! 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 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