restructured stress integration. Double loop for stress integration (Lp and stress) with cutback step in IntegrateStress is replaced by single loop for Lp without cutback. loop counter and limits are accordingly renamed and implemented

This commit is contained in:
Christoph Kords 2009-05-28 16:38:40 +00:00
parent aead2b8d20
commit ab57a40bab
5 changed files with 356 additions and 332 deletions

View File

@ -837,19 +837,19 @@ END FUNCTION
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '+------------------------------+'
write(6,*) '+ ERROR +'
write(6,*) '+ +'
write(6,*) msg
if (present(ext_msg)) write(6,*) ext_msg
write(6,'(a38)') '+------------------------------------+'
write(6,'(a38)') '+ error +'
write(6,'(a38)') '+ +'
write(6,*) '+ ',msg
if (present(ext_msg)) write(6,*) '+ ',ext_msg
if (present(e)) then
if (present(i) .and. present(g)) then
write(6,'(a10,x,i6,x,a2,x,i2,x,a5,x,i4)') 'at element',e,'IP',i,'grain',g
write(6,'(a12,x,i6,x,a2,x,i2,x,a5,x,i4,a2)') '+ at element',e,'IP',i,'grain',g,' +'
else
write(6,'(a2,x,i6)') 'at',e
write(6,'(a17,i6,a14)') '+ at ',e,' +'
endif
endif
write(6,*) '+------------------------------+'
write(6,'(a38)') '+------------------------------------+'
call debug_info()
call flush(6)
@ -877,29 +877,29 @@ END FUNCTION
character(len=80) msg
select case (ID)
case (650)
msg = 'Polar decomposition failed'
case (600)
msg = 'Crystallite responds elastically'
msg = '+ Crystallite responds elastically +'
case (650)
msg = '+ Polar decomposition failed +'
case default
msg = 'Unknown warning number...'
msg = '+ Unknown warning number... +'
end select
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '+------------------------------+'
write(6,*) '+ warning +'
write(6,*) '+ +'
write(6,*) msg
if (present(ext_msg)) write(6,*) ext_msg
write(6,'(a38)') '+------------------------------------+'
write(6,'(a38)') '+ warning +'
write(6,'(a38)') '+ +'
write(6,'(a38)') msg
if (present(ext_msg)) write(6,*) '+ ',ext_msg
if (present(e)) then
if (present(i) .and. present(g)) then
write(6,'(a10,x,i6,x,a2,x,i2,x,a5,x,i4)') 'at element',e,'IP',i,'grain',g
write(6,'(a12,x,i6,x,a2,x,i2,x,a5,x,i4,a2)') '+ at element',e,'IP',i,'grain',g,' +'
else
write(6,'(a2,x,i6)') 'at',e
write(6,'(a17,i6,a14)') '+ at ',e,' +'
endif
endif
write(6,*) '+------------------------------+'
write(6,'(a38)') '+------------------------------------+'
END SUBROUTINE

View File

@ -164,7 +164,7 @@ MODULE crystallite
return
end subroutine
endsubroutine
!********************************************************************
@ -176,7 +176,7 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
use debug
use IO, only: IO_warning
use math
use FEsolving, only: FEsolving_execElem, FEsolving_execIP
use FEsolving, only: FEsolving_execElem, FEsolving_execIP, theInc
use mesh, only: mesh_element
use material, only: homogenization_Ngrains
use constitutive
@ -185,18 +185,18 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
logical, intent(in) :: updateJaco
real(pReal), dimension(3,3) :: invFp,Fe_guess,PK2,myF,myFp,myFe,myLp,myP
real(pReal), dimension(constitutive_maxSizeState) :: myState
integer(pInt) crystallite_Niteration
integer(pInt) NiterationCrystallite, NiterationState
integer(pInt) g,i,e,k,l, myNgrains, mySizeState
logical converged
logical onTrack,converged
! ------ initialize to starting condition ------
write (6,*)
write (6,*) 'Crystallite request from Materialpoint'
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedF0 of 1 8 1',crystallite_partionedF0(1:3,:,1,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedFp0 of 1 8 1',crystallite_partionedFp0(1:3,:,1,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedF of 1 8 1',crystallite_partionedF(1:3,:,1,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedLp0 of 1 8 1',crystallite_partionedLp0(1:3,:,1,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedF0 of 1 1 1',crystallite_partionedF0(1:3,:,1,1,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedFp0 of 1 1 1',crystallite_partionedFp0(1:3,:,1,1,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedF of 1 1 1',crystallite_partionedF(1:3,:,1,1,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'crystallite_partionedLp0 of 1 1 1',crystallite_partionedLp0(1:3,:,1,1,1)
!$OMP PARALLEL DO
@ -222,19 +222,24 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
! ------ cutback loop ------
NiterationCrystallite = 0_pInt
do while (any(crystallite_subStep(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) > subStepMin)) ! cutback loop for crystallites
write(6,*)
write(6,*) 'entering cutback at crystallite_stress'
NiterationCrystallite = NiterationCrystallite + 1
if (any(.not. crystallite_converged(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) .and. & ! any non-converged grain
.not. crystallite_localConstitution(:,:,FEsolving_execELem(1):FEsolving_execElem(2))) ) & ! has non-local constitution?
