! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH ! ! This file is part of DAMASK, ! the Düsseldorf Advanced MAterial Simulation Kit. ! ! DAMASK is free software: you can redistribute it and/or modify ! it under the terms of the GNU General Public License as published by ! the Free Software Foundation, either version 3 of the License, or ! (at your option) any later version. ! ! DAMASK is distributed in the hope that it will be useful, ! but WITHOUT ANY WARRANTY; without even the implied warranty of ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ! GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License ! along with DAMASK. If not, see . ! !############################################################## !* $Id$ !******************************************************************** ! 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 mpie_spectral PathToGeomFile/NameOfGeom.geom ! PathToLoadFile/NameOfLoadFile.load ! - PathToGeomFile will be the working directory ! - make sure the file "material.config" exists in the working ! directory. For further configuration use "numerics.config" !******************************************************************** program mpie_spectral !******************************************************************** use mpie_interface use prec, only: pInt, pReal use IO use math use CPFEM, only: CPFEM_general, CPFEM_initAll use numerics, only: err_div_tol, err_stress_tol, err_stress_tolrel, err_defgrad_tol,& itmax, memory_efficient, mpieNumThreadsInt use homogenization, only: materialpoint_sizeResults, materialpoint_results !$ use OMP_LIB ! the openMP function library implicit none include 'fftw3.f' ! header file for fftw3 (declaring variables). Library files are also needed ! compile FFTW 3.2.2 with ./configure --enable-threads ! variables to read from loadcase and geom file real(pReal), dimension(9) :: valuevector ! stores information temporarily from loadcase file integer(pInt), parameter :: maxNchunksInput = 24 ! 4 identifiers, 18 values for the matrices and 2 scalars integer(pInt), dimension (1+maxNchunksInput*2) :: posInput integer(pInt), parameter :: maxNchunksGeom = 7 ! 4 identifiers, 3 values integer(pInt), dimension (1+2*maxNchunksGeom) :: posGeom integer(pInt) unit, N_l, N_s, N_t, N_n ! numbers of identifiers character(len=1024) path, line logical gotResolution,gotDimension,gotHomogenization logical, dimension(9) :: bc_maskvector ! variables storing information from loadcase file real(pReal) timeinc real(pReal), dimension (:,:,:), allocatable :: bc_velocityGrad, & bc_stress ! velocity gradient and stress BC real(pReal), dimension(:), allocatable :: bc_timeIncrement ! length of increment integer(pInt) N_Loadcases, steps integer(pInt), dimension(:), allocatable :: bc_steps ! number of steps logical, dimension(:,:,:,:), allocatable :: bc_mask ! mask of boundary conditions ! variables storing information from geom file real(pReal) wgt real(pReal), dimension(3) :: geomdimension integer(pInt) homog integer(pInt), dimension(3) :: resolution ! stress etc. real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, damper,& pstress, pstress_av, cstress_av, defgrad_av,& defgradAim, defgradAimOld, defgradAimCorr, defgradAimCorrPrev,& mask_stress, mask_defgrad real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0 real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation real(pReal), dimension(6,6) :: dsde, c066, s066 ! Mandel notation of 4th order tensors real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold ! variables storing information for spectral method complex(pReal) :: img complex(pReal), dimension(3,3) :: temp33_Complex real(pReal), dimension(3,3) :: xinormdyad real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat real(pReal), dimension(3) :: xi, xi_central integer(pInt), dimension(3) :: k_s integer*8, dimension(2) :: plan_fft ! loop variables, convergence etc. real(pReal) guessmode, err_div, err_stress, err_defgrad, sigma0 integer(pInt) i, j, k, l, m, n, p integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode, ierr logical errmatinv real(pReal) temperature ! not used, but needed for call to CPFEM_general !Initializing !