! 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_spectral.f90 769 2011-02-21 14:37:38Z MPIE\m.diehl $
!********************************************************************
! Material subroutine for BVP solution using spectral method
!
! 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 PathToGeomFile/NameOfGeom.geom
! PathToLoadFile/NameOfLoadFile.load
! - PathToGeomFile will be the working directory
! - make sure the file "material.config" exists in the working
! directory. For further configuration use "numerics.config"
!********************************************************************
program DAMASK_spectral
!********************************************************************
use DAMASK_interface
use prec, only: pInt, pReal
use IO
use math
use CPFEM, only: CPFEM_general, CPFEM_initAll
use numerics, only: err_div_tol, err_stress_tol, err_stress_tolrel, err_defgrad_tol,&
itmax, memory_efficient, mpieNumThreadsInt
use homogenization, only: materialpoint_sizeResults, materialpoint_results
!$ use OMP_LIB ! the openMP function library
implicit none
include 'fftw3.f' !header file for fftw3 (declaring variables). Library files are also needed
! compile FFTW 3.2.2 with ./configure --enable-threads
! variables to read from loadcase and geom 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 :: maxNchunksGeom = 7 ! 4 identifiers, 3 values
integer(pInt), dimension (1+2*maxNchunksGeom) :: posGeom
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 geom file
real(pReal) wgt
real(pReal), dimension(3) :: geomdimension
integer(pInt) homog
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 ! Mandel notation of 4th order tensors
real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold
! variables storing information for spectral method
complex(pReal) :: img
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(3,3) :: xinormdyad
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat
real(pReal), dimension(3) :: xi, xi_central
integer(pInt), dimension(3) :: k_s
integer*8, dimension(2) :: plan_fft
! loop variables, convergence etc.
real(pReal) guessmode, err_div, err_stress, err_defgrad, sigma0
integer(pInt) i, j, k, l, m, n, p
integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode, ierr
logical errmatinv
real(pReal) temperature ! not used, but needed for call to CPFEM_general
!Initializing
!$ call omp_set_num_threads(mpieNumThreadsInt) ! set number of threads for parallel execution set by MPIE_NUM_THREADS
bc_maskvector = ''
unit = 234_pInt
ones = 1.0_pReal; zeroes = 0.0_pReal
img = cmplx(0.0,1.0)
N_l = 0_pInt; N_s = 0_pInt
N_t = 0_pInt; N_n = 0_pInt
gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false.
resolution = 1_pInt; geomdimension = 0.0_pReal
temperature = 300.0_pReal
if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments
! Reading the loadcase file and assign variables
path = getLoadcaseName()
print '(a,/,a)', 'Loadcase: ',trim(path)
print '(a,/,a)', 'Workingdir: ',trim(getSolverWorkingDirectoryName())
print '(a,/,a)', 'SolverJobName: ',trim(getSolverJobName())
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
enddo
101 N_Loadcases = N_l
! allocate memory depending on lines in input file
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) = transpose(reshape(bc_maskvector,(/3,3/)))
bc_velocityGrad(:,:,i) = math_transpose3x3(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) = transpose(reshape(bc_maskvector,(/3,3/)))
bc_stress(:,:,i) = math_transpose3x3(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(46,i) ! bc_mask consistency
if (bc_timeIncrement(i) < 0.0_pReal) call IO_error(47,i) ! negative time increment forbidden
if (bc_steps(i) < 1_pInt) call IO_error(48,i) ! non-positive increments requested
print '(a,/,3(3(f12.6,x)/))','L:' ,math_transpose3x3(bc_velocityGrad(:,:,i))
print '(a,/,3(3(f12.6,x)/))','bc_stress:',math_transpose3x3(bc_stress(:,:,i))
print '(a,/,3(3(l,x)/))', 'bc_mask for velocitygrad:',transpose(bc_mask(:,:,1,i))
print '(a,/,3(3(l,x)/))', 'bc_mask for stress:' ,transpose(bc_mask(:,:,2,i))
print '(a,f12.6)','time: ',bc_timeIncrement(i)
print '(a,i5)','incs: ',bc_steps(i)
print *, ''
enddo
!read header of geom file to get the information needed before the complete geom file is intepretated by mesh.f90
path = getModelName()
print '(a,a)', 'GeomName: ',trim(path)
if (.not. IO_open_file(unit,trim(path)//InputFileExtension)) call IO_error(101,ext_msg = trim(path)//InputFileExtension)
rewind(unit)
do
read(unit,'(a1024)',END = 100) line
if (IO_isBlank(line)) cycle ! skip empty lines
posGeom = IO_stringPos(line,maxNchunksGeom)
select case ( IO_lc(IO_StringValue(line,posGeom,1)) )
case ('dimension')
gotDimension = .true.
do i = 2,6,2
select case (IO_lc(IO_stringValue(line,posGeom,i)))
case('x')
geomdimension(1) = IO_floatValue(line,posGeom,i+1)
case('y')
geomdimension(2) = IO_floatValue(line,posGeom,i+1)
case('z')
geomdimension(3) = IO_floatValue(line,posGeom,i+1)
end select
enddo
case ('homogenization')
gotHomogenization = .true.
