From 3837dad51e7ac5dc9ae9dc62bdc3743f42ce1bec Mon Sep 17 00:00:00 2001 From: Martin Diehl Date: Wed, 20 Oct 2010 08:59:00 +0000 Subject: [PATCH] fixed bug in mpie_spectral.f90 concerning spectral method (now deltaF hat get the right value) added mpie_spectral2.f90, a version that should get the new algorithm proposed in 2010. until now, it is the same as mpie_spectral.f90 (large strain formulation by suquet et al) but with c2c, c2c FFT --- code/mpie_spectral.f90 | 360 ++++++++++++------------ code/mpie_spectral2.f90 | 592 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 760 insertions(+), 192 deletions(-) create mode 100644 code/mpie_spectral2.f90 diff --git a/code/mpie_spectral.f90 b/code/mpie_spectral.f90 index 49bb790a7..fbe9dc1bb 100644 --- a/code/mpie_spectral.f90 +++ b/code/mpie_spectral.f90 @@ -29,7 +29,7 @@ program mpie_spectral use IO use math use CPFEM, only: CPFEM_general - use numerics, only: relevantStrain, rTol_crystalliteStress, rTol_defgradAvg + use numerics, only: relevantStrain, rTol_crystalliteStress implicit none include 'fftw3.f' !header file for fftw3 (declaring variables). Library file is also needed @@ -62,28 +62,27 @@ program mpie_spectral ! stress etc. real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, damper,& - pstress, cstress_av, defgrad_av,& + 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 - real(pReal), dimension(9,9) :: s099 - real(pReal), dimension(:,:,:), allocatable :: ddefgrad + real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation + real(pReal), dimension(6,6) :: dsde, c066, s066 + real(pReal), dimension(:,:,:), allocatable :: ddefgrad real(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field, defgrad, defgradold, cstress_field - + ! variables storing information for spectral method complex(pReal), dimension(:,:,:,:,:), allocatable :: workfft complex(pReal), dimension(3,3) :: temp33_Complex + real(pReal), dimension(3,3) :: xinormdyad real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat - real(pReal), dimension(:,:,:,:,:), allocatable :: xinormdyad real(pReal), dimension(:,:,:,:), allocatable :: xi integer(pInt), dimension(3) :: k_s integer*8, dimension(2,3,3) :: plan_fft ! convergence etc. real(pReal) err_div, err_stress, err_defgrad - real(pReal) err_div_tol, err_stress_tol, err_defgrad_tol, sigma0 + real(pReal) err_div_tol, err_stress_tol, err_stress_tolrel, sigma0 integer(pInt) itmax, ierr logical errmatinv @@ -113,15 +112,11 @@ program mpie_spectral N_n = 0_pInt resolution = 1_pInt; meshdimension = 0.0_pReal - xi = 0.0_pReal - c0 = 0.0_pReal err_div_tol = 1.0e-4 - err_stress_tol = 1.0e6 - err_defgrad_tol = 1.0e-12 - - itmax = 50_pInt - + itmax = 250_pInt + err_stress_tolrel=0.01 + temperature = 300.0_pReal gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false. @@ -179,7 +174,7 @@ program mpie_spectral 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 + if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the velocity gradient matrix enddo bc_mask(:,:,1,i) = reshape(bc_maskvector,(/3,3/)) bc_velocityGrad(:,:,i) = reshape(valuevector,(/3,3/)) @@ -255,14 +250,13 @@ program mpie_spectral enddo 100 close(unit) - print '(a,/,i3,i3,i3)','resolution a b c', resolution - print '(a,/,f6.2,f6.2,f6.2)','dimension x y z', meshdimension + print '(a,/,i4,i4,i4)','resolution a b c', resolution + print '(a,/,f6.1,f6.1,f6.1)','dimension x y z', meshdimension print *,'homogenization',homog print *, '' - + allocate (workfft(resolution(1)/2+1,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal - allocate (xinormdyad(resolution(1)/2+1,resolution(2),resolution(3),3,3)); xinormdyad = 0.0_pReal allocate (xi(resolution(1)/2+1,resolution(2),resolution(3),3)); xi = 0.0_pReal allocate (pstress_field(resolution(1),resolution(2),resolution(3),3,3)); pstress_field = 0.0_pReal allocate (cstress_field(resolution(1),resolution(2),resolution(3),3,3)); cstress_field = 0.0_pReal @@ -270,7 +264,7 @@ program mpie_spectral 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 (ddefgrad(resolution(1),resolution(2),resolution(3))); ddefgrad = 0.0_pReal - + ! Initialization of fftw (see manual on fftw.org for more details) call dfftw_init_threads(ierr) call dfftw_plan_with_nthreads(4) @@ -288,13 +282,19 @@ program mpie_spectral defgrad_av = math_I3 ! