corrected calculation of divergence in Fourier space, removed normalization of normdyad (was useless), now using correct compliance for calculation of stress BC.
This commit is contained in:
Martin Diehl
parent
18a5841bc5
commit
a561ef1cf5
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@ -56,7 +56,7 @@ program DAMASK_spectral
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implicit none
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include 'include/fftw3.f' ! header file for fftw3 (declaring variables). Library files are also needed
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! compile FFTW 3.2.2 with ./configure --enable-threads
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! compile FFTW 3.2.2 with ./configure --enable-threads
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! variables to read from loadcase and geom file
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real(pReal), dimension(9) :: valuevector ! stores information temporarily from loadcase file
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integer(pInt), parameter :: maxNchunksInput = 26 ! 5 identifiers, 18 values for the matrices and 3 scalars
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@ -90,7 +90,8 @@ program DAMASK_spectral
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pstress, pstress_av, cstress_av, defgrad_av,&
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defgradAim, defgradAimOld, defgradAimCorr, defgradAimCorrPrev,&
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mask_stress, mask_defgrad
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real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0
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real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0, c0_temp
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real(pReal), dimension(9,9) :: s099
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real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation
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real(pReal), dimension(6,6) :: dsde, c066, s066 ! Mandel notation of 4th order tensors
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real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold
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@ -99,14 +100,14 @@ program DAMASK_spectral
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! variables storing information for spectral method
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complex(pReal) :: img
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complex(pReal), dimension(3,3) :: temp33_Complex
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real(pReal), dimension(3,3) :: xinormdyad
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real(pReal), dimension(3,3) :: xidyad
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat
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real(pReal), dimension(3) :: xi, xi_central
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real(pReal), dimension(:,:,:,:), allocatable :: xi
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integer(pInt), dimension(3) :: k_s
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integer*8, dimension(2) :: plan_fft
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! loop variables, convergence etc.
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real(pReal) guessmode, err_div, err_stress, err_defgrad, sigma0
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real(pReal) guessmode, err_div, err_stress, err_defgrad, pHatAv
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integer(pInt) i, j, k, l, m, n, p
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integer(pInt) loadcase, ielem, iter, calcmode, CPFEM_mode, ierr
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logical errmatinv
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@ -281,7 +282,8 @@ program DAMASK_spectral
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allocate (defgrad (resolution(1),resolution(2),resolution(3),3,3)); defgrad = 0.0_pReal
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allocate (defgradold(resolution(1),resolution(2),resolution(3),3,3)); defgradold = 0.0_pReal
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allocate (coordinates(3,resolution(1),resolution(2),resolution(3))); coordinates = 0.0_pReal
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allocate (coordinates(3,resolution(1),resolution(2),resolution(3))); coordinates = 0.0_pReal
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allocate (xi (3,resolution(1)/2+1,resolution(2),resolution(3))); xi = 0.0_pReal
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wgt = 1.0_pReal/real(resolution(1)*resolution(2)*resolution(3), pReal)
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defgradAim = math_I3
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@ -301,49 +303,43 @@ program DAMASK_spectral
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c066 = c066 + dsde
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enddo; enddo; enddo
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c066 = c066 * wgt
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c0 = math_mandel66to3333(c066)
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call math_invert(6, c066, s066,i, errmatinv)
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if(errmatinv) call IO_error(800) ! Matrix inversion error
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s0 = math_mandel66to3333(s066)
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c0 = math_mandel66to3333(c066) ! linear reference material stiffness
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do k = 1, resolution(3) ! calculation of discrete frequencies, order as in FFTW (wrap around)
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k_s(3) = k-1
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if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3)
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do j = 1, resolution(2)
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k_s(2) = j-1
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if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
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do i = 1, resolution(1)/2+1
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k_s(1) = i-1
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xi(3,i,j,k) = 0.0_pReal ! 2D case
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if(resolution(3) > 1) xi(3,i,j,k) = real(k_s(3), pReal)*2*pi/geomdimension(3) ! 3D case ToDo: Check if to multiply by 2 pi?