$ call omp_set_num_threads(mpieNumThreadsInt) ! set number of threads for parallel execution set by MPIE_NUM_THREADS bc_maskvector = '' unit = 234_pInt ones = 1.0_pReal; zeroes = 0.0_pReal img = cmplx(0.0,1.0) N_l = 0_pInt; N_s = 0_pInt N_t = 0_pInt; N_n = 0_pInt gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false. resolution = 1_pInt; geomdimension = 0.0_pReal temperature = 300.0_pReal if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments ! Reading the loadcase file and assign variables path = getLoadcaseName() print '(a,/,a)', 'Loadcase: ',trim(path) print '(a,/,a)', 'Workingdir: ',trim(getSolverWorkingDirectoryName()) print '(a,/,a)', 'SolverJobName: ',trim(getSolverJobName()) if (.not. IO_open_file(unit,path)) call IO_error(45,ext_msg = path) rewind(unit) do read(unit,'(a1024)',END = 101) line if (IO_isBlank(line)) cycle ! skip empty lines posInput = IO_stringPos(line,maxNchunksInput) do i = 1, maxNchunksInput, 1 select case (IO_lc(IO_stringValue(line,posInput,i))) case('l','velocitygrad') N_l = N_l+1 case('s','stress') N_s = N_s+1 case('t','time','delta') N_t = N_t+1 case('n','incs','increments','steps') N_n = N_n+1 end select enddo ! count all identifiers to allocate memory and do sanity check enddo 101 N_Loadcases = N_l ! allocate memory depending on lines in input file allocate (bc_velocityGrad(3,3,N_Loadcases)); bc_velocityGrad = 0.0_pReal allocate (bc_stress(3,3,N_Loadcases)); bc_stress = 0.0_pReal allocate (bc_mask(3,3,2,N_Loadcases)); bc_mask = .false. allocate (bc_timeIncrement(N_Loadcases)); bc_timeIncrement = 0.0_pReal allocate (bc_steps(N_Loadcases)); bc_steps = 0_pInt rewind(unit) i = 0_pInt do read(unit,'(a1024)',END = 200) line if (IO_isBlank(line)) cycle ! skip empty lines i = i + 1 posInput = IO_stringPos(line,maxNchunksInput) do j = 1,maxNchunksInput,2 select case (IO_lc(IO_stringValue(line,posInput,j))) case('l','velocitygrad') valuevector = 0.0_pReal forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '#' do k = 1,9 if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the velocity gradient matrix enddo bc_mask(:,:,1,i) = transpose(reshape(bc_maskvector,(/3,3/))) bc_velocityGrad(:,:,i) = math_transpose3x3(reshape(valuevector,(/3,3/))) case('s','stress') valuevector = 0.0_pReal forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '#' do k = 1,9 if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the bc_stress matrix enddo bc_mask(:,:,2,i) = transpose(reshape(bc_maskvector,(/3,3/))) bc_stress(:,:,i) = math_transpose3x3(reshape(valuevector,(/3,3/))) case('t','time','delta') ! increment time bc_timeIncrement(i) = IO_floatValue(line,posInput,j+1) case('n','incs','increments','steps') ! bc_steps bc_steps(i) = IO_intValue(line,posInput,j+1) end select enddo; enddo 200 close(unit) do i = 1, N_Loadcases ! consistency checks if (any(bc_mask(:,:,1,i) == bc_mask(:,:,2,i))) call IO_error(46,i) ! exclisive or masking only if (bc_timeIncrement(i) < 0.0_pReal) call IO_error(47,i) ! negative time increment if (bc_steps(i) < 1_pInt) call IO_error(48,i) ! non-positive increment count print '(a,/,3(3(f12.6,x)/))','L:' ,math_transpose3x3(bc_velocityGrad(:,:,i)) print '(a,/,3(3(f12.6,x)/))','bc_stress:',math_transpose3x3(bc_stress(:,:,i)) print '(a,/,3(3(l,x)/))', 'bc_mask for velocitygrad:',transpose(bc_mask(:,:,1,i)) print '(a,/,3(3(l,x)/))', 'bc_mask for stress:' ,transpose(bc_mask(:,:,2,i)) print '(a,f12.6)','time: ',bc_timeIncrement(i) print '(a,i5)','incs: ',bc_steps(i) print *, '' enddo !read header of geom file to get the information needed before the complete geom file is intepretated by mesh.f90 path = getModelName() print '(a,a)', 'GeomName: ',trim(path) if (.not. IO_open_file(unit,trim(path)//InputFileExtension)) call IO_error(101,ext_msg = trim(path)//InputFileExtension) rewind(unit) do read(unit,'(a1024)',END = 100) line if (IO_isBlank(line)) cycle ! skip empty lines posGeom = IO_stringPos(line,maxNchunksGeom) select case ( IO_lc(IO_StringValue(line,posGeom,1)) ) case ('dimension') gotDimension = .true. do i = 2,6,2 select case (IO_lc(IO_stringValue(line,posGeom,i))) case('x') geomdimension(1) = IO_floatValue(line,posGeom,i+1) case('y') geomdimension(2) = IO_floatValue(line,posGeom,i+1) case('z') geomdimension(3) = IO_floatValue(line,posGeom,i+1) end select enddo case ('homogenization') gotHomogenization = .true. homog = IO_intValue(line,posGeom,2) case ('resolution') gotResolution = .true. do i = 2,6,2 select case (IO_lc(IO_stringValue(line,posGeom,i))) case('a') resolution(1) = IO_intValue(line,posGeom,i+1) case('b') resolution(2) = IO_intValue(line,posGeom,i+1) case('c') resolution(3) = IO_intValue(line,posGeom,i+1) end select enddo end select if (gotDimension .and. gotHomogenization .and. gotResolution) exit enddo 100 close(unit) if(mod(resolution(1),2)/=0 .or. mod(resolution(2),2)/=0 .or. mod(resolution(3),2)/=0) call IO_error(103) print '(a,/,i4,i4,i4)','resolution a b c:', resolution print '(a,/,f6.1,f6.1,f6.1)','dimension x y z:', geomdimension print '(a,i4)','homogenization: ',homog allocate (defgrad (resolution(1),resolution(2),resolution(3),3,3)); defgrad = 0.0_pReal allocate (defgradold(resolution(1),resolution(2),resolution(3),3,3)); defgradold = 0.0_pReal wgt = 1.0_pReal/real(resolution(1)*resolution(2)*resolution(3), pReal) defgradAim = math_I3 defgradAimOld = math_I3 defgrad_av = math_I3 ! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field call CPFEM_initAll(temperature,1_pInt,1_pInt) ielem = 0_pInt c066 = 0.0_pReal do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) defgradold(i,j,k,:,:) = math_I3 ! no deformation at the beginning defgrad(i,j,k,:,:) = math_I3 ielem = ielem +1 call CPFEM_general(2,math_I3,math_I3,temperature,0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF) c066 = c066 + dsde enddo; enddo; enddo c066 = c066 * wgt c0 = math_mandel66to3333(c066) call math_invert(6, c066, s066,i, errmatinv) if(errmatinv) call IO_error(800) ! Matrix inversion error s0 = math_mandel66to3333(s066) if(memory_efficient) then ! allocate just single fourth order tensor allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal else ! precalculation of gamma_hat field allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal do k = 1, resolution(3) k_s(3) = k-1 if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3) do j = 1, resolution(2) k_s(2) = j-1 if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2) do i = 1, resolution(1)/2+1 k_s(1) = i-1 xi(3) = 0.0_pReal ! for the 2D case if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) ! 3D case xi(2) = real(k_s(2), pReal)/geomdimension(2) xi(1) = real(k_s(1), pReal)/geomdimension(1) if (any(xi /= 0.0_pReal)) then do l = 1,3; do m = 1,3 xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2) ! unit sphere, unit vectors in Fourier space enddo; enddo temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad)) else xinormdyad = 0.0_pReal temp33_Real = 0.0_pReal endif do l=1,3; do m=1,3; do n=1,3; do p=1,3 gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *& (xinormdyad(m,p)+xinormdyad(p,m)) enddo; enddo; enddo; enddo enddo; enddo; enddo endif ! calculate xi for the calculation of divergence in Fourier space (central frequency) xi_central(3) = 0.0_pReal ! 2D case if(resolution(3) > 1) xi_central(3) = real(resolution(3)/2, pReal)/geomdimension(3) ! 3D case xi_central(2) = real(resolution(2)/2, pReal)/geomdimension(2) xi_central(1) = real(resolution(1)/2, pReal)/geomdimension(1) allocate (workfft(resolution(1)+2,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal ! Initialization of fftw (see manual on fftw.org for more details) call dfftw_init_threads(ierr) if(ierr == 0) call IO_error(104,ierr) call dfftw_plan_with_nthreads(mpieNumThreadsInt) 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), 'increments', sum(bc_steps+1) ! +1 to store initial situation write(538), 'eoh' write(538) materialpoint_results(:,1,:) ! initial (non-deformed) results ! Initialization done !************************************************************* ! Loop over loadcases defined in the loadcase file do loadcase = 1, N_Loadcases !************************************************************* timeinc = bc_timeIncrement(loadcase)/bc_steps(loadcase) guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first step mask_defgrad = merge(ones,zeroes,bc_mask(:,:,1,loadcase)) mask_stress = merge(ones,zeroes,bc_mask(:,:,2,loadcase)) damper = ones/10 !************************************************************* ! loop oper steps defined in input file for current loadcase do steps = 1, bc_steps(loadcase) !