DAMASK_EICMD/trunk/crystallite.f90

399 lines
18 KiB
Fortran

!##############################################################
MODULE crystallite
!##############################################################
! *** Solution at single crystallite level ***
!
CONTAINS
!
!
!********************************************************************
! Calculates the stress for a single component
!********************************************************************
!***********************************************************************
!*** calculation of stress (P), stiffness (dPdF), ***
!*** and announcment of any ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
subroutine SingleCrystallite(&
msg,& ! return message
P,& ! first PK stress
dPdF,& ! consistent tangent
post_results,& ! plot results from constitutive model
Lp,& ! plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
state_new,& ! new state variable array
dt,& ! time increment
cp_en,& ! element number
ip,& ! integration point number
grain,& ! grain number
updateJaco,& ! update of Jacobian required
Temperature,& ! temperature of crystallite
Fg_new,& ! new global deformation gradient
Fg_old,& ! old global deformation gradient
Fp_old,& ! old plastic deformation gradient
state_old) ! old state variable array
!
use prec, only: pReal,pInt,pert_Fg,subStepMin, nCutback
use debug
use constitutive, only: constitutive_Nstatevars,constitutive_Nresults
use mesh, only: mesh_element
use math
implicit none
!
character(len=*) msg
logical updateJaco,error,success,guessNew
integer(pInt) cp_en,ip,grain,k,l, nCutbacks, maxCutbacks
real(pReal) Temperature
real(pReal) dt,dt_aim,subFrac,subStep,det
real(pReal), dimension(3,3) :: Lp,Lp_interpolated,Lp_pert,inv
real(pReal), dimension(3,3) :: Fg_old,Fg_current,Fg_new,Fg_pert,Fg_aim,deltaFg
real(pReal), dimension(3,3) :: Fp_old,Fp_current,Fp_new,Fp_pert
real(pReal), dimension(3,3) :: Fe_current,Fe_new,Fe_pert
real(pReal), dimension(3,3) :: P,P_pert
real(pReal), dimension(3,3,3,3) :: dPdF
real(pReal), dimension(constitutive_Nstatevars(grain,ip,cp_en)) :: state_old,state_new
real(pReal), dimension(constitutive_Nstatevars(grain,ip,cp_en)) :: state_current,state_bestguess,state_pert
real(pReal), dimension(constitutive_Nresults(grain,ip,cp_en)) :: post_results
deltaFg = Fg_new - Fg_old
subFrac = 0.0_pReal
subStep = 1.0_pReal
nCutbacks = 0_pInt
maxCutbacks = 0_pInt
Fg_current = Fg_old ! initialize to start of inc
Fp_current = Fp_old
call math_invert3x3(Fp_old,inv,det,error)
Fe_current = math_mul33x33(Fg_old,inv)
state_current = state_old
success = .false. ! pretend cutback
dt_aim = 0.0_pReal ! prevent initial Lp interpolation
! begin the cutback loop
do while (subStep > subStepMin) ! continue until finished or too much cut backing
if (success) then ! wind forward
Fg_current = Fg_aim
Fe_current = Fe_new
Fp_current = Fp_new
state_current = state_new
elseif (dt_aim > 0.0_pReal) then
call math_invert3x3(Fg_aim,inv,det,error) ! inv of Fg_aim
Lp_interpolated = 0.5_pReal*Lp + &
0.5_pReal*(math_I3 - math_mul33x33(Fp_current,&
math_mul33x33(inv,Fe_current)))/dt_aim ! interpolate Lp and L
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) 'Lp interpolation'
write (6,'(a,/,3(3(f12.7,x)/))') 'from',Lp(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'to',Lp_interpolated(1:3,:)
!$OMP END CRITICAL (write2out)
endif
Lp = Lp_interpolated
endif
Fg_aim = Fg_current + subStep*deltaFg ! aim for Fg
dt_aim = subStep*dt ! aim for dt
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) 'using these values'
write (6,'(a,/,3(4(f9.3,x)/))') 'state current / MPa',state_current/1e6_pReal
write (6,'(a,/,3(4(f9.3,x)/))') 'state new / MPa',state_new/1e6_pReal
write (6,'(a,/,3(3(f12.7,x)/))') 'Fe current',Fe_current(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'Fp current',Fp_current(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'Lp (old=new guess)',Lp(1:3,:)
write (6,'(a20,f,x,a2,x,f)') 'integrating from ',subFrac,'to',(subFrac+subStep)
!$OMP END CRITICAL (write2out)
endif
call TimeIntegration(msg,Lp,Fp_new,Fe_new,P,state_new,post_results, & ! def gradients and PK2 at end of time step
maxval(abs(Fg_aim-Fg_new)) < relevantStrain, & ! post results only if asking for final values
dt_aim,cp_en,ip,grain,Temperature,Fg_aim,Fp_current,state_current)
if (msg == 'ok') then
subFrac = subFrac + subStep
subStep = min(1.0_pReal-subFrac, subStep*2.0_pReal) ! accelerate
nCutbacks = 0_pInt ! reset cutback counter
success = .true. ! keep current Lp
else
nCutbacks = nCutbacks + 1 ! record additional cutback
maxCutbacks = max(nCutbacks,maxCutbacks)! remember maximum number of cutbacks
subStep = subStep / 2.0_pReal ! cut time step in half
success = .false. ! force Lp interpolation
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) '>>>>>>>>>>>>>>>>>>>> cutback <<<<<<<<<<<<<<<<<<<<<<'
!$OMP END CRITICAL (write2out)
endif
endif
enddo ! potential substepping
!