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xi(2,i,j,k) = real(k_s(2), pReal)*2*pi/geomdimension(2)
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xi(1,i,j,k) = real(k_s(1), pReal)*2*pi/geomdimension(1)
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enddo; enddo; enddo
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if(memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal
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do k = 1, resolution(3)
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k_s(3) = k-1
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if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3)
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do j = 1, resolution(2)
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k_s(2) = j-1
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if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
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do i = 1, resolution(1)/2+1
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k_s(1) = i-1
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xi(3) = 0.0_pReal ! for the 2D case
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if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) ! 3D case
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xi(2) = real(k_s(2), pReal)/geomdimension(2)
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xi(1) = real(k_s(1), pReal)/geomdimension(1)
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if (any(xi /= 0.0_pReal)) then
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do l = 1,3; do m = 1,3
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xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2) ! unit sphere, unit vectors in Fourier space
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enddo; enddo
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temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad))
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else
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xinormdyad = 0.0_pReal
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temp33_Real = 0.0_pReal
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endif
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do l=1,3; do m=1,3; do n=1,3; do p=1,3
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gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
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(xinormdyad(m,p)+xinormdyad(p,m))
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enddo; enddo; enddo; enddo
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do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
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if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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do l = 1,3; do m = 1,3
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xidyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
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enddo; enddo
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temp33_Real = math_inv3x3(math_mul3333xx33(c0, xidyad))
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else
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xidyad = 0.0_pReal
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temp33_Real = 0.0_pReal
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endif
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do l=1,3; do m=1,3; do n=1,3; do p=1,3
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gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
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(xidyad(m,p)+xidyad(p,m))
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enddo; enddo; enddo; enddo
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enddo; enddo; enddo
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endif
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! calculate xi for the calculation of divergence in Fourier space (central frequency)
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xi_central(3) = 0.0_pReal ! 2D case
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if(resolution(3) > 1) xi_central(3) = real(resolution(3)/2, pReal)/geomdimension(3) ! 3D case
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xi_central(2) = real(resolution(2)/2, pReal)/geomdimension(2)
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xi_central(1) = real(resolution(1)/2, pReal)/geomdimension(1)
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allocate (workfft(resolution(1)+2,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal
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! Initialization of fftw (see manual on fftw.org for more details)
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@ -392,7 +388,7 @@ program DAMASK_spectral
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! loop oper steps defined in input file for current loadcase
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do step = 1, bc_steps(loadcase)
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!*************************************************************
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if (bc_logscale(loadcase) == 1) then ! loglinear scale
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if (bc_logscale(loadcase) == 1) then ! loglinear scale
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if (loadcase == 1) then ! 1st loadcase of loglinear scale
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if (step == 1) then ! 1st step of 1st loadcase of loglinear scale
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timeinc = bc_timeIncrement(1)*(2.0**(1 - bc_steps(1))) ! assume 1st step is equal to 2nd
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@ -444,7 +440,7 @@ program DAMASK_spectral
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print*, ' '
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print '(3(A,I5.5,tr2))', ' Loadcase = ',loadcase, ' Step = ',step, ' Iteration = ',iter
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cstress_av = 0.0_pReal
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workfft = 0.0_pReal !needed because of the padding for FFTW
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workfft = 0.0_pReal ! needed because of the padding for FFTW
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!*************************************************************
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! adjust defgrad to fulfill BCs
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@ -460,6 +456,7 @@ program DAMASK_spectral
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cstress,dsde, pstress, dPdF)
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enddo; enddo; enddo
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c0_temp = 0.0_pReal !for calculation of s0
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ielem = 0_pInt
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do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
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ielem = ielem + 1_pInt
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@ -469,10 +466,15 @@ program DAMASK_spectral
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temperature,timeinc,ielem,1_pInt,&
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cstress,dsde, pstress, dPdF)
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CPFEM_mode = 2_pInt
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workfft(i,j,k,:,:) = pstress ! prepare Fourier transform of first P--K stress
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c0_temp = c0_temp + dPdF
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workfft(i,j,k,:,:) = pstress ! build up average P-K stress
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cstress_av = cstress_av + math_mandel6to33(cstress) ! build up average Cauchy stress
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enddo; enddo; enddo
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call math_invert(9, math_plain3333to99(c0_temp),s099,i,errmatinv)
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if(errmatinv) call IO_error(800,ext_msg = "problem in c0 inversion")
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s0 = math_plain99to3333(s099) *real(resolution(1)*resolution(2)*resolution(3), pReal) ! average s0 for calculation of BC
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cstress_av = cstress_av * wgt
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do n = 1,3; do m = 1,3
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pstress_av(m,n) = sum(workfft(1:resolution(1),1:resolution(2),1:resolution(3),m,n)) * wgt