crystallite_converged(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) = &
crystallite_converged(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) .and. &
crystallite_localConstitution(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) ! reset non-local grains' convergence status
crystallite_converged(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) .and. &
crystallite_localConstitution(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) ! reset non-local grains' convergence status
!$OMP PARALLEL DO
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1,myNgrains
debugger = (g == 1 .and. i == 1 .and. e == 1)
if (crystallite_converged(g,i,e)) then
crystallite_subFrac(g,i,e) = crystallite_subFrac(g,i,e) + crystallite_subStep(g,i,e)
crystallite_subStep(g,i,e) = min(1.0_pReal-crystallite_subFrac(g,i,e), 2.0_pReal * crystallite_subStep(g,i,e))
@ -244,11 +249,26 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
crystallite_subLp0(:,:,g,i,e) = crystallite_Lp(:,:,g,i,e) ! ...plastic velocity gradient
constitutive_subState0(g,i,e)%p = constitutive_state(g,i,e)%p ! ...microstructure
endif
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a21,f6.4,a28,f6.4,a35)') 'winding forward from ', &
crystallite_subFrac(g,i,e)-crystallite_subStep(g,i,e),' to new crystallite_subfrac ', &
crystallite_subFrac(g,i,e),' in crystallite_stressAndItsTangent'
write(6,*)
!$OMP END CRITICAL (write2out)
endif
else
crystallite_subStep(g,i,e) = 0.5_pReal * crystallite_subStep(g,i,e) ! cut step in half and restore...
crystallite_Fp(:,:,g,i,e) = crystallite_subFp0(:,:,g,i,e) ! ...plastic def grad
crystallite_Lp(:,:,g,i,e) = crystallite_subLp0(:,:,g,i,e) ! ...plastic velocity grad
constitutive_state(g,i,e)%p = constitutive_subState0(g,i,e)%p ! ...microstructure
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a78,f6.4)') 'cutback step in crystallite_stressAndItsTangent with new crystallite_subStep: ',&
crystallite_subStep(g,i,e)
write(6,*)
!$OMP END CRITICAL (write2out)
endif
endif
crystallite_onTrack(g,i,e) = crystallite_subStep(g,i,e) > subStepMin ! still on track or already done (beyond repair)
@ -257,6 +277,12 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
crystallite_subStep(g,i,e) * &
(crystallite_partionedF(:,:,g,i,e) - crystallite_partionedF0(:,:,g,i,e))
crystallite_subdt(g,i,e) = crystallite_subStep(g,i,e) * crystallite_dt(g,i,e)
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a36,e8.3)') 'current timestep crystallite_subdt: ',crystallite_subdt(g,i,e)
write(6,*)
!$OMP END CRITICAL (write2out)
endif
crystallite_converged(g,i,e) = .false. ! start out non-converged
endif
enddo
@ -266,14 +292,15 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
! ------ convergence loop for stress and state ------
crystallite_Niteration = 0_pInt
NiterationState = 0_pInt
if (debugger) write(6,*) 'state integration started'
do while (any( crystallite_requested(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) &
.and. crystallite_onTrack(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) &
.and. .not. crystallite_converged(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) &
) .and. crystallite_Niteration < nCryst) ! convergence loop for crystallite
crystallite_Niteration = crystallite_Niteration + 1
) .and. NiterationState < nState) ! convergence loop for crystallite
NiterationState = NiterationState + 1
! --+>> stress integration <<+--
!
@ -283,6 +310,8 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
! to account for substepping within _integrateStress
! results in crystallite_Fp,.._Lp
if (debugger) write(6,*) 'stress integration started'
!$OMP PARALLEL DO
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
@ -296,8 +325,11 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
enddo
!$OMP END PARALLEL DO
write(6,'(i2,x,a10,x,16(l,x))') crystallite_Niteration,'cryst_onT',crystallite_onTrack
write (6,'(a,/,3(3(f12.7,x)/))') 'Lp of 1 8 1',crystallite_Lp(1:3,:,1,8,1)
if (crystallite_requested(1,1,1) .and. crystallite_onTrack(1,1,1)) then
write(6,*) 'stress integration converged'
write(6,'(a,/,3(3(e15.7,x)/))') 'P of 1 1 1',crystallite_P(:,:,1,1,1)
write(6,'(a,/,3(3(f12.7,x)/))') 'Lp of 1 1 1',crystallite_Lp(:,:,1,1,1)
endif
! --+>> state integration <<+--
!
@ -315,9 +347,12 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
crystallite_converged(g,i,e) = crystallite_updateState(g,i,e)
if (crystallite_converged(g,i,e)) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(crystallite_Niteration) = &
debug_StateLoopDistribution(crystallite_Niteration) + 1
debug_StateLoopDistribution(NiterationState) = debug_StateLoopDistribution(NiterationState) + 1
!$OMP END CRITICAL (distributionState)
!$OMP CRITICAL (distributionCrystallite)
debug_CrystalliteLoopDistribution(NiterationCrystallite) = &
debug_CrystalliteLoopDistribution(NiterationCrystallite) + 1
!$OMP END CRITICAL (distributionCrystallite)
endif
endif
enddo
@ -325,15 +360,14 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
enddo
!$OMP END PARALLEL DO
if (crystallite_requested(1,1,1) .and. crystallite_onTrack(1,1,1) .and. crystallite_converged(1,1,1)) then
write(6,*) 'state integration converged'
write(6,'(a20,e8.3)') 'state of 1 1 1: ', constitutive_state(1,1,1)%p(1)
write(6,*)
endif
enddo ! crystallite convergence loop
write(6,*)
write(6,'(a10,x,16(f6.4,x))') 'cryst_frac',crystallite_subFrac
write(6,'(a10,x,16(f6.4,x))') 'cryst_step',crystallite_subStep
write(6,'(a10,x,16(l,x))') 'cryst_req',crystallite_requested
write(6,'(a10,x,16(l,x))') 'cryst_onT',crystallite_onTrack
write(6,'(a10,x,16(l,x))') 'cryst_cvg',crystallite_converged
write(6,'(a10,x,16(e8.3,x))') 'cryst_dt',crystallite_subdt
enddo ! cutback loop
@ -368,9 +402,9 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
if(updateJaco) then ! Jacobian required
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) 'Jacobian calc'
write(6,'(a10,x,16(f6.4,x))') 'cryst_dt',crystallite_subdt
write (6,*) 'Stiffness calculation started'
!$OMP CRITICAL (write2out)
! write(6,'(a10,x,16(f6.4,x))') 'cryst_dt',crystallite_subdt
!$OMP END CRITICAL (write2out)
endif
@ -387,30 +421,63 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
myFe = crystallite_Fe(:,:,g,i,e)
myLp = crystallite_Lp(:,:,g,i,e)
myP = crystallite_P(:,:,g,i,e)
if (debugger) then
write (6,*) '#############'
write (6,*) 'central solution'
write (6,*) '#############'
write (6,'(a,/,3(3(f12.4,x)/))') ' P of 1 1 1',myP(1:3,:)/1e6
write (6,'(a,/,3(3(f12.8,x)/))') ' Fp of 1 1 1',myFp(1:3,:)
write (6,'(a,/,3(3(f12.8,x)/))') ' Lp of 1 1 1',myLp(1:3,:)
write (6,'(a,/,f12.4)') 'state of 1 1 1',myState/1e6
endif
do k = 1,3 ! perturbation...