************************************************************* temp33_Real = defgradAim defgradAim = defgradAim & ! update macroscopic displacement gradient (defgrad BC) + guessmode * mask_stress * (defgradAim - defgradAimOld) & + math_mul33x33(bc_velocityGrad(:,:,loadcase), defgradAim)*timeinc defgradAimOld = temp33_Real do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) temp33_Real = defgrad(i,j,k,:,:) defgrad(i,j,k,:,:) = defgrad(i,j,k,:,:)& ! old fluctuations as guess for new step, no fluctuations for new loadcase + guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& + (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,k,:,:))*timeinc defgradold(i,j,k,:,:) = temp33_Real enddo; enddo; enddo guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase if(all(bc_mask(:,:,1,loadcase))) then calcmode = 1_pInt ! if no stress BC is given (calmode 0 is not needed) else calcmode = 0_pInt ! start calculation of BC fulfillment endif CPFEM_mode = 1_pInt ! winding forward iter = 0_pInt err_div= 2_pReal * err_div_tol ! go into loop defgradAimCorr = 0.0_pReal ! reset damping calculation damper = damper * 0.9_pReal !************************************************************* ! convergence loop do while(iter < itmax .and. & (err_div > err_div_tol .or. & err_stress > err_stress_tol .or. & err_defgrad > err_defgrad_tol)) iter = iter + 1_pInt print*, ' ' print '(3(A,I5.5,tr2))', ' Loadcase = ',loadcase, ' Step = ',steps,'Iteration = ',iter cstress_av = 0.0_pReal workfft = 0.0_pReal !needed because of the padding for FFTW !************************************************************* ! adjust defgrad to fulfill BCs select case (calcmode) case (0) print *, 'Update Stress Field (constitutive evaluation P(F))' ielem = 0_pInt do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) ielem = ielem + 1 call CPFEM_general(3, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& temperature,timeinc,ielem,1_pInt,& cstress,dsde, pstress, dPdF) enddo; enddo; enddo ielem = 0_pInt do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) ielem = ielem + 1_pInt call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& ! others get 2 (saves winding forward effort) temperature,timeinc,ielem,1_pInt,& cstress,dsde, pstress, dPdF) CPFEM_mode = 2_pInt workfft(i,j,k,:,:) = pstress cstress_av = cstress_av + math_mandel6to33(cstress) enddo; enddo; enddo cstress_av = cstress_av * wgt do m = 1,3; do n = 1,3 pstress_av(m,n) = sum(workfft(1:resolution(1),:,:,m,n)) * wgt defgrad_av(m,n) = sum(defgrad(:,:,:,m,n)) * wgt enddo; enddo err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(:,:,loadcase)))) err_stress_tol = maxval(abs(pstress_av))*err_stress_tolrel print*, 'Correcting deformation gradient to fullfill BCs' defgradAimCorrPrev = defgradAimCorr defgradAimCorr = -mask_stress * math_mul3333xx33(s0, (mask_stress*(pstress_av - bc_stress(:,:,loadcase)))) do m=1,3; do n =1,3 ! calculate damper (correction is far to strong) if ( sign(1.0_pReal,defgradAimCorr(m,n))/=sign(1.0_pReal,defgradAimCorrPrev(m,n))) then damper(m,n) = max(0.01_pReal,damper(m,n)*0.8) else damper(m,n) = min(1.0_pReal,damper(m,n) *1.2) endif enddo; enddo defgradAimCorr = mask_Stress*(damper * defgradAimCorr) defgradAim = defgradAim + defgradAimCorr do m = 1,3; do n = 1,3 defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + (defgradAim(m,n) - defgrad_av(m,n)) ! anticipated target minus current state enddo; enddo err_div = 2 * err_div_tol err_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim))) print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient:',math_transpose3x3(defgrad_av) print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress / MPa: ' ,math_transpose3x3(cstress_av)/1.e6 print '(2(a,E8.2))', ' error stress: ',err_stress, ' Tol. = ', err_stress_tol print '(2(a,E8.2))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol*0.8 if(err_stress < err_stress_tol*0.8) then calcmode = 1_pInt endif ! Using the spectral method to calculate the change of deformation gradient, check divergence of stress field in fourier space case (1) print *, 'Update Stress Field (constitutive evaluation P(F))' ielem = 0_pInt do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) ielem = ielem + 1_pInt call