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@ -486,7 +488,7 @@ program DAMASK_spectral
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defgradAimCorrPrev = defgradAimCorr
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defgradAimCorr = -mask_stress * math_mul3333xx33(s0, (mask_stress*(pstress_av - bc_stress(:,:,loadcase))))
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do m=1,3; do n =1,3 ! calculate damper (correction is far too strong)
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do m=1,3; do n =1,3 ! calculate damper (correction is far too strong) !ToDo:
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if ( sign(1.0_pReal,defgradAimCorr(m,n))/=sign(1.0_pReal,defgradAimCorrPrev(m,n))) then
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damper(m,n) = max(0.01_pReal,damper(m,n)*0.8)
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else
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@ -537,47 +539,38 @@ program DAMASK_spectral
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enddo; enddo
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print *, 'Calculating equilibrium using spectral method'
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err_div = 0.0_pReal; sigma0 = 0.0_pReal
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err_div = 0.0_pReal; pHatAv = 0.0_pReal
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call dfftw_execute_dft_r2c(plan_fft(1),workfft,workfft) ! FFT of pstress
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do m = 1,3 ! L infinity Norm of stress tensor
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sigma0 = max(sigma0, sum(abs(workfft(1,1,1,m,:) + workfft(2,1,1,m,:)*img)))
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pHatAv = max(pHatAv, sum(abs(workfft(1,1,1,m,:) + workfft(2,1,1,m,:)*img)))
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enddo
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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)
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workfft(resolution(1)+2,resolution(2)/2+1,resolution(3)/2+1,:,:)*img,xi_central))))
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err_div = err_div/sigma0 ! weighting of error
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do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
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err_div = max(err_div, maxval(abs(math_mul33x3_complex(workfft(i*2-1,j,k,:,:)+& ! L infinity norm of div(stress)
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workfft(i*2, j,k,:,:)*img,xi(:,i,j,k)))))
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enddo; enddo; enddo
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err_div = err_div/pHatAv ! Criterion as supposed in Suquet 2001
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if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
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do k = 1, resolution(3)
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k_s(3) = k-1
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if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3)
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do j = 1, resolution(2)
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k_s(2) = j-1
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if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
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do i = 1, resolution(1)/2+1
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k_s(1) = i-1
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xi(3) = 0.0_pReal ! for the 2D case
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if(resolution(3) > 1) xi(3) = real(k_s(3), pReal)/geomdimension(3) ! 3D case
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xi(2) = real(k_s(2), pReal)/geomdimension(2)
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xi(1) = real(k_s(1), pReal)/geomdimension(1)
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if (any(xi(:) /= 0.0_pReal)) then
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do l = 1,3; do m = 1,3
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xinormdyad(l,m) = xi(l)*xi(m)/sum(xi**2)
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enddo; enddo
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temp33_Real = math_inv3x3(math_mul3333xx33(c0, xinormdyad))
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else
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xinormdyad = 0.0_pReal
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temp33_Real = 0.0_pReal
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endif
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do l=1,3; do m=1,3; do n=1,3; do p=1,3
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gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
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(xinormdyad(m,p) +xinormdyad(p,m))
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enddo; enddo; enddo; enddo
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do m = 1,3; do n = 1,3
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temp33_Complex(m,n) = sum(gamma_hat(1,1,1,m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
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+workfft(i*2 ,j,k,:,:)*img))
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enddo; enddo
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workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of strain
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workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
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do k = 1, resolution(3); do j = 1, resolution(2) ;do i = 1, resolution(1)/2+1
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if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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do l = 1,3; do m = 1,3
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xidyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
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enddo; enddo
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temp33_Real = math_inv3x3(math_mul3333xx33(c0, xidyad))
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else
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xidyad = 0.0_pReal
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temp33_Real = 0.0_pReal
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endif
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do l=1,3; do m=1,3; do n=1,3; do p=1,3
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gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
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(xidyad(m,p) +xidyad(p,m))
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enddo; enddo; enddo; enddo
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do m = 1,3; do n = 1,3
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temp33_Complex(m,n) = sum(gamma_hat(1,1,1,m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
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+workfft(i*2 ,j,k,:,:)*img))
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enddo; enddo
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workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of av strain
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workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
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enddo; enddo; enddo
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else ! use precalculated gamma-operator
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do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
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@ -585,7 +578,7 @@ program DAMASK_spectral
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temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
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+ workfft(i*2 ,j,k,:,:)*img))
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enddo; enddo
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workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of strain
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workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of av strain
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workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
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enddo; enddo; enddo
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endif
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