do l = 1,3 ! ...components
crystallite_subF(:,:,g,i,e) = myF ! initialize perturbed F to match converged
crystallite_subF(k,l,g,i,e) = crystallite_subF(k,l,g,i,e) + pert_Fg ! perturb single component
converged = .false.
crystallite_Niteration = 0_pInt
do while(.not. converged .and. crystallite_Niteration < nCryst) ! keep cycling until done (potentially non-converged)
crystallite_Niteration = crystallite_Niteration + 1_pInt
if(crystallite_integrateStress(g,i,e)) & ! stress of perturbed situation (overwrites_P,_Tstar_v,_Fp,_Lp,_Fe)
converged = crystallite_updateState(g,i,e)
end do
if (converged) & ! converged state warrants stiffness update
crystallite_dPdF(:,:,k,l,g,i,e) =(crystallite_p(:,:,g,i,e) - myP)/pert_Fg ! tangent dP_ij/dFg_kl
do l = 1,3 ! ...components
crystallite_subF(:,:,g,i,e) = myF ! initialize perturbed F to match converged
crystallite_subF(k,l,g,i,e) = crystallite_subF(k,l,g,i,e) + pert_Fg ! perturb single component
onTrack = .true.
converged = .false.
NiterationState = 0_pInt
if (debugger) then
write (6,*) '============='
write (6,'(i1,x,i1)') k,l
write (6,*) '============='
write (6,'(a,/,3(3(f12.6,x)/))') 'pertF of 1 1 1',crystallite_subF(1:3,:,g,i,e)
endif
do while(.not. converged .and. onTrack .and. NiterationState < nState) ! keep cycling until done (potentially non-converged)
NiterationState = NiterationState + 1_pInt
if (debugger) write (6,'(a4,x,i6)') 'loop',NiterationState
onTrack = crystallite_integrateStress(g,i,e) ! stress of perturbed situation (overwrites _P,_Tstar_v,_Fp,_Lp,_Fe)
if(onTrack) converged = crystallite_updateState(g,i,e)
if (debugger) then
write (6,*) '-------------'
write (6,'(l,x,l)') onTrack,converged
write (6,'(a,/,3(3(f12.4,x)/))') 'pertP of 1 1 1',crystallite_P(1:3,:,g,i,e)/1e6
write (6,'(a,/,3(3(f12.4,x)/))') 'DP of 1 1 1',(crystallite_P(1:3,:,g,i,e)-myP(1:3,:))/1e6
write (6,'(a,/,f12.4)') 'state of 1 1 1',constitutive_state(g,i,e)%p/1e6
write (6,'(a,/,f12.4)') 'Dstate of 1 1 1',(constitutive_state(g,i,e)%p-myState)/1e6
endif
enddo
if (converged) & ! converged state warrants stiffness update
crystallite_dPdF(:,:,k,l,g,i,e) = (crystallite_P(:,:,g,i,e) - myP)/pert_Fg ! tangent dP_ij/dFg_kl
constitutive_state(g,i,e)%p = myState ! restore unperturbed, converged state...
crystallite_Fp(:,:,g,i,e) = myFp ! ... and kinematics
crystallite_Fe(:,:,g,i,e) = myFe
crystallite_Lp(:,:,g,i,e) = myLp
crystallite_P(:,:,g,i,e) = myP
!$OMP CRITICAL (out)
debug_StiffnessStateLoopDistribution(crystallite_Niteration) = &
debug_StiffnessstateLoopDistribution(crystallite_Niteration) + 1
debug_StiffnessStateLoopDistribution(NiterationState) = &
debug_StiffnessstateLoopDistribution(NiterationState) + 1
!$OMP END CRITICAL (out)
end do
end do
enddo
enddo
constitutive_state(g,i,e)%p = myState ! restore unperturbed, converged state...
