DAMASK_EICMD/code/DAMASK_spectral.f90

832 lines
48 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
! -g (--geom, --geometry) PathToGeomFile/NameOfGeom.geom
! -l (--load, --loadcase) 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 debug, only: debug_Verbosity
use math
use mesh, only: mesh_ipCenterOfGravity
use CPFEM, only: CPFEM_general, CPFEM_initAll
use FEsolving, only: restartWrite
use numerics, only: err_div_tol, err_stress_tol, err_stress_tolrel , rotation_tol,&
itmax, memory_efficient, DAMASK_NumThreadsInt,&
fftw_planner_flag, fftw_timelimit
use homogenization, only: materialpoint_sizeResults, materialpoint_results
!$ use OMP_LIB ! the openMP function library
implicit none
! variables to read from loadcase and geom file
real(pReal), dimension(9) :: valueVector ! stores information temporarily from loadcase file
integer(pInt), parameter :: maxNchunksLoadcase = &
(1_pInt + 9_pInt)*3_pInt + & ! deformation, rotation, and stress
(1_pInt + 1_pInt)*5_pInt + & ! time, (log)incs, temp, restartfrequency, and outputfrequency
1_pInt ! dropguessing
integer(pInt), dimension (1 + maxNchunksLoadcase*2) :: posLoadcase
integer(pInt), parameter :: maxNchunksGeom = 7_pInt ! 4 identifiers, 3 values
integer(pInt), dimension (1 + maxNchunksGeom*2) :: posGeom
integer(pInt) :: myUnit, N_l, N_s, N_t, N_n, N_Fdot, headerLength ! numbers of identifiers
character(len=1024) :: path, line, keyword
logical :: gotResolution, gotDimension, gotHomogenization
! variables storing information from loadcase file
!ToDo: create Data Structure loadcase
real(pReal), dimension (:,:,:), allocatable :: bc_deformation, & ! applied velocity gradient or time derivative of deformation gradient
bc_stress, & ! stress BC (if applicable)
bc_rotation ! rotation of BC (if applicable)
real(pReal), dimension(:), allocatable :: bc_timeIncrement, & ! length of increment
bc_temperature ! isothermal starting conditions
integer(pInt), dimension(:), allocatable :: bc_steps, & ! number of steps
bc_outputfrequency, & ! frequency of result writes
bc_restartfrequency, & ! frequency of result writes
bc_logscale ! linear/logaritmic time step flag
logical, dimension(:), allocatable :: bc_followFormerTrajectory,& ! follow trajectory of former loadcase
bc_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
character(len=3) :: loadcase_string
! 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
logical :: spectralPictureMode ! indicating 1 to 1 mapping of FP to microstructure
! stress etc.
real(pReal), dimension(3,3) :: pstress, pstress_av, defgrad_av, &
defgradAim, defgradAimOld, defgradAimCorr,&
mask_stress, mask_defgrad, fDot, &
pstress_av_load, defgradAim_lab ! quantities rotated to other coordinate system
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 :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
integer(pInt) :: size_reduced ! number of stress BCs
! pointwise data
real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
real(pReal), dimension(:,:,:), allocatable :: temperature
! variables storing information for spectral method and FFTW
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) :: fftw_plan ! plans for fftw (forward and backward)
integer*8 :: fftw_flag ! planner flag for fftw
! loop variables, convergence etc.