CPFEM_general(3, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& temperature,timeinc,ielem,1_pInt,& cstress,dsde, pstress, dPdF) enddo; enddo; enddo ielem = 0_pInt do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) ielem = ielem + 1_pInt call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& temperature,timeinc,ielem,1_pInt,& cstress,dsde, pstress, dPdF) CPFEM_mode = 2_pInt workfft(i,j,k,:,:) = pstress cstress_av = cstress_av + math_mandel6to33(cstress) enddo; enddo; enddo cstress_av = cstress_av * wgt do m = 1,3; do n = 1,3 pstress_av(m,n) = sum(workfft(1:resolution(1),:,:,m,n))*wgt enddo; enddo print *, 'Calculating equilibrium using spectral method' err_div = 0.0_pReal; sigma0 = 0.0_pReal call dfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress do m = 1,3 ! L infinity Norm of stress tensor sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:) + (workfft(2,1,1,m,:))*img))) enddo err_div = (maxval(abs(math_mul33x3_complex(workfft(resolution(1)+1,resolution(2)/2+1,resolution(3)/2+1,:,:)+& ! L infinity norm of div(stress) workfft(resolution(1)+2,resolution(2)/2+1,resolution(3)/2+1,:,:)*img,xi_central)))) err_div = err_div/sigma0 ! weighting of error if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat do k = 1, resolution(3) k_s(3) = k-1 if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3) do j = 1, resolution(2) k_s(2) = j-1 if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2) do i = 1, resolution(1)/2+1 k_s(1) = i-1 xi(3) = 0.0_pReal ! for the 2D case if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) ! 3D case xi(2) = real(k_s(2), pReal)/geomdimension(2) xi(1) = real(k_s(1), pReal)/geomdimension(1) if (any(xi(:) /= 0.0_pReal)) then do l = 1,3; do m = 1,3 xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2) enddo; enddo temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad)) else xinormdyad = 0.0_pReal temp33_Real = 0.0_pReal endif do l=1,3; do m=1,3; do n=1,3; do p=1,3 gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*& (xinormdyad(m,p) +xinormdyad(p,m)) enddo; enddo; enddo; enddo do m = 1,3; do n = 1,3 temp33_Complex(m,n) = sum(gamma_hat(1,1,1,m,n,:,:) *(workfft(i*2-1,j,k,:,:)& +workfft(i*2 ,j,k,:,:)*img)) enddo; enddo workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of strain 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) ! change of strain workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex) enddo; enddo; enddo endif workfft(1,1,1,:,:) = defgrad_av - math_I3 ! zero frequency (real part) workfft(2,1,1,:,:) = 0.0_pReal ! zero frequency (imaginary part) call 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 err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(:,:,loadcase)))) err_stress_tol = maxval(abs(pstress_av))*err_stress_tolrel ! accecpt relative error specified err_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim))) print '(2(a,E8.2))', ' error divergence: ',err_div, ' Tol. = ', err_div_tol print '(2(a,E8.2))', ' error stress: ',err_stress, ' Tol. = ', err_stress_tol print '(2(a,E8.2))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol if((err_stress > err_stress_tol .or. err_defgrad > err_defgrad_tol) .and. err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc. calcmode = 0_pInt defgradAimCorr = 0.0_pReal damper = damper * 0.9_pReal endif end select enddo ! end looping when convergency is achieved write(538) materialpoint_results(:,1,:) ! write to output file print '(a,x,f12.7)' , ' Determinant of Deformation Aim: ', math_det3x3(defgradAim) print '(a,/,3(3(f12.7,x)/))', ' Deformation Aim: ',math_transpose3x3(defgradAim) print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient:',math_transpose3x3(defgrad_av) print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress / MPa: ',math_transpose3x3(cstress_av)/1.e6 print '(A)', '************************************************************' enddo ! end looping over steps in current loadcase enddo ! end looping over loadcases close(538) call dfftw_destroy_plan(plan_fft(1)); call dfftw_destroy_plan(plan_fft(2)) end program mpie_spectral !******************************************************************** ! quit subroutine to satisfy IO_error ! !******************************************************************** subroutine quit(id) use prec implicit none integer(pInt) id stop end subroutine