crystallite_Fp(:,:,g,i,e) = myFp ! ... and kinematics
crystallite_Fe(:,:,g,i,e) = myFe
crystallite_Lp(:,:,g,i,e) = myLp
crystallite_P(:,:,g,i,e) = myP
if (e == 1 .and. i == 1 .and. g == 1) then
write (6,'(a,/,9(9(f12.4,x)/))') 'dPdF/GPa',crystallite_dPdF(:,:,:,:,1,1,1)/1e9
endif
else ! grain has not converged
crystallite_dPdF(:,:,:,:,g,i,e) = crystallite_fallbackdPdF(:,:,:,:,g,i,e) ! use fallback
endif
@ -420,7 +487,7 @@ subroutine crystallite_stressAndItsTangent(updateJaco)
!$OMP END PARALLEL DO
endif
end subroutine
endsubroutine
@ -434,9 +501,13 @@ end subroutine
i,& ! integration point number
e & ! element number
)
use prec, only: pReal,pInt,rTol_crystalliteState
use constitutive, only: constitutive_dotState,constitutive_sizeDotState,&
constitutive_subState0,constitutive_state
use prec, only: pReal, &
pInt, &
rTol_crystalliteState
use constitutive, only: constitutive_dotState, &
constitutive_sizeDotState, &
constitutive_subState0, &
constitutive_state
use debug
logical crystallite_updateState
@ -455,18 +526,21 @@ end subroutine
debug_cumDotStateCalls = debug_cumDotStateCalls + 1_pInt
debug_cumDotStateTicks = debug_cumDotStateTicks + tock-tick
if (tock < tick) debug_cumDotStateTicks = debug_cumDotStateTicks + maxticks
if (any(constitutive_state(g,i,e)%p(1:mySize)/=constitutive_state(g,i,e)%p(1:mySize))) return ! NaN occured?
constitutive_state(g,i,e)%p(1:mySize) = constitutive_state(g,i,e)%p(1:mySize) - residuum ! update of microstructure
crystallite_updateState = maxval(abs(residuum/constitutive_state(g,i,e)%p(1:mySize)),&
constitutive_state(g,i,e)%p(1:mySize) /= 0.0_pReal) < rTol_crystalliteState
return
end function
endfunction
!***********************************************************************
!*** calculation of stress (P), stiffness (dPdF), ***
!*** and announcement of any ***
!*** calculation of stress (P) with time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
function crystallite_integrateStress(&
@ -474,266 +548,226 @@ end subroutine
i,& ! integration point number
e) ! element number
use prec, only: pReal,pInt,subStepMin
use debug
use constitutive, only: constitutive_state,constitutive_subState0,constitutive_sizeState
use math
implicit none
integer(pInt), intent(in) :: e,i,g
integer(pInt) mySize, Niteration
real(pReal) dt_aim,subFrac,subStep,det
real(pReal), dimension(3,3) :: inv
real(pReal), dimension(3,3) :: Fg_current,Fg_aim,deltaFg
real(pReal), dimension(3,3) :: Fp_current,Fp_new
real(pReal), dimension(3,3) :: Fe_current,Fe_new
real(pReal), dimension(constitutive_sizeState(g,i,e)) :: interpolatedState
logical crystallite_integrateStress ! still on track?
mySize = constitutive_sizeState(g,i,e)
deltaFg = crystallite_subF(:,:,g,i,e) - crystallite_subF0(:,:,g,i,e)
Fg_current = crystallite_subF0(:,:,g,i,e) ! initialize to start of inc
Fp_current = crystallite_subFp0(:,:,g,i,e)
Fe_current = math_mul33x33(Fg_current,math_inv3x3(Fp_current))
subFrac = 0.0_pReal
subStep = 1.0_pReal
Niteration = 0_pInt
crystallite_integrateStress = .false. ! be pessimisitc
! begin the cutback loop
do while (subStep > subStepMin) ! continue until finished or too much cut backing
Niteration = Niteration + 1
Fg_aim = Fg_current + subStep*deltaFg ! aim for Fg
dt_aim = subStep*crystallite_subdt(g,i,e) ! aim for dt
debugger = (g == 1 .and. i == 8 .and. e == 1)
call TimeIntegration(crystallite_integrateStress,&
crystallite_Lp(:,:,g,i,e),crystallite_Fp(:,:,g,i,e),crystallite_Fe(:,:,g,i,e),&
crystallite_Tstar_v(:,g,i,e),crystallite_P(:,:,g,i,e), &
Fg_aim,Fp_current,crystallite_Temperature(g,i,e),&
( subFrac+subStep)*constitutive_state(g,i,e)%p(1:mySize) + &
(1.0_pReal-subFrac-subStep)*constitutive_subState0(g,i,e)%p(1:mySize),& ! interpolated state
dt_aim,g,i,e)
if (crystallite_integrateStress) then ! happy with time integration
if (e == 1 .and. i == 8 .and. g == 1) then
write(6,*) '*** winding forward in IntegrateStress ***'
write(6,*) subFrac, subFrac+subStep
write (6,'(a,/,3(3(f12.7,x)/))') 'Lp of 1 8 1',crystallite_Lp(1:3,:,1,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'Fp of 1 8 1',crystallite_Fp(1:3,:,1,8,1)
endif
Fg_current = Fg_aim ! wind forward
Fe_current = crystallite_Fe(:,:,g,i,e)
Fp_current = crystallite_Fp(:,:,g,i,e)
subFrac = subFrac + subStep
subStep = min(1.0_pReal-subFrac, subStep*2.0_pReal) ! accelerate
else ! time integration encountered trouble
subStep = 0.5_pReal * subStep ! cut time step in half
crystallite_Lp(:,:,g,i,e) = 0.5_pReal*(crystallite_Lp(:,:,g,i,e) + & ! interpolate Lp and L
(math_I3 - math_mul33x33(Fp_current,&
math_mul33x33(math_inv3x3(Fg_aim),Fe_current)))/dt_aim)
endif
enddo ! potential substepping
!$OMP CRITICAL (distributionStress)
debug_StressLoopDistribution(Niteration) = debug_StressLoopDistribution(Niteration) + 1
!$OMP END CRITICAL (distributionStress)
return ! with final happyness
end function
!***********************************************************************
!*** fully-implicit two-level time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
subroutine TimeIntegration(&
happy,& ! return status
Lpguess,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
Tstar_v,& ! Stress vector
P,& ! 1st PK stress (taken as initial guess if /= 0)
!