real(pReal) :: time, time0, timeinc ! elapsed time, begin of interval, time interval
real(pReal) :: guessmode, err_div, err_stress, p_hat_avg
complex(pReal), parameter :: img = cmplx(0.0_pReal,1.0_pReal)
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(3,3) :: temp33_Real
integer(pInt) :: i, j, k, l, m, n, p
integer(pInt) :: N_Loadcases, loadcase, step, iter, ielem, CPFEM_mode, ierr, notConvergedCounter, totalStepsCounter
logical errmatinv
!Initializing
!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
if (.not.(command_argument_count()==4 .or. command_argument_count()==6)) call IO_error(error_ID=102) ! check for correct number of given arguments
call DAMASK_interface_init()
!$OMP CRITICAL (write2out)
print '(a)', ''
print '(a,a)', '<<<+- DAMASK_spectral init -+>>>'
print '(a,a)', '$Id$'
print '(a)', ''
print '(a,a)', 'Working Directory: ',trim(getSolverWorkingDirectoryName())
print '(a,a)', 'Solver Job Name: ',trim(getSolverJobName())
print '(a)', ''
!$OMP END CRITICAL (write2out)
! Reading the loadcase file and allocate variables
myUnit = 234_pInt
path = getLoadcaseName()
if (.not. IO_open_file(myUnit,path)) call IO_error(error_ID=30,ext_msg = trim(path))
N_l = 0_pInt
N_Fdot = 0_pInt
N_t = 0_pInt
N_n = 0_pInt
rewind(myUnit)
do
read(myUnit,'(a1024)',END = 100) line
if (IO_isBlank(line)) cycle ! skip empty lines
posLoadcase = IO_stringPos(line,maxNchunksLoadcase)
do i = 1, maxNchunksLoadcase, 1 ! reading compulsory parameters for loadcase
select case (IO_lc(IO_stringValue(line,posLoadcase,i)))
case('l', 'velocitygrad', 'velgrad','velocitygradient')
N_l = N_l+1
case('fdot')
N_Fdot = N_Fdot+1
case('t', 'time', 'delta')
N_t = N_t+1
case('n', 'incs', 'increments', 'steps', 'logincs', 'logsteps')
N_n = N_n+1
end select
enddo ! count all identifiers to allocate memory and do sanity check
enddo
100 N_Loadcases = N_n
if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
call IO_error(error_ID=37,ext_msg = trim(path)) ! error message for incomplete loadcase
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 (bc_velGradApplied(N_Loadcases)); bc_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_outputfrequency(N_Loadcases)); bc_outputfrequency = 1_pInt
allocate (bc_restartfrequency(N_Loadcases)); bc_restartfrequency = 1_pInt
allocate (bc_followFormerTrajectory(N_Loadcases)); bc_followFormerTrajectory = .true.
allocate (bc_rotation(3,3,N_Loadcases)); bc_rotation = 0.0_pReal
rewind(myUnit)
loadcase = 0_pInt
do
read(myUnit,'(a1024)',END = 101) line
if (IO_isBlank(line)) cycle ! skip empty lines
loadcase = loadcase + 1
bc_rotation(:,:,loadcase) = math_I3 ! assume no rotation, overwrite later in case rotation of loadcase is given
posLoadcase = IO_stringPos(line,maxNchunksLoadcase)
do j = 1,maxNchunksLoadcase
select case (IO_lc(IO_stringValue(line,posLoadcase,j)))
case('fdot','l','velocitygrad','velgrad','velocitygradient') ! assign values for the deformation BC matrix
bc_velGradApplied(loadcase) = (IO_lc(IO_stringValue(line,posLoadcase,j)) == 'l' .or. &
IO_lc(IO_stringValue(line,posLoadcase,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,posLoadcase,j+k) /= '*'
do k = 1,9
if (bc_maskvector(k,1,loadcase)) valueVector(k) = IO_floatValue(line,posLoadcase,j+k)
enddo
bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector(1:9,1,loadcase),(/3,3/)))
bc_deformation(:,:,loadcase) = math_plain9to33(valueVector)
case('p', 'pk1', 'piolakirchhoff', 'stress')
valueVector = 0.0_pReal
forall (k = 1:9) bc_maskvector(k,2,loadcase) = IO_stringValue(line,posLoadcase,j+k) /= '*'
do k = 1,9
if (bc_maskvector(k,2,loadcase)) valueVector(k) = IO_floatValue(line,posLoadcase,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,posLoadcase,j+1)
case('temp','temperature') ! starting temperature
bc_temperature(loadcase) = IO_floatValue(line,posLoadcase,j+1)
case('n','incs','increments','steps') ! bc_steps
bc_steps(loadcase) = IO_intValue(line,posLoadcase,j+1)
case('logincs','logsteps') ! true, if log scale
bc_steps(loadcase) = IO_intValue(line,posLoadcase,j+1)
bc_logscale(loadcase) = 1_pInt
case('f','freq','frequency','outputfreq') ! frequency of result writings
bc_outputfrequency(loadcase) = IO_intValue(line,posLoadcase,j+1)
case('r','restart','restartwrite') ! frequency of writing restart information
bc_restartfrequency(loadcase) = IO_intValue(line,posLoadcase,j+1)
case('guessreset','dropguessing')
bc_followFormerTrajectory(loadcase) = .false. ! do not continue to predict deformation along former trajectory
case('euler') ! rotation of loadcase given in euler angles
p = 0_pInt ! assuming values given in radians
l = 1_pInt ! assuming keyword indicating degree/radians
select case (IO_lc(IO_stringValue(line,posLoadcase,j+1)))
case('deg','degree')
p = 1_pInt ! for conversion from degree to radian
case('rad','radian')
case default
l = 0_pInt ! imediately reading in angles, assuming radians
end select
forall(k = 1:3) temp33_Real(k,1) = IO_floatValue(line,posLoadcase,j +l +k) * real(p,pReal) * inRad
bc_rotation(:,:,loadcase) = math_EulerToR(temp33_Real(:,1))
case('rotation','rot') ! assign values for the rotation of loadcase matrix
valueVector = 0.0_pReal
forall (k = 1:9) valueVector(k) = IO_floatValue(line,posLoadcase,j+k)
bc_rotation(:,:,loadcase) = math_plain9to33(valueVector)
end select
enddo; enddo
101 close(myUnit)
!read header of geom file to get the information needed before the complete geom file is intepretated by mesh.f90
gotResolution =.false.
