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DAMASK_EICMD
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DEBUGGING VERSION for calculation of Divergence (various methods implemented). DO NOT USE. Wait for next update coming in a few minutes

This commit is contained in:
Martin Diehl 2011-08-10 16:02:13 +00:00
parent bb1ca2330b
commit 34de2e301b
3 changed files with 281 additions and 699 deletions
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code/DAMASK_spectral.f90
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@ -93,12 +93,17 @@ program DAMASK_spectral
pstress, pstress_av, cstress_av, defgrad_av,&
defgradAim, defgradAimOld, defgradAimCorr, defgradAimCorrPrev,&
mask_stress, mask_defgrad, deltaF
real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0 !, c0_temp ! ToDo
real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation
real(pReal), dimension(6,6) :: dsde, c066, s066 ! Mandel notation of 4th order tensors
real(pReal), dimension(3,3,3,3) :: dPdF, c_current, s_current, c0_reference ! ToDo
real(pReal), dimension(6) :: cstress, stress_res, delta_defgrad ! cauchy stress, residuum_stress, change of defgrad in Mandel notation
real(pReal), dimension(6,6) :: dsde, c_current66, s_current66 ! Mandel notation of 4th order tensors
real(pReal), dimension(9,9) :: s_current99, c_current99
real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
real(pReal), dimension(:,:,:), allocatable :: temperature
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced
logical, dimension(6) :: mask_stress6
logical, dimension(9) :: mask_stress9
integer(pInt) size_reduced
! variables storing information for spectral method
complex(pReal) :: img
@ -121,6 +126,8 @@ program DAMASK_spectral
integer*8 plan_div(3)
real(pReal), dimension(:,:,:,:), allocatable :: divergence
complex(pReal), dimension(:,:,:,:), allocatable :: divergence_hat
complex(pReal), dimension(:,:,:,:), allocatable :: divergence_hat_full
complex(pReal), dimension(:,:,:,:), allocatable :: divergence_hat_full2
complex(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field_hat, pstress_field
real(pReal) ev1, ev2, ev3
real(pReal), dimension(3,3) :: evb1, evb2, evb3
@ -128,6 +135,7 @@ program DAMASK_spectral
err_div_avg_inf, err_div_avg_two, err_div_max_inf, err_div_max_two, &
err_div_avg_inf2, err_div_avg_two2, err_div_max_two2, err_div_max_inf2, &
err_real_div_avg_inf, err_real_div_avg_two, err_real_div_max_inf, err_real_div_max_two, &
err_real_div_avg_inf2, err_real_div_avg_two2, err_real_div_max_inf2, err_real_div_max_two2, &
rho
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
@ -267,7 +275,7 @@ program DAMASK_spectral
print '(a,i5)', 'Loadcase:', loadcase
if (.not. followFormerTrajectory(loadcase)) &
print '(a)', 'drop guessing along trajectory'
if (any(bc_mask(:,:,1,loadcase) .and. bc_mask(:,:,2,loadcase)))& ! check whther stress and strain is prescribed simultaneously
if (any(bc_mask(:,:,1,loadcase) .eqv. bc_mask(:,:,2,loadcase)))& ! exclusive or masking only
call IO_error(31,loadcase)
if (velGradApplied(loadcase)) then
do j = 1, 3
@ -354,6 +362,8 @@ program DAMASK_spectral
allocate (xi (3,resolution(1),resolution(2),resolution(3))); xi = 0.0_pReal
allocate (divergence (resolution(1) ,resolution(2),resolution(3),3)); divergence = 0.0_pReal
allocate (divergence_hat (resolution(1)/2+1,resolution(2),resolution(3),3)); divergence_hat = 0.0_pReal
allocate (divergence_hat_full(resolution(1),resolution(2),resolution(3),3)); divergence_hat_full = 0.0_pReal
allocate (divergence_hat_full2(resolution(1),resolution(2),resolution(3),3)); divergence_hat_full2 = 0.0_pReal
allocate (pstress_field_hat(resolution(1),resolution(2),resolution(3),3,3)); pstress_field_hat = 0.0_pReal
allocate (pstress_field (resolution(1),resolution(2),resolution(3),3,3)); pstress_field = 0.0_pReal
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
@ -366,20 +376,16 @@ program DAMASK_spectral
! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field
call CPFEM_initAll(bc_temperature(1),1_pInt,1_pInt)
ielem = 0_pInt
c066 = 0.0_pReal
c_current = 0.0_pReal
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
defgradold(i,j,k,:,:) = math_I3 ! no deformation at the beginning
defgrad(i,j,k,:,:) = math_I3
ielem = ielem +1
coordinates(1:3,i,j,k) = mesh_ipCenterOfGravity(1:3,1,ielem) ! set to initial coordinates ToDo: SHOULD BE UPDATED TO CURRENT POSITION IN FUTURE REVISIONS!!!
call CPFEM_general(2,coordinates(1:3,i,j,k),math_I3,math_I3,temperature(i,j,k),0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c066 = c066 + dsde
c_current = c_current + dPdF
enddo; enddo; enddo
c066 = c066 * wgt
c0 = math_mandel66to3333(c066) ! linear reference material stiffness
call math_invert(6, math_Mandel66toPlain66(c066), s066,i, errmatinv) ! ToDo
if(errmatinv) call IO_error(800) ! Matrix inversion error ToDo
s0 = math_mandel66to3333(math_Plain66toMandel66(s066)) ! ToDo
c0_reference = c_current * wgt ! linear reference material stiffness
do k = 1, resolution(3) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
k_s(3) = k-1
@ -409,7 +415,7 @@ program DAMASK_spectral
do l = 1,3; do m = 1,3
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
enddo; enddo
temp33_Real = math_inv3x3(math_mul3333xx33(c0, xiDyad))
temp33_Real = math_inv3x3(math_mul3333xx33(c0_reference, xiDyad))
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
@ -425,9 +431,11 @@ program DAMASK_spectral
! Initialization of fftw (see manual on fftw.org for more details)
if(DAMASK_NumThreadsInt>0_pInt) then
call dfftw_init_threads(ierr)
if(ierr == 0_pInt) call IO_error(104,ierr)
call dfftw_plan_with_nthreads(DAMASK_NumThreadsInt)
endif
call dfftw_plan_many_dft_r2c(plan_fft(1),3,(/resolution(1),resolution(2),resolution(3)/),9,&
workfft,(/resolution(1) +2,resolution(2),resolution(3)/),1,(resolution(1) +2)*resolution(2)*resolution(3),&
@ -441,10 +449,14 @@ program DAMASK_spectral
pstress_field, (/resolution(1),resolution(2),resolution(3)/),1,(resolution(1)*resolution(2)*resolution(3)),&
pstress_field_hat,(/resolution(1),resolution(2),resolution(3)/),1,(resolution(1)*resolution(2)*resolution(3)),&