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field 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) + s0 = math_mandel66to3333(s066) + !calculation of xinormdyad (to calculate gamma_hat) and xi (waves, for proof of equilibrium) do k = 1, resolution(3) k_s(3) = k-1 @@ -304,19 +304,26 @@ program mpie_spectral 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(i,j,k,3) = 0.0_pReal + xi(i,j,k,3) = 0.0_pReal if(resolution(3) > 1) xi(i,j,k,3) = real(k_s(3), pReal)/meshdimension(3) xi(i,j,k,2) = real(k_s(2), pReal)/meshdimension(2) xi(i,j,k,1) = real(k_s(1), pReal)/meshdimension(1) - - if (any(xi(i,j,k,:) /= 0.0_pReal)) then + if (any(xi(i,j,k,:) /= 0.0_pReal)) then do l = 1,3; do m = 1,3 - xinormdyad(i,j,k, l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2) + xinormdyad(l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2) enddo; enddo + else + xinormdyad = 0.0_pReal endif - + temp33_Real = math_mul3333xx33(c0, xinormdyad) + temp33_Real = math_inv3x3(temp33_Real) + 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) = - temp33_Real(l,n) * xinormdyad(m,p) + ! gamma_hat(i,j,k, l,m,n,p) = - 0.5_pReal * temp33_Real(l,n) * xinormdyad(m,p)& ! symmetrization???????? + ! - 0.5_pReal * temp33_Real(m,n) * xinormdyad(l,p) + enddo; enddo; enddo; enddo enddo; enddo; enddo - + open(539,file='stress-strain.out') ! Initialization done @@ -330,7 +337,7 @@ program mpie_spectral 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) @@ -350,177 +357,142 @@ program mpie_spectral enddo; enddo; enddo guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase - calcmode = 1_pInt ! start calculation of BC fullfillment + calcmode = 0_pInt ! start calculation of BC fullfillment CPFEM_mode = 1_pInt ! winding forward iter = 0_pInt - err_stress= 2_pReal * err_stress_tol ! go into loop + err_div= 2_pReal * err_div_tol ! go into loop defgradAimCorr = 0.0_pReal ! reset damping calculation - damper = ones/10 - 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(i,j,k,3) = 0.0_pReal - if(resolution(3) > 1) xi(i,j,k,3) = real(k_s(3), pReal)/(meshdimension(3)*defgrad_av(3,3)) - xi(i,j,k,2) = real(k_s(2), pReal)/(meshdimension(2)*defgrad_av(2,2)) - xi(i,j,k,1) = real(k_s(1), pReal)/(meshdimension(1)*defgrad_av(1,1)) + damper = damper * 0.9_pReal - if (any(xi(i,j,k,:) /= 0.0_pReal)) then - do l = 1,3; do m = 1,3 - xinormdyad(i,j,k, l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2) - enddo; enddo - endif - - enddo; enddo; enddo !************************************************************* ! 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 print '(A,I5.5,tr2,A,I5.5)', ' Step = ',steps,'Iteration = ',iter - !************************************************************* -! Calculate stress field for current deformation gradient using CPFEM_general - 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 - cstress_av = 0.0_pReal - c0 = 0.0_pReal; c066 = 0.0_pReal - ielem = 0_pInt - do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) - ielem = ielem + 1 - call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1, others get 2 (saves winding forward effort) - defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& - temperature,timeinc,ielem,1_pInt,& - cstress,dsde, pstress, dPdF) - CPFEM_mode = 2 - c0 = c0 + dPdF - c066 = c066 + dsde - pstress_field(i,j,k,:,:) = pstress - cstress_field(i,j,k,:,:) = math_mandel6to33(cstress) - cstress_av = cstress_av + math_mandel6to33(cstress) ! average stress - enddo; enddo; enddo - cstress_av = cstress_av*wgt ! do the weighting of average stress - err_stress = maxval(abs(mask_stress * (cstress_av - bc_stress(:,:,loadcase)))) - err_stress_tol = maxval(abs(cstress_av))/100.0_pReal !accecpt one % of error - print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol - -! Update gamma_hat with new reference stiffness, calculate new compliance - if(iter == 1) then - c0 = c0 * wgt - c066 = c066 * wgt - call math_invert(9, math_plain3333to99(c0), s099, i, errmatinv) -errmatinv = .true. - if(errmatinv) then - call math_invert(6, c066, s066,i, errmatinv) - if(errmatinv) then - print *, 'Compliance not updated' - else - s0 = math_mandel66to3333(s066) - endif - else - s0 = math_plain99to3333(s099) - endif - if(errmatinv == .false.) then - do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1 - temp33_Real = 0.0_pReal - do l = 1,3; do m = 1,3; do n = 1,3; do p = 1,3 - temp33_Real(l,m) = temp33_Real(l,m) + c0(l,n,m,p) * xinormdyad(i,j,k, n,p) - enddo; enddo; enddo; enddo - temp33_Real = math_inv3x3(temp33_Real) - 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) = - temp33_Real(l,n) * xinormdyad(i,j,k, m,p) - enddo; enddo; enddo; enddo - enddo; enddo; enddo - print *, 'Gamma hat updated' - endif - endif - - select case (calcmode) - case (0) ! Using the spectral method to calculate the change of deformation gradient, check divergence of stress field in fourier space - print *, 'Calculating equilibrium using spectral method' - err_div = 0.0_pReal; sigma0 = 0.0_pReal - do m = 1,3; do n = 1,3 - call dfftw_execute_dft_r2c(plan_fft(1,m,n), cstress_field(:,:,:,m,n),workfft(:,:,:,m,n)) - if(n==3) sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:)))) ! L infinity Norm of stress tensor - 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, defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& + temperature,timeinc,ielem,1_pInt,& + cstress,dsde, pstress, dPdF) + enddo; enddo; 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,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress) - temp33_Complex = 0.0_pReal - do m = 1,3; do n = 1,3 - temp33_Complex(m,n) = sum(gamma_hat(i,j,k,m,n,:,:) * workfft(i,j,k,:,:)) - enddo; enddo - workfft(i,j,k,:,:) = temp33_Complex(:,:) - enddo; enddo; enddo - - err_div = err_div/real((prodnn/resolution(1)*(resolution(1)/2+1)), pReal)/sigma0 !weighting of error - - do m = 1,3; do n = 1,3 - call dfftw_execute_dft_c2r(plan_fft(2,m,n), workfft(:,:,:,m,n),ddefgrad(:,:,:)) - ddefgrad = ddefgrad * wgt - defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + ddefgrad - enddo; enddo - - print '(2(a,E8.2))', ' error divergence ',err_div,' Tol. = ', err_div_tol - - if(err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc. - calcmode = 1 - defgradAimCorr = 0.0_pReal - damper = ones/10 - endif + ielem = 0_pInt + do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) + ielem = ielem + 1 + 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 + pstress_field(i,j,k,:,:) = pstress + cstress_field(i,j,k,:,:) = math_mandel6to33(cstress) + enddo; enddo; enddo - case (1) ! adjust defgrad to fulfill BCs s - print*, 'Correcting deformation gradient to fullfill BCs' - defgrad_av = 0.0_pReal - do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) - defgrad_av = defgrad_av + defgrad(i,j,k,:,:) - enddo; enddo; enddo - defgrad_av = defgrad_av * wgt ! weight by number of FP + do m = 1,3; do n = 1,3 + pstress_av(m,n) = sum(pstress_field(:,:,:,m,n)) * wgt + cstress_av(m,n) = sum(cstress_field(:,:,:,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)))) - defgradAimCorrPrev = defgradAimCorr - defgradAimCorr = -mask_stress * math_mul3333xx33(s0, (mask_stress*(cstress_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(0.0_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_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim))) - print '(a,/,3(3(f12.7,x)/))', ' defgrad Aim: ',defgradAim(1:3,:) - print '(a,/,3(3(f12.7,x)/))', ' damper: ',damper(1:3,:) - print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6 - print '(2(a,E8.2))', ' error defgrad ',err_defgrad,' Tol. = ',err_defgrad_tol - print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol*0.8 - if(err_stress < err_stress_tol*0.8) then - calcmode = 0 - err_div = 2* err_div_tol + 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 - - end select - + 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: ',defgrad_av(1:3,:) + print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6 + print '(a,E8.2)', ' error defgrad ',err_defgrad + print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol*0.8 + if(err_stress < err_stress_tol*0.8) then + calcmode = 1 + 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 + 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 + call CPFEM_general(2,& + defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& + temperature,timeinc,ielem,1_pInt,& + cstress,dsde, pstress, dPdF) + pstress_field(i,j,k,:,:) = pstress + cstress_field(i,j,k,:,:) = math_mandel6to33(cstress) + enddo; enddo; enddo + + print *, 'Calculating equilibrium using spectral method' + err_div = 0.0_pReal; sigma0 = 0.0_pReal + do m = 1,3; do n = 1,3 + call dfftw_execute_dft_r2c(plan_fft(1,m,n), pstress_field(:,:,:,m,n),workfft(:,:,:,m,n)) + if(n==3) sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:)))) ! L infinity Norm of stress tensor + enddo; 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,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress) + temp33_Complex = 0.0_pReal + do m = 1,3; do n = 1,3 + temp33_Complex(m,n) = sum(gamma_hat(i,j,k,m,n,:,:) * workfft(i,j,k,:,:)) + enddo; enddo + workfft(i,j,k,:,:) = temp33_Complex(:,:) + enddo; enddo; enddo + workfft(1,1,1,:,:) = defgrad_av - math_I3 + err_div = err_div/real((prodnn/resolution(1)*(resolution(1)/2+1)), pReal)/sigma0 !weighting of error + + do m = 1,3; do n = 1,3 + call dfftw_execute_dft_c2r(plan_fft(2,m,n), workfft(:,:,:,m,n),ddefgrad(:,:,:)) + defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + ddefgrad * wgt + pstress_av(m,n) = sum(pstress_field(:,:,:,m,n))*wgt + cstress_av(m,n) = sum(cstress_field(:,:,:,m,n))*wgt + 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 relativ error specified + + 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 + if(err_stress > err_stress_tol .and. err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc. + calcmode = 0 + defgradAimCorr = 0.0_pReal + damper = damper * 0.9_pReal + endif + end select enddo ! end looping when convergency is achieved write(539,'(E12.6,a,E12.6)'),defgrad_av(3,3)-1,' ', cstress_av(3,3) @@ -530,22 +502,25 @@ errmatinv = .true. print '(A)', '************************************************************' ! Postprocessing (gsmh output) -if(mod(steps-1,10)==0) then + temp33_Real(1,:) = 0.0_pReal; temp33_Real(1,3) = -(real(resolution(3))/meshdimension(3)) ! start just below origin do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) if((j==1).and.(i==1)) then - temp33_Real(1,:) = temp33_Real(1,:) + math_mul33x3(defgrad(i,j,k,:,:),(/0.0_pReal,0.0_pReal,(real(resolution(3))/meshdimension(3))/)) + temp33_Real(1,:) = temp33_Real(1,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/0.0_pReal,0.0_pReal,(real(resolution(3))/meshdimension(3))/)) temp33_Real(2,:) = temp33_Real(1,:) temp33_Real(3,:) = temp33_Real(1,:) displacement(i,j,k,:) = temp33_Real(1,:) else if(i==1) then - temp33_Real(2,:) = temp33_Real(2,:) + math_mul33x3(defgrad(i,j,k,:,:),(/0.0_pReal,(real(resolution(2))/meshdimension(2)),0.0_pReal/)) + temp33_Real(2,:) = temp33_Real(2,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/0.0_pReal,(real(resolution(2))/meshdimension(2)),0.0_pReal/)) temp33_Real(3,:) = temp33_Real(2,:) displacement(i,j,k,:) = temp33_Real(2,:) else - temp33_Real(3,:) = temp33_Real(3,:) + math_mul33x3(defgrad(i,j,k,:,:),(/(real(resolution(1))/meshdimension(1)),0.0_pReal,0.0_pReal/)) + temp33_Real(3,:) = temp33_Real(3,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/(real(resolution(1))/meshdimension(1)),0.0_pReal,0.0_pReal/)) displacement(i,j,k,:) = temp33_Real(3,:) endif