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DAMASK_EICMD
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altered stress and strain "language" to first PK and deformation gradient. 

plot_results are now part of the crystallite result and not explicitly called from the homogenization layer.
This commit is contained in:
Denny Tjahjanto 2008-03-14 14:19:10 +00:00
parent 6f06133b90
commit 6950eee59b
1 changed files with 205 additions and 223 deletions
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trunk/CPFEM.f90
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@ -1,4 +1,3 @@
!##############################################################
MODULE CPFEM
!##############################################################
@ -10,27 +9,24 @@
! ****************************************************************
! *** General variables for the material behaviour calculation ***
! ****************************************************************
real(pReal), dimension (:,:), allocatable :: CPFEM_Temperature
real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobi_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ini_ori
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_old
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobian
real(pReal), dimension (:,:), allocatable :: CPFEM_Temperature
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ini_ori
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
real(pReal), dimension (:,:,:,:,:,:),allocatable :: CPFEM_dPdF_bar
real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
integer(pInt) :: CPFEM_inc_old = 0_pInt
integer(pInt) :: CPFEM_subinc_old = 1_pInt
integer(pInt) :: CPFEM_cycle_old = -1_pInt
integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction
logical :: CPFEM_first_call = .true.
!
CONTAINS
!
!*********************************************************
!*** allocate the arrays defined in module CPFEM ***
!*** and initialize them ***
@ -43,7 +39,7 @@
use constitutive
!
implicit none
!
integer(pInt) e,i,g
!
! *** mpie.marc parameters ***
@ -51,17 +47,12 @@
allocate(CPFEM_ffn_all (3,3,mesh_maxNips,mesh_NcpElems))
forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_all(:,:,i,e) = math_I3
allocate(CPFEM_ffn1_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_all = CPFEM_ffn_all
allocate(CPFEM_stress_all( 6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_all = 0.0_pReal
allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobi_all = 0.0_pReal
allocate(CPFEM_PK1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_bar = 0.0_pReal
!
! *** User defined results !!! MISSING incorporate consti_Nresults ***
allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
CPFEM_results = 0.0_pReal
!
! *** Second Piola-Kirchoff stress tensor at (t=t0) and (t=t1) ***
allocate(CPFEM_sigma_old(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_old = 0.0_pReal
allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_new = 0.0_pReal
!
! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
allocate(CPFEM_Fp_old(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:constitutive_maxNgrains) &
@ -69,8 +60,7 @@
allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal
!
! *** FEM jacobian (consistent tangent) ***
allocate(CPFEM_jacobian(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobian = 0.0_pReal
!
allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal
!
! *** Output to MARC output file ***
write(6,*)
@ -78,18 +68,15 @@
write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature)
write(6,*) 'CPFEM_ffn_all: ', shape(CPFEM_ffn_all)
write(6,*) 'CPFEM_ffn1_all: ', shape(CPFEM_ffn1_all)
write(6,*) 'CPFEM_stress_all: ', shape(CPFEM_stress_all)
write(6,*) 'CPFEM_jacobi_all: ', shape(CPFEM_jacobi_all)
write(6,*) 'CPFEM_PK1_bar: ', shape(CPFEM_PK1_bar)
write(6,*) 'CPFEM_results: ', shape(CPFEM_results)
write(6,*) 'CPFEM_sigma_old: ', shape(CPFEM_sigma_old)
write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new)
write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old)
write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new)
write(6,*) 'CPFEM_jacobian: ', shape(CPFEM_jacobian)
write(6,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar)
write(6,*)
call flush(6)
return
!
END SUBROUTINE
!
!
