From 4fb1cb8f876a6013b8123e72666a99b05d8abaa9 Mon Sep 17 00:00:00 2001 From: Martin Diehl Date: Fri, 26 Aug 2011 14:06:37 +0000 Subject: [PATCH] merged calcmodes, i.e. equilibrium and fulfilling of stress BC is done in one step, made convergence independent of size and resolution, polishing output in DAMASK_spectral.f90 added function to compute eigenvalues without eigenvectors and function to convert a 3x3 logical to a 9 vector in math.f90 removed obsolete variable in numerics.f90 --- code/DAMASK_spectral.f90 | 483 +++++++++++++++------------------------ code/IO.f90 | 2 + code/math.f90 | 64 +++++- code/numerics.f90 | 14 +- 4 files changed, 258 insertions(+), 305 deletions(-) diff --git a/code/DAMASK_spectral.f90 b/code/DAMASK_spectral.f90 index ca6f59aab..da394ac20 100644 --- a/code/DAMASK_spectral.f90 +++ b/code/DAMASK_spectral.f90 @@ -1,7 +1,7 @@ -! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH +! Copyright 2011 Max-Planck-Institut fuer Eisenforschung GmbH ! ! This file is part of DAMASK, -! the Düsseldorf Advanced MAterial Simulation Kit. +! 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 @@ -49,8 +49,8 @@ program DAMASK_spectral 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, err_defgrad_tol,& - relevantStrain,itmax, memory_efficient, DAMASK_NumThreadsInt + 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 @@ -66,7 +66,6 @@ program DAMASK_spectral 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 - logical, dimension(9) :: bc_maskvector ! variables storing information from loadcase file real(pReal) time, time0, timeinc ! elapsed time, begin of interval, time interval @@ -81,49 +80,52 @@ program DAMASK_spectral 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 - integer(pInt) homog - integer(pInt), dimension(3) :: resolution + 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, damper,& - pstress, pstress_av, cstress_av, defgrad_av,& - defgradAim, defgradAimOld, defgradAimCorr, defgradAimCorrPrev,& + real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, & + pstress, pstress_av, defgrad_av,& + defgradAim, defgradAimOld, defgradAimCorr,& mask_stress, mask_defgrad, deltaF - real(pReal), dimension(3,3,3,3) :: dPdF, c_current, s_current, c0_reference ! ToDo - real(pReal), dimension(6) :: cstress, stress_res, delta_defgrad ! cauchy stress, residuum_stress, change of defgrad in Mandel notation - real(pReal), dimension(6,6) :: dsde, c_current66, s_current66 ! Mandel notation of 4th order tensors - real(pReal), dimension(9,9) :: s_current99, c_current99 + 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 - logical, dimension(6) :: mask_stress6 - logical, dimension(9) :: mask_stress9 - integer(pInt) size_reduced + 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 - real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat - real(pReal), dimension(:,:,:,:), allocatable :: xi - integer(pInt), dimension(3) :: k_s - integer*8, dimension(2) :: plan_fft + 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, err_defgrad, p_hat_avg + real(pReal) guessmode, err_div, err_stress, p_hat_avg integer(pInt) i, j, k, l, m, n, p - integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode, ierr, not_converged_counter + 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 - bc_maskvector = .false. + 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) @@ -179,12 +181,13 @@ program DAMASK_spectral 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 inp !ToDo:change message + 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 @@ -198,36 +201,29 @@ program DAMASK_spectral loadcase = 0_pInt do read(unit,'(a1024)',END = 200) line - if (IO_isBlank(line)) cycle ! skip empty lines + 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') ! assign values for the deformation BC matrix (in case of given fdot) + 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) = IO_stringValue(line,posInput,j+k) /= '*' + forall (k = 1:9) bc_maskvector(k,1,loadcase) = IO_stringValue(line,posInput,j+k) /= '*' do k = 1,9 - if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) + if (bc_maskvector(k,1,loadcase)) valuevector(k) = IO_floatValue(line,posInput,j+k) enddo - bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector,(/3,3/))) - bc_deformation(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/))) - case('l','velocitygrad') ! assign