DAMASK_EICMD/code/DAMASK_spectral.f90

682 lines
38 KiB
Fortran

! Copyright 2011 Max-Planck-Institut fuer Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Duesseldorf 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/>.
!
!##############################################################
!* $Id$
!********************************************************************
! 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 DAMASK_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 mesh, only: mesh_ipCenterOfGravity
use CPFEM, only: CPFEM_general, CPFEM_initAll
use numerics, only: err_div_tol, err_stress_tol, err_stress_tolrel,&
relevantStrain, itmax, memory_efficient, DAMASK_NumThreadsInt
use homogenization, only: materialpoint_sizeResults, materialpoint_results
!$ use OMP_LIB ! the openMP function library
implicit none
include '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 = 26 ! 5 identifiers, 18 values for the matrices and 3 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, N_freq, N_Fdot, N_temperature ! numbers of identifiers
character(len=1024) path, line
logical gotResolution,gotDimension,gotHomogenization
! variables storing information from loadcase file
real(pReal) time, time0, timeinc ! elapsed time, begin of interval, time interval
real(pReal), dimension (:,:,:), allocatable :: bc_deformation, & ! applied velocity gradient or time derivative of deformation gradient
bc_stress ! stress BC (if applicable)
real(pReal), dimension(:), allocatable :: bc_timeIncrement, & ! length of increment
bc_temperature ! isothermal starting conditions
integer(pInt) N_Loadcases, step ! ToDo: rename?
integer(pInt), dimension(:), allocatable :: bc_steps, & ! number of steps
bc_frequency, & ! frequency of result writes
bc_logscale ! linear/logaritmic time step flag
logical, dimension(:), allocatable :: followFormerTrajectory,& ! follow trajectory of former loadcase
velGradApplied ! decide wether velocity gradient or fdot is given
logical, dimension(:,:,:,:), allocatable :: bc_mask ! mask of boundary conditions
logical, dimension(:,:,:), allocatable :: bc_maskvector ! linear mask of boundary conditions
! variables storing information from geom file
real(pReal) wgt
real(pReal), dimension(3) :: geomdimension ! physical dimension of volume element in each direction
integer(pInt) homog ! homogenization scheme used
integer(pInt), dimension(3) :: resolution ! resolution (number of Fourier points) in each direction
! stress etc.
real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, &
pstress, pstress_av, defgrad_av,&
defgradAim, defgradAimOld, defgradAimCorr,&
mask_stress, mask_defgrad, fDot
real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current, s_prev, c_prev ! stiffness and compliance
real(pReal), dimension(6) :: cstress ! cauchy stress
real(pReal), dimension(6,6) :: dsde ! small strain stiffness
real(pReal), dimension(9,9) :: s_prev99, c_prev99 ! compliance and stiffness in matrix notation
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 ! reduced compliance and stiffness (only for stress BC)
integer(pInt) size_reduced ! number of stress BCs
! variables storing information for spectral method
complex(pReal) :: img
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field
integer(pInt), dimension(3) :: k_s
integer*8, dimension(2) :: plan_fft ! plans for fftw (forward and backward)
! loop variables, convergence etc.
real(pReal) guessmode, err_div, err_stress, p_hat_avg
integer(pInt) i, j, k, l, m, n, p
integer(pInt) loadcase, ielem, iter, CPFEM_mode, ierr, not_converged_counter
logical errmatinv
!Initializing
!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
print*, ''
print*, '<<<+- DAMASK_spectral init -+>>>'
print*, '$Id$'
print*, ''
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_temperature = 0_pInt
time = 0.0_pReal
N_n = 0_pInt
N_freq = 0_pInt
N_Fdot = 0_pInt
not_converged_counter = 0_pInt
gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false.
resolution = 1_pInt
geomdimension = 0.0_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(30,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('fdot')
N_Fdot = N_Fdot+1
case('s', 'stress', 'pk1', 'piolakirchhoff')
N_s = N_s+1
case('t', 'time', 'delta')
N_t = N_t+1
case('n', 'incs', 'increments', 'steps', 'logincs', 'logsteps')
N_n = N_n+1
case('f', 'freq', 'frequency')
N_freq = N_freq+1
case('temp','temperature')
N_temperature = N_temperature+1
end select
enddo ! count all identifiers to allocate memory and do sanity check
enddo
101 N_Loadcases = N_n
if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
call IO_error(31,ext_msg = path) ! error message for incomplete loadcase
! allocate memory depending on lines in input file
allocate (bc_deformation(3,3,N_Loadcases)); bc_deformation = 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_maskvector(9,2,N_Loadcases)); bc_maskvector = .false.