FFTW_FORWARD,FFTW_PATIENT)
call dfftw_plan_many_dft_c2r(plan_div(2),3,(/resolution(1),resolution(2),resolution(3)/),3/3,&
call dfftw_plan_many_dft_c2r(plan_div(2),3,(/resolution(1),resolution(2),resolution(3)/),3,&
divergence_hat, (/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),&
divergence ,(/resolution(1), resolution(2),resolution(3)/),1, resolution(1)* resolution(2)*resolution(3),&
FFTW_PATIENT)
call dfftw_plan_many_dft(plan_div(3),3,(/resolution(1),resolution(2),resolution(3)/),3,&
divergence_hat_full,(/resolution(1),resolution(2),resolution(3)/),1,resolution(1)*resolution(2)*resolution(3),&
divergence_hat_full2,(/resolution(1),resolution(2),resolution(3)/),1,resolution(1)* resolution(2)*resolution(3),&
FFTW_BACKWARD,FFTW_PATIENT)
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
! write header of output file
@ -483,6 +495,7 @@ program DAMASK_spectral
mask_defgrad = merge(ones,zeroes,bc_mask(:,:,1,loadcase))
mask_stress = merge(ones,zeroes,bc_mask(:,:,2,loadcase))
deltaF = bc_deformation(:,:,loadcase) ! only valid for given fDot. will be overwritten later in case L is given
!*************************************************************
! loop oper steps defined in input file for current loadcase
@ -567,7 +580,7 @@ program DAMASK_spectral
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
! c0_temp = 0.0_pReal !for calculation of s0 ToDo
c_current = 0.0_pReal
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1_pInt
@ -577,29 +590,110 @@ program DAMASK_spectral
temperature(i,j,k),timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
CPFEM_mode = 2_pInt
! c0_temp = c0_temp + dPdF ToDo
workfft(i,j,k,:,:) = pstress ! build up average P-K stress
cstress_av = cstress_av + math_mandel6to33(cstress) ! build up average Cauchy stress
c_current = c_current + dPdF
enddo; enddo; enddo
! call math_invert(9, math_plain3333to99(c0_temp),s099,i,errmatinv) ToDo
! if(errmatinv) call IO_error(800,ext_msg = "problem in c0 inversion") ToDo
! s0 = math_plain99to3333(s099) *real(resolution(1)*resolution(2)*resolution(3), pReal) ! average s0 for calculation of BC ToDo
c_current = c_current * wgt
cstress_av = cstress_av * wgt
do n = 1,3; do m = 1,3
pstress_av(m,n) = sum(workfft(1:resolution(1),1:resolution(2),1:resolution(3),m,n)) * wgt
defgrad_av(m,n) = sum(defgrad(1:resolution(1),1:resolution(2),1:resolution(3),m,n)) * wgt
pstress_av(m,n) = sum(workfft(1:resolution(1),:,:,m,n)) * wgt
defgrad_av(m,n) = sum(defgrad(: ,:,:,m,n)) * wgt
enddo; enddo
err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(:,:,loadcase))))
err_stress_tol = maxval(abs(pstress_av))*0.8*err_stress_tolrel
print*, 'Correcting deformation gradient to fullfill BCs'
defgradAimCorrPrev = defgradAimCorr
defgradAimCorr = - (1.0_pReal - mask_defgrad) & ! allow alteration of all non-fixed defgrad components
* math_mul3333xx33(s0, (mask_stress*(pstress_av - bc_stress(:,:,loadcase)))) ! residual on given stress components
call math_invert(9, math_plain3333to99(c_current),s_current99,i,errmatinv)
if(errmatinv) then
print*, 'using symmetric compliance'
pause !somehow not working, maybe we don't need it
!mask_stress6 = math_Plain33to6_logical(bc_mask(:,:,2,loadcase))
size_reduced = count(mask_stress6)
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
c_current66 = math_Plain3333to66(c_current)
k = 0_pInt
do n = 1,6
if(mask_stress6(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,6
if(mask_stress6(m)) then
j = j + 1_pInt
c_reduced(k,j) = c_current66(n,m)
endif
enddo
endif
enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv)
if(errmatinv) call IO_error(800)
s_current66 = 0.0_pReal
k = 0_pInt
do n = 1,6
if(mask_stress6(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,6
if(mask_stress6(m)) then
j = j + 1_pInt
s_current66(n,m) = s_reduced(k,j)
endif
enddo
endif
enddo
s_current = math_Plain66to3333(s_current66)
else
print*, 'using non-symmetric compliance'
mask_stress9 = reshape(bc_mask(:,:,2,loadcase),(/9/))
size_reduced = count(mask_stress9)
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
c_current99 = math_Plain3333to99(c_current)
k = 0_pInt
do n = 1,9
if(mask_stress9(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,9
if(mask_stress9(m)) then
j = j + 1_pInt
c_reduced(k,j) = c_current99(n,m)
endif
enddo
endif
enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv)
if(errmatinv) call IO_error(800)
s_current99 = 0.0_pReal
k = 0_pInt
do n = 1,9
if(mask_stress9(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,9
if(mask_stress9(m)) then
j = j + 1_pInt
s_current99(n,m) = s_reduced(k,j)
endif
enddo
endif
enddo
s_current = math_Plain99to3333(s_current99)
endif
deallocate(c_reduced)
deallocate(s_reduced)
print*, 'Correcting deformation gradient to fullfill BCs'
defgradAimCorr = - math_mul3333xx33(s_current, ((pstress_av - bc_stress(:,:,loadcase)))) ! residual on given stress components
print*, 'change of Stress:'
print '(3(f10.4,x))', -math_transpose3x3(math_mul3333xx33(c_current,defgradAimCorr))/1.e6
print*, 'defgradAimCorr:'
print '(3(e12.3,x))', math_transpose3x3(defgradAimCorr)
do m=1,3; do n =1,3 ! calculate damper
! if ( sign(1.0_pReal,defgradAimCorr(m,n))/=sign(1.0_pReal,defgradAimCorrPrev(m,n))) then
if (defgradAimCorr(m,n) * defgradAimCorrPrev(m,n) < -relevantStrain ** 2.0_pReal) then ! insignificant within relevantstrain around zero
damper(m,n) = max(0.01_pReal,damper(m,n)*0.8)
else
@ -633,6 +727,9 @@ program DAMASK_spectral
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
ielem = 0_pInt
!!!!!!!!!!!!!!!!!!!!!!!! start divergence debugging
pstress_field = cmplx(0.0_pReal,0.0_pReal)
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1_pInt
call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
@ -655,8 +752,8 @@ program DAMASK_spectral
print *, 'Calculating equilibrium using spectral method'
err_div = 0.0_pReal
p_hat_avg = 0.0_pReal
!!!!!!!!!!!!!!!!!!!!!!!! start divergence debugging
p_hat_avg_inf = 0.0_pReal
p_hat_avg_two = 0.0_pReal
p_real_avg_inf = 0.0_pReal
@ -673,6 +770,10 @@ program DAMASK_spectral
