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VUMAT_dynamics.for
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cccccccccccccccccccccccccccccccccccccccccccccc
c
c Fan Zhang
c June.03.09
c Based on Hopperstad, Borvik, Berstad and Benallal, J Phys IV France 134(2006), 435
c
c Props
c E=props(1)
c nu=props(2)
c Q0=props(3)
c SRS0=props(4)
c H=props(5)
c alpha=props(6)
c td=props(7)
c HQ1=props(8)
c HQ2=props(9)
c HC1=props(10)
c HC2=props(11)
c pR0=props(12)
c Omega=props(13)
c state variables
c p0=stateOld(kb,1)
c ta0=stateOld(kb,2)
c
cccccccccccccccccccccccccccccccccccccccccccccc
subroutine vumat(
C Read only (unmodifiable)variables -
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,
5 stressOld, stateOld, enerInternOld, enerInelasOld,
6 tempNew, stretchNew, defgradNew, fieldNew,
C Write only (modifiable) variables -
7 stressNew, stateNew, enerInternNew, enerInelasNew )
C
include 'vaba_param.inc'
c IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
dimension props(nprops), density(nblock), coordMp(nblock,*),
1 charLength(nblock), strainInc(nblock,ndir+nshr),
2 relSpinInc(nblock,nshr), tempOld(nblock),
3 stretchOld(nblock,ndir+nshr),
4 defgradOld(nblock,ndir+nshr+nshr),
5 fieldOld(nblock,nfieldv), stressOld(nblock,ndir+nshr),
6 stateOld(nblock,nstatev), enerInternOld(nblock),
7 enerInelasOld(nblock), tempNew(nblock),
8 stretchNew(nblock,ndir+nshr),
8 defgradNew(nblock,ndir+nshr+nshr),
9 fieldNew(nblock,nfieldv),
1 stressNew(nblock,ndir+nshr), stateNew(nblock,nstatev),
2 enerInternNew(nblock), enerInelasNew(nblock)
C
character*80 cmname
C
c Local variables
INTEGER nds,kb
c
c
c
c WRITE(*,*) 'VUMAT',TotalTime !debug
nds=ndir+nshr
IF (TotalTime>0) THEN
DO kb=1,nblock
c WRITE(*,*) 'Normal,kb=',kb !debug
CALL TimeInc(nblock,nstatev,ndir,nshr,nds,kb,nprops,
1 props,stateOld,stateNew,stressOld,stressNew,strainInc,
2 dt,StepTime,TotalTime,EIOld,EInEOld,EINew,EInENew,density)
END DO
ELSE ! initialize
DO kb=1,nblock
c WRITE(*,*) 'Initial,kb=',kb !debug
CALL Initial(nblock,nstatev,ndir,nshr,nds,kb,nprops,
1 props,stateOld,stateNew,stressOld,stressNew,strainInc,
2 dt,StepTime,TotalTime,EIOld,EInEOld,EINew,EInENew,density)
END DO
END IF
RETURN
END
c
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! MAIN SUBROUTINES
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!
!***********************************************************************
!
! Time increment updates
!
