! 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 . ! !############################################################## !* $Id$ !******************************************************************** ! 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 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)*4_pInt + & ! time, (log)incs, temp, and frequency 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_frequency, & ! 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_frequency(N_Loadcases)); bc_frequency = 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') ! frequency of result writings bc_frequency(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_frequency(loadcase) < 1_pInt) call IO_error(error_ID=36,ext_msg=loadcase_string) ! non-positive result frequency !$OMP CRITICAL (write2out) print '(a,i5)','Freq. of Output: ',bc_frequency(loadcase) !$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) !$OMP CRITICAL (write2out) if (debug_verbosity > 1) then write (6,*) 'FFTW initialized' endif ! write header of output file open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())& //'.spectralOut',form='UNFORMATTED',status='REPLACE')!,access='DIRECT') write(538), 'load', trim(getLoadcaseName()) write(538), 'workingdir', trim(getSolverWorkingDirectoryName()) write(538), 'geometry', trim(getSolverJobName())//InputFileExtension write(538), 'resolution', resolution write(538), 'dimension', geomdimension write(538), 'materialpoint_sizeResults', materialpoint_sizeResults write(538), 'loadcases', N_Loadcases write(538), 'logscale', bc_logscale ! one entry per loadcase (0: linear, 1: log) write(538), 'frequencies', bc_frequency ! one entry per loadcase write(538), 'times', bc_timeIncrement ! one entry per loadcase bc_steps(1)= bc_steps(1) + 1_pInt write(538), 'increments', bc_steps ! one entry per loadcase ToDo: rename keyword to steps bc_steps(1)= bc_steps(1) - 1_pInt write(538), 'startingIncrement', totalStepsCounter write(538), 'eoh' ! end of header write(538), materialpoint_results(:,1,:) ! initial (non-deformed) results !$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 (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(step,bc_frequency(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