err_real_div_avg_two = 0.0_pReal
err_real_div_max_inf = 0.0_pReal
err_real_div_max_two = 0.0_pReal
err_real_div_avg_inf2 = 0.0_pReal
err_real_div_avg_two2 = 0.0_pReal
err_real_div_max_inf2 = 0.0_pReal
err_real_div_max_two2 = 0.0_pReal
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
call dfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress
@ -690,9 +791,11 @@ program DAMASK_spectral
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
! print*, workfft(2*i-1,j,k,:,:)+workfft(i*2,j,k,:,:)*cmplx(0.0,1.0)-pstress_field_hat(i,j,k,:,:)
err_div = max(err_div, maxval(abs(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+& ! maximum of L infinity norm of div(stress), Suquet 2001
workfft(i*2, j,k,:,:)*img,xi(:,i,j,k)*minval(geomdimension)))))
!!!!!!!!!!!!!!!!!!!!!!!! start divergence debugging
!if(abs(sqrt(sum(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+workfft(i*2,j,k,:,:)*img,xi(:,i,j,k)*minval(geomdimension)))**2.0))>err_div_max_two) print*, i,j,k
err_div_max_two = max(err_div_max_two,abs(sqrt(sum(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+& ! maximum of L two norm of div(stress), Suquet 2001
workfft(i*2,j,k,:,:)*img,xi(:,i,j,k)*minval(geomdimension)))**2.0)))
err_div_avg_inf = err_div_avg_inf + (maxval(abs(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+& ! sum of squared L infinity norm of div(stress), Suquet 1998
@ -708,20 +811,24 @@ program DAMASK_spectral
do k = 1, resolution(3)
n = 1
do j = 1, resolution(2)
!print*, xi(:,resolution(1)-i,j,k) + xi(:,i+2,n,m), resolution(1)-i,j,k
err_div_avg_inf = err_div_avg_inf + (maxval(abs(math_mul33x3_complex&
(workfft(3+2*i,n,m,:,:)+workfft(4+i*2,n,m,:,:)*img,xi(:,resolution(1)-i,j,k)*minval(geomdimension)))))**2.0
err_div_avg_two = err_div_avg_two + abs(sum((math_mul33x3_complex(workfft(3+2*i,n,m,:,:)+workfft(4+i*2,n,m,:,:)*img,&
(workfft(3+2*i,n,m,:,:)+workfft(4+i*2,n,m,:,:)*cmplx(0.0,-1.0),xi(:,resolution(1)-i,j,k)*minval(geomdimension)))))**2.0
err_div_avg_two = err_div_avg_two + abs(sum((math_mul33x3_complex(workfft(3+2*i,n,m,:,:)+workfft(4+i*2,n,m,:,:)*cmplx(0.0,-1.0),&
xi(:,resolution(1)-i,j,k)*minval(geomdimension)))**2.0))
! workfft(resolution(1)-i,j,k,:,:) = conjg(workfft(2+i,n,m,:,:)) original code for complex array, above little bit confusing because compley data is stored in real array
! print*, workfft(3+2*i,n,m,:,:)+workfft(4+i*2,n,m,:,:)*cmplx(0.0,-1.0)-pstress_field_hat(resolution(1)-i,j,k,:,:)
! workfft(resolution(1)-i,j,k,:,:) = conjg(workfft(2+i,n,m,:,:)) original code for complex array, code above is a little bit confusing because compley data is stored in real array
if(n == 1) n = resolution(2) +1
n = n-1
enddo
if(m == 1) m = resolution(3) +1
m = m -1
enddo; enddo
! print*, 'new'
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) !calculating divergence criteria for full field (no complex symmetry)
err_div_max_two2 = max(err_div_max_two,abs(sqrt(sum(math_mul33x3_complex(pstress_field_hat(i,j,k,:,:),xi(:,i,j,k)*&
if (abs(sqrt(sum(math_mul33x3_complex(pstress_field_hat(i,j,k,:,:),xi(:,i,j,k)*minval(geomdimension)))**2.0))>err_div_max_two2) print*, i,j,k
err_div_max_two2 = max(err_div_max_two2,abs(sqrt(sum(math_mul33x3_complex(pstress_field_hat(i,j,k,:,:),xi(:,i,j,k)*&
minval(geomdimension)))**2.0)))
err_div_max_inf2 = max(err_div_max_inf2,(maxval(abs(math_mul33x3_complex(pstress_field_hat(i,j,k,:,:),xi(:,i,j,k)*&
minval(geomdimension))))))
@ -745,29 +852,64 @@ program DAMASK_spectral
err_div = err_div/p_hat_avg !weigthting of error by average stress (L infinity norm)
!!!!!!!!!!!!!!!!!!!!!!!! start divergence debugging
divergence_hat_full=0.0
!divergence in real space
do k = 1, resolution(3) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
k_s(3) = k-1
if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3)
do j = 1, resolution(2)
k_s(2) = j-1
if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
do i = 1, resolution(1)/2+1
k_s(1) = i-1
divergence_hat(i,j,k,1) = (workfft(i*2-1,j,k,1,1)+ workfft(i*2,j,k,1,1)*img)*(real(k_s(1))*img*pi*2.0)/geomdimension(1)&
+ (workfft(i*2-1,j,k,2,1)+ workfft(i*2,j,k,2,1)*img)*(real(k_s(2))*img*pi*2.0)/geomdimension(2)&
+ (workfft(i*2-1,j,k,3,1)+ workfft(i*2,j,k,3,1)*img)*(real(k_s(3))*img*pi*2.0)/geomdimension(3)
divergence_hat(i,j,k,2) = (workfft(i*2-1,j,k,1,2)+ workfft(i*2,j,k,1,2)*img)*(real(k_s(1))*img*pi*2.0)/geomdimension(1)&
+ (workfft(i*2-1,j,k,2,2)+ workfft(i*2,j,k,2,2)*img)*(real(k_s(2))*img*pi*2.0)/geomdimension(2)&
+ (workfft(i*2-1,j,k,3,2)+ workfft(i*2,j,k,3,2)*img)*(real(k_s(3))*img*pi*2.0)/geomdimension(3)
divergence_hat(i,j,k,3) = (workfft(i*2-1,j,k,1,3)+ workfft(i*2,j,k,1,3)*img)*(real(k_s(1))*img*pi*2.0)/geomdimension(1)&
+ (workfft(i*2-1,j,k,2,3)+ workfft(i*2,j,k,2,3)*img)*(real(k_s(2))*img*pi*2.0)/geomdimension(2)&
+ (workfft(i*2-1,j,k,3,3)+ workfft(i*2,j,k,3,3)*img)*(real(k_s(3))*img*pi*2.0)/geomdimension(3)
divergence_hat(i,j,k,1) = (workfft(i*2-1,j,k,1,1)+ workfft(i*2,j,k,1,1)*img)*xi(1,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,2,1)+ workfft(i*2,j,k,2,1)*img)*xi(2,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,3,1)+ workfft(i*2,j,k,3,1)*img)*xi(3,i,j,k)*img*pi*2.0
divergence_hat(i,j,k,2) = (workfft(i*2-1,j,k,1,2)+ workfft(i*2,j,k,1,2)*img)*xi(1,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,2,2)+ workfft(i*2,j,k,2,2)*img)*xi(2,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,3,2)+ workfft(i*2,j,k,3,2)*img)*xi(3,i,j,k)*img*pi*2.0
divergence_hat(i,j,k,3) = (workfft(i*2-1,j,k,1,3)+ workfft(i*2,j,k,1,3)*img)*xi(1,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,2,3)+ workfft(i*2,j,k,2,3)*img)*xi(2,i,j,k)*img*pi*2.0&
+ (workfft(i*2-1,j,k,3,3)+ workfft(i*2,j,k,3,3)*img)*xi(3,i,j,k)*img*pi*2.0
enddo; enddo; enddo
do k = 1, resolution(3) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
do j = 1, resolution(2)
do i = 1, resolution(1)/2+1
divergence_hat_full(i,j,k,1) = pstress_field_hat(i,j,k,1,1)*xi(1,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,2,1)*xi(2,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,3,1)*xi(3,i,j,k)*img*pi*2.0