allocate (velGradApplied(N_Loadcases)); velGradApplied = .false.
allocate (bc_timeIncrement(N_Loadcases)); bc_timeIncrement = 0.0_pReal
allocate (bc_temperature(N_Loadcases)); bc_temperature = 300.0_pReal
allocate (bc_steps(N_Loadcases)); bc_steps = 0_pInt
allocate (bc_logscale(N_Loadcases)); bc_logscale = 0_pInt
allocate (bc_frequency(N_Loadcases)); bc_frequency = 1_pInt
allocate (followFormerTrajectory(N_Loadcases)); followFormerTrajectory = .true.
rewind(unit)
loadcase = 0_pInt
do
read(unit,'(a1024)',END = 200) line
if (IO_isBlank(line)) cycle ! skip empty lines
loadcase = loadcase + 1
posInput = IO_stringPos(line,maxNchunksInput)
do j = 1,maxNchunksInput,2
select case (IO_lc(IO_stringValue(line,posInput,j)))
case('fdot','l','velocitygrad') ! assign values for the deformation BC matrix
velGradApplied(loadcase) = (IO_lc(IO_stringValue(line,posInput,j)) == 'l' .or. &
IO_lc(IO_stringValue(line,posInput,j)) == 'velocitygrad') ! in case of given L, set flag to true
valuevector = 0.0_pReal
forall (k = 1:9) bc_maskvector(k,1,loadcase) = IO_stringValue(line,posInput,j+k) /= '*'
do k = 1,9
if (bc_maskvector(k,1,loadcase)) valuevector(k) = IO_floatValue(line,posInput,j+k)
enddo
bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector(1:9,1,loadcase),(/3,3/)))
bc_deformation(:,:,loadcase) = math_plain9to33(valuevector)
case('s', 'stress', 'pk1', 'piolakirchhoff')
valuevector = 0.0_pReal
forall (k = 1:9) bc_maskvector(k,2,loadcase) = IO_stringValue(line,posInput,j+k) /= '*'
do k = 1,9
if (bc_maskvector(k,2,loadcase)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the bc_stress matrix
enddo
bc_mask(:,:,2,loadcase) = transpose(reshape(bc_maskvector(1:9,2,loadcase),(/3,3/)))
bc_stress(:,:,loadcase) = math_plain9to33(valuevector)
case('t','time','delta') ! increment time
bc_timeIncrement(loadcase) = IO_floatValue(line,posInput,j+1)
case('temp','temperature') ! starting temperature
bc_temperature(loadcase) = IO_floatValue(line,posInput,j+1)
case('n','incs','increments','steps') ! bc_steps
bc_steps(loadcase) = IO_intValue(line,posInput,j+1)
case('logincs','logsteps') ! true, if log scale
bc_steps(loadcase) = IO_intValue(line,posInput,j+1)
bc_logscale(loadcase) = 1_pInt
case('f','freq','frequency') ! frequency of result writings
bc_frequency(loadcase) = IO_intValue(line,posInput,j+1)
case('guessreset','dropguessing')
followFormerTrajectory(loadcase) = .false. ! do not continue to predict deformation along former trajectory
end select
enddo; enddo
200 close(unit)
if (followFormerTrajectory(1)) then
call IO_warning(33) ! cannot guess along trajectory for first step of first loadcase
followFormerTrajectory(1) = .false.