SUBROUTINE TimeInc(nblock,nstatev,ndir,nshr,nds,kb,nprops,
1 props,stateOld,stateNew,stressOld,stressNew,strainInc,
2 dt,StepTime,TotalTime,EIOld,EInEOld,EINew,EInENew,dens)
c IMPLICIT NONE
include 'vaba_param.inc'
INTEGER,PARAMETER :: itermax=100
DOUBLE PRECISION,PARAMETER :: err=0.0001
INTEGER nblock,nstatev,ndir,nshr,nds,kb,nprops
c DOUBLE PRECISION stressOld,stressNew,stateOld,stateNew,strainInc,
c 1 props
c DOUBLE PRECISION EIOld,EInEOld,EINew,EInENew,dens,dt,
c 1 StepTime,TotalTime
DIMENSION stressOld(nblock,nds),stressNew(nblock,nds),
1 stateOld(nblock,nstatev),stateNew(nblock,nstatev),
2 strainInc(nblock,nds),props(nprops)
c Local variables
INTEGER i
DOUBLE PRECISION Str(nds),Snew(nds)
DOUBLE PRECISION E,nu,Q0,SRS0,H,alpha,td,HQ1,HQ2,HC1,HC2,pR0,Omega
DOUBLE PRECISION p0,ta0,p,ta,dp,pR,dpR
DOUBLE PRECISION QY,R,Qv,DQY,DR,DQv,RHS,DRHS,dta,tt
DOUBLE PRECISION G,twoG,lamda,means,Qtr,Qnew,ratio
c
c Parameters
E=props(1)
nu=props(2)
Q0=props(3)
SRS0=props(4)
H=props(5)
alpha=props(6)
td=props(7)
HQ1=props(8)
HQ2=props(9)
HC1=props(10)
HC2=props(11)
pR0=props(12)
Omega=props(13)
c state variables
p0=stateOld(kb,1)
ta0=stateOld(kb,2)
p=p0
ta=ta0
c
G=E/(2.D0*(1.D0+nu))
twoG=2.D0*G
lamda=twoG*nu/(1.D0-2.D0*nu)
means=strainInc(kb,1)+strainInc(kb,2)+strainInc(kb,3)
Str(1:nds)=stressOld(kb,1:nds)+twoG*strainInc(kb,1:ndir)
Str(1:ndir)=Str(1:ndir)+lamda*means
means=(Str(1)+Str(2)+Str(3))/3.D0
Str(1:ndir)=Str(1:ndir)-means
Qtr=DSQRT(1.5D0*(SUM(Str(1:ndir)*Str(1:ndir))
1 +3.D0*SUM(Str(ndir+1:nds)*Str(ndir+1:nds))))
c
QY=Q0+SRS0*H*(1.D0-DEXP(-(ta/td)**alpha))
R=HQ1*(1.D0-DEXP(-HC1*p))+HQ2*(1.D0-DEXP(-HC2*p))
pR=0.D0
Qv=0.D0
c WRITE(*,*) 'QY,R,Qtr' !debug
c WRITE(*,*) QY,R,Qtr !debug
IF (Qtr>QY+R) THEN !Plastic
! solve pR
DO i=1,itermax
p=p0+pR*dt
ta=(ta0+dt)/(1.D0+dt*pR/Omega)
c dta=-(ta0+dt)*dt/((1.D0+dt*pR/Omega)**2*Omega)
tt=(ta/td)**alpha
QY=Q0+SRS0*H*(1.D0-DEXP(-tt))
R=HQ1*(1.D0-DEXP(-HC1*p))+HQ2*(1.D0-DEXP(-HC2*p))
Qv=SRS0*DLOG(1.D0+pR/pR0)
DQY=-SRS0*H*DEXP(-tt)*tt*alpha*dt/(Omega+pR*dt)
DR1=HQ1*HC1*DEXP(-HC1*p)
DR2=HQ2*HC2*DEXP(-HC2*p)
DQv=SRS0/(pR0+pR)
RHS=Qtr-3.D0*G*pR*dt-QY-R-Qv
DRHS=dt*(-DQY+DR1+DR2+3.D0*G)+DQv
dpR=RHS/DRHS
pR=pR+dpR
IF (DABS(dpR)<DABS(err*pR)) EXIT
IF (i>itermax/2) THEN
WRITE(*,*) 'RHS,DRHS,pR'
WRITE(*,*) RHS,DRHS,pR
WRITE(*,*) 'DQY,DR1,DR2,DQv,dt'
WRITE(*,*) DQY,DR1,DR2,DQv,dt
END IF
END DO
IF (i>itermax) THEN
WRITE(*,*) '***ERRORZF: NOT CONV'
WRITE(*,*) 'Qtr,QY,R,Qv,p,pR'
WRITE(*,*) Qtr,QY,R,Qv,p,pR
WRITE(*,*) 'DQY,DR,DQv'
WRITE(*,*) DQY,DR,DQv
c CALL XIT
END IF
END IF
c
dp=pR*dt
p=p0+dp
Qnew=Qtr-3.D0*G*dp
ta=(ta0+dt)/(1.D0+dt*pR/Omega)
IF (Qnew>1.D-20) THEN
ratio=1.D0/(1.D0+3.D0*G*dp/Qnew)
ELSE
ratio=1.D0
END IF
Snew=Str*ratio
c Update stressNew and stateNew
stressNew(kb,1:ndir)=Snew(1:ndir)+means
stressNew(kb,ndir+1:nds)=Snew(ndir+1:nds)
stateNew(kb,1)=p
stateNew(kb,2)=ta
stateNew(kb,3)=R ! output debug
stateNew(kb,4)=Qv ! output debug
stateNew(kb,5)=QY-QR ! output debug
EINew=EIOld
1 +(0.5*SUM((stressOld(kb,1:ndir)+stressNew(kb,1:ndir))
2 *strainInc(kb,1:ndir))+
3 SUM((stressOld(kb,ndir+1:nds)+stressNew(kb,ndir+1:nds))
4 *strainInc(kb,ndir+1:nds)))/dens
EInENew=EInEOld+Qnew*dp/dens
c WRITE(*,*) '***Final QY,R,Qv,Qnew,pR' !debug
c WRITE(*,'(5F12.4)') QY,R,Qv,Qnew,pR !debug
c WRITE(*,*) 'i,RHS,pR,dpR' !debug
c WRITE(*,'(I4,3F12.4)') i,RHS,pR,dpR !debug
RETURN
END
!***********************************************************************
!