divergence_hat_full(i,j,k,2) = pstress_field_hat(i,j,k,1,2)*xi(1,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,2,2)*xi(2,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,3,2)*xi(3,i,j,k)*img*pi*2.0
divergence_hat_full(i,j,k,3) = pstress_field_hat(i,j,k,1,3)*xi(1,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,2,3)*xi(2,i,j,k)*img*pi*2.0&
+ pstress_field_hat(i,j,k,3,3)*xi(3,i,j,k)*img*pi*2.0
enddo; enddo; enddo
! do i = 0, resolution(1)/2-2 ! reconstruct data of conjugated complex (symmetric) part in Fourier spaced
! m = 1
! do k = 1, resolution(3)
! n = 1
! do j = 1, resolution(2)
! divergence_hat_full(resolution(1)-i,j,k,1) = pstress_field_hat(resolution(1)-i,j,k,1,1)*xi(1,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,2,1)*xi(2,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,3,1)*xi(3,2+i,n,m)*img*pi*2.0
! divergence_hat_full(resolution(1)-i,j,k,2) = pstress_field_hat(resolution(1)-i,j,k,1,2)*xi(1,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,2,2)*xi(2,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,3,2)*xi(3,2+i,n,m)*img*pi*2.0
! divergence_hat_full(resolution(1)-i,j,k,3) = pstress_field_hat(resolution(1)-i,j,k,1,3)*xi(1,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,2,3)*xi(2,2+i,n,m)*img*pi*2.0&
! + pstress_field_hat(resolution(1)-i,j,k,3,3)*xi(3,2+i,n,m)*img*pi*2.0
! if(n == 1) n = resolution(2) +1
! n = n-1
! enddo
! if(m == 1) m = resolution(3) +1
! m = m -1
! enddo; enddo
print*, divergence_hat_full
pause
call dfftw_execute_dft_c2r(plan_div(2), divergence_hat, divergence)
call dfftw_execute_dft(plan_div(3), divergence_hat_full, divergence_hat_full2)
divergence = divergence*wgt
divergence_hat_full2 = divergence_hat_full2*wgt
print*, divergence_hat_full2
do m = 1,3 ! L infinity norm of stress tensor
p_real_avg_inf = max(p_real_avg_inf, sum(abs(pstress_av(:,m))))
@ -779,15 +921,23 @@ program DAMASK_spectral
do k = 1, resolution(3); do j = 1, resolution(2) ;do i = 1, resolution(1)
err_real_div_max_inf = max(err_real_div_max_inf, maxval(divergence(i,j,k,:)))
err_real_div_max_inf2 = max(err_real_div_max_inf2, maxval(real(divergence_hat_full2(i,j,k,:))))
err_real_div_max_two = max(err_real_div_max_two, sqrt(sum(divergence(i,j,k,:)**2.0)))
err_real_div_max_two2 = max(err_real_div_max_two2, sqrt(sum(real(divergence_hat_full2(i,j,k,:))**2.0)))
err_real_div_avg_inf = err_real_div_avg_inf + (maxval(divergence(i,j,k,:)))**2.0
err_real_div_avg_inf2 = err_real_div_avg_inf2 + (maxval(real(divergence_hat_full2(i,j,k,:))))**2.0
err_real_div_avg_two = err_real_div_avg_two + sum(divergence(i,j,k,:)**2.0) ! don't take square root just to square it again
err_real_div_avg_two2 = err_real_div_avg_two2 + sum(real(divergence_hat_full2(i,j,k,:))**2.0) ! don't take square root just to square it again
enddo; enddo; enddo
err_real_div_max_inf = err_real_div_max_inf/p_real_avg_inf
err_real_div_max_inf2 = err_real_div_max_inf2/p_real_avg_inf
err_real_div_max_two = err_real_div_max_two/p_real_avg_two
err_real_div_max_two2 = err_real_div_max_two2/p_real_avg_two
err_real_div_avg_inf = sqrt(err_real_div_avg_inf*wgt)/p_real_avg_inf
err_real_div_avg_inf2 = sqrt(err_real_div_avg_inf2*wgt)/p_real_avg_inf
err_real_div_avg_two = sqrt(err_real_div_avg_two*wgt)/p_real_avg_two
err_real_div_avg_two2 = sqrt(err_real_div_avg_two2*wgt)/p_real_avg_two
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
@ -796,7 +946,7 @@ program DAMASK_spectral
do l = 1,3; do m = 1,3
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
enddo; enddo
temp33_Real = math_inv3x3(math_mul3333xx33(c0, xiDyad))
temp33_Real = math_inv3x3(math_mul3333xx33(c0_reference, xiDyad))
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
@ -839,18 +989,22 @@ program DAMASK_spectral
print '(2(a,E8.2))', ' error divergence: ',err_div, ' Tol. = ', err_div_tol
!!!!!!!!!!!!!!!!!!!!!!!! start divergence debugging
print '((a,E12.7))', ' error divergence FT (max,inf): ',err_div_max_inf
print '((a,E12.7))', ' error divergence FT (max,inf2): ',err_div_max_inf2
print '((a,E12.7))', ' error divergence FT (max,two): ',err_div_max_two
print '((a,E12.7))', ' error divergence FT (max,two2): ',err_div_max_two2
print '((a,E12.6))', ' error divergence FT (avg,inf): ',err_div_avg_inf
print '((a,E12.6))', ' error divergence FT (avg,inf2): ',err_div_avg_inf2
print '((a,E12.7))', ' error divergence FT (avg,two): ',err_div_avg_two
print '((a,E12.7))', ' error divergence FT (avg,two2): ',err_div_avg_two2
print '((a,E16.11))', ' error divergence FT (max,inf): ',err_div_max_inf
print '((a,E16.11))', ' error divergence FT (max,inf2): ',err_div_max_inf2
print '((a,E16.11))', ' error divergence FT (max,two): ',err_div_max_two
print '((a,E16.11))', ' error divergence FT (max,two2): ',err_div_max_two2
print '((a,E16.11))', ' error divergence FT (avg,inf): ',err_div_avg_inf
print '((a,E16.11))', ' error divergence FT (avg,inf2): ',err_div_avg_inf2
print '((a,E16.11))', ' error divergence FT (avg,two): ',err_div_avg_two
print '((a,E16.11))', ' error divergence FT (avg,two2): ',err_div_avg_two2
print '((a,E8.2))', ' error divergence Real (max,inf): ',err_real_div_max_inf
print '((a,E8.2))', ' error divergence Real (max,inf2): ',err_real_div_max_inf2
print '((a,E8.2))', ' error divergence Real (max,two): ',err_real_div_max_two
print '((a,E8.2))', ' error divergence Real (max,two2): ',err_real_div_max_two2
print '((a,E8.2))', ' error divergence Real (avg,inf): ',err_real_div_avg_inf
print '((a,E8.2))', ' error divergence Real (avg,inf2): ',err_real_div_avg_inf2
print '((a,E8.2))', ' error divergence Real (avg,two): ',err_real_div_avg_two
print '((a,E8.2))', ' error divergence Real (avg,two2): ',err_real_div_avg_two2
!!!!!!!!!!!!!!!!!!!!!!!! end divergence debugging
print '(2(a,E8.2))', ' error stress: ',err_stress, ' Tol. = ', err_stress_tol
print '(2(a,E8.2))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol
@ -858,7 +1012,7 @@ program DAMASK_spectral
if((err_stress > err_stress_tol .or. err_defgrad > err_defgrad_tol) .and. err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc.