homog = IO_intValue(line,posGeom,2)
case ('resolution')
gotResolution = .true.
do i = 2,6,2
select case (IO_lc(IO_stringValue(line,posGeom,i)))
case('a')
resolution(1) = IO_intValue(line,posGeom,i+1)
case('b')
resolution(2) = IO_intValue(line,posGeom,i+1)
case('c')
resolution(3) = IO_intValue(line,posGeom,i+1)
end select
enddo
end select
if (gotDimension .and. gotHomogenization .and. gotResolution) exit
enddo
100 close(unit)
if(mod(resolution(1),2)/=0 .or. mod(resolution(2),2)/=0 .or. mod(resolution(3),2)/=0) call IO_error(103)
print '(a,/,i4,i4,i4)','resolution a b c:', resolution
print '(a,/,f6.1,f6.1,f6.1)','dimension x y z:', geomdimension
print '(a,i4)','homogenization: ',homog
allocate (defgrad (resolution(1),resolution(2),resolution(3),3,3)); defgrad = 0.0_pReal
allocate (defgradold(resolution(1),resolution(2),resolution(3),3,3)); defgradold = 0.0_pReal
wgt = 1.0_pReal/real(resolution(1)*resolution(2)*resolution(3), pReal)
defgradAim = math_I3
defgradAimOld = math_I3
defgrad_av = math_I3
! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field
call CPFEM_initAll(temperature,1_pInt,1_pInt)
ielem = 0_pInt
c066 = 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
call CPFEM_general(2,math_I3,math_I3,temperature,0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c066 = c066 + dsde
enddo; enddo; enddo
c066 = c066 * wgt
c0 = math_mandel66to3333(c066)
call math_invert(6, c066, s066,i, errmatinv)
if(errmatinv) call IO_error(800) !Matrix inversion error
s0 = math_mandel66to3333(s066)
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal
else ! precalculation of gamma_hat field
allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal
do k = 1, resolution(3)
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
xi(3) = 0.0_pReal !for the 2D case
if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) !3D case
xi(2) = real(k_s(2), pReal)/geomdimension(2)
xi(1) = real(k_s(1), pReal)/geomdimension(1)
if (any(xi /= 0.0_pReal)) then
do l = 1,3; do m = 1,3
xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2)
enddo; enddo
temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad))
else
xinormdyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
do l=1,3; do m=1,3; do n=1,3; do p=1,3
gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
(xinormdyad(m,p)+xinormdyad(p,m))
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
! calculate xi for the calculation of divergence in Fourier space (central frequency)
xi_central(3) = 0.0_pReal !2D case
if(resolution(3) > 1) xi_central(3) = real(resolution(3)/2, pReal)/geomdimension(3) !3D case
xi_central(2) = real(resolution(2)/2, pReal)/geomdimension(2)
xi_central(1) = real(resolution(1)/2, pReal)/geomdimension(1)
allocate (workfft(resolution(1)+2,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal
! Initialization of fftw (see manual on fftw.org for more details)
call sfftw_init_threads(ierr)
if(ierr == 0) call IO_error(104,ierr)
call sfftw_plan_with_nthreads(mpieNumThreadsInt)
call sfftw_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),&
workfft,(/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),FFTW_PATIENT)
call sfftw_plan_many_dft_c2r(plan_fft(2),3,(/resolution(1),resolution(2),resolution(3)/),9,&
workfft,(/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),&
workfft,(/resolution(1) +2,resolution(2),resolution(3)/),1,(resolution(1) +2)*resolution(2)*resolution(3),FFTW_PATIENT)
! write header of output file
open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
//'.spectralOut',form='UNFORMATTED')
write(538), 'load',trim(getLoadcaseName())
write(538), 'workingdir',trim(getSolverWorkingDirectoryName())
write(538), 'geometry',trim(getSolverJobName())//InputFileExtension
write(538), 'resolution',resolution
write(538), 'dimension',geomdimension
write(538), 'materialpoint_sizeResults', materialpoint_sizeResults
write(538), 'increments', sum(bc_steps)
write(538), 'eoh'
write(538) materialpoint_results(:,1,:)
write(538) materialpoint_results(:,1,:) !to be conform with t16 Marc format
! 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 k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,k,:,:)
defgrad(i,j,k,:,:) = defgrad(i,j,k,:,:)& ! old fluctuations as guess for new step, no fluctuations for new loadcase
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))&
+ (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,k,:,:))*timeinc
defgradold(i,j,k,:,:) = temp33_Real
enddo; enddo; enddo
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
if(all(bc_mask(:,:,1,loadcase))) then
calcmode = 1_pInt ! if no stress BC is given (calmode 0 is not needed)
else
calcmode = 0_pInt ! start calculation of BC fulfillment
endif
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 .or. &
err_defgrad > err_defgrad_tol))
iter = iter + 1_pInt
print*, ' '
print '(3(A,I5.5,tr2))', ' Loadcase = ',loadcase, ' Step = ',steps,'Iteration = ',iter
cstress_av = 0.0_pReal
workfft = 0.0_pReal !needed because of the padding for FFTW
!*************************************************************
! adjust defgrad to fulfill BCs
select case (calcmode)
case (0)
print *, 'Update Stress Field (constitutive evaluation P(F))'
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
call CPFEM_general(3, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