values for the deformation BC matrix (in case of given L) - velGradApplied(loadcase) = .true. ! in case of given L, set flag to true - 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) - enddo - bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector,(/3,3/))) - bc_deformation(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/))) + 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) = IO_stringValue(line,posInput,j+k) /= '*' + forall (k = 1:9) bc_maskvector(k,2,loadcase) = 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 + 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,(/3,3/))) - bc_stress(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/))) + 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 @@ -328,16 +324,16 @@ program DAMASK_spectral 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,/,i4,i4,i4)','resolution a b c:', resolution - print '(a,/,f8.4,f8.5,f8.5)','dimension x y z:', geomdimension + + 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 + 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 @@ -357,7 +353,7 @@ program DAMASK_spectral 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) @@ -370,7 +366,13 @@ program DAMASK_spectral 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 + 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 @@ -437,16 +439,19 @@ program DAMASK_spectral !************************************************************* time0 = time ! loadcase start time - if (followFormerTrajectory(loadcase)) then + 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 - damper = 1.0_pReal 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 deltaF = 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 @@ -463,17 +468,13 @@ program DAMASK_spectral 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 - else ! linear scale - timeinc = bc_timeIncrement(loadcase)/bc_steps(loadcase) endif - time = time + timeinc - -! update macroscopic deformation gradient (defgrad BC) if (velGradApplied(loadcase)) & ! calculate deltaF from given L and current F deltaF = math_mul33x33(bc_deformation(:,:,loadcase), defgradAim) +!winding forward of deformation aim temp33_Real = defgradAim defgradAim = defgradAim & + guessmode * mask_stress * (defgradAim - defgradAimOld) & @@ -483,217 +484,117 @@ program DAMASK_spectral ! 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)) & ! using velocity gradient to calculate new deformation gradient (if not guessing) + if (velGradApplied(loadcase)) & ! use velocity gradient to calculate new deformation gradient (if not guessing) deltaF = 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 (addon only for applied deformation) - + guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& - + (1.0_pReal-guessmode) * mask_defgrad * deltaF *timeinc + 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 * deltaF *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 - 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 + CPFEM_mode = 1_pInt ! winding forward iter = 0_pInt - err_div= 2.0_pReal * err_div_tol ! go into loop - + 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 .or. & - err_defgrad > err_defgrad_tol)) + err_stress > err_stress_tol)) iter = iter + 1_pInt if (iter == itmax) not_converged_counter = not_converged_counter + 1 - print*, ' ' - print '(3(A,I5.5,tr2))', ' Loadcase = ',loadcase, ' Step = ',step, ' Iteration = ',iter - cstress_av = 0.0_pReal - workfft = 0.0_pReal ! needed because of the padding for FFTW + print '(A,/)', '============================================================' + print '(3(A,I5.5,tr2)/)', 'Loadcase = ',loadcase, ' Step = ',step, ' Iteration = ',iter + workfft = 0.0_pReal ! needed because of the padding for FFTW !************************************************************* + 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 -! 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,& ! 