Fg_new,& ! new total def gradient
Fp_old,& ! former plastic def gradient
Temperature,& ! temperature
state,& ! microstructural state
dt,& ! time increment
grain,& ! grain number
ip,& ! integration point number
cp_en & ! element number
)
use prec
use debug
use mesh, only: mesh_element
use constitutive, only: constitutive_microstructure,constitutive_homogenizedC,constitutive_LpAndItsTangent,&
constitutive_sizeState
use constitutive, only: constitutive_microstructure, &
constitutive_homogenizedC, &
constitutive_LpAndItsTangent
use math
use IO
implicit none
logical, intent(out) :: happy
real(pReal), dimension(3,3), intent(inout) :: Lpguess
real(pReal), dimension(3,3), intent(out) :: Fp_new,Fe_new,P
real(pReal), dimension(6), intent(out) :: Tstar_v
real(pReal), dimension(3,3), intent(in) :: Fg_new,Fp_old
real(pReal), intent(in) :: Temperature,dt
integer(pInt), intent(in) :: cp_en, ip, grain
real(pReal), dimension(constitutive_sizeState(grain,ip,cp_en)), intent(in) :: state
logical error
integer(pInt) Niteration,dummy, i,j,k,l,m,n
integer(pLongInt) tick,tock,tickrate,maxticks
real(pReal) p_hydro,det, leapfrog,maxleap
real(pReal), dimension(3,3,3,3) :: C
real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2
real(pReal), dimension(6,6) :: C_66
real(pReal), dimension(3,3) :: invFp_new,invFp_old,Lp,Lpguess_old,Rinner,Rinner_old,A,B,BT,AB,BTA
happy = .false. ! be pessimistic
eye2 = math_identity2nd(9)
invFp_old = math_inv3x3(Fp_old) ! inversion of Fp_old
if (all(invFp_old == 0.0_pReal)) return ! failed
! write (6,'(a,/,3(3(f12.7,x)/))') 'Fp old',Fp_old
! write (6,'(a,/,3(3(f12.7,x)/))') 'Fp old inv',invFp_old
!*** input variables ***!
integer(pInt), intent(in) :: e, & ! element index
i, & ! integration point index
g ! grain index
A = math_mul33x33(transpose(invFp_old), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_old)))
!*** output variables ***!
logical crystallite_integrateStress ! flag indicating if integration suceeded
!*** internal variables ***!
real(pReal), dimension(3,3) :: Fg_current, & ! deformation gradient at start of timestep
Fg_new, & ! deformation gradient at end of timestep
Fp_current, & ! plastic deformation gradient at start of timestep
Fp_new, & ! plastic deformation gradient at end of timestep
Fe_current, & ! elastic deformation gradient at start of timestep
Fe_new, & ! elastic deformation gradient at end of timestep
invFp_new, & ! inverse of Fp_new
invFp_current, & ! inverse of Fp_current
Lpguess, & ! current guess for plastic velocity gradient
Lpguess_old, & ! known last good guess for plastic velocity gradient
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
residuum, & ! current residuum of plastic velocity gradient
residuum_old, & ! last residuum of plastic velocity gradient
A, &
B, &
BT, &
AB, &
BTA
real(pReal), dimension(6) :: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
real(pReal), dimension(9,9) :: dLp_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
dTdLp, & ! partial derivative of 2nd Piola-Kirchhoff stress
dRdLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
invdRdLp ! inverse of dRdLp
real(pReal), dimension(3,3,3,3) :: C ! 4th rank elasticity tensor
real(pReal), dimension(6,6) :: C_66 ! simplified 2nd rank elasticity tensor
real(pReal) p_hydro, & ! volumetric part of 2nd Piola-Kirchhoff Stress
det, & ! determinant
leapfrog, & ! acceleration factor for Newton-Raphson scheme
maxleap ! maximum acceleration factor
logical error ! flag indicating an error
integer(pInt) NiterationStress, & ! number of stress integrations
dummy, &
h, &
j, &
k, &
l, &
m, &
n
integer(pLongInt) tick, &
tock, &
tickrate, &
maxticks
!$OMP CRITICAL (write2out)
! if (debugger) write (6,'(a,/,3(3(f12.7,x)/))') 'Fg to be calculated',Fg_new
!$OMP END CRITICAL (write2out)
! be pessimistic
crystallite_integrateStress = .false.
call constitutive_microstructure(Temperature,grain,ip,cp_en)
C_66 = constitutive_homogenizedC(grain,ip,cp_en)
C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor
! feed local variables
Fg_current = crystallite_subF0(:,:,g,i,e)
Fg_new = crystallite_subF(:,:,g,i,e)
Fp_current = crystallite_subFp0(:,:,g,i,e)
Fe_current = math_mul33x33(Fg_current,math_inv3x3(Fp_current))
Tstar_v = crystallite_Tstar_v(:,g,i,e)
Lpguess_old = crystallite_Lp(:,:,g,i,e) ! consider present Lp good (i.e. worth remembering) ...