! Time increment updates
!
SUBROUTINE Initial(nblock,nstatev,ndir,nshr,nds,kb,nprops,
1 props,stateOld,stateNew,stressOld,stressNew,strainInc,
2 dt,StepTime,TotalTime,EIOld,EInEOld,EINew,EInENew,dens)
c IMPLICIT NONE
include 'vaba_param.inc'
INTEGER nblock,nstatev,ndir,nshr,nds,kb,nprops
c DOUBLE PRECISION stressOld,stressNew,stateOld,stateNew,strainInc,
c 1 props
c DOUBLE PRECISION EIOld,EInEOld,EINew,EInENew,dens,dt,
c 1 StepTime,TotalTime
DIMENSION stressOld(nblock,nds),stressNew(nblock,nds),
1 stateOld(nblock,nstatev),stateNew(nblock,nstatev),
2 strainInc(nblock,nds),props(nprops)
c Local variables
INTEGER i
DOUBLE PRECISION Str(nds),Snew(nds)
DOUBLE PRECISION E,nu,Q0,SRS0,H,alpha,td,HQ1,HQ2,HC1,HC2,pR0,Omega
DOUBLE PRECISION p0,ta0,p,ta,dp,pR,dpR
DOUBLE PRECISION QY,R,Qv,DQY,DR,DQv,RHS,DRHS,dta,tt
DOUBLE PRECISION G,twoG,lamda,means,Qtr,Qnew,ratio
c
c Parameters
E=props(1)
nu=props(2)
c state variables
G=E/(2.D0*(1.D0+nu))
twoG=2.D0*G
lamda=twoG*nu/(1.D0-2.D0*nu)
means=strainInc(kb,1)+strainInc(kb,2)+strainInc(kb,3)
Str(1:nds)=stressOld(kb,1:nds)+twoG*strainInc(kb,1:ndir)
Str(1:ndir)=Str(1:ndir)+lamda*means
means=(Str(1)+Str(2)+Str(3))/3.D0
Str(1:ndir)=Str(1:ndir)-means
Qtr=DSQRT(1.5D0*(SUM(Str(1:ndir)*Str(1:ndir))
1 +3.D0*SUM(Str(ndir+1:nds)*Str(ndir+1:nds))))
p0=0.D0
ta0=0.D0
c
pR=0.D0
dp=pR*dt
p=p0+dp
ta=0.D0
Qnew=Qtr-3.D0*G*dp
IF (Qnew>1.D-20) THEN
ratio=1.D0/(1.D0+3.D0*G*dp/Qnew)
ELSE
ratio=1.D0
END IF
Snew=Str*ratio
c Update stressNew and stateNew
stressNew(kb,1:ndir)=Snew(1:ndir)+means
stressNew(kb,ndir+1:nds)=Snew(ndir+1:nds)
stateNew(kb,1)=p
stateNew(kb,2)=ta
EINew=EIOld
1 +(0.5*SUM((stressOld(kb,1:ndir)+stressNew(kb,1:ndir))
2 *strainInc(kb,1:ndir))+
3 SUM((stressOld(kb,ndir+1:nds)+stressNew(kb,ndir+1:nds))
4 *strainInc(kb,ndir+1:nds)))/dens
EInENew=EInEOld+Qnew*dp/dens
RETURN
END