!$OMP CRITICAL (cutback)
debug_cutbackDistribution(min(nCutback,maxCutbacks)+1) = debug_cutbackDistribution(min(nCutback,maxCutbacks)+1)+1
!$OMP END CRITICAL (cutback)
!
if (msg /= 'ok') return ! solution not reached --> report back
if (updateJaco) then ! consistent tangent using
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) 'Jacobian calc'
!$OMP END CRITICAL (write2out)
endif
do k=1,3
do l=1,3
Fg_pert = Fg_new ! initialize perturbed Fg
Fg_pert(k,l) = Fg_pert(k,l) + pert_Fg ! perturb single component
Lp_pert = Lp
state_pert = state_new ! initial guess from end of time step
call TimeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,P_pert,state_pert,post_results,.false., & ! def gradients and PK2 at end of time step
dt_aim,cp_en,ip,grain,Temperature,Fg_pert,Fp_current,state_current)
if (msg == 'ok') &
dPdF(:,:,k,l) = (P_pert-P)/pert_Fg ! constructing tangent dP_ij/dFg_kl only if valid forward difference
! otherwise leave component unchanged
enddo
enddo
endif
!
msg = 'ok' ! a new consistent tangent was computed even if msg was not ok for all components
!
return
!
END SUBROUTINE
!
!***********************************************************************
!*** fully-implicit two-level time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
SUBROUTINE TimeIntegration(&
msg,& ! return message
Lpguess,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
P,& ! 1nd PK stress (taken as initial guess if /= 0)
state,& ! current microstructure at end of time inc (taken as guess if /= 0)
results,& ! post results from constitutive
wantsConstitutiveResults,& ! its flag
!
dt,& ! time increment
cp_en,& ! element number
ip,& ! integration point number
grain,& ! grain number
Temperature,& ! temperature
Fg_new,& ! new total def gradient
Fp_old,& ! former plastic def gradient
state_old) ! former microstructure
use prec
use debug
use mesh, only: mesh_element
use constitutive, only: constitutive_Nstatevars,&
constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent,&
constitutive_Nresults,constitutive_Microstructure,constitutive_post_results
use math
use IO
implicit none
!
character(len=*) msg
logical failed,wantsConstitutiveResults
integer(pInt) cp_en, ip, grain
integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n
real(pReal) dt, Temperature, det, p_hydro, leapfrog,maxleap
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2
real(pReal), dimension(6,6) :: C_66
real(pReal), dimension(3,3) :: Fg_new,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new
real(pReal), dimension(3,3) :: P,Tstar
real(pReal), dimension(3,3) :: Lp,Lpguess,Lpguess_old,Rinner,Rinner_old,A,B,BT,AB,BTA
real(pReal), dimension(3,3,3,3) :: C
real(pReal), dimension(constitutive_Nstatevars(grain, ip, cp_en)) :: state_old,state,ROuter
real(pReal), dimension(constitutive_Nresults(grain,ip,cp_en)) :: results
!
msg = 'ok' ! error-free so far
eye2 = math_identity2nd(9)
call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp_old
if (failed) then
msg = 'inversion Fp_old'
return
endif
A = math_mul33x33(transpose(invFp_old), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_old)))
!
if (all(state == 0.0_pReal)) state = state_old ! former state guessed, if none specified
iOuter = 0_pInt ! outer counter
!
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,'(a,/,3(3(f12.7,x)/))') 'Fg to be calculated',Fg_new
!$OMP END CRITICAL (write2out)
endif
!
Outer: do ! outer iteration: State
iOuter = iOuter+1
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,'(a,i3)') '---outer ',iOuter
write (6,'(a,/,3(4(f9.3,x)/))') 'state old / MPa',state_old/1e6_pReal
write (6,'(a,/,3(4(f9.3,x)/))') 'state / MPa',state/1e6_pReal
write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:)
!$OMP END CRITICAL (write2out)
endif
if (iOuter > nOuter) then
msg = 'limit Outer iteration'
!$OMP CRITICAL (out)
debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1
!$OMP END CRITICAL (out)
return
endif
call constitutive_Microstructure(state,Temperature,grain,ip,cp_en)
C_66 = constitutive_HomogenizedC(state, grain, ip, cp_en)
C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor
!
iInner = 0_pInt
leapfrog = 1.0_pReal ! correction as suggested by invdRdLp-step
maxleap = 1024.0_pReal ! preassign maximum acceleration level
!
Lpguess_old = Lpguess ! consider present Lpguess good
!