endif
do loadcase = 1, N_Loadcases ! consistency checks and output
print *, '------------------------------------------------------'
print '(a,i5)', 'Loadcase:', loadcase
if (.not. followFormerTrajectory(loadcase)) &
print '(a)', 'drop guessing along trajectory'
if (any(bc_mask(:,:,1,loadcase) .eqv. bc_mask(:,:,2,loadcase)))& ! exclusive or masking only
call IO_error(31,loadcase)
if (any(bc_mask(1:3,1:3,2,loadcase).and.transpose(bc_mask(1:3,1:3,2,loadcase)).and.&
reshape((/.false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false./),(/3,3/))))&
call IO_error(38,loadcase)
if (velGradApplied(loadcase)) then
do j = 1, 3
if (any(bc_mask(j,:,1,loadcase) .eqv. .true.) .and.&
any(bc_mask(j,:,1,loadcase) .eqv. .false.)) call IO_error(32,loadcase) ! each line should be either fully or not at all defined
enddo
print '(a,/,3(3(f12.6,x)/))','L:' ,math_transpose3x3(bc_deformation(:,:,loadcase))
print '(a,/,3(3(l,x)/))', 'bc_mask for L:',transpose(bc_mask(:,:,1,loadcase))
else
print '(a,/,3(3(f12.6,x)/))','Fdot:' ,math_transpose3x3(bc_deformation(:,:,loadcase))
print '(a,/,3(3(l,x)/))', 'bc_mask for Fdot:',transpose(bc_mask(:,:,1,loadcase))
endif
print '(a,/,3(3(f12.6,x)/))','bc_stress/MPa:',math_transpose3x3(bc_stress(:,:,loadcase))*1e-6
print '(a,/,3(3(l,x)/))', 'bc_mask for stress:' ,transpose(bc_mask(:,:,2,loadcase))
if (bc_timeIncrement(loadcase) < 0.0_pReal) call IO_error(34,loadcase) ! negative time increment
print '(a,f12.6)','temperature: ',bc_temperature(loadcase)
print '(a,f12.6)','time: ',bc_timeIncrement(loadcase)
if (bc_steps(loadcase) < 1_pInt) call IO_error(35,loadcase) ! non-positive increment count
print '(a,i6)','incs: ',bc_steps(loadcase)
if (bc_frequency(loadcase) < 1_pInt) call IO_error(36,loadcase) ! non-positive result frequency
print '(a,i6)','freq: ',bc_frequency(loadcase)
enddo
!read header of geom file to get the information needed before the complete geom file is intepretated by mesh.f90
path = getModelName()
print *, '------------------------------------------------------'
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_pInt)/=0_pInt .or.&
mod(resolution(2),2_pInt)/=0_pInt .or.&
(mod(resolution(3),2_pInt)/=0_pInt .and. resolution(3)/= 1_pInt)) call IO_error(103)
print '(a,/,i5,i5,i5)','resolution a b c:', resolution
print '(a,/,f12.5,f12.5,f12.5)','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
allocate (coordinates(3,resolution(1),resolution(2),resolution(3))); coordinates = 0.0_pReal
allocate (temperature( resolution(1),resolution(2),resolution(3))); temperature = bc_temperature(1) ! start out isothermally
allocate (xi (3,resolution(1)/2+1,resolution(2),resolution(3))); xi =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(bc_temperature(1),1_pInt,1_pInt)
ielem = 0_pInt
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)
c_current = c_current + dPdF
enddo; enddo; enddo
c0_reference = c_current * wgt ! linear reference material stiffness
c_prev = c0_reference
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
xi(3,i,j,k) = 0.0_pReal ! 2D case
if(resolution(3) > 1) xi(3,i,j,k) = real(k_s(3), pReal)/geomdimension(3) ! 3D case
xi(2,i,j,k) = real(k_s(2), pReal)/geomdimension(2)
xi(1,i,j,k) = real(k_s(1), pReal)/geomdimension(1)
enddo; enddo; enddo
! remove highest frequencies for calculation of divergence (CAREFULL, they will be used for pre calculatet gamma operator!)