Lpguess = crystallite_Lp(:,:,g,i,e) ! ... and take it as first guess
! inversion of Fp_current...
invFp_current = math_inv3x3(Fp_current)
if (all(invFp_current == 0.0_pReal)) then ! ... failed?
if (debugger) write(6,*) '::: integrateStress failed on invFp_current inversion'
return
endif
A = math_mul33x33(transpose(invFp_current), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_current)))
! update microstructure
call constitutive_microstructure(crystallite_Temperature(g,i,e),g,i,e)
! get elasticity tensor
C_66 = constitutive_homogenizedC(g,i,e)
C = math_Mandel66to3333(C_66)
! start LpLoop with no acceleration
NiterationStress = 0_pInt
leapfrog = 1.0_pReal
maxleap = 1024.0_pReal
Niteration = 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 (i.e. worth remembering)
Inner: do ! inner iteration: Lp
Niteration = Niteration + 1
if (Niteration > nLp) then ! too many loops required
Lpguess = Lpguess_old ! do not trust the last update but resort to former one
LpLoop: do
! increase loop counter
NiterationStress = NiterationStress + 1
! too many loops required ?
if (NiterationStress > nStress) then
if (debugger) write(6,*) '::: integrateStress exceeded nStress loopcount'
return
endif
! write(6,*) 'iteration',Niteration
! write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess
B = math_i3 - dt*Lpguess
B = math_i3 - crystallite_subdt(g,i,e)*Lpguess
BT = transpose(B)
AB = math_mul33x33(A,B)
BTA = math_mul33x33(BT,A)
! calculate 2nd Piola-Kirchhoff stress tensor
Tstar_v = 0.5_pReal*math_mul66x6(C_66,math_mandel33to6(math_mul33x33(BT,AB)-math_I3))
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
! write (6,'(a,/,6(f12.7,x))') 'Tstar',Tstar_v
p_hydro = sum(Tstar_v(1:3))/3.0_pReal
forall(n=1:3) Tstar_v(n) = Tstar_v(n) - p_hydro ! get deviatoric stress tensor
! calculate plastic velocity gradient and its tangent according to constitutive law
call system_clock(count=tick,count_rate=tickrate,count_max=maxticks)
call constitutive_LpAndItsTangent(Lp,dLp, Tstar_v,Temperature,grain,ip,cp_en)
call constitutive_LpAndItsTangent(Lp_constitutive,dLp_constitutive,Tstar_v,crystallite_Temperature(g,i,e),g,i,e)
call system_clock(count=tock,count_rate=tickrate,count_max=maxticks)
debug_cumLpCalls = debug_cumLpCalls + 1_pInt
debug_cumLpTicks = debug_cumLpTicks + tock-tick
if (tock < tick) debug_cumLpTicks = debug_cumLpTicks + maxticks
Rinner = Lpguess - Lp ! update current residuum
! write (6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp
! write (6,'(a,/,3(3(f12.7,x)/))') 'Residuum',Rinner
! update current residuum
residuum = Lpguess - Lp_constitutive
if (.not.(any(Rinner/=Rinner)) .and. & ! exclude any NaN in residuum
( ( maxval(abs(Rinner)) < aTol_crystalliteStress) .or. & ! below abs tol .or.
( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and.
maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < rTol_crystalliteStress & ! below rel tol
! Check for convergence of loop
if (.not.(any(residuum/=residuum)) .and. & ! exclude any NaN in residuum
( maxval(abs(residuum)) < aTol_crystalliteStress .or. & ! below absolute tolerance .or.
( any(abs(crystallite_subdt(g,i,e)*Lpguess) > relevantStrain) .and. & ! worth checking? .and.
maxval(abs(residuum/Lpguess), abs(crystallite_subdt(g,i,e)*Lpguess) > relevantStrain) < rTol_crystalliteStress & ! below relative tolerance
) &
) &
) &
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 and croak for cutback
) &
) &
exit LpLoop
! NaN occured at regular speed?
if (any(residuum/=residuum) .and. leapfrog == 1.0) then
if (debugger) write(6,*) '::: integrateStress encountered NaN at iteration', NiterationStress
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
! something went wrong at accelerated speed?
elseif (leapfrog > 1.0_pReal .and. & ! at fast pace .and.
( sum(residuum*residuum) > sum(residuum_old*residuum_old) .or. & ! worse residuum .or.
sum(residuum*residuum_old) < 0.0_pReal .or. & ! residuum changed sign (overshoot) .or.
any(residuum/=residuum) & ! NaN occured
) &
) then
maxleap = 0.5_pReal * leapfrog ! limit next acceleration
leapfrog = 1.0_pReal ! grinding halt
! restore old residuum and Lp
Lpguess = Lpguess_old
residuum = residuum_old
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
! residuum got better
else
! calculate Jacobian for correction term
dTdLp = 0.0_pReal
forall (h=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
dTdLp(3*(h-1)+j,3*(k-1)+l) = dTdLp(3*(h-1)+j,3*(k-1)+l) + &
C(h,j,l,n)*AB(k,n)+C(h,j,m,l)*BTA(m,k)
dTdLp = -0.5_pReal*crystallite_subdt(g,i,e)*dTdLp
dRdLp = math_identity2nd(9) - math_mul99x99(dLp_constitutive,dTdLp)
invdRdLp = 0.0_pReal
call math_invert(9,dRdLp,invdRdLp,dummy,error) ! invert dR/dLp --> dLp/dR
call math_invert(9,dRdLp,invdRdLp,dummy,error) ! invert dR/dLp --> dLp/dR
if (error) then
if (debugger) then
!$OMP CRITICAL (write2out)
write (6,*) 'inversion dR/dLp failed',grain,ip,cp_en
! write (6,'(a,/,9(9(e9.3,x)/))') 'dRdLp', dRdLp(1:9,:)
! write (6,'(a,/,3(4(f9.3,x)/))') 'state_new / 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
!$OMP END CRITICAL (write2out)
endif
if (debugger) write(6,*) '::: integrateStress failed on dR/dLp inversion at iteration', NiterationStress
return
endif
Rinner_old = Rinner ! remember current residuum
Lpguess_old = Lpguess ! remember current Lp guess
if (Niteration > 1 .and. leapfrog < maxleap) leapfrog = 2.0_pReal * leapfrog ! accelerate if ok
! remember current residuum and Lpguess
residuum_old = residuum
Lpguess_old = Lpguess
! accelerate?