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 - cstress_av = cstress_av + math_mandel6to33(cstress) ! build up average Cauchy stress - c_current = c_current + dPdF - enddo; enddo; enddo - c_current = c_current * wgt - cstress_av = cstress_av * wgt - do n = 1,3; do m = 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 + 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 + 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,/,3(3(f12.7,x)/))', 'Piola-Kirchhoff Stress / MPa: ',math_transpose3x3(pstress_av)/1.e6 - err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(:,:,loadcase)))) - err_stress_tol = maxval(abs(pstress_av)) * 0.8 * err_stress_tolrel - - call math_invert(9, math_plain3333to99(c_current),s_current99,i,errmatinv) - if(errmatinv) then - print*, 'using symmetric compliance' - pause !maybe we don't need it. Code below is not working - !mask_stress6 = math_Plain33to6_logical(bc_mask(:,:,2,loadcase)) - !if the symmetrized stiffness is not used at all, the allocate terms only needed at the beginning of a load case - size_reduced = count(mask_stress6) - allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal - allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal - ! c_current66 = math_Plain3333to66(c_current) - k = 0_pInt - do n = 1,6 - if(mask_stress6(n)) then - k = k + 1_pInt - j = 0_pInt - do m = 1,6 - if(mask_stress6(m)) then - j = j + 1_pInt - c_reduced(k,j) = c_current66(n,m) - endif - enddo - endif - enddo - call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) - if(errmatinv) call IO_error(800) - s_current66 = 0.0_pReal - k = 0_pInt - do n = 1,6 - if(mask_stress6(n)) then - k = k + 1_pInt - j = 0_pInt - do m = 1,6 - if(mask_stress6(m)) then - j = j + 1_pInt - s_current66(n,m) = s_reduced(k,j) - endif - enddo - endif - enddo - ! s_current = math_Plain66to3333(s_current66) - else - mask_stress9 = reshape(bc_mask(:,:,2,loadcase),(/9/)) - size_reduced = count(mask_stress9) - allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal - allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal - c_current99 = math_Plain3333to99(c_current) - k = 0_pInt ! build reduced stiffness - do n = 1,9 - if(mask_stress9(n)) then - k = k + 1_pInt - j = 0_pInt - do m = 1,9 - if(mask_stress9(m)) then - j = j + 1_pInt - c_reduced(k,j) = c_current99(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_current99 = 0.0_pReal ! build full compliance - k = 0_pInt - do n = 1,9 - if(mask_stress9(n)) then - k = k + 1_pInt - j = 0_pInt - do m = 1,9 - if(mask_stress9(m)) then - j = j + 1_pInt - s_current99(n,m) = s_reduced(k,j) - endif; enddo; endif; enddo - s_current = math_Plain99to3333(s_current99) - endif - - deallocate(c_reduced) - deallocate(s_reduced) - print*, 'Correcting deformation gradient to fullfill BCs' - - defgradAimCorr = - math_mul3333xx33(s_current, ((pstress_av - bc_stress(:,:,loadcase)))) ! residual on given stress components - 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 = 2.0_pReal * 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)/))', ' Piola-Kirchhoff Stress / MPa: ',math_transpose3x3(pstress_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 - if(err_stress < err_stress_tol) 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, 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 - 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,:,:),& - temperature(i,j,k),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 n = 1,3; do m = 1,3 - pstress_av(m,n) = sum(workfft(1:resolution(1),1:resolution(2),1:resolution(3),m,n)) * wgt - enddo; enddo - - print *, 'Calculating equilibrium using spectral method' - err_div = 0.0_pReal - p_hat_avg = 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 - p_hat_avg = max(p_hat_avg, sum(abs(workfft(1,1,1,:,m)))) ! ignore imaginary part as it is always zero (Nyquist freq for real only input) + 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) + do m = 1,3 + err_stress_tol = max(err_stress_tol, sum(abs(pstress_av(m,1:3)))) ! L_inf norm of average stress enddo + 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 + endif + print '(A,/)', '== Calculating Equilibrium Using Spectral Method ==' + err_div = 0.0_pReal + p_hat_avg = 0.0_pReal - - do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1 - err_div = max(err_div, maxval(abs(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+& ! maximum of L infinity norm of div(stress), Suquet 2001 - workfft(i*2, j,k,:,:)*img,xi(:,i,j,k)*minval(geomdimension))))) - enddo; enddo; enddo + call dfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress + do m =1,3 ! L_inf norm of average stress in fourier space + p_hat_avg = max(p_hat_avg,sum(abs(workfft(1,1,1,m,1:3)))) ! ignore imaginary part as it is always zero for real only input)) + enddo + + do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1 + err_div = err_div + maxval(abs(math_mul33x3_complex(workfft(i*2-1,j,k,1:3,1:3)+& ! avg of L_inf 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)))) + enddo; enddo; enddo - err_div = err_div/p_hat_avg !weigthting of error by average stress (L infinity norm) + err_div = err_div*wgt/p_hat_avg*(minval(geomdimension)*wgt**(-1/4)) ! weigthting, multiplying by minimum dimension to get rid of dimension dependency - if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat + 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 @@ -712,59 +613,53 @@ program DAMASK_spectral 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 average strain + 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 + 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 average strain + workfft(i*2-1,j,k,:,:) = real (temp33_Complex) 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,E13.8))', ' error divergence: ',err_div, ' Tol. = ', err_div_tol - print '(2(a,E13.8))', ' error stress: ',err_stress, ' Tol. = ', err_stress_tol - print '(2(a,E13.8))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol - !ToDo: usefull .and. for err_div? - 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 = 1.0_pReal - endif - end select + 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 + + do m = 1,3; do n = 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 '(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 - - print '(A)', '------------------------------------------------------------' - 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,/,3(3(f10.4,x)/))', ' Piola-Kirchhoff Stress / MPa: ',math_transpose3x3(pstress_av)/1.e6 - print '(A)', '************************************************************' + print '(2(A,I5.5),A,/)', 'Step = ',step, ' of Loadcase = ',loadcase, ' Converged' + 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)/))', 'Piola-Kirchhoff Stress / MPa (prev. Iteration): ',math_transpose3x3(pstress_av)/1.e6 + print '(A,/)', '************************************************************' enddo ! end looping over steps in current loadcase - enddo ! end looping over loadcases - print '(a,i10,a)', 'A Total of ', not_converged_counter, ' Steps did not converge!' + deallocate(c_reduced) + deallocate(s_reduced) + enddo ! end looping over loadcases + print '(a,i10,a)', 'A Total of ', not_converged_counter, ' Steps did not Converge!' close(538) call dfftw_destroy_plan(plan_fft(1)); call dfftw_destroy_plan(plan_fft(2)) diff --git a/code/IO.f90 b/code/IO.f90 index 49b7efa08..c432bd82c 100644 --- a/code/IO.f90 +++ b/code/IO.f90 @@ -1196,6 +1196,8 @@ endfunction msg = 'non-positive increments in spectral loadcase' case (36) msg = 'non-positive result frequency in spectral loadcase' + case (37) + msg = 'incomplete loadcase' case (40) msg = 'path rectification error' case (41) diff --git a/code/math.f90 b/code/math.f90 index eb84d99f3..639731204 100644 --- a/code/math.f90 +++ b/code/math.f90 @@ -1165,6 +1165,23 @@ pure function math_transpose3x3(A) forall (i=1:9) math_Plain33to9(i) = m33(mapPlain(1,i),mapPlain(2,i)) endfunction math_Plain33to9 + + !******************************************************************** +! convert 3x3 matrix into vector 9x1 +!******************************************************************** + pure function math_Plain33to9_logical(m33) + + use prec, only: pReal,pInt + implicit none + + logical, dimension(3,3), intent(in) :: m33 + logical, dimension(9) :: math_Plain33to9_logical + integer(pInt) i + + forall (i=1:9) math_Plain33to9_logical(i) = m33(mapPlain(1,i),mapPlain(2,i)) + + endfunction math_Plain33to9_logical + !******************************************************************** ! convert Plain 9x1 back to 3x3 matrix !******************************************************************** @@ -2048,7 +2065,7 @@ endfunction math_sampleGaussVar real(pReal) CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det error = .false. - ce = math_mul33x33(transpose(FE),FE) + ce = math_mul33x33(math_transpose3x3(FE),FE) CALL math_spectral1(CE,EW1,EW2,EW3,EB1,EB2,EB3) U=sqrt(EW1)*EB1+sqrt(EW2)*EB2+sqrt(EW3)*EB3 @@ -2154,6 +2171,51 @@ endfunction math_sampleGaussVar ENDSUBROUTINE math_spectral1 +!