gotDimension =.false.
gotHomogenization = .false.
spectralPictureMode = .false.
resolution = 1_pInt
geomdimension = 0.0_pReal
path = getModelName()
if (.not. IO_open_file(myUnit,trim(path)//InputFileExtension))&
call IO_error(error_ID=101,ext_msg = trim(path)//InputFileExtension)
rewind(myUnit)
read(myUnit,'(a1024)') line
posGeom = IO_stringPos(line,2)
keyword = IO_lc(IO_StringValue(line,posGeom,2))
if (keyword(1:4) == 'head') then
headerLength = IO_intValue(line,posGeom,1) + 1_pInt
else
call IO_error(error_ID=42)
endif
rewind(myUnit)
do i = 1, headerLength
read(myUnit,'(a1024)') line
posGeom = IO_stringPos(line,maxNchunksGeom)
select case ( IO_lc(IO_StringValue(line,posGeom,1)) )
case ('dimension')
gotDimension = .true.
do j = 2,6,2
select case (IO_lc(IO_stringValue(line,posGeom,j)))
case('x')
geomdimension(1) = IO_floatValue(line,posGeom,j+1)
case('y')
geomdimension(2) = IO_floatValue(line,posGeom,j+1)
case('z')
geomdimension(3) = IO_floatValue(line,posGeom,j+1)
end select
enddo
case ('homogenization')
gotHomogenization = .true.
homog = IO_intValue(line,posGeom,2)
case ('resolution')
gotResolution = .true.
do j = 2,6,2
select case (IO_lc(IO_stringValue(line,posGeom,j)))
case('a')
resolution(1) = IO_intValue(line,posGeom,j+1)
case('b')
resolution(2) = IO_intValue(line,posGeom,j+1)
case('c')
resolution(3) = IO_intValue(line,posGeom,j+1)
end select
enddo
case ('picture')
spectralPictureMode = .true.
end select
enddo
close(myUnit)
if (.not.(gotDimension .and. gotHomogenization .and. gotResolution)) call IO_error(error_ID=45)
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(error_ID=103)
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)
!Output of geom file
!$OMP CRITICAL (write2out)
print '(a)', ''
print '(a)', '*************************************************************'
print '(a)', 'DAMASK spectral:'
print '(a)', 'The spectral method boundary value problem solver for'
print '(a)', 'the Duesseldorf Advanced Material Simulation Kit'
print '(a)', '*************************************************************'
print '(a,a)', 'Geom File Name: ',trim(path)//'.geom'
print '(a)', '-------------------------------------------------------------'
print '(a,/,i12,i12,i12)','resolution a b c:', resolution
print '(a,/,f12.5,f12.5,f12.5)','dimension x y z:', geomdimension
print '(a,i5)','homogenization: ',homog
print '(a,L)','spectralPictureMode: ',spectralPictureMode
print '(a)', '************************************************************'
print '(a,a)','Loadcase File Name: ',trim(getLoadcaseName())
!$OMP END CRITICAL (write2out)
if (bc_followFormerTrajectory(1)) then
call IO_warning(warning_ID=33_pInt) ! cannot guess along trajectory for first step of first loadcase
bc_followFormerTrajectory(1) = .false.
