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DAMASK_EICMD
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cleaning up, added new output to gmsh and to screen, prepared calculation of deformed mesh 

new convergence criteria: divergence of stressfield (in fourier space)
This commit is contained in:
Martin Diehl 2010-09-21 15:38:25 +00:00
parent 8488cafe3a
commit 6920d8d939
1 changed files with 141 additions and 116 deletions
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257
code/mpie_spectral.f90
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@ -63,26 +63,26 @@ program mpie_spectral
real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation (not needed)
real(pReal), dimension(3,3) :: pstress ! Piola-Kirchhoff stress in Matrix notation
real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0 ! ??, reference stiffnes, compliance
real(pReal), dimension(6,6) :: dsde, s066
real(pReal), dimension(6,6) :: dsde, s066
real(pReal), dimension(3,3) :: defgradmacro
real(pReal), dimension(3,3) :: pstress_av, defgrad_av, temp33_Real
real(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field, defgrad, defgradold, ddefgrad
real(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field, defgrad, defgradold
real(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(:,:,:,:,:,:,:), allocatable :: gamma_hat
real(pReal), dimension(:,:,:,:,:), allocatable :: xknormdyad
real(pReal), dimension(3) :: xk
real(pReal), dimension(:,:,:,:), allocatable :: xi
integer(pInt), dimension(3) :: k_s
integer*8, dimension(2,3,3) :: plan_fft
! convergency etc.
logical errmatinv
integer(pInt) itmax, ierr
real(pReal) error, err_stress_av, err_stress_max, err_strain_av, err_strain_max
real(pReal), dimension(3,3) :: strain_err, pstress_err
real(pReal) error, err_div, sigma0
! loop variables etc.
integer(pInt) i, j, k, l, m, n, p
integer(pInt) loadcase, ielem, iter, calcmode
@ -93,6 +93,7 @@ program mpie_spectral
!gmsh output
character(len=1024) :: nriter
character(len=1024) :: nrstep
real(pReal), dimension(:,:,:,:), allocatable :: displacement
!gmsh output
!Initializing
@ -104,11 +105,11 @@ program mpie_spectral
N_t = 0_pInt
N_n = 0_pInt
pstress_err = .0_pReal; strain_err = .0_pReal
resolution = 1_pInt; meshdimension = .0_pReal
error = 0.001_pReal
itmax = 50_pInt
resolution = 1_pInt; meshdimension = 0.0_pReal
xi = 0.0_pReal
error = 1.0e-7_pReal
itmax = 100_pInt
temperature = 300.0_pReal
@ -248,65 +249,62 @@ program mpie_spectral
print *,'homogenization',homog
print *, ''
allocate (workfft(resolution(1)/2+1,resolution(2),resolution(3),3,3)); workfft = .0_pReal
allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = .0_pReal
allocate (xknormdyad(resolution(1)/2+1,resolution(2),resolution(3),3,3)); xknormdyad = .0_pReal
allocate (pstress_field(resolution(1),resolution(2),resolution(3),3,3)); pstress_field = .0_pReal
allocate (defgrad(resolution(1),resolution(2),resolution(3),3,3)); defgrad = .0_pReal
allocate (defgradold(resolution(1),resolution(2),resolution(3),3,3)); defgradold = .0_pReal
allocate (ddefgrad(resolution(1),resolution(2),resolution(3),3,3)); ddefgrad = .0_pReal
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 (xknormdyad(resolution(1)/2+1,resolution(2),resolution(3),3,3)); xknormdyad = 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 (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
call dfftw_init_threads(ierr)
call dfftw_plan_with_nthreads(4)
do m = 1,3; do n = 1,3
call dfftw_plan_dft_r2c_3d(plan_fft(1,m,n),resolution(1),resolution(2),resolution(3),&
pstress_field(:,:,:,m,n), workfft(:,:,:,m,n), FFTW_PATIENT, FFTW_DESTROY_INPUT)
pstress_field(:,:,:,m,n), workfft(:,:,:,m,n), FFTW_PATIENT)
call dfftw_plan_dft_c2r_3d(plan_fft(2,m,n),resolution(1),resolution(2),resolution(3),&
workfft(:,:,:,m,n), ddefgrad(:,:,:,m,n), FFTW_PATIENT)