if (NiterationStress > 1 .and. leapfrog < maxleap) leapfrog = 2.0_pReal * leapfrog
endif
Lpguess = Lpguess_old ! start from current guess
Rinner = Rinner_old ! use current residuum
forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess
Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l)
enddo Inner
! leapfrog to updated Lp
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
Lpguess(k,l) = Lpguess(k,l) - leapfrog*invdRdLp(3*(k-1)+l,3*(m-1)+n)*residuum(m,n)
enddo LpLoop
!$OMP CRITICAL (distributionLp)
debug_LpLoopDistribution(Niteration) = debug_LpLoopDistribution(Niteration) + 1
!$OMP END CRITICAL (distributionLp)
invFp_new = math_mul33x33(invFp_old,B)
if (debugger) then
write (6,'(a,x,f10.6,/,3(3(f12.7,x)/))') 'Lp(guess)',dt,Lpguess(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'invFp_old',invFp_old(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'B',B(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'invFp_new',invFp_new(1:3,:)
endif
! calculate new plastic and elastic deformation gradient
invFp_new = math_mul33x33(invFp_current,B)
invFp_new = invFp_new/math_det3x3(invFp_new)**(1.0_pReal/3.0_pReal) ! regularize by det
call math_invert3x3(invFp_new,Fp_new,det,error)
if (debugger) then
write (6,'(a,/,3(3(f12.7,x)/))') 'invFp_new',invFp_new(1:3,:)
write (6,'(a,/,3(3(f12.7,x)/))') 'Fp_new',Fp_new(1:3,:)
write (6,'(a,x,l,x,a,f10.6)') 'with inversion error:',error,'and determinant:',det
if (error) then
if (debugger) write(6,*) '::: integrateStress failed on invFp_new inversion at iteration', NiterationStress
return
endif
if (error) return ! inversion failed
Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !!
forall (i=1:3) Tstar_v(i) = Tstar_v(i) + p_hydro ! add hydrostatic component back
Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
P = math_mul33x33(Fe_new,math_mul33x33(math_Mandel6to33(Tstar_v),transpose(invFp_new))) ! first PK stress
! add volumetric component to 2nd Piola-Kirchhoff stress
forall (n=1:3) Tstar_v(n) = Tstar_v(n) + p_hydro
! calculate 1st Piola-Kirchhoff stress
crystallite_P(:,:,g,i,e) = math_mul33x33(Fe_new,math_mul33x33(math_Mandel6to33(Tstar_v),transpose(invFp_new)))
! store local values in global variables
crystallite_Lp(:,:,g,i,e) = Lpguess
crystallite_Tstar_v(:,g,i,e) = Tstar_v
crystallite_Fp(:,:,g,i,e) = Fp_new
crystallite_Fe(:,:,g,i,e) = Fe_new
happy = .true. ! now smile...
! set return flag to true
crystallite_integrateStress = .true.
if (debugger) write(6,*) '::: integrateStress finished at iteration', NiterationStress
!$OMP CRITICAL (distributionStress)
debug_StressLoopDistribution(NiterationStress) = debug_StressLoopDistribution(NiterationStress) + 1
!$OMP END CRITICAL (distributionStress)
return
end subroutine
endfunction
!********************************************************************
! return results of particular grain
@ -780,8 +814,9 @@ function crystallite_postResults(&
constitutive_postResults(Tstar_v,Temperature,dt,g,i,e)
return
end function
endfunction
END MODULE
!##############################################################
!##############################################################

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@ -6,10 +6,10 @@
implicit none
integer(pInt), dimension(nLp) :: debug_LpLoopDistribution = 0_pInt
integer(pInt), dimension(nStress) :: debug_StressLoopDistribution = 0_pInt
integer(pInt), dimension(nCryst) :: debug_StateLoopDistribution = 0_pInt
integer(pInt), dimension(nCryst) :: debug_StiffnessStateLoopDistribution = 0_pInt
integer(pInt), dimension(nState) :: debug_StateLoopDistribution = 0_pInt
integer(pInt), dimension(nState) :: debug_StiffnessStateLoopDistribution = 0_pInt
integer(pInt), dimension(nCryst) :: debug_CrystalliteLoopDistribution = 0_pInt
integer(pLongInt) :: debug_cumLpTicks = 0_pInt
integer(pLongInt) :: debug_cumDotStateTicks = 0_pInt
integer(pInt) :: debug_cumLpCalls = 0_pInt
@ -27,10 +27,10 @@ SUBROUTINE debug_reset()
use prec
implicit none
debug_LpLoopDistribution = 0_pInt ! initialize debugging data
debug_StressLoopDistribution = 0_pInt
debug_StressLoopDistribution = 0_pInt ! initialize debugging data
debug_StateLoopDistribution = 0_pInt
debug_StiffnessStateLoopDistribution = 0_pInt
debug_CrystalliteLoopDistribution = 0_pInt