endif @@ -560,8 +535,10 @@ if(mod(steps-1,10)==0) then ielem = 0_pInt do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) ielem = ielem + 1 - write(589, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) - write(588, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) + write(589, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) !for deformed configuration + write(588, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) + ! write(589, '(4(I10,tr2))'), ielem, i-1,j-1,k-1 !for undeformed configuration + ! write(588, '(4(I10,tr2))'), ielem, i-1,j-1,k-1 enddo; enddo; enddo write(589, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn @@ -589,7 +566,6 @@ if(mod(steps-1,10)==0) then write(589, *), '$EndNodeData' write(588, *), '$EndNodeData' close(589); close(588) -endif enddo ! end looping over steps in current loadcase enddo ! end looping over loadcases close(539) diff --git a/code/mpie_spectral2.f90 b/code/mpie_spectral2.f90 new file mode 100644 index 000000000..4895cd741 --- /dev/null +++ b/code/mpie_spectral2.f90 @@ -0,0 +1,592 @@ +!* $Id: mpie_spectral.f90 665 2010-10-13 16:04:44Z MPIE\m.diehl $ +!******************************************************************** +! 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 PathToMeshFile/NameOfMesh.mesh +! PathToLoadFile/NameOfLoadFile.load +! - PathToLoadFile will be the working directory +! - make sure the file "material.config" exists in the working +! directory +!******************************************************************** +program mpie_spectral +!******************************************************************** + + use mpie_interface + use prec, only: pInt, pReal + use IO + use math + use CPFEM, only: CPFEM_general + use numerics, only: relevantStrain, rTol_crystalliteStress + + implicit none + include 'fftw3.f' !header file for fftw3 (declaring variables). Library file is also needed + +! variables to read from loadcase and mesh 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 :: maxNchunksMesh = 7 ! 4 identifiers, 3 values + integer(pInt), dimension (1+2*maxNchunksMesh) :: posMesh + 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 mesh file + real(pReal) wgt + real(pReal), dimension(3) :: meshdimension + integer(pInt) homog, prodnn + 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 + real(pReal), dimension(:,:,:,:,:), allocatable :: defgrad, defgradold, cstress_field + complex(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field + complex(pReal), dimension(:,:,:), allocatable :: ddefgrad + +! variables storing information for spectral method + complex(pReal), dimension(:,:,:,:,:), allocatable :: workfft + complex(pReal), dimension(3,3) :: temp33_Complex + real(pReal), dimension(3,3) :: xinormdyad + real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat + real(pReal), dimension(:,:,:,:), allocatable :: xi + integer(pInt), dimension(3) :: k_s + integer*8, dimension(2,3,3) :: plan_fft + +! convergence etc. + real(pReal) err_div, err_stress, err_defgrad + real(pReal) err_div_tol, err_stress_tol, err_stress_tolrel, sigma0 + integer(pInt) itmax, ierr + logical errmatinv + +! loop variables etc. + real(pReal) guessmode ! flip-flop to guess defgrad fluctuation field evolution + integer(pInt) i, j, k, l, m, n, p + integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode + + real(pReal) temperature ! not used, but needed for call to CPFEM_general + +!gmsh output + character(len=1024) :: nriter + character(len=1024) :: nrstep + real(pReal), dimension(:,:,:,:), allocatable :: displacement +!gmsh output + +!Initializing + bc_maskvector = '' + unit = 234_pInt + + ones = 1.0_pReal + zeroes = 0.0_pReal + + N_l = 0_pInt + N_s = 0_pInt + N_t = 0_pInt + N_n = 0_pInt + + resolution = 1_pInt; meshdimension = 0.0_pReal + + err_div_tol = 1.0e-4 + itmax = 250_pInt + err_stress_tolrel=0.01 + + temperature = 300.0_pReal + + gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false. + + if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments + +! Reading the loadcase file and assign variables + path = getLoadcaseName() + print*,'Loadcase: ',trim(path) + print*,'Workingdir: ',trim(getSolverWorkingDirectoryName()) + + 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 + if ((N_l /= N_s).or.