endif
! consistency checks and output of loadcase
do loadcase = 1, N_Loadcases
!$OMP CRITICAL (write2out)
print '(a)', '-------------------------------------------------------------'
print '(a,i5)', 'Loadcase: ', loadcase
write (loadcase_string, '(i3)' ) loadcase
if (.not. bc_followFormerTrajectory(loadcase)) &
print '(a)', 'Drop Guessing Along Trajectory'
!$OMP END CRITICAL (write2out)
if (any(bc_mask(:,:,1,loadcase) .eqv. bc_mask(1:3,1:3,2,loadcase)))& ! exclusive or masking only
call IO_error(error_ID=31,ext_msg=loadcase_string)
if (any(bc_mask(1:3,1:3,2,loadcase).and.transpose(bc_mask(1:3,1:3,2,loadcase)).and.& !checking if no rotation is allowed by stress BC
reshape((/.false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false./),(/3,3/))))&
call IO_error(error_ID=38,ext_msg=loadcase_string)
if (bc_velGradApplied(loadcase)) then
do j = 1, 3
if (any(bc_mask(j,1:3,1,loadcase) .eqv. .true.) .and.&
any(bc_mask(j,1:3,1,loadcase) .eqv. .false.)) call IO_error(error_ID=32,ext_msg=loadcase_string) ! each line should be either fully or not at all defined
enddo
!$OMP CRITICAL (write2out)
print '(a,/,3(3(f12.6,x)/))','Velocity Gradient:', merge(math_transpose3x3(bc_deformation(1:3,1:3,loadcase)),&
reshape(spread(DAMASK_NaN,1,9),(/3,3/)),&
transpose(bc_mask(1:3,1:3,1,loadcase)))
!$OMP END CRITICAL (write2out)
else
!$OMP CRITICAL (write2out)
print '(a,/,3(3(f12.6,x)/))','Change of Deformation Gradient:', merge(math_transpose3x3(bc_deformation(1:3,1:3,loadcase)),&
reshape(spread(DAMASK_NaN,1,9),(/3,3/)),&
transpose(bc_mask(1:3,1:3,1,loadcase)))
!$OMP END CRITICAL (write2out)
endif
!$OMP CRITICAL (write2out)
print '(a,/,3(3(f12.6,x)/))','Stress Boundary Condition/MPa:',merge(math_transpose3x3(bc_stress(1:3,1:3,loadcase)),&
reshape(spread(DAMASK_NaN,1,9),(/3,3/)),&
transpose(bc_mask(:,:,2,loadcase)))*1e-6
!$OMP END CRITICAL (write2out)
if (any(abs(math_mul33x33(bc_rotation(1:3,1:3,loadcase),math_transpose3x3(bc_rotation(1:3,1:3,loadcase)))-math_I3)&
>reshape(spread(rotation_tol,1,9),(/3,3/)))&
.or. abs(math_det3x3(bc_rotation(1:3,1:3,loadcase)))>1.0_pReal + rotation_tol) call IO_error(error_ID=46,ext_msg=loadcase_string)
!$OMP CRITICAL (write2out)
if (any(bc_rotation(1:3,1:3,loadcase)/=math_I3)) &
print '(a,/,3(3(f12.6,x)/))','Rotation of BCs:',math_transpose3x3(bc_rotation(1:3,1:3,loadcase))
!$OMP END CRITICAL (write2out)
if (bc_timeIncrement(loadcase) < 0.0_pReal) call IO_error(error_ID=34,ext_msg=loadcase_string) ! negative time increment
!$OMP CRITICAL (write2out)
print '(a,f12.6)','Temperature: ',bc_temperature(loadcase)
print '(a,f12.6)','Time: ',bc_timeIncrement(loadcase)
!$OMP END CRITICAL (write2out)
if (bc_steps(loadcase) < 1_pInt) call IO_error(error_ID=35,ext_msg=loadcase_string) ! non-positive increment count
!$OMP CRITICAL (write2out)
print '(a,i5)','Increments: ',bc_steps(loadcase)
!$OMP END CRITICAL (write2out)
if (bc_outputfrequency(loadcase) < 1_pInt) call IO_error(error_ID=36,ext_msg=loadcase_string) ! non-positive result frequency
!$OMP CRITICAL (write2out)
print '(a,i5)','Freq. of Restults Output: ',bc_outputfrequency(loadcase)
!$OMP END CRITICAL (write2out)
if (bc_restartfrequency(loadcase) < 1_pInt) call IO_error(error_ID=39,ext_msg=loadcase_string) ! non-positive result frequency