@ -99,21 +86,22 @@
!***********************************************************************
SUBROUTINE CPFEM_general(ffn, ffn1, Temperature, CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_stress_recovery, CPFEM_dt,&
CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_jaco, CPFEM_ngens)
! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de
!
use prec, only: pReal,pInt
use debug
use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33
use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33,math_det3x3,math_I3
use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element
use crystal, only: crystal_Init
use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new,material_Cslip_66
implicit none
integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i, e
real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens)
!
integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n, e
real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens),Kirchhoff_bar(3,3), &
H_bar(3,3,3,3),J_inverse
logical CPFEM_stress_recovery
!
! calculate only every second cycle
if (mod(CPFEM_cn,2) /= 0) then ! odd cycle: record data for use in even cycle and return stiff result for this odd cycle
cp_en = mesh_FEasCP('elem',CPFEM_en)
CPFEM_Temperature(CPFEM_in, cp_en) = Temperature
@ -122,9 +110,8 @@
CPFEM_stress(1:CPFEM_ngens) = CPFEM_odd_stress
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens)
CPFEM_cycle_old = CPFEM_cn
!
else ! even cycle: really calculate only in first call of new cycle and when in stress recovery
if (CPFEM_cn /= CPFEM_cycle_old .and. CPFEM_stress_recovery) then
if (CPFEM_first_call) then ! initialization step
! three dimensional stress state ?
@ -135,51 +122,55 @@
call CPFEM_init()
CPFEM_Temperature = Temperature
CPFEM_first_call = .false.
endif
!
if (CPFEM_inc == CPFEM_inc_old) then ! not a new increment
if (CPFEM_subinc > CPFEM_subinc_old) then ! new subincrement: update starting with subinc 2
CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new
CPFEM_subinc_old = CPFEM_subinc
endif
else ! new increment
CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new
CPFEM_inc_old = CPFEM_inc
CPFEM_subinc_old = 1_pInt
endif
CPFEM_cycle_old = CPFEM_cn
debug_cutbackDistribution = 0_pInt ! initialize debugging data
debug_cutbackDistribution = 0_pInt ! initialize debugging data
debug_InnerLoopDistribution = 0_pInt
debug_OuterLoopDistribution = 0_pInt
!
! this shall be done in a parallel loop in the future
do e=1,mesh_NcpElems
do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e)))
debugger = (e==1 .and. i==1)
call CPFEM_stressIP(CPFEM_cn, CPFEM_dt, i, e)
enddo
enddo
call debug_info() ! output of debugging/performance statistics
end if
! return stress and jacobi
!
! return stress and the jacobian
cp_en = mesh_FEasCP('elem', CPFEM_en)
CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_all(1:CPFEM_ngens, CPFEM_in, cp_en)
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jacobian(1:CPFEM_ngens,1:CPFEM_ngens, CPFEM_in, cp_en)
Kirchhoff_bar = matmul(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_all(:,:,CPFEM_in, cp_en)))
J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_all(:,:,CPFEM_in, cp_en))
CPFEM_stress(1:CPFEM_ngens) = math_Mandel33to6(J_inverse*Kirchhoff_bar)
!
H_bar = 0.0_pReal
forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
H_bar(i,j,k,l) = H_bar(i,j,k,l) + &
(CPFEM_ffn1_all(j,m,CPFEM_in, cp_en)*CPFEM_ffn1_all(l,n,CPFEM_in, cp_en)*CPFEM_dPdF_bar(i,m,k,n,CPFEM_in, cp_en) - &
math_I3(j,l)*CPFEM_ffn1_all(i,m,CPFEM_in, cp_en)*CPFEM_PK1_bar(k,m, CPFEM_in, cp_en)) + &
0.5_pReal*(math_I3(i,k)*Kirchhoff_bar(j,l) + math_I3(j,l)*Kirchhoff_bar(i,k) + &
math_I3(i,l)*Kirchhoff_bar(j,k) + math_I3(j,k)*Kirchhoff_bar(i,l))
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = math_Mandel3333to66(J_inverse*H_bar)
end if
!
return
!
END SUBROUTINE
!