debug_cumLpTicks = 0_pInt
debug_cumDotStateTicks = 0_pInt
debug_cumLpCalls = 0_pInt
@ -67,49 +67,49 @@ END SUBROUTINE
write(6,'(a33,x,i12)') 'total CPU ticks :',debug_cumDotStateTicks
endif
integral = 0_pInt
write(6,*)
write(6,*) 'distribution_LpLoop :'
do i=1,nLp
if (debug_LpLoopDistribution(i) /= 0) then
integral = integral + i*debug_LpLoopDistribution(i)
write(6,*) i,debug_LpLoopDistribution(i)
endif
enddo
write(6,*) 'total',sum(debug_LpLoopDistribution),integral
integral = 0_pInt
write(6,*)
write(6,*) 'distribution_StressLoop :'
do i=1,nStress
if (debug_StressLoopDistribution(i) /= 0) then
integral = integral + i*debug_StressLoopDistribution(i)
write(6,*) i,debug_StressLoopDistribution(i)
write(6,'(i25,i10)') i,debug_StressLoopDistribution(i)
endif
enddo
write(6,*) 'total',sum(debug_StressLoopDistribution),integral
write(6,'(a15,i10,i10)') ' total',sum(debug_StressLoopDistribution),integral
integral = 0_pInt
write(6,*)
write(6,*) 'distribution_StateLoop :'
do i=1,nCryst
do i=1,nState
if (debug_StateLoopDistribution(i) /= 0) then
integral = integral + i*debug_StateLoopDistribution(i)
write(6,*) i,debug_StateLoopDistribution(i)
write(6,'(i25,i10)') i,debug_StateLoopDistribution(i)
endif
enddo
write(6,*) 'total',sum(debug_StateLoopDistribution),integral
write(6,'(a15,i10,i10)') ' total',sum(debug_StateLoopDistribution),integral
integral = 0_pInt
write(6,*)
write(6,*) 'distribution_StiffnessStateLoop :'
do i=1,nCryst
do i=1,nState
if (debug_StiffnessStateLoopDistribution(i) /= 0) then
integral = integral + i*debug_StiffnessStateLoopDistribution(i)
write(6,*) i,debug_StiffnessStateLoopDistribution(i)
write(6,'(i25,i10)') i,debug_StiffnessStateLoopDistribution(i)
endif
enddo
write(6,*) 'total',sum(debug_StiffnessStateLoopDistribution),integral
write(6,'(a15,i10,i10)') ' total',sum(debug_StiffnessStateLoopDistribution),integral
integral = 0_pInt
write(6,*)
write(6,*) 'distribution_CrystalliteLoop :'
do i=1,nCryst
if (debug_CrystalliteLoopDistribution(i) /= 0) then
integral = integral + i*debug_CrystalliteLoopDistribution(i)
write(6,'(i25,i10)') i,debug_CrystalliteLoopDistribution(i)
endif
enddo
write(6,'(a15,i10,i10)') ' total',sum(debug_CrystalliteLoopDistribution),integral
write(6,*)
END SUBROUTINE

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@ -257,17 +257,6 @@ subroutine materialpoint_stressAndItsTangent(&
enddo
!$OMP END PARALLEL DO
! tell what is requested
write(6,'(a14,x,16(l,x))') 'matpnt_req',materialpoint_requested
write(6,'(a14,x,16(l,x))') 'matpnt_don',materialpoint_doneAndHappy(1,:,:)
write(6,'(a14,x,16(l,x))') 'matpnt_hpy',materialpoint_doneAndHappy(1,:,:)
write(6,'(a14,x,16(f6.4,x))') 'matpnt_frac',materialpoint_subFrac
write(6,'(a14,x,16(f6.4,x))') 'matpnt_step',materialpoint_subStep
write(6,'(a10,x,16(e8.3,x))') 'matpnt_dt',materialpoint_subdt
write(6,*)
write (6,'(a,/,3(3(f12.7,x)/))') 'subF0 of 8 1',materialpoint_subF0(1:3,:,8,1)
write (6,'(a,/,3(3(f12.7,x)/))') 'subF of 8 1',materialpoint_subF(1:3,:,8,1)
! ------ convergence loop material point homogenization ------
homogenization_Niteration = 0_pInt

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@ -23,9 +23,9 @@
real(pReal), parameter :: pert_Fg = 1.0e-6_pReal ! strain perturbation for FEM Jacobi
integer(pInt), parameter :: nReg = 1_pInt ! regularization attempts for Jacobi inversion
integer(pInt), parameter :: nHomog = 10_pInt ! homogenization loop limit
integer(pInt), parameter :: nCryst = 10_pInt ! crystallite loop limit (state update)
integer(pInt), parameter :: nStress = 20_pInt ! stress loop limit
integer(pInt), parameter :: nLp = 40_pInt ! stress loop limit
integer(pInt), parameter :: nCryst = 20_pInt ! crystallite loop limit (only for debugging info, real loop limit is "subStepMin")
integer(pInt), parameter :: nState = 10_pInt ! state loop limit
integer(pInt), parameter :: nStress = 40_pInt ! stress loop limit
real(pReal), parameter :: rTol_crystalliteState = 1.0e-5_pReal ! relative tolerance in crystallite state loop
real(pReal), parameter :: rTol_crystalliteStress = 1.0e-6_pReal ! relative tolerance in crystallite stress loop
real(pReal), parameter :: aTol_crystalliteStress = 1.0e-8_pReal ! absolute tolerance in crystallite stress loop