!$OMP CRITICAL (write2out)
print '(a,i5)','Freq. of Restart Information Output: ',bc_restartfrequency(loadcase)
!$OMP END CRITICAL (write2out)
enddo
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 = math_rotate_forward3x3x3x3(c0_reference,bc_rotation(1:3,1:3,loadcase)) ! rotate_forward: lab -> load system
if (debug_verbosity > 1) then
!$OMP CRITICAL (write2out)
write (6,*) 'First Call to CPFEM_general finished'
!$OMP END CRITICAL (write2out)
endif
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)
#ifdef _OPENMP
if(DAMASK_NumThreadsInt>0_pInt) then
call dfftw_init_threads(ierr)
if(ierr == 0_pInt) call IO_error(error_ID=104)
call dfftw_plan_with_nthreads(DAMASK_NumThreadsInt)
endif
#endif
!is not working, have to find out how it is working in FORTRAN
!call dfftw_timelimit(fftw_timelimit)
! setting parameters for the plan creation of FFTW. Basically a translation from fftw3.f
! ordered from slow execution (but fast plan creation) to fast execution
select case(IO_lc(fftw_planner_flag))
case('estimate','fftw_estimate')
fftw_flag = 64
case('measure','fftw_measure')
fftw_flag = 0
case('patient','fftw_patient')
fftw_flag= 32
case('exhaustive','fftw_exhaustive')
fftw_flag = 8
case default
!$OMP CRITICAL (write2out)
write (6,*) 'No valid parameter for FFTW given, using FFTW_PATIENT'
!$OMP END CRITICAL (write2out)
fftw_flag = 32
end select
call dfftw_plan_many_dft_r2c(fftw_plan(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_flag)
call dfftw_plan_many_dft_c2r(fftw_plan(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_flag)
!$OMP CRITICAL (write2out)
if (debug_verbosity > 1) then
write (6,*) 'FFTW initialized'
endif
! write header of output file
open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
//'.spectralOut',form='UNFORMATTED',status='REPLACE')!,access='DIRECT')
write(538), 'load', trim(getLoadcaseName())
write(538), 'workingdir', trim(getSolverWorkingDirectoryName())
write(538), 'geometry', trim(getSolverJobName())//InputFileExtension
write(538), 'resolution', resolution
write(538), 'dimension', geomdimension
write(538), 'materialpoint_sizeResults', materialpoint_sizeResults
write(538), 'loadcases', N_Loadcases
write(538), 'logscale', bc_logscale ! one entry per loadcase (0: linear, 1: log)
write(538), 'frequencies', bc_outputfrequency ! one entry per loadcase
write(538), 'times', bc_timeIncrement ! one entry per loadcase
bc_steps(1)= bc_steps(1) + 1_pInt
write(538), 'increments', bc_steps ! one entry per loadcase ToDo: rename keyword to steps
bc_steps(1)= bc_steps(1) - 1_pInt
write(538), 'startingIncrement', totalStepsCounter
write(538), 'eoh' ! end of header
write(538), materialpoint_results(:,1,:) ! initial (non-deformed) results
!$OMP END CRITICAL (write2out)
! Initialization done
time = 0.0_pReal
notConvergedCounter = 0_pInt
totalStepsCounter = 1_pInt
!*************************************************************
! Loop over loadcases defined in the loadcase file
do loadcase = 1, N_Loadcases
!*************************************************************
time0 = time ! loadcase start time
if (bc_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 (mod(step,bc_restartFrequency(loadcase))==0_pInt) then ! setting restart parameter for FEsolving
restartWrite = .true.
else
restartWrite = .false.