!**********************************************************
!*** calculate the material behaviour at IP level ***
!**********************************************************
@ -188,36 +179,36 @@
CPFEM_dt,& ! Time increment (dt)
CPFEM_in,& ! Integration point number
cp_en) ! Element number
!
use prec, only: pReal,pInt,ijaco,nCutback
use debug
use math, only: math_pDecomposition,math_RtoEuler, inDeg, math_I3, math_invert3x3
use IO, only: IO_error
use mesh, only: mesh_element
use constitutive
implicit none
!
integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt
character(len=128) msg
integer(pInt) CPFEM_cn,cp_en,CPFEM_in,grain,i,max_cutbacks
logical updateJaco,error,cutback
logical updateJaco,error,cutback,post_flag
real(pReal) CPFEM_dt,dt,t,volfrac,det
real(pReal), dimension(6) :: cs,Tstar_v
real(pReal), dimension(6,6) :: cd
real(pReal), dimension(3,3) :: Fe,U,R,deltaFg,invFgthen,invFpnow,Lp
real(pReal), dimension(3,3,2) :: Fg,Fp
real(pReal), dimension(3,3) :: PK1
real(pReal), dimension(3,3,3,3) :: dPdF
real(pReal), dimension(3,3) :: Fe,U,R,deltaFg,invFgthen,invFpnow,Lp
real(pReal), dimension(3,3,2) :: Fg,Fp
real(pReal), dimension(constitutive_maxNstatevars,2) :: state
real(pReal), dimension (:), allocatable :: post_results
!
updateJaco = (mod(CPFEM_cn,2_pInt*ijaco)==0) ! update consistent tangent every ijaco'th iteration
CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress
if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent
!
CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average first PK stress
if (updateJaco) CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average consistent tangent
!
! -------------- grain loop -----------------
do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
! -------------------------------------------
allocate(post_results(constitutive_Nresults(grain,CPFEM_in,cp_en))) ; post_results = 0.0_pReal
!
i = 0_pInt ! cutback counter
max_cutbacks = 0_pInt ! maximum depth of cut backing
dt = CPFEM_dt
@ -233,35 +224,37 @@
else
Lp = 0.0_pReal ! fully elastic guess
endif
!
deltaFg = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess
Fg(:,:,i_then) = Fg(:,:,i_now)
Fp(:,:,i_then) = Fp(:,:,i_now)
state(:,i_then) = 0.0_pReal ! state_old as initial guess
t = 0.0_pReal
cutback = .false. ! no cutback has happened so far
msg = ''
!
! ------- crystallite integration -----------
do
! -------------------------------------------
do while ((t < CPFEM_dt) .or. (msg /= 'ok'))
!
if (t+dt < CPFEM_dt) then ! intermediate solution
t = t+dt ! next time inc
Fg(:,:,i_then) = Fg(:,:,i_then)+deltaFg ! corresponding Fg
post_flag = .false.
else ! full step solution
t = CPFEM_dt ! final time
Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg
Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg
post_flag = .true.
endif
call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Lp,Fp(:,:,i_then),Fe,state(:,i_then),&
!
call CPFEM_stressCrystallite(msg,PK1,dPdF,post_results,post_flag,Lp,Fp(:,:,i_then),Fe,state(:,i_then),&
t,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,&
Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now))
if (msg == 'ok') then ! solution converged
if (t == CPFEM_dt) then
debug_cutbackDistribution(max_cutbacks+1) = debug_cutbackDistribution(max_cutbacks+1)+1
exit ! reached final "then"
endif
if (cutback == .false.) then ! stable solution at current speed?