ielem = 0_pInt
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,
defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& ! others get 2 (saves winding forward effort)
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
CPFEM_mode = 2_pInt
workfft(i,j,k,:,:) = pstress
cstress_av = cstress_av + math_mandel6to33(cstress)
enddo; enddo; enddo
cstress_av = cstress_av * wgt
do m = 1,3; do n = 1,3
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))*err_stress_tolrel
print*, 'Correcting deformation gradient to fullfill BCs'
defgradAimCorrPrev = defgradAimCorr
defgradAimCorr = -mask_stress * math_mul3333xx33(s0, (mask_stress*(pstress_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:',math_transpose3x3(defgrad_av)
print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress / MPa: ' ,math_transpose3x3(cstress_av)/1.e6
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*0.8
if(err_stress < err_stress_tol*0.8) then
calcmode = 1_pInt
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 k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1_pInt
call CPFEM_general(3, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
ielem = 0_pInt
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,
defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),&
temperature,timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
CPFEM_mode = 2_pInt
workfft(i,j,k,:,:) = pstress
cstress_av = cstress_av + math_mandel6to33(cstress)
enddo; enddo; enddo
cstress_av = cstress_av * wgt
do m = 1,3; do n = 1,3
pstress_av(m,n) = sum(workfft(1:resolution(1),:,:,m,n))*wgt
enddo; enddo
print *, 'Calculating equilibrium using spectral method'
err_div = 0.0_pReal; sigma0 = 0.0_pReal
call sfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress
do m = 1,3 ! L infinity Norm of stress tensor
sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:) + (workfft(2,1,1,m,:))*img)))
enddo
err_div = (maxval(abs(math_mul33x3_complex(workfft(resolution(1)+1,resolution(2)/2+1,resolution(3)/2+1,:,:)+& ! L infinity Norm of div(stress)
workfft(resolution(1)+2,resolution(2)/2+1,resolution(3)/2+1,:,:)*img,xi_central))))
err_div = err_div/sigma0 !weighting of error
if(memory_efficient) then ! memory saving version, in-time calculation of gamma_hat
do k = 1, resolution(3)
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
xi(3) = 0.0_pReal !for the 2D case
if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) !3D case
xi(2) = real(k_s(2), pReal)/geomdimension(2)
xi(1) = real(k_s(1), pReal)/geomdimension(1)
if (any(xi(:) /= 0.0_pReal)) then
do l = 1,3; do m = 1,3
xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2)
enddo; enddo
temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad))
else
xinormdyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
do l=1,3; do m=1,3; do n=1,3; do p=1,3
gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
(xinormdyad(m,p) +xinormdyad(p,m))
enddo; enddo; enddo; enddo
do m = 1,3; do n = 1,3
temp33_Complex(m,n) = sum(gamma_hat(1,1,1,m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
+workfft(i*2 ,j,k,:,:)*img))
enddo; enddo
workfft(i*2-1,j,k,:,:) = real (temp33_Complex)
workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
enddo; enddo; enddo
else !use precalculated gamma-operator
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
do m = 1,3; do n = 1,3
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
+ workfft(i*2 ,j,k,:,:)*img))
enddo; enddo
workfft(i*2-1,j,k,:,:) = real (temp33_Complex)
workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
enddo; enddo; enddo
endif
workfft(1,1,1,:,:) = defgrad_av - math_I3 !zero frequency (real part)
workfft(2,1,1,:,:) = 0.0_pReal !zero frequency (imaginary part)
call sfftw_execute_dft_c2r(plan_fft(2),workfft,workfft)
defgrad = defgrad + workfft(1:resolution(1),:,:,:,:)*wgt
do m = 1,3; do n = 1,3
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 * (pstress_av - bc_stress(:,:,loadcase))))
err_stress_tol = maxval(abs(pstress_av))*err_stress_tolrel !accecpt relativ error specified
err_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim)))
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
print '(2(a,E8.2))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol
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
endif
end select
enddo ! end looping when convergency is achieved
write(538) materialpoint_results(:,1,:) !write to output file
print '(a,x,f12.7)' , ' Determinant of Deformation Aim: ', math_det3x3(defgradAim)
print '(a,/,3(3(f12.7,x)/))', ' Deformation Aim: ',math_transpose3x3(defgradAim)
print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient:',math_transpose3x3(defgrad_av)
print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress / MPa: ',math_transpose3x3(cstress_av)/1.e6
print '(A)', '************************************************************'
enddo ! end looping over steps in current loadcase
enddo ! end looping over loadcases
close(538)
call sfftw_destroy_plan(plan_fft(1)); call sfftw_destroy_plan(plan_fft(2))
end program DAMASK_spectral
!********************************************************************
! quit subroutine to satisfy IO_error
!
!********************************************************************
subroutine quit(id)
use prec
implicit none
integer(pInt) id
stop
end subroutine