAQUS user manual. there are two questions:
where was STATE(*,i)(i=1,2,3,4,5) defined?andwhere was props(i)(i=1,2,3,4) defined？
subroutine vumat(
C Read only –
1 nblock, ndir, nshr, nstatev, nfieldv, nprops, lanneal,
2 stepTime, totalTime, dt, cmname, coordMp, charLength,
3 props, density, strainInc, relSpinInc,
4 tempOld, stretchOld, defgradOld, fieldOld,
3 stressOld, stateOld, enerInternOld, enerInelasOld,
6 tempNew, stretchNew, defgradNew, fieldNew,
C Write only –只写
5 stressNew, stateNew, enerInternNew, enerInelasNew )
C
include 'vaba_param.inc'
C
C J2 Mises Plasticity with kinematic hardening for plane
C strain case.
C Elastic predictor, radial corrector algorithm.
C
C The state variables are stored as:
C STATE(*,1) = back stress component 11 ***（where was STATE(*,1) defined?）
C STATE(*,2) = back stress component 22 ****（where was STATE(*,2) defined？）
C STATE(*,3) = back stress component 33 ****（where was STATE(*,3) defined？）
C STATE(*,4) = back stress component 12 ****（where was STATE(*,4) defined？）
C STATE(*,5) = equivalent plastic strain *****（where was STATE(*,5) defined？）
C
C
C All arrays dimensioned by (*) are not used in this algorithm
dimension props(nprops), density(nblock),
1 coordMp(nblock,*),
2 charLength(*), strainInc(nblock,ndir+nshr),
3 relSpinInc(*), tempOld(*),
4 stretchOld(*), defgradOld(*),
5 fieldOld(*), stressOld(nblock,ndir+nshr),
6 stateOld(nblock,nstatev), enerInternOld(nblock),
7 enerInelasOld(nblock), tempNew(*),
8 stretchNew(*), defgradNew(*), fieldNew(*),
9 stressNew(nblock,ndir+nshr), stateNew(nblock,nstatev),
1 enerInternNew(nblock), enerInelasNew(nblock)
C
character*80 cmname
C
parameter( zero = 0., one = 1., two = 2., three = 3.,
1 third = one/three, half = .5, twoThirds = two/three,
2 threeHalfs = 1.5 )
C
e = props(1)*****（where was props(1) defined？）
xnu = props(2)*****（where was props(2) defined？）
yield = props(3)*****（where was props(3) defined？）
hard = props(4)*****（where was props(4) defined？）
C
twomu = e / ( one + xnu )
thremu = threeHalfs * twomu
sixmu = three * twomu
alamda = twomu * ( e - twomu ) / ( sixmu - two * e )
term = one / ( twomu * ( one + hard/thremu ) )
con1 = sqrt( twoThirds )
C
do 100 i = 1,nblock
C
C Trial stress
trace = strainInc(i,1) + strainInc(i,2) + strainInc(i,3)
sig1 = stressOld(i,1) + alamda*trace + twomu*strainInc(i,1)
sig2 = stressOld(i,2) + alamda*trace + twomu*strainInc(i,2)
sig3 = stressOld(i,3) + alamda*trace + twomu*strainInc(i,3)
sig4 = stressOld(i,4) + twomu*strainInc(i,4)
C
C Trial stress measured from the back stress
s1 = sig1 - stateOld(i,1)
s2 = sig2 - stateOld(i,2)
s3 = sig3 - stateOld(i,3)
s4 = sig4 - stateOld(i,4)
C
C Deviatoric part of trial stress measured from the back stress
smean = third * ( s1 + s2 + s3 )
ds1 = s1 - smean
ds2 = s2 - smean
ds3 = s3 - smean
C
C Magnitude of the deviatoric trial stress difference
dsmag = sqrt( ds1**2 + ds2**2 + ds3**2 + 2.*s4**2 )
C
C Check for yield by determining the factor for plasticity,
C zero for elastic, one for yield
radius = con1 * yield
facyld = zero
if( dsmag - radius .ge. zero ) facyld = one
C
C Add a protective addition factor to prevent a divide by zero
C when dsmag is zero. If dsmag is zero, we will not have exceeded
C the yield stress and facyld will be zero.
dsmag = dsmag + ( one - facyld )
C
C Calculated increment in gamma (this explicitly includes the
C time step)
diff = dsmag - radius
dgamma = facyld * term * diff
C
C Update equivalent plastic strain
deqps = con1 * dgamma
stateNew(i,5) = stateOld(i,5) + deqps
C
C Divide dgamma by dsmag so that the deviatoric stresses are
C explicitly converted to tensors of unit magnitude in the
C following calculations
dgamma = dgamma / dsmag
C
C Update back stress
factor = hard * dgamma * twoThirds
stateNew(i,1) = stateOld(i,1) + factor * ds1
stateNew(i,2) = stateOld(i,2) + factor * ds2
stateNew(i,3) = stateOld(i,3) + factor * ds3
stateNew(i,4) = stateOld(i,4) + factor * s4
C
C Update the stress
factor = twomu * dgamma
stressNew(i,1) = sig1 - factor * ds1
stressNew(i,2) = sig2 - factor * ds2
stressNew(i,3) = sig3 - factor * ds3
stressNew(i,4) = sig4 - factor * s4
C
C Update the specific internal energy -
stressPower = half * (
1 ( stressOld(i,1)+stressNew(i,1) )*strainInc(i,1)
1 + ( stressOld(i,2)+stressNew(i,2) )*strainInc(i,2)
1 + ( stressOld(i,3)+stressNew(i,3) )*strainInc(i,3)
1 + two*( stressOld(i,4)+stressNew(i,4) )*strainInc(i,4) )
C
enerInternNew(i) = enerInternOld(i)
1 + stressPower / density(i)
C
C Update the dissipated inelastic specific energy -
smean = third * ( stressNew(i,1) + stressNew(i,2)
1 + stressNew(i,3) )
equivStress = sqrt( threeHalfs *
1 ( (stressNew(i,1)-smean)**2
1 + (stressNew(i,2)-smean)**2
1 + (stressNew(i,3)-smean)**2
1 + two * stressNew(i,4)**2 ) )
plasticWorkInc = equivStress * deqps
enerInelasNew(i) = enerInelasOld(i)
1 + plasticWorkInc / density(i)
100 continue
C
return
end