! if (t == CPFEM_dt) then
! debug_cutbackDistribution(max_cutbacks+1) = debug_cutbackDistribution(max_cutbacks+1)+1
! exit ! reached final "then"
! endif
if (.not. cutback) then ! stable solution at current speed?
dt = 2.0_pReal*dt ! double time-step
i = i-1_pInt ! dec cutback counter
endif
@ -271,8 +264,9 @@
max_cutbacks = max(i,max_cutbacks)
cutback = .true.
if (i > nCutback) then ! limit exceeded?
debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1
write(6,'(x,a,x,i6,x,a,x,i2,x,a,x,i2)') 'element:',cp_en,'IP:',CPFEM_in,'grain:',grain
debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1
write(6,'(x,a,x,f10.8,x,a,x,f10.8,x,a,x,i6,x,a,x,i2,x,a,x,i2)') &
'inc fraction:',t/CPFEM_dt,'from',(t-dt)/CPFEM_dt,'element:',cp_en,'IP:',CPFEM_in,'grain:',grain
write(6,*) 'cutback limit --> '//msg
call IO_error(600)
return ! byebye
@ -284,18 +278,21 @@
endif
endif
enddo ! crystallite integration (cutback loop)
! ---- update crystallite matrices at t = t1 ----
debug_cutbackDistribution(max_cutbacks+1) = debug_cutbackDistribution(max_cutbacks+1)+1
!
! update crystallite matrices at t = t1
CPFEM_Fp_new(:,:,grain,CPFEM_in,cp_en) = Fp(:,:,i_then)
constitutive_state_new(:,grain,CPFEM_in,cp_en) = state(:,i_then)
CPFEM_sigma_new(:,grain,CPFEM_in,cp_en) = Tstar_v
! ---- contribute to IP result ----
!
! contribute to IP result
volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en)
CPFEM_stress_all(:,CPFEM_in,cp_en) = CPFEM_stress_all(:,CPFEM_in,cp_en)+volfrac*cs ! average Cauchy stress
if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = CPFEM_jacobian(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent
! ---- update results plotted in MENTAT ----
CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = CPFEM_PK1_bar(:,:,CPFEM_in,cp_en)+volfrac*PK1 ! average Cauchy stress
if (updateJaco) CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en)+volfrac*dPdF ! consistent tangent
!
! update results plotted in MENTAT
call math_pDecomposition(Fe,U,R,error) ! polar decomposition
if (error) then
write(6,*) Fe
write(6,*) 'polar decomposition'
write(6,*) 'Grain: ',grain
write(6,*) 'Integration point: ',CPFEM_in
@ -305,23 +302,24 @@
endif
CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R))*inDeg ! orientation
CPFEM_results(4 ,grain,CPFEM_in,cp_en) = volfrac ! volume fraction of orientation
CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = &
constitutive_post_results(Tstar_v,state(:,i_then),CPFEM_dt,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = post_results
!
deallocate(post_results)
enddo ! grain loop
!
return
!
END SUBROUTINE
!
!********************************************************************
! Calculates the stress for a single component
!********************************************************************
subroutine CPFEM_stressCrystallite(&
msg,& ! return message
cs,& ! Cauchy stress vector
dcs_de,& ! consistent tangent
Tstar_v,& ! second Piola-Kirchhoff stress tensor
P,& ! first PK stress
dPdF,& ! consistent tangent
post_results,& ! plot results from constitutive model
post_flag,& ! its flag
Lp,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
@ -335,33 +333,28 @@
Fg_new,& ! new global deformation gradient
Fp_old,& ! old plastic deformation gradient
state_old) ! old state variable array
!
use prec, only: pReal,pInt,pert_Fg
use debug
use constitutive, only: constitutive_Nstatevars
use constitutive, only: constitutive_Nstatevars,constitutive_Nresults
use mesh, only: mesh_element
use math, only: math_Mandel6to33,math_Mandel33to6,math_Mandel3333to66,&
math_I3,math_det3x3,math_invert3x3
implicit none
!