(N_s /= N_t).or.(N_t /= N_n)) & ! sanity check + call IO_error(46,ext_msg = path) !error message for incomplete input file + + enddo + +! allocate memory depending on lines in input file +101 N_Loadcases = N_l + + 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) = reshape(bc_maskvector,(/3,3/)) + bc_velocityGrad(:,:,i) = 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) = reshape(bc_maskvector,(/3,3/)) + bc_stress(:,:,i) = 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 + if (any(bc_mask(:,:,1,i) == bc_mask(:,:,2,i))) call IO_error(47,i) ! bc_mask consistency + print '(a,/,3(3(f12.6,x)/))','L',bc_velocityGrad(:,:,i) + print '(a,/,3(3(f12.6,x)/))','bc_stress',bc_stress(:,:,i) + print '(a,/,3(3(l,x)/))','bc_mask for velocitygrad',bc_mask(:,:,1,i) + print '(a,/,3(3(l,x)/))','bc_mask for stress',bc_mask(:,:,2,i) + print *,'time',bc_timeIncrement(i) + print *,'incs',bc_steps(i) + print *, '' + enddo + +!read header of mesh file to get the information needed before the complete mesh file is intepretated by mesh.f90 + path = getSolverJobName() + print*,'JobName: ',trim(path) + if (.not. IO_open_file(unit,trim(path)//InputFileExtension)) call IO_error(101,ext_msg = path) + + rewind(unit) + do + read(unit,'(a1024)',END = 100) line + if (IO_isBlank(line)) cycle ! skip empty lines + posMesh = IO_stringPos(line,maxNchunksMesh) + + select case ( IO_lc(IO_StringValue(line,posMesh,1)) ) + case ('dimension') + gotDimension = .true. + do i = 2,6,2 + select case (IO_lc(IO_stringValue(line,posMesh,i))) + case('x') + meshdimension(1) = IO_floatValue(line,posMesh,i+1) + case('y') + meshdimension(2) = IO_floatValue(line,posMesh,i+1) + case('z') + meshdimension(3) = IO_floatValue(line,posMesh,i+1) + end select + enddo + case ('homogenization') + gotHomogenization = .true. + homog = IO_intValue(line,posMesh,2) + case ('resolution') + gotResolution = .true. + do i = 2,6,2 + select case (IO_lc(IO_stringValue(line,posMesh,i))) + case('a') + resolution(1) = IO_intValue(line,posMesh,i+1) + case('b') + resolution(2) = IO_intValue(line,posMesh,i+1) + case('c') + resolution(3) = IO_intValue(line,posMesh,i+1) + end select + enddo + end select + if (gotDimension .and. gotHomogenization .and. gotResolution) exit + enddo + 100 close(unit) + + print '(a,/,i4,i4,i4)','resolution a b c', resolution + print '(a,/,f6.1,f6.1,f6.1)','dimension x y z', meshdimension + print *,'homogenization',homog + print *, '' + + allocate (workfft(resolution(1),resolution(2),resolution(3),3,3)); workfft = 0.0_pReal + allocate (gamma_hat(resolution(1),resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal + allocate (xi(resolution(1),resolution(2),resolution(3),3)); xi = 0.0_pReal + allocate (pstress_field(resolution(1),resolution(2),resolution(3),3,3)); pstress_field = 0.0_pReal + allocate (cstress_field(resolution(1),resolution(2),resolution(3),3,3)); cstress_field = 0.0_pReal + allocate (displacement(resolution(1),resolution(2),resolution(3),3)); displacement = 0.0_pReal + 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 (ddefgrad(resolution(1),resolution(2),resolution(3))); ddefgrad = 0.0_pReal + +! Initialization of fftw (see manual on fftw.org for more details) + call dfftw_init_threads(ierr) + call dfftw_plan_with_nthreads(4) + do m = 1,3; do n = 1,3 + call dfftw_plan_dft_3d(plan_fft(1,m,n),resolution(1),resolution(2),resolution(3),& + pstress_field(:,:,:,m,n), workfft(:,:,:,m,n), FFTW_PATIENT, FFTW_FORWARD) + call dfftw_plan_dft_3d(plan_fft(2,m,n),resolution(1),resolution(2),resolution(3),& + workfft(:,:,:,m,n), ddefgrad(:,:,:), FFTW_PATIENT, FFTW_BACKWARD) + enddo; enddo + + prodnn = resolution(1)*resolution(2)*resolution(3) + wgt = 1_pReal/real(prodnn, pReal) + defgradAim = math_I3 + defgradAimOld = math_I3 + defgrad_av = math_I3 +! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field + 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) + s0 = math_mandel66to3333(s066) + +!calculation of xinormdyad (to calculate gamma_hat) and xi (waves, for proof of equilibrium) + 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) + k_s(1) = i-1 + if(i > resolution(1)/2+1) k_s(1) = k_s(1)-resolution(1) + xi(i,j,k,3) = 0.0_pReal + if(resolution(3) > 1) xi(i,j,k,3) = real(k_s(3), pReal)/meshdimension(3) + xi(i,j,k,2) = real(k_s(2), pReal)/meshdimension(2) + xi(i,j,k,1) = real(k_s(1), pReal)/meshdimension(1) + if (any(xi(i,j,k,:) /= 0.0_pReal)) then + do l = 1,3; do m = 1,3 + xinormdyad(l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2) + enddo; enddo + else + xinormdyad = 0.0_pReal + endif + temp33_Real = math_mul3333xx33(c0, xinormdyad) + temp33_Real = math_inv3x3(temp33_Real) + 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) = - temp33_Real(l,n) * xinormdyad(m,p) + ! gamma_hat(i,j,k, l,m,n,p) = - 0.5_pReal * temp33_Real(l,n) * xinormdyad(m,p)& ! symmetrization???????? + ! - 0.5_pReal * temp33_Real(m,n) * xinormdyad(l,p) + enddo; enddo; enddo; enddo + enddo; enddo; enddo + + open(539,file='stress-strain.out') +! 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 + calcmode = 0_pInt ! start calculation of BC fullfillment + 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)) + iter = iter + 1 + print '(A,I5.5,tr2,A,I5.5)', ' Step = ',steps,'Iteration = ',iter +!************************************************************* + +! 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 + 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 + pstress_field(i,j,k,:,:) = pstress + cstress_field(i,j,k,:,:) = math_mandel6to33(cstress) + enddo; enddo; enddo + + do m = 1,3; do n = 1,3 + pstress_av(m,n) = sum(pstress_field(:,:,:,m,n)) * wgt + cstress_av(m,n) = sum(cstress_field(:,:,:,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: ',defgrad_av(1:3,:) + print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6 + print '(a,E8.2)', ' error defgrad ',err_defgrad + print '(2(a,E8.2))', ' error stress ',err_stress,' Tol. = ', err_stress_tol*0.8 + if(err_stress < err_stress_tol*0.8) then + calcmode = 1 + 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 + 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 + call CPFEM_general(2,& + defgradold(i,j,k,:,:), defgrad(i,j,k,:,:),& + temperature,timeinc,ielem,1_pInt,& + cstress,dsde, pstress, dPdF) + pstress_field(i,j,k,:,:) = pstress + cstress_field(i,j,k,:,:) = math_mandel6to33(cstress) + enddo; enddo; enddo + + print *, 'Calculating equilibrium using spectral method' + err_div = 0.0_pReal; sigma0 = 0.0_pReal + do m = 1,3; do n = 1,3 + call dfftw_execute_dft(plan_fft(1,m,n), pstress_field(:,:,:,m,n),workfft(:,:,:,m,n)) + if(n==3) sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:)))) ! L infinity Norm of stress tensor + enddo; 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,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress) + temp33_Complex = 0.0_pReal + do m = 1,3; do n = 1,3 + temp33_Complex(m,n) = sum(gamma_hat(i,j,k,m,n,:,:) * workfft(i,j,k,:,:)) + enddo; enddo + workfft(i,j,k,:,:) = temp33_Complex(:,:) + enddo; enddo; enddo + workfft(1,1,1,:,:) = defgrad_av - math_I3 + err_div = err_div/real((prodnn/resolution(1)*(resolution(1)/2+1)), pReal)/sigma0 !weighting of error + + do m = 1,3; do n = 1,3 + call dfftw_execute_dft_c2r(plan_fft(2,m,n), workfft(:,:,:,m,n),ddefgrad(:,:,:)) + defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + real(ddefgrad, pReal) * wgt + pstress_av(m,n) = sum(pstress_field(:,:,:,m,n))*wgt + cstress_av(m,n) = sum(cstress_field(:,:,:,m,n))*wgt + 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 relativ error specified + + 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 + if(err_stress > err_stress_tol .and. err_div < err_div_tol) then ! change to calculation of BCs, reset damper etc. + calcmode = 0 + defgradAimCorr = 0.0_pReal + damper = damper * 0.9_pReal + endif + end select + enddo ! end looping when convergency is achieved + + write(539,'(E12.6,a,E12.6)'),defgrad_av(3,3)-1,' ', cstress_av(3,3) + print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient: ',defgrad_av(1:3,:) + print *, '' + print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress [MPa]: ',cstress_av(1:3,:)/1.e6 + print '(A)', '************************************************************' + +! Postprocessing (gsmh output) + + temp33_Real(1,:) = 0.0_pReal; temp33_Real(1,3) = -(real(resolution(3))/meshdimension(3)) ! start just below origin + + do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) + if((j==1).and.(i==1)) then + temp33_Real(1,:) = temp33_Real(1,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/0.0_pReal,0.0_pReal,(real(resolution(3))/meshdimension(3))/)) + temp33_Real(2,:) = temp33_Real(1,:) + temp33_Real(3,:) = temp33_Real(1,:) + displacement(i,j,k,:) = temp33_Real(1,:) + else + if(i==1) then + temp33_Real(2,:) = temp33_Real(2,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/0.0_pReal,(real(resolution(2))/meshdimension(2)),0.0_pReal/)) + temp33_Real(3,:) = temp33_Real(2,:) + displacement(i,j,k,:) = temp33_Real(2,:) + else + temp33_Real(3,:) = temp33_Real(3,:) + math_mul33x3(defgrad(i,j,k,:,:),& + (/(real(resolution(1))/meshdimension(1)),0.0_pReal,0.0_pReal/)) + displacement(i,j,k,:) = temp33_Real(3,:) + endif + endif + enddo; enddo; enddo + + write(nriter, *) iter; write(nrstep, *) steps + open(589,file = 'stress' //trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh') + open(588,file = 'disgrad'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh') + write(589, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn + write(588, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn + + ielem = 0_pInt + do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) + ielem = ielem + 1 + write(589, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) !for deformed configuration + write(588, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:) + ! write(589, '(4(I10,tr2))'), ielem, i-1,j-1,k-1 !for undeformed configuration + ! write(588, '(4(I10,tr2))'), ielem, i-1,j-1,k-1 + enddo; enddo; enddo + + write(589, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn + write(588, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn + + do i = 1, prodnn + write(589, '(I10, A, I10)'), i, ' 15 2 1 2', i + write(588, '(I10, A, I10)'), i, ' 15 2 1 2', i + enddo + + write(589, '(A)'), '$EndElements' + write(588, '(A)'), '$EndElements' + write(589, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('stress'//trim(adjustl(nrstep))//& + '-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn + write(588, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('disgrad'//trim(adjustl(nrstep))//& + '-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn + + ielem = 0_pInt + do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1) + ielem = ielem + 1 + write(589, '(i10, 9(tr2, E14.8))'), ielem, cstress_field(i,j,k,:,:) + write(588, '(i10, 9(tr2, E14.8))'), ielem, defgrad(i,j,k,:,:) - math_I3 + enddo; enddo; enddo + + write(589, *), '$EndNodeData' + write(588, *), '$EndNodeData' + close(589); close(588) + enddo ! end looping over steps in current loadcase + enddo ! end looping over loadcases +close(539) + +do i=1,2; do m = 1,3; do n = 1,3 + call dfftw_destroy_plan(plan_fft(i,m,n)) +enddo; enddo; enddo + +end program mpie_spectral + +!******************************************************************** +! quit subroutine to satisfy IO_error +! +!******************************************************************** +subroutine quit(id) + use prec + implicit none + + integer(pInt) id + + stop +end subroutine \ No newline at end of file