calcmode = 0_pInt
defgradAimCorr = 0.0_pReal
damper = damper * 0.9_pReal
damper = 1.0_pReal
endif
end select
enddo ! end looping when convergency is achieved

54
code/math.f90
View File

@ -1167,6 +1167,23 @@ pure function math_transpose3x3(A)
endfunction math_Plain33to9
!********************************************************************
! convert symmetric 3x3 matrix into plain vector 6x1
!********************************************************************
pure function math_Plain33to6(m33)
use prec, only: pReal,pInt
implicit none
real(pReal), dimension(3,3), intent(in) :: m33
real(pReal), dimension(6) :: math_Plain33to6
integer(pInt) i
forall (i=1:6) math_Plain33to6(i) = m33(mapMandel(1,i),mapMandel(2,i))
endfunction math_Plain33to6
!********************************************************************
! convert Plain 9x1 back to 3x3 matrix
!********************************************************************
@ -1313,6 +1330,43 @@ pure function math_transpose3x3(A)
endfunction math_Mandel3333to66
!********************************************************************
! convert symmetric 3x3x3x3 tensor into Plain matrix 6x6
!********************************************************************
pure function math_Plain3333to66(m3333)
use prec, only: pReal,pInt
implicit none
real(pReal), dimension(3,3,3,3), intent(in) :: m3333
real(pReal), dimension(6,6) :: math_Plain3333to66
integer(pInt) i,j
forall (i=1:6,j=1:6) math_Plain3333to66(i,j) = &
m3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j))
endfunction math_Plain3333to66
!********************************************************************
! convert Plain matrix 6x6 back to symmetric 3x3x3x3 tensor
!********************************************************************
pure function math_Plain66to3333(m66)
use prec, only: pReal,pInt
implicit none
real(pReal), dimension(6,6), intent(in) :: m66
real(pReal), dimension(3,3,3,3) :: math_Plain66to3333
integer(pInt) i,j
forall (i=1:6,j=1:6)
math_Plain66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j)) = m66(i,j)
math_Plain66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(1,j),mapMandel(2,j)) = m66(i,j)
math_Plain66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(2,j),mapMandel(1,j)) = m66(i,j)
math_Plain66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(2,j),mapMandel(1,j)) = m66(i,j)
end forall
endfunction math_Plain66to3333
!********************************************************************

626
code/mpie_spectral2d.f90
View File

@ -1,626 +0,0 @@
! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##############################################################
!* $Id: mpie_spectral2d.f90 665 2010-10-13 16:04:44Z MPIE\m.diehl $
!********************************************************************
! Material subroutine for BVP solution using spectral method
! Version for 2D Problems, suitable for testing and implementation of new features
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Not working by now due to changes on other routines
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! written by P. Eisenlohr,
! F. Roters,
! L. Hantcherli,
! W.A. Counts
! D.D. Tjahjanto
! C. Kords
! M. Diehl
! R. Lebensohn
!
! MPI fuer Eisenforschung, Duesseldorf
!
!********************************************************************
! Usage:
! - start program with mpie_spectral PathToMeshFile/NameOfMesh.mesh
! PathToLoadFile/NameOfLoadFile.load
! - PathToLoadFile will be the working directory
! - make sure the file "material.config" exists in the working
! directory
!********************************************************************
program DAMASK_spectral
!********************************************************************
use DAMASK_interface
use prec, only: pInt, pReal
use IO
use math
use CPFEM, only: CPFEM_general
use numerics, only: relevantStrain, rTol_crystalliteStress
implicit none
include 'include/fftw3.f' !header file for fftw3 (declaring variables). Library file is also needed
! variables to read from loadcase and mesh file
real(pReal), dimension(9) :: valuevector ! stores information temporarily from loadcase file
integer(pInt), parameter :: maxNchunksInput = 24 ! 4 identifiers, 18 values for the matrices and 2 scalars
integer(pInt), dimension (1+maxNchunksInput*2) :: posInput
integer(pInt), parameter :: maxNchunksMesh = 7 ! 4 identifiers, 3 values
integer(pInt), dimension (1+2*maxNchunksMesh) :: posMesh
integer(pInt) unit, N_l, N_s, N_t, N_n ! numbers of identifiers
character(len=1024) path, line
logical gotResolution,gotDimension,gotHomogenization
logical, dimension(9) :: bc_maskvector
! variables storing information from loadcase file
real(pReal) timeinc
real(pReal), dimension (:,:,:), allocatable :: bc_velocityGrad, &
bc_stress ! velocity gradient and stress BC
real(pReal), dimension(:), allocatable :: bc_timeIncrement ! length of increment
integer(pInt) N_Loadcases, steps
integer(pInt), dimension(:), allocatable :: bc_steps ! number of steps
logical, dimension(:,:,:,:), allocatable :: bc_mask ! mask of boundary conditions
! variables storing information from mesh file
real(pReal) wgt
real(pReal), dimension(3) :: meshdimension
integer(pInt) homog, prodnn
integer(pInt), dimension(3) :: resolution
! stress etc.
real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, damper,&
pstress, pstress_av, cstress_av, defgrad_av,&
defgradAim, defgradAimOld, defgradAimCorr, defgradAimCorrPrev,&
mask_stress, mask_defgrad
real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0
real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation
real(pReal), dimension(6,6) :: dsde, c066, s066
real(pReal), dimension(:,:,:,:), allocatable :: defgradold, cstress_field, defgrad
complex(pReal), dimension(:,:,:,:), allocatable :: pstress_field, tau
complex(pReal), dimension(:,:), allocatable :: ddefgrad
! variables storing information for spectral method
complex(pReal), dimension(:,:,:,:), allocatable :: workfft
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(3,3) :: xinormdyad
real(pReal), dimension(:,:,:,:,:,:), allocatable :: gamma_hat
real(pReal), dimension(:,:,:), allocatable :: xi
integer(pInt), dimension(2) :: k_s
integer*8, dimension(3,3,3) :: plan_fft
! convergence etc.
real(pReal) err_div, err_stress, err_defgrad
real(pReal) err_div_tol, err_stress_tol, err_stress_tolrel, sigma0
integer(pInt) itmax, ierr
logical errmatinv
! loop variables etc.