character(len=*) msg
logical updateJaco,error
logical updateJaco,error,post_flag
integer(pInt) cp_en,CPFEM_in,grain,i,j,k,l,m,n
real(pReal) dt,invJ,det
real(pReal), dimension(3,3,3,3) :: A,H
real(pReal), dimension(3,3) :: Lp,Lp_pert,Fg_new,Fg_pert,Fp_old,Fp_new,invFp_new,Fp_pert,invFp_pert
real(pReal), dimension(3,3) :: Fe_new,Fe_pert,Tstar,tau,P,P_pert
real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert
real(pReal), dimension(6,6) :: dcs_de
real(pReal), dimension(3,3) :: Lp,Lp_pert,Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,invFp_new,Fp_pert,invFp_pert
real(pReal), dimension(3,3) :: Fe_new,Fe_pert,Tstar,tau,P,P_pert,E_pert
real(pReal), dimension(3,3,3,3) :: dPdF
real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert
call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step
real(pReal), dimension(constitutive_Nresults(grain,CPFEM_in,cp_en)) :: post_results
!
call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,P,state_new,post_results,post_flag, & ! def gradients and PK2 at end of time step
dt,cp_en,CPFEM_in,grain,Fg_new,Fp_old,state_old)
if (msg /= 'ok') return ! solution not reached --> report back
Tstar = math_Mandel6to33(Tstar_v) ! second PK in intermediate
tau = matmul(Fe_new,matmul(Tstar,transpose(Fe_new))) ! Kirchhoff stress
invJ = 1.0_pReal/math_det3x3(Fe_new) ! inverse dilatation of Fe
cs = math_Mandel33to6(invJ*tau) ! Cauchy stress
if (updateJaco) then ! consistent tangent using
! numerical perturbation of Fg (D. Tjahjanto Diss p.106)
call math_invert3x3(Fp_new,invFp_new,det,error)
@ -369,46 +362,34 @@
msg = 'inversion of Fp_new'
return
endif
P = matmul(Fe_new,&
matmul(Tstar,transpose(invFp_new))) ! first PK at center
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 CPFEM_timeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, &
call CPFEM_timeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,P_pert,state_pert,post_results,.false., &
dt,cp_en,CPFEM_in,grain,Fg_pert,Fp_old,state_old)
if (msg /= 'ok') then
msg = 'consistent tangent --> '//msg
return
endif
!
call math_invert3x3(Fp_pert,invFp_pert,det,error)
if (error) then
msg = 'inversion of Fp_pert'
return
endif
P_pert = matmul(Fe_pert,&
matmul(math_mandel6to33(Tstar_v_pert),transpose(invFp_pert))) ! perturbed first PK
A(:,:,k,l) = (P_pert-P)/pert_Fg ! dP_ij/dFg_kl
!
dPdF(:,:,k,l) = (P_pert-P)/pert_Fg ! constructin the tangent dP_ij/dFg_kl
enddo
enddo
H = 0.0_pReal
forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
H(i,j,k,l) = H(i,j,k,l) + &
(Fg_new(j,m)*Fg_new(l,n)*A(i,m,k,n) - math_I3(j,l)*Fg_new(i,m)*P(k,m)) + &
0.5_pReal*(math_I3(i,k)*tau(j,l) + math_I3(j,l)*tau(i,k) + &
math_I3(i,l)*tau(j,k) + math_I3(j,k)*tau(i,l))
dcs_de = math_Mandel3333to66(invJ*H) ! Mandel version of stiffness tensor
endif
!
return
!
END SUBROUTINE
!
!***********************************************************************
!*** fully-implicit two-level time integration ***
!*** based on a residuum in Lp and intermediate ***
@ -419,8 +400,10 @@
Lpguess,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0)
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
@ -429,33 +412,32 @@
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_Microstructure
constitutive_Nresults,constitutive_Microstructure,constitutive_post_results
use math
implicit none
!
character(len=*) msg
logical failed,wantsConstitutiveResults
integer(pInt) cp_en, CPFEM_in, grain
integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n
real(pReal) dt, 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,invFg_new,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new,Fe_old
real(pReal), dimension(3,3) :: Tstar
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, CPFEM_in, cp_en)) :: state_old,state,ROuter
logical failed
real(pReal), dimension(constitutive_Nresults(grain,CPFEM_in,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
@ -467,113 +449,113 @@
msg = 'inversion Fg_new'
return
endif
!