do k = 1,resolution(3); do j = 1,resolution(2); do i = 1,resolution(1)/2+1
if(k==resolution(3)/2+1) xi(3,i,j,k)= 0.0_pReal
if(j==resolution(2)/2+1) xi(2,i,j,k)= 0.0_pReal
if(i==resolution(1)/2+1) xi(1,i,j,k)= 0.0_pReal
enddo; enddo; enddo
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); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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_reference, xiDyad))
else
xiDyad = 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)) *&
(xiDyad(m,p)+xiDyad(p,m))
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
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)
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),&
workfft,(/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),FFTW_PATIENT)
call dfftw_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), 'loadcases', N_Loadcases
write(538), 'logscale', bc_logscale ! one entry per loadcase (0: linear, 1: log)
write(538), 'frequencies', bc_frequency ! one entry per loadcase
write(538), 'times', bc_timeIncrement ! one entry per loadcase
bc_steps(1) = bc_steps(1)+1 ! +1 to store initial situation
write(538), 'increments', bc_steps ! one entry per loadcase
bc_steps(1) = bc_steps(1)-1 ! re-adjust for correct looping
write(538), 'eoh' ! end of header
write(538) materialpoint_results(:,1,:) ! initial (non-deformed) results
! Initialization done
!*************************************************************
! Loop over loadcases defined in the loadcase file
do loadcase = 1, N_Loadcases
!*************************************************************
time0 = time ! loadcase start time
if (followFormerTrajectory(loadcase)) then ! continue to guess along former trajectory where applicable
guessmode = 1.0_pReal
else
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first step
endif
mask_defgrad = merge(ones,zeroes,bc_mask(:,:,1,loadcase))
mask_stress = merge(ones,zeroes,bc_mask(:,:,2,loadcase))
size_reduced = count(bc_maskvector(1:9,2,loadcase))
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
timeinc = bc_timeIncrement(loadcase)/bc_steps(loadcase) ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
fDot = 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
do step = 1, bc_steps(loadcase)
!*************************************************************
if (bc_logscale(loadcase) == 1_pInt) then ! loglinear scale
if (loadcase == 1_pInt) then ! 1st loadcase of loglinear scale
if (step == 1_pInt) then ! 1st step of 1st loadcase of loglinear scale
timeinc = bc_timeIncrement(1)*(2.0**(1 - bc_steps(1))) ! assume 1st step is equal to 2nd
else ! not-1st step of 1st loadcase of loglinear scale
timeinc = bc_timeIncrement(1)*(2.0**(step - (1 + bc_steps(1))))
endif
else ! not-1st loadcase of loglinear scale
timeinc = time0 * ( ((1.0_pReal+bc_timeIncrement(loadcase)/time0)**(float( step )/(bc_steps(loadcase)))) &
- ((1.0_pReal+bc_timeIncrement(loadcase)/time0)**(float((step-1))/(bc_steps(loadcase)))) )
endif
endif
time = time + timeinc
if (velGradApplied(loadcase)) & ! calculate fDot from given L and current F
fDot = math_mul33x33(bc_deformation(:,:,loadcase), defgradAim)
!winding forward of deformation aim
temp33_Real = defgradAim
defgradAim = defgradAim &
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
+ mask_defgrad * fDot * timeinc
defgradAimOld = temp33_Real
! update local deformation gradient
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,k,:,:)
if (velGradApplied(loadcase)) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc_deformation(:,:,loadcase),defgradold(i,j,k,:,:))
defgrad(i,j,k,:,:) = defgrad(i,j,k,:,:) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& ! guessing...
+ (1.0_pReal-guessmode) * mask_defgrad * fDot *timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,:,:) = temp33_Real
enddo; enddo; enddo
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
CPFEM_mode = 1_pInt ! winding forward
iter = 0_pInt
err_div = 2.0_pReal * err_div_tol ! go into loop
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
c_prev99 = math_Plain3333to99(c_prev)
k = 0_pInt ! build reduced stiffness
do n = 1,9
if(bc_maskvector(n,2,loadcase)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,9
if(bc_maskvector(m,2,loadcase)) then
j = j + 1_pInt
c_reduced(k,j) = c_prev99(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(800)
s_prev99 = 0.0_pReal ! build full compliance
k = 0_pInt
do n = 1,9
if(bc_maskvector(n,2,loadcase)) then
k = k + 1_pInt
j = 0_pInt
do m = 1,9
if(bc_maskvector(m,2,loadcase)) then
j = j + 1_pInt
s_prev99(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
s_prev = (math_Plain99to3333(s_prev99))
endif
!*************************************************************
! convergence loop
do while(iter < itmax .and. &
(err_div > err_div_tol .or. &
err_stress > err_stress_tol))
iter = iter + 1_pInt