real(pReal) guessmode ! flip-flop to guess defgrad fluctuation field evolution
integer(pInt) i, j, k, l, m, n, p
integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode
real(pReal) temperature ! not used, but needed for call to CPFEM_general
!gmsh output
character(len=1024) :: nriter
character(len=1024) :: nrstep
character(len=1024) :: nrloadcase
real(pReal), dimension(:,:,:), allocatable :: displacement
!gmsh output
!Initializing
bc_maskvector = ''
unit = 234_pInt
ones = 1.0_pReal
zeroes = 0.0_pReal
N_l = 0_pInt
N_s = 0_pInt
N_t = 0_pInt
N_n = 0_pInt
resolution = 1_pInt; meshdimension = 0.0_pReal
err_div_tol = 1.0e-4
itmax = 250_pInt
err_stress_tolrel=0.01
temperature = 300.0_pReal
gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false.
if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments
! Reading the loadcase file and assign variables
path = getLoadcaseName()
print*,'Loadcase: ',trim(path)
print*,'Workingdir: ',trim(getSolverWorkingDirectoryName())
if (.not. IO_open_file(unit,path)) call IO_error(45,ext_msg = path)
rewind(unit)
do
read(unit,'(a1024)',END = 101) line
if (IO_isBlank(line)) cycle ! skip empty lines
posInput = IO_stringPos(line,maxNchunksInput)
do i = 1, maxNchunksInput, 1
select case (IO_lc(IO_stringValue(line,posInput,i)))
case('l','velocitygrad')
N_l = N_l+1
case('s','stress')
N_s = N_s+1
case('t','time','delta')
N_t = N_t+1
case('n','incs','increments','steps')
N_n = N_n+1
end select
enddo ! count all identifiers to allocate memory and do sanity check
if ((N_l /= N_s).or.(N_s /= N_t).or.(N_t /= N_n)) & ! sanity check
call IO_error(46,ext_msg = path) !error message for incomplete input file
enddo
! allocate memory depending on lines in input file
101 N_Loadcases = N_l
allocate (bc_velocityGrad(3,3,N_Loadcases)); bc_velocityGrad = 0.0_pReal
allocate (bc_stress(3,3,N_Loadcases)); bc_stress = 0.0_pReal
allocate (bc_mask(3,3,2,N_Loadcases)); bc_mask = .false.
allocate (bc_timeIncrement(N_Loadcases)); bc_timeIncrement = 0.0_pReal
allocate (bc_steps(N_Loadcases)); bc_steps = 0_pInt
rewind(unit)
i = 0_pInt
do
read(unit,'(a1024)',END = 200) line
if (IO_isBlank(line)) cycle ! skip empty lines
i = i + 1
posInput = IO_stringPos(line,maxNchunksInput)
do j = 1,maxNchunksInput,2
select case (IO_lc(IO_stringValue(line,posInput,j)))
case('l','velocitygrad')
valuevector = 0.0_pReal
forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '#'
do k = 1,9
if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the velocity gradient matrix
enddo
bc_mask(:,:,1,i) = reshape(bc_maskvector,(/3,3/))
bc_velocityGrad(:,:,i) = reshape(valuevector,(/3,3/))
case('s','stress')
valuevector = 0.0_pReal
forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '#'
do k = 1,9
if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the bc_stress matrix
enddo
bc_mask(:,:,2,i) = reshape(bc_maskvector,(/3,3/))
bc_stress(:,:,i) = reshape(valuevector,(/3,3/))
case('t','time','delta') ! increment time
bc_timeIncrement(i) = IO_floatValue(line,posInput,j+1)
case('n','incs','increments','steps') ! bc_steps
bc_steps(i) = IO_intValue(line,posInput,j+1)
end select
enddo; enddo
200 close(unit)
do i = 1, N_Loadcases
if (any(bc_mask(:,:,1,i) == bc_mask(:,:,2,i))) call IO_error(47,i) ! bc_mask consistency
print '(a,/,3(3(f12.6,x)/))','L',bc_velocityGrad(:,:,i)
print '(a,/,3(3(f12.6,x)/))','bc_stress',bc_stress(:,:,i)
print '(a,/,3(3(l,x)/))','bc_mask for velocitygrad',bc_mask(:,:,1,i)
print '(a,/,3(3(l,x)/))','bc_mask for stress',bc_mask(:,:,2,i)
print *,'time',bc_timeIncrement(i)
print *,'incs',bc_steps(i)
print *, ''
enddo
!read header of mesh file to get the information needed before the complete mesh file is intepretated by mesh.f90
path = getSolverJobName()
print*,'JobName: ',trim(path)
if (.not. IO_open_file(unit,trim(path)//InputFileExtension)) call IO_error(101,ext_msg = path)
rewind(unit)
do
read(unit,'(a1024)',END = 100) line
if (IO_isBlank(line)) cycle ! skip empty lines
posMesh = IO_stringPos(line,maxNchunksMesh)
select case ( IO_lc(IO_StringValue(line,posMesh,1)) )
case ('dimension')
gotDimension = .true.
do i = 2,6,2
select case (IO_lc(IO_stringValue(line,posMesh,i)))
case('x')
meshdimension(1) = IO_floatValue(line,posMesh,i+1)
case('y')
meshdimension(2) = IO_floatValue(line,posMesh,i+1)
case('z')
meshdimension(3) = IO_floatValue(line,posMesh,i+1)
end select
enddo
case ('homogenization')
gotHomogenization = .true.
homog = IO_intValue(line,posMesh,2)
case ('resolution')
gotResolution = .true.