Fe_old = matmul(Fg_new,invFp_old)
A = matmul(transpose(Fe_old), Fe_old)
!
if (all(state == 0.0_pReal)) state = state_old ! former state guessed, if none specified
iOuter = 0_pInt ! outer counter
!
!
Outer: do ! outer iteration: State
iOuter = iOuter+1
if (iOuter > nOuter) then
msg = 'limit Outer iteration'
debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1
debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1
return
endif
call constitutive_Microstructure(state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
C_66 = constitutive_HomogenizedC(state, grain, CPFEM_in, cp_en)
call constitutive_Microstructure(state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
C_66 = constitutive_HomogenizedC(state, grain, CPFEM_in, 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
Inner: do ! inner iteration: Lp
iInner = iInner+1
if (iInner > nInner) then ! too many loops required
msg = 'limit Inner iteration'
debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1
!
Inner: do ! inner iteration: Lp
iInner = iInner+1
if (iInner > nInner) then ! too many loops required
msg = 'limit Inner iteration'
debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1
return
endif
B = math_i3 - dt*Lpguess
BT = transpose(B)
AB = matmul(A,B)
BTA = matmul(BT,A)
Tstar_v = 0.5_pReal*matmul(C_66,math_mandel33to6(matmul(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,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
Rinner = Lpguess - Lp ! update current residuum
if ((maxval(abs(Rinner)) < abstol_Inner) .or. &
(any(abs(dt*Lpguess) > relevantStrain) .and. &
maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner)) &
exit Inner
!
! check for acceleration/deceleration in Newton--Raphson correction
if (leapfrog > 1.0_pReal .and. &
(sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum
sum(Rinner*Rinner_old) < 0.0_pReal)) then ! residuum changed sign (overshoot)
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 - matmul(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'
return
endif
B = math_i3 - dt*Lpguess
BT = transpose(B)
AB = matmul(A,B)
BTA = matmul(BT,A)
Tstar_v = 0.5_pReal*matmul(C_66,math_mandel33to6(matmul(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,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
Rinner = Lpguess - Lp ! update current residuum
if (( maxval(abs(Rinner)) < abstol_Inner ) .or. &
( any(abs(dt*Lpguess) > relevantStrain) .and. &
maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner )&
) exit Inner
! check for acceleration/deceleration in Newton--Raphson correction
if (leapfrog > 1.0_pReal .and. &
(sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum
sum(Rinner*Rinner_old) < 0.0_pReal)) then ! residuum changed sign (overshoot)
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 - matmul(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'
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
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
!
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
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
!
debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
ROuter = state - state_old - &
dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),&
grain,CPFEM_in,cp_en) ! residuum from evolution of microstructure
ROuter = state - state_old - &
dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),&
grain,CPFEM_in,cp_en) ! residuum from evolution of microstructure
state = state - ROuter ! update of microstructure
if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer
enddo Outer
enddo Outer
!
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
invFp_new = matmul(invFp_old,B)
call math_invert3x3(invFp_new,Fp_new,det,failed)
if (failed) then
msg = 'inversion Fp_new'
return
msg = 'inversion Fp_new'
return
endif
!
if (wantsConstitutiveResults) then ! get the post_results upon request
results = 0.0_pReal
results = constitutive_post_results(Tstar_v,state,dt,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
endif
!
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !!
Fe_new = matmul(Fg_new,invFp_new) ! calc resulting Fe
forall (i=1:3) Tstar_v(i) = Tstar_v(i)+p_hydro ! add hydrostatic component back
P = matmul(Fe_new,matmul(Tstar,transpose(invFp_new))) ! first PK stress
!
return
!
END SUBROUTINE
!
END MODULE
!##############################################################