workfft(:,:,:,m,n), ddefgrad(:,:,:), FFTW_PATIENT)
enddo; enddo
prodnn = resolution(1)*resolution(2)*resolution(3)
wgt = 1._pReal/real(prodnn, pReal)
wgt = 1_pReal/real(prodnn, pReal)
defgradmacro = math_I3
c0 = .0_pReal
ielem = 0_pInt
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)
c0 = c0 + dPdF
enddo; enddo; enddo
call math_invert(6,math_Mandel3333to66(c0),s066,i,errmatinv) !i is just a dummy variable
if(errmatinv) call IO_error(45,ext_msg = "problem in c0 inversion") ! todo: change number and add message to io.f90 (and remove No. 48)
s0 = math_Mandel66to3333(s066)*real(prodnn, pReal)
!calculation of xknormdyad (needed to calculate gamma_hat)
!calculation of xknormdyad (needed to calculate gamma_hat) and xi (waves, needed 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)
xk(3) = .0_pReal
if(resolution(3) > 1) xk(3) = real(k_s(3), pReal)/meshdimension(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)
xk(2) = real(k_s(2), pReal)/meshdimension(2)
do i = 1, resolution(1)/2+1
k_s(1) = i-1
xk(1) = real(k_s(1), pReal)/meshdimension(1)
if (any(xk /= .0_pReal)) then
do l = 1,3; do m = 1,3
xknormdyad(i,j,k, l,m) = xk(l)*xk(m)/(xk(1)**2+xk(2)**2+xk(3)**2)
enddo; enddo
endif
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_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_pReal)) then
do l = 1,3; do m = 1,3
xknormdyad(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
open(539,file='stress-strain.out')
! Initialization done
open(539,file='stress-strain.out')
!*************************************************************
!Loop over loadcases defined in the loadcase file
@ -320,36 +318,31 @@ program mpie_spectral
! loop oper steps defined in input file for current loadcase
do steps = 1, bc_steps(loadcase)
!*************************************************************
write(*,*) '***************************************************'
write(*,*) 'STEP = ',steps
defgradmacro = defgradmacro&
defgradmacro = defgradmacro&
+ math_mul33x33(bc_velocityGrad(:,:,loadcase), defgradmacro)*timeinc !update macroscopic displacement gradient (stores the desired BCs of defgrad)
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,:,:)&
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& ! old fluctuations as guess for new step
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& ! old fluctuations as guess for new step
+ (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,k,:,:))*timeinc ! no fluctuations for new loadcase
defgradold(i,j,k,:,:) = temp33_Real
enddo; enddo; enddo
guessmode = 1.0_pReal ! keep guessing along former trajectory
guessmode = 1_pReal ! keep guessing along former trajectory
calcmode = 1_pInt
iter = 0_pInt
err_stress_av = 2.*error; err_strain_av = 2.*error
err_div= 2_pInt * error
!*************************************************************
! convergency loop
do while((iter <= itmax).and.((err_stress_av > error).or.(err_strain_av > error)))
do while((iter <= itmax).and.(err_div > error))
iter = iter + 1
write(*,*) 'ITER = ',iter
print '(A,I5.5,tr2,A,I5.5)' ' Step = ',steps,'Iteration = ',iter
!*************************************************************
err_strain_av = .0_pReal; err_stress_av = .0_pReal
err_strain_max = .0_pReal; err_stress_max = .0_pReal
err_div = .0_pReal; sigma0 = .0_pReal
pstress_av = .0_pReal; defgrad_av=.0_pReal
write(*,*) 'UPDATE STRESS FIELD'
print *, 'Update Stress Field'
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
@ -359,7 +352,6 @@ program mpie_spectral
enddo; enddo; enddo
c0 = .0_pReal
l = 0_pInt
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
@ -369,24 +361,18 @@ program mpie_spectral
cstress,dsde, pstress, dPdF)
calcmode = 2
c0 = c0 + dPdF
temp33_Real = pstress
do m = 1,3; do n = 1,3 ! calculate stress error
if(abs(temp33_Real(m,n)) > 0.1_pReal * abs(pstress_err(m,n))) then ! only stress components larger than 10% are taking under consideration