print '(A)', '************************************************************'
print '(3(A,I5.5,tr2)A)', '**** Loadcase = ',loadcase, 'Step = ',step, 'Iteration = ',iter,'****'
print '(A)', '************************************************************'
workfft = 0.0_pReal ! needed because of the padding for FFTW
!*************************************************************
do n = 1,3; do m = 1,3
defgrad_av(m,n) = sum(defgrad(:,:,:,m,n)) * wgt
enddo; enddo
print '(a,/,3(3(f12.7,x)/))', 'Deformation Gradient:',math_transpose3x3(defgrad_av)
print '(A,/)', '== 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,& ! collect cycle
coordinates(1:3,i,j,k), defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),&
temperature(i,j,k),timeinc,ielem,1_pInt,&
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
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
call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
coordinates(1:3,i,j,k),&
defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& ! others get 2 (saves winding forward effort)
temperature(i,j,k),timeinc,ielem,1_pInt,&
cstress,dsde, pstress,dPdF)
CPFEM_mode = 2_pInt
workfft(i,j,k,:,:) = pstress ! build up average P-K stress
c_current = c_current + dPdF
enddo; enddo; enddo
do n = 1,3; do m = 1,3
pstress_av(m,n) = sum(workfft(1:resolution(1),:,:,m,n)) * wgt
enddo; enddo
print '(a,/,3(3(f12.7,x)/))', 'Piola-Kirchhoff Stress / MPa: ',math_transpose3x3(pstress_av)/1.e6
err_stress_tol = 0.0_pReal
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(1:3,1:3,loadcase)))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = maxval(abs(mask_defgrad * pstress_av)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
err_stress_tol = err_stress_tol * err_stress_tolrel ! weighting by relative criterion
print '(A,/)', '== Correcting Deformation Gradient to Fullfill BCs ========='
print '(2(a,E10.5)/)', 'Error Stress = ',err_stress, ', Tol. = ', err_stress_tol
defgradAimCorr = - math_mul3333xx33(s_prev, ((pstress_av - bc_stress(1:3,1:3,loadcase)))) ! residual on given stress components
defgradAim = defgradAim + defgradAimCorr
print '(a,/,3(3(f12.7,x)/))', 'Deformation Aim: ',math_transpose3x3(defgradAim)
print '(a,x,f12.7,/)' , 'Determinant of Deformation Aim: ', math_det3x3(defgradAim)
endif
print '(A,/)', '== Calculating Equilibrium Using Spectral Method ==========='
call dfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress
p_hat_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(workfft(1,1,1,1:3,1:3),& ! L_2 norm of average stress in fourier space,
math_transpose3x3(workfft(1,1,1,1:3,1:3)))))) ! ignore imaginary part as it is always zero for real only input))
err_div = 0.0_pReal
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
err_div = err_div + sqrt(sum((math_mul33x3_complex(workfft(i*2-1,j,k,1:3,1:3)+& ! avg of L_2 norm of div(stress) in fourier space (Suquet small strain)
workfft(i*2, j,k,1:3,1:3)*img,xi(1:3,i,j,k)))**2.0))
enddo; enddo; enddo
err_div = err_div*wgt/p_hat_avg*(minval(geomdimension)*wgt**(-1/4)) ! weigthting, multiplying by minimum dimension to get rid of dimension dependency and phenomenologigal factor wgt**(-1/4) to get rid of resolution dependency
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1, resolution(3); do j = 1, resolution(2) ;do i = 1, resolution(1)/2+1
if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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_reference, xiDyad))
else
xiDyad = 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))*&
(xiDyad(m,p) +xiDyad(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
! average strain
workfft(1,1,1,:,:) = defgrad_av - math_I3 ! zero frequency (real part)
workfft(2,1,1,:,:) = 0.0_pReal ! zero frequency (imaginary part)
call dfftw_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
print '(2(a,E10.5)/)', 'Error Divergence = ',err_div, ', Tol. = ', err_div_tol
enddo ! end looping when convergency is achieved
c_prev = c_current*wgt ! calculate stiffness for next step
if (mod(step,bc_frequency(loadcase)) == 0_pInt) & ! at output frequency
write(538) materialpoint_results(:,1,:) ! write result to file
if(err_div<err_div_tol .and. err_stress<err_stress_tol) then
print '(2(A,I5.5),A,/)', '== Step = ',step, ' of Loadcase = ',loadcase, ' Converged =============='
else
print '(2(A,I5.5),A,/)', '== Step = ',step, ' of Loadcase = ',loadcase, ' NOT Converged =========='
not_converged_counter = not_converged_counter + 1
endif
enddo ! end looping over steps in current loadcase
deallocate(c_reduced)
deallocate(s_reduced)
enddo ! end looping over loadcases
print '(A,/)', '############################################################'
print '(a,i5.5,a)', 'A Total of ', not_converged_counter, ' Steps did not Converge!'
close(538)
call dfftw_destroy_plan(plan_fft(1)); call dfftw_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