Inner: do ! inner iteration: Lp
iInner = iInner+1
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,'(a,i3)') 'inner ',iInner
if (wantsConstitutiveResults .and. iOuter == 1 .and. iInner < 3) then
write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:)
endif
!$OMP END CRITICAL (write2out)
endif
if (iInner > nInner) then ! too many loops required
Lpguess = Lpguess_old ! do not trust the last update but resort to former one
msg = 'limit Inner iteration'
!$OMP CRITICAL (in)
debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1
!$OMP END CRITICAL (in)
return
endif
!
B = math_i3 - dt*Lpguess
BT = transpose(B)
AB = math_mul33x33(A,B)
BTA = math_mul33x33(BT,A)
Tstar_v = 0.5_pReal*math_mul66x6(C_66,math_mandel33to6(math_mul33x33(BT,AB)-math_I3))
Tstar = math_Mandel6to33(Tstar_v)
p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal
forall(i=1:3) Tstar_v(i) = Tstar_v(i)-p_hydro ! subtract hydrostatic pressure
call constitutive_LpAndItsTangent(Lp,dLp, &
Tstar_v,state,Temperature,grain,ip,cp_en)
!
Rinner = Lpguess - Lp ! update current residuum
!
if (.not.(any(Rinner/=Rinner)) .and. & ! exclude any NaN in residuum
( (maxval(abs(Rinner)) < abstol_Inner) .or. & ! below abs tol .or.
( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and.
maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner & ! below rel tol
) &
) &
) &
exit Inner ! convergence
!
! check for acceleration/deceleration in Newton--Raphson correction
!
if (any(Rinner/=Rinner) .and. & ! NaN occured at regular speed
leapfrog == 1.0) then
Lpguess = Lpguess_old ! restore known good guess
msg = 'NaN present' ! croak for cutback
return
elseif (leapfrog > 1.0_pReal .and. & ! at fast pace ?
(sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum
sum(Rinner*Rinner_old) < 0.0_pReal) .or. & ! residuum changed sign (overshoot)
any(Rinner/=Rinner) ) then ! NaN
maxleap = 0.5_pReal * leapfrog ! limit next acceleration
leapfrog = 1.0_pReal ! grinding halt
else ! better residuum
dTdLp = 0.0_pReal ! calc dT/dLp
forall (i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
dTdLp(3*(i-1)+j,3*(k-1)+l) = dTdLp(3*(i-1)+j,3*(k-1)+l) + &
C(i,j,l,n)*AB(k,n)+C(i,j,m,l)*BTA(m,k)
dTdLp = -0.5_pReal*dt*dTdLp
dRdLp = eye2 - math_mul99x99(dLp,dTdLp) ! calc dR/dLp
invdRdLp = 0.0_pReal
call math_invert(9,dRdLp,invdRdLp,dummy,failed) ! invert dR/dLp --> dLp/dR
if (failed) then
msg = 'inversion dR/dLp'
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) msg
write (6,'(a,/,9(9(e9.3,x)/))') 'dRdLp', dRdLp(1:9,:)
write (6,'(a,/,3(4(f9.3,x)/))') 'state / MPa',state/1e6_pReal
write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:)
write (6,'(a,/,3(3(e12.7,x)/))') 'Lp',Lp(1:3,:)
write (6,'(a,/,6(f9.3,x))') 'Tstar / MPa',Tstar_v/1e6_pReal
!$OMP END CRITICAL (write2out)
endif
return
endif
!
Rinner_old = Rinner ! remember current residuum
Lpguess_old = Lpguess ! remember current Lp guess
if (iInner > 1 .and. leapfrog < maxleap) &
leapfrog = 2.0_pReal * leapfrog ! accelerate if ok
endif
!
Lpguess = Lpguess_old ! start from current guess
Rinner = Rinner_old ! use current residuum
forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess
Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l)
enddo Inner
!
!$OMP CRITICAL (in)
debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
!$OMP END CRITICAL (in)
ROuter = state - state_old - &
dt*constitutive_dotState(Tstar_v,state,Temperature,&
grain,ip,cp_en) ! residuum from evolution of microstructure
state = state - ROuter ! update of microstructure
if (iOuter==nOuter) then
!!$OMP CRITICAL (write2out)
write (6,*) 'Terminated outer loop at el,ip,grain',cp_en,ip,grain
!!$OMP END CRITICAL (write2out)
exit Outer
endif
if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer
enddo Outer
!
!$OMP CRITICAL (out)
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
!$OMP END CRITICAL (out)
invFp_new = math_mul33x33(invFp_old,B)
call math_invert3x3(invFp_new,Fp_new,det,failed)
if (failed) then
msg = 'inversion Fp_new^-1'
return
endif
!
if (wantsConstitutiveResults) then ! get the post_results upon request
results = 0.0_pReal
results = constitutive_post_results(Tstar_v,state,Temperature,dt,grain,ip,cp_en)
endif
!
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !!
forall (i=1:3) Tstar_v(i) = Tstar_v(i)+p_hydro ! add hydrostatic component back
Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
P = math_mul33x33(Fe_new,math_mul33x33(Tstar,transpose(invFp_new))) ! first PK stress
return
!
END SUBROUTINE
!
!
END MODULE
!##############################################################