endif
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 (bc_velGradApplied(loadcase)) & ! calculate fDot from given L and current F
fDot = math_mul33x33(bc_deformation(1:3,1:3,loadcase), defgradAim)
!winding forward of deformation aim in loadcase system
temp33_Real = defgradAim
defgradAim = defgradAim &
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
+ mask_defgrad * fDot * timeinc
defgradAimOld = temp33_Real
! update local deformation gradient
if (any(bc_rotation(1:3,1:3,loadcase)/=math_I3)) then ! lab and loadcase coordinate system are NOT the same
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc_velGradApplied(loadcase)) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc_deformation(1:3,1:3,loadcase),&
math_rotate_forward3x3(defgradold(i,j,k,1:3,1:3),bc_rotation(1:3,1:3,loadcase)))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ math_rotate_backward3x3((1.0_pReal-guessmode) * mask_defgrad * fDot,&
bc_rotation(1:3,1:3,loadcase)) *timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
else ! one coordinate system for lab and loadcase, save some multiplication
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc_velGradApplied(loadcase)) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc_deformation(1:3,1:3,loadcase),defgradold(i,j,k,1:3,1:3))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ (1.0_pReal-guessmode) * mask_defgrad * fDot * timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
endif
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(error_ID=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
!$OMP CRITICAL (write2out)
print '(A)', '************************************************************'
print '(3(A,I5.5,tr2)A)', '**** Loadcase = ',loadcase, 'Step = ',step, 'Iteration = ',iter,'****'
print '(A)', '************************************************************'
!$OMP END CRITICAL (write2out)
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
!$OMP CRITICAL (write2out)
print '(a,/,3(3(f12.7,x)/))', 'Deformation Gradient:',math_transpose3x3(defgrad_av)
print '(A,/)', '== Update Stress Field (Constitutive Evaluation P(F)) ======'
!$OMP END CRITICAL (write2out)
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
!$OMP CRITICAL (write2out)
print '(a,/,3(3(f12.7,x)/))', 'Piola-Kirchhoff Stress / MPa: ',math_transpose3x3(pstress_av)/1.e6
err_stress_tol = 0.0_pReal
pstress_av_load = math_rotate_forward3x3(pstress_av,bc_rotation(1:3,1:3,loadcase))
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (pstress_av_load - bc_stress(1:3,1:3,loadcase)))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = maxval(abs(mask_defgrad * pstress_av_load)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
print '(A,/)', '== Correcting Deformation Gradient to Fullfill BCs ========='
print '(2(a,E10.5)/)', 'Error Stress = ',err_stress, ', Tol. = ', err_stress_tol
defgradAimCorr = - math_mul3333xx33(s_prev, ((pstress_av_load - bc_stress(1:3,1:3,loadcase)))) ! residual on given stress components
defgradAim = defgradAim + defgradAimCorr
print '(a,/,3(3(f12.7,x)/))', 'Deformation Aim: ',math_transpose3x3(math_rotate_backward3x3(&
defgradAim,bc_rotation(1:3,1:3,loadcase)))
print '(a,x,f12.7,/)' , 'Determinant of Deformation Aim: ', math_det3x3(defgradAim)
endif
print '(A,/)', '== Calculating Equilibrium Using Spectral Method ==========='
!$OMP END CRITICAL (write2out)
call dfftw_execute_dft_r2c(fftw_plan(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(fftw_plan(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
enddo; enddo
defgradAim_lab = math_rotate_backward3x3(defgradAim,bc_rotation(1:3,1:3,loadcase))
do m = 1,3; do n = 1,3
defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + (defgradAim_lab(m,n) - defgrad_av(m,n)) ! anticipated target minus current state
enddo; enddo
!$OMP CRITICAL (write2out)
print '(2(a,E10.5)/)', 'Error Divergence = ',err_div, ', Tol. = ', err_div_tol
!$OMP END CRITICAL (write2out)
enddo ! end looping when convergency is achieved
c_prev = math_rotate_forward3x3x3x3(c_current*wgt,bc_rotation(1:3,1:3,loadcase)) ! calculate stiffness for next step
!ToDo: Incfluence for next loadcase
if (mod(totalStepsCounter,bc_outputfrequency(loadcase)) == 0_pInt) then ! at output frequency
write(538), materialpoint_results(:,1,:) ! write result to file
endif
totalStepsCounter = totalStepsCounter + 1_pInt
!$OMP CRITICAL (write2out)
if(err_div<=err_div_tol .and. err_stress<=err_stress_tol) then
print '(3(A,I5.5),A,/)', '== Step ',step, ' of Loadcase ',loadcase,' (Total ', totalStepsCounter,') Converged ===='
else
print '(3(A,I5.5),A,/)', '== Step ',step, ' of Loadcase ',loadcase,' (Total ', totalStepsCounter,') NOT Converged '
notConvergedCounter = notConvergedCounter + 1
endif
!$OMP END CRITICAL (write2out)
enddo ! end looping over steps in current loadcase
deallocate(c_reduced)
deallocate(s_reduced)
enddo ! end looping over loadcases
!$OMP CRITICAL (write2out)
print '(A,/)', '############################################################'
print '(a,i5.5,a,i5.5,a)', 'Of ', totalStepsCounter, ' Total Steps,', notConvergedCounter, ' Steps did not Converge!'
!$OMP END CRITICAL (write2out)
close(538)
call dfftw_destroy_plan(fftw_plan(1)); call dfftw_destroy_plan(fftw_plan(2))
end program DAMASK_spectral
!********************************************************************
! quit subroutine to satisfy IO_error
!
!********************************************************************
subroutine quit(id)
use prec
implicit none
integer(pInt) id
stop
end subroutine