do i = 2,6,2
select case (IO_lc(IO_stringValue(line,posMesh,i)))
case('a')
resolution(1) = IO_intValue(line,posMesh,i+1)
case('b')
resolution(2) = IO_intValue(line,posMesh,i+1)
case('c')
resolution(3) = IO_intValue(line,posMesh,i+1)
end select
enddo
end select
if (gotDimension .and. gotHomogenization .and. gotResolution) exit
if (resolution(3) /=1) exit
enddo
100 close(unit)
print '(a,/,i4,i4,i4)','resolution a b c', resolution
print '(a,/,f6.1,f6.1,f6.1)','dimension x y z', meshdimension
print *,'homogenization',homog
print *, ''
allocate (workfft(resolution(1),resolution(2),3,3)); workfft = 0.0_pReal
allocate (gamma_hat(resolution(1),resolution(2),3,3,3,3)); gamma_hat = 0.0_pReal
allocate (xi(resolution(1),resolution(2),3)); xi = 0.0_pReal
allocate (pstress_field(resolution(1),resolution(2),3,3)); pstress_field = 0.0_pReal
allocate (cstress_field(resolution(1),resolution(2),3,3)); cstress_field = 0.0_pReal
allocate (tau(resolution(1),resolution(2),3,3)); tau = 0.0_pReal
allocate (displacement(resolution(1),resolution(2),3)); displacement = 0.0_pReal
allocate (defgrad(resolution(1),resolution(2),3,3)); defgrad = 0.0_pReal
allocate (defgradold(resolution(1),resolution(2),3,3)); defgradold = 0.0_pReal
allocate (ddefgrad(resolution(1),resolution(2))); ddefgrad = 0.0_pReal
! Initialization of fftw (see manual on fftw.org for more details)
call dfftw_init_threads(ierr)
call dfftw_plan_with_nthreads(4)
do m = 1,3; do n = 1,3
call dfftw_plan_dft_2d(plan_fft(1,m,n),resolution(1),resolution(2),&
cstress_field(:,:,m,n), workfft(:,:,m,n), FFTW_PATIENT, FFTW_FORWARD) !only for calculation of div (P)
call dfftw_plan_dft_2d(plan_fft(2,m,n),resolution(1),resolution(2),&
tau(:,:,m,n), workfft(:,:,m,n), FFTW_PATIENT, FFTW_FORWARD)
call dfftw_plan_dft_2d(plan_fft(3,m,n),resolution(1),resolution(2),&
workfft(:,:,m,n), ddefgrad(:,:), FFTW_PATIENT, FFTW_BACKWARD)
enddo; enddo
prodnn = resolution(1)*resolution(2)
wgt = 1_pReal/real(prodnn, pReal)
defgradAim = math_I3
defgradAimOld = math_I3
defgrad_av = math_I3
! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field
ielem = 0_pInt
c066 = 0.0_pReal
do j = 1, resolution(3); do i = 1, resolution(2)
defgradold(i,j,:,:) = math_I3 !no deformation at the beginning
defgrad(i,j,:,:) = math_I3
ielem = ielem +1
call CPFEM_general(2,math_I3,math_I3,temperature,0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c066 = c066 + dsde
enddo; enddo
c066 = c066 * wgt
c0 = math_mandel66to3333(c066)
call math_invert(6, c066, s066,i, errmatinv)
s0 = math_mandel66to3333(s066)
!calculation of xinormdyad (to calculate gamma_hat) and xi (waves, for proof of equilibrium)
do j = 1, resolution(2)
k_s(2) = j-1
if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
do i = 1, resolution(1)
k_s(1) = i-1
if(i > resolution(1)/2+1) k_s(1) = k_s(1)-resolution(1)
xi(i,j,3) = 0.0_pReal
xi(i,j,2) = real(k_s(2), pReal)/meshdimension(2)
xi(i,j,1) = real(k_s(1), pReal)/meshdimension(1)
if (any(xi(i,j,:) /= 0.0_pReal)) then
do l = 1,2; do m = 1,2
xinormdyad(l,m) = xi(i,j, l)*xi(i,j, m)/sum(xi(i,j,:)**2)
enddo; enddo
else
xinormdyad = 0.0_pReal
endif
temp33_Real = math_mul3333xx33(c0, xinormdyad)
temp33_Real = math_inv3x3(temp33_Real)
do l=1,3; do m=1,3; do n=1,3; do p=1,3
gamma_hat(i,j, l,m,n,p) = - temp33_Real(l,n) * xinormdyad(m,p)
! gamma_hat(i,j,k, l,m,n,p) = - 0.5_pReal * temp33_Real(l,n) * xinormdyad(m,p)& ! symmetrization????????
! - 0.5_pReal * temp33_Real(m,n) * xinormdyad(l,p)
enddo; enddo; enddo; enddo
enddo; enddo
open(539,file='stress-strain.out')
! Initialization done
!*************************************************************
!Loop over loadcases defined in the loadcase file
do loadcase = 1, N_Loadcases
!*************************************************************
timeinc = bc_timeIncrement(loadcase)/bc_steps(loadcase)
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first step
mask_defgrad = merge(ones,zeroes,bc_mask(:,:,1,loadcase))
mask_stress = merge(ones,zeroes,bc_mask(:,:,2,loadcase))
damper = ones/10
!*************************************************************
! loop oper steps defined in input file for current loadcase
do steps = 1, bc_steps(loadcase)
!*************************************************************
temp33_Real = defgradAim
defgradAim = defgradAim & ! update macroscopic displacement gradient (defgrad BC)
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
+ math_mul33x33(bc_velocityGrad(:,:,loadcase), defgradAim)*timeinc
defgradAimOld = temp33_Real
do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,:,:)
defgrad(i,j,:,:) = defgrad(i,j,:,:)& ! old fluctuations as guess for new step, no fluctuations for new loadcase
+ guessmode * (defgrad(i,j,:,:) - defgradold(i,j,:,:))&
+ (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,:,:))*timeinc
defgradold(i,j,:,:) = temp33_Real
enddo; enddo
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
calcmode = 0_pInt ! start calculation of BC fullfillment
CPFEM_mode = 1_pInt ! winding forward
iter = 0_pInt
err_div= 2_pReal * err_div_tol ! go into loop
defgradAimCorr = 0.0_pReal ! reset damping calculation
damper = damper * 0.9_pReal
!*************************************************************
! convergence loop
do while( iter <= itmax .and. &
(err_div > err_div_tol .or. &
err_stress > err_stress_tol))
iter = iter + 1
print '(A,I5.5,tr2,A,I5.5)', ' Step = ',steps,'Iteration = ',iter
!*************************************************************
! adjust defgrad to fulfill BCs
select case (calcmode)
case (0)
print *, 'Update Stress Field (constitutive evaluation P(F))'
ielem = 0_pInt
do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
call CPFEM_general(3, defgradold(i,j,:,:), defgrad(i,j,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo
ielem = 0_pInt
do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
defgradold(i,j,:,:), defgrad(i,j,:,:),& ! others get 2 (saves winding forward effort)
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
CPFEM_mode = 2_pInt
pstress_field(i,j,:,:) = pstress
cstress_field(i,j,:,:) = math_mandel6to33(cstress)
enddo; enddo
do m = 1,3; do n = 1,3
pstress_av(m,n) = sum(pstress_field(:,:,m,n)) * wgt
cstress_av(m,n) = sum(cstress_field(:,:,m,n)) * wgt
defgrad_av(m,n) = sum(defgrad(:,:,m,n)) * wgt
enddo; enddo
err_stress = maxval(abs(mask_stress * (cstress_av - bc_stress(:,:,loadcase))))
err_stress_tol = maxval(abs(cstress_av))*err_stress_tolrel
print*, 'Correcting deformation gradient to fullfill BCs'
defgradAimCorrPrev = defgradAimCorr
defgradAimCorr = -mask_stress * math_mul3333xx33(s0, (mask_stress*(cstress_av - bc_stress(:,:,loadcase))))
do m=1,3; do n =1,3 ! calculate damper (correction is far to strong)
if ( sign(1.0_pReal,defgradAimCorr(m,n))/=sign(1.0_pReal,defgradAimCorrPrev(m,n))) then