********************************************************************** + function math_eigenvalues3x3(M) +!**** Eigenvalues of symmetric 3X3 matrix M + + use prec, only: pReal, pInt + implicit none + + real(pReal), intent(in) :: M(3,3) + real(pReal), dimension(3,3) :: EB1(3,3),EB2(3,3),EB3(3,3) + real(pReal), dimension(3) :: math_eigenvalues3x3 + real(pReal) HI1M,HI2M,HI3M,TOL,R,S,T,P,Q,RHO,PHI,Y1,Y2,Y3,arg,EW1,EW2,EW3 + TOL=1.e-14_pReal + CALL math_hi(M,HI1M,HI2M,HI3M) + R=-HI1M + S= HI2M + T=-HI3M + P=S-R**2.0_pReal/3.0_pReal + Q=2.0_pReal/27.0_pReal*R**3.0_pReal-R*S/3.0_pReal+T + EB1=0.0_pReal + EB2=0.0_pReal + EB3=0.0_pReal + if((abs(P) < TOL) .and. (abs(Q) < TOL)) THEN +! three equivalent eigenvalues + math_eigenvalues3x3(1) = HI1M/3.0_pReal + math_eigenvalues3x3(2)=math_eigenvalues3x3(1) + math_eigenvalues3x3(3)=math_eigenvalues3x3(1) +! this is not really correct, but this way U is calculated +! correctly in PDECOMPOSITION (correct is EB?=I) + EB1(1,1)=1.0_pReal + EB2(2,2)=1.0_pReal + EB3(3,3)=1.0_pReal + else + RHO=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal + arg=-Q/RHO/2.0_pReal + if(arg.GT.1) arg=1 + if(arg.LT.-1) arg=-1 + PHI=acos(arg) + Y1=2*RHO**(1.0_pReal/3.0_pReal)*cos(PHI/3.0_pReal) + Y2=2*RHO**(1.0_pReal/3.0_pReal)*cos(PHI/3.0_pReal+2.0_pReal/3.0_pReal*PI) + Y3=2*RHO**(1.0_pReal/3.0_pReal)*cos(PHI/3.0_pReal+4.0_pReal/3.0_pReal*PI) + math_eigenvalues3x3(1) = Y1-R/3.0_pReal + math_eigenvalues3x3(2) = Y2-R/3.0_pReal + math_eigenvalues3x3(3) = Y3-R/3.0_pReal + endif + endfunction math_eigenvalues3x3 !********************************************************************** !**** HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M diff --git a/code/numerics.f90 b/code/numerics.f90 index b7a8e1663..2bab441dc 100644 --- a/code/numerics.f90 +++ b/code/numerics.f90 @@ -67,9 +67,8 @@ real(pReal) relevantStrain, & ! strain !* spectral parameters: err_div_tol, & ! error of divergence in fourier space err_stress_tol, & ! absolut stress error, will be computed from err_stress_tolrel (dont prescribe a value) - err_stress_tolrel, & ! factor to multiply with highest stress to get err_stress_tol - err_defgrad_tol ! tolerance for error of defgrad compared to prescribed defgrad -logical memory_efficient ! for fast execution (pre calculation of gamma_hat) + err_stress_tolrel ! factor to multiply with highest stress to get err_stress_tol +logical memory_efficient ! for fast execution (pre calculation of gamma_hat) integer(pInt) itmax , & ! maximum number of iterations @@ -163,10 +162,9 @@ subroutine numerics_init() volDiscrPow_RGC = 5.0 !* spectral parameters: - err_div_tol = 1.0e-2 ! proposed by Suquet, less strict criteria are usefull, e.g. 5e-3 - err_defgrad_tol = 1.0e-3 ! relative tolerance for fullfillment of average deformation gradient (is usually passively fullfilled) + err_div_tol = 1.0e-4 ! 1.0e-4 proposed by Suquet err_stress_tolrel = 0.01 ! relative tolerance for fullfillment of stress BC - itmax = 40_pInt ! Maximum iteration number + itmax = 20_pInt ! Maximum iteration number memory_efficient = .true. ! Precalculate Gamma-operator (81 double per point) !* Random seeding parameters: added <<>> @@ -274,8 +272,6 @@ subroutine numerics_init() !* spectral parameters case ('err_div_tol') err_div_tol = IO_floatValue(line,positions,2) - case ('err_defgrad_tol') - err_defgrad_tol = IO_floatValue(line,positions,2) case ('err_stress_tolrel') err_stress_tolrel = IO_floatValue(line,positions,2) case ('itmax') @@ -345,7 +341,6 @@ subroutine numerics_init() !* spectral parameters write(6,'(a24,x,e8.1)') 'err_div_tol: ',err_div_tol - write(6,'(a24,x,e8.1)') 'err_defgrad_tol: ',err_defgrad_tol write(6,'(a24,x,e8.1)') 'err_stress_tolrel: ',err_stress_tolrel write(6,'(a24,x,i8)') 'itmax: ',itmax write(6,'(a24,x,L8)') 'memory_efficient: ',memory_efficient @@ -403,7 +398,6 @@ subroutine numerics_init() !* spectral parameters if (err_div_tol <= 0.0_pReal) call IO_error(49) - if (err_defgrad_tol <= 0.0_pReal) call IO_error(49) if (err_stress_tolrel <= 0.0_pReal) call IO_error(49) if (itmax <= 1.0_pInt) call IO_error(49)