err_stress_av = err_stress_av + abs((pstress_field(i,j,k,m,n)-temp33_Real(m,n))/temp33_Real(m,n))
err_stress_max = max(err_stress_max, abs((pstress_field(i,j,k,m,n)-temp33_Real(m,n))/temp33_Real(m,n)))
l=l+1
endif
enddo; enddo
pstress_field(i,j,k,:,:) = temp33_Real
pstress_av = pstress_av + temp33_Real ! average stress
pstress_field(i,j,k,:,:) = pstress
pstress_av = pstress_av + pstress ! average stress
enddo; enddo; enddo
err_stress_av = err_stress_av/l ! do the weighting of the error
pstress_av = pstress_av*wgt ! do the weighting of average stress
pstress_err = pstress_av
if(iter==1) then !update gamma_hat with new reference stiffness
pstress_av = pstress_av*wgt ! do the weighting of average stress
if(iter==1) then !update gamma_hat with new reference stiffness
if(steps==1) then !prevent updating of s0
call math_invert(6,math_mandel3333to66(c0),s066,i,errmatinv) !i is just a dummy variable
if(errmatinv) call IO_error(45,ext_msg = "problem in c0 inversion") ! todo: change number and add message to io.f90 (and remove No. 48)
s0 = math_mandel66to3333(s066)*real(prodnn, pReal)
endif
c0 = c0 *wgt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
temp33_Real = .0_pReal
@ -398,68 +384,80 @@ program mpie_spectral
gamma_hat(i,j,k, l,m,n,p) = -temp33_Real(l,n)*xknormdyad(i,j,k, m,p)
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
endif
write(*,*) 'SPECTRAL METHOD TO GET CHANGE OF DEFORMATION GRADIENT FIELD'
print *, 'Update Deformation Gradient Field'
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))
enddo; enddo
if(n == 3) sigma0 = max(sigma0, sum(abs(real(workfft(1,1,1,m,:))))) ! L infinity Norm of stress tensor in Fourier space
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_mul33x3c(workfft(i,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress tensor) in Fourier space
temp33_Complex = .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)))/sigma0 !calculate error (divergence of stress field)
do m = 1,3; do n = 1,3
call dfftw_execute_dft_c2r(plan_fft(2,m,n), workfft(:,:,:,m,n),ddefgrad(:,:,:,m,n))
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
ddefgrad = ddefgrad * wgt
defgrad = defgrad + ddefgrad
l = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
defgrad_av(:,:) = defgrad_av(:,:) + defgrad(i,j,k,:,:) ! calculate average strain
do m = 1,3; do n = 1,3 ! calculate strain error
if(abs(defgrad(i,j,k,m,n)) > 0.1 * abs(strain_err(m,n))) then
err_strain_av = err_strain_av + abs(real(ddefgrad(i,j,k,m,n), pReal)/defgrad(i,j,k,m,n))
err_strain_max = max(err_strain_max, abs(real(ddefgrad(i,j,k,m,n), pReal)/defgrad(i,j,k,m,n)))
l=l+1
endif
enddo; enddo
defgrad_av= defgrad_av + defgrad(i,j,k,:,:)
enddo; enddo; enddo
defgrad_av = defgrad_av * wgt ! weight by number of FP
err_strain_av = err_strain_av/l ! weight by number of non-zero strain components
defgrad_av = defgrad_av * wgt ! weight by number of points
strain_err = defgrad_av
do m = 1,3; do n = 1,3
if(bc_mask(m,n,1,loadcase)) then ! adjust defgrad to fulfill displacement BC (defgradmacro)
defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + (defgradmacro(m,n)-defgrad_av(m,n))
else ! adjust defgrad to fulfill stress BC
defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + sum( s0(m,n,:,:)*(bc_stress(:,:,loadcase)-pstress_av(:,:)), &
mask = bc_mask(:,:,2,loadcase) ) !works at the moment only for 0 Stress as BC
mask = bc_mask(:,:,2,loadcase) )
endif
enddo; enddo
write(*,*) 'STRESS FIELD ERROR AV = ',err_stress_av
write(*,*) 'STRAIN FIELD ERROR AV = ',err_strain_av
write(*,*) 'STRESS FIELD ERROR MAX = ',err_stress_max
write(*,*) 'STRAIN FIELD ERROR MAX = ',err_strain_max
write(*,'(2(a,E9.3))') ' Error = ',err_div,' Tolerance = ', error
write(*,'(A)') '----------------------------------'
enddo ! end looping when convergency is achieved
write(