damper(m,n) = max(0.01_pReal,damper(m,n)*0.8)
else
damper(m,n) = min(1.0_pReal,damper(m,n) *1.2)
endif
enddo; enddo
defgradAimCorr = mask_Stress*(damper * defgradAimCorr)
defgradAim = defgradAim + defgradAimCorr
do m = 1,3; do n = 1,3
defgrad(:,:,m,n) = defgrad(:,:,m,n) + (defgradAim(m,n) - defgrad_av(m,n)) !anticipated target minus current state
enddo; enddo
err_div = 2 * err_div_tol
err_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim)))
print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient: ',defgrad_av(1:3,:)
print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6
print '(a,E8.2)', ' error defgrad ',err_defgrad
print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol*0.8
if(err_stress < err_stress_tol*0.8) then
calcmode = 1
endif
! Using the spectral method to calculate the change of deformation gradient, check divergence of stress field in fourier space
case (1)
print *, 'Update Stress Field (constitutive evaluation P(F))'
ielem = 0_pInt
do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
call CPFEM_general(3, defgradold(i,j,:,:), defgrad(i,j,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo
ielem = 0_pInt
do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
call CPFEM_general(2,&
defgradold(i,j,:,:), defgrad(i,j,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
pstress_field(i,j,:,:) = pstress
cstress_field(i,j,:,:) = math_mandel6to33(cstress)
enddo; enddo
do j = 1, resolution(2); do i = 1, resolution(1)
tau(i,j,:,:) = cstress_field(i,j,:,:) - math_mul3333xx33(c0, defgrad(i,j,:,:)-math_I3)
enddo; enddo
print *, 'Calculating equilibrium using spectral method'
err_div = 0.0_pReal; sigma0 = 0.0_pReal
do m = 1,3; do n = 1,3
call dfftw_execute_dft(plan_fft(1,m,n), cstress_field(:,:,m,n),workfft(:,:,m,n))
if(n==3) sigma0 = max(sigma0, sum(abs(workfft(1,1,m,:)))) ! L infinity Norm of stress tensor
enddo; enddo
do j = 1, resolution(2); do i = 1, resolution(1)
err_div = err_div + (maxval(abs(math_mul33x3_complex(workfft(i,j,:,:),xi(i,j,:))))) ! L infinity Norm of div(stress)
enddo; enddo
err_div = err_div/real(prodnn, pReal)/sigma0 !weighting of error
do m = 1,3; do n = 1,3
call dfftw_execute_dft(plan_fft(2,m,n), tau(:,:,m,n), workfft(:,:,m,n))
enddo; enddo
do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Complex = 0.0_pReal
do m = 1,3; do n = 1,3
temp33_Complex(m,n) = sum(gamma_hat(i,j,m,n,:,:) * workfft(i,j,:,:))
enddo; enddo
workfft(i,j,:,:) = temp33_Complex(:,:)
enddo; enddo
workfft(1,1,:,:) = zeroes!????
do m = 1,3; do n = 1,3
call dfftw_execute_dft(plan_fft(3,m,n), workfft(:,:,m,n),ddefgrad(:,:))
defgrad(:,:,m,n) = defgrad_av(m,n) + real(ddefgrad, pReal) * wgt
pstress_av(m,n) = sum(pstress_field(:,:,m,n))*wgt
cstress_av(m,n) = sum(cstress_field(:,:,m,n))*wgt
defgrad_av(m,n) = sum(defgrad(:,:,m,n))*wgt
defgrad(:,:,m,n) = defgrad(:,:,m,n) + (defgradAim(m,n) - defgrad_av(m,n)) !anticipated target minus current state
enddo; enddo
err_stress = maxval(abs(mask_stress * (cstress_av - bc_stress(:,:,loadcase))))
err_stress_tol = maxval(abs(cstress_av))*err_stress_tolrel !accecpt relativ error specified
print '(2(a,E8.2))', ' error divergence ',err_div,' Tol. = ', err_div_tol
print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol
if(err_stress > err_stress_tol .and. err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc.
calcmode = 0
defgradAimCorr = 0.0_pReal
damper = damper * 0.9_pReal
endif
end select
enddo ! end looping when convergency is achieved
write(539,'(E12.6,a,E12.6)'),defgrad_av(3,3)-1,' ', cstress_av(3,3)
print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient: ',defgrad_av(1:3,:)
print *, ''
print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6
print '(A)', '************************************************************'
! Postprocessing (gsmh output)
temp33_Real(1,:) = 0.0_pReal; temp33_Real(1,3) = -(real(resolution(3))/meshdimension(3)) ! start just below origin
k=1
do j = 1, resolution(2); do i = 1, resolution(1)
if((j==1).and.(i==1)) then
temp33_Real(1,:) = temp33_Real(1,:) + math_mul33x3(defgrad(i,j,:,:),&
(/0.0_pReal,0.0_pReal,(real(resolution(3))/meshdimension(3))/))
temp33_Real(2,:) = temp33_Real(1,:)
temp33_Real(3,:) = temp33_Real(1,:)
displacement(i,j,:) = temp33_Real(1,:)
else
if(i==1) then
temp33_Real(2,:) = temp33_Real(2,:) + math_mul33x3(defgrad(i,j,:,:),&
(/0.0_pReal,(real(resolution(2))/meshdimension(2)),0.0_pReal/))
temp33_Real(3,:) = temp33_Real(2,:)
displacement(i,j,:) = temp33_Real(2,:)
else
temp33_Real(3,:) = temp33_Real(3,:) + math_mul33x3(defgrad(i,j,:,:),&
(/(real(resolution(1))/meshdimension(1)),0.0_pReal,0.0_pReal/))
displacement(i,j,:) = temp33_Real(3,:)
endif
endif
enddo; enddo
write(nrloadcase, *) loadcase; write(nriter, *) iter; write(nrstep, *) steps
open(589,file = 'stress' //trim(adjustl(nrloadcase))//'-'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh')
open(588,file = 'disgrad'//trim(adjustl(nrloadcase))//'-'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh')
write(589, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
write(588, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,:) !for deformed configuration
write(588, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,:)
! write(589, '(4(I10,tr2))'), ielem, i-1,j-1,k-1 !for undeformed configuration
! write(588, '(4(I10,tr2))'), ielem, i-1,j-1,k-1
enddo; enddo; enddo
write(589, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn
write(588, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn
do i = 1, prodnn
write(589, '(I10, A, I10)'), i, ' 15 2 1 2', i
write(588, '(I10, A, I10)'), i, ' 15 2 1 2', i
enddo
write(589, '(A)'), '$EndElements'
write(588, '(A)'), '$EndElements'
write(589, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('stress'//trim(adjustl(nrloadcase))//'-'//&
trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn
write(588, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('disgrad'//trim(adjustl(nrloadcase))//'-'//&
trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(i10, 9(tr2, E14.8))'), ielem, cstress_field(i,j,:,:)
write(588, '(i10, 9(tr2, E14.8))'), ielem, defgrad(i,j,:,:) - math_I3
enddo; enddo; enddo
write(589, *), '$EndNodeData'
write(588, *), '$EndNodeData'
close(589); close(588)
enddo ! end looping over steps in current loadcase
enddo ! end looping over loadcases
close(539)
do i=1,3; do m = 1,3; do n = 1,3
call dfftw_destroy_plan(plan_fft(i,m,n))
enddo; enddo; enddo
end program DAMASK_spectral
!********************************************************************
! quit subroutine to satisfy IO_error
!
!********************************************************************
subroutine quit(id)
use prec
implicit none
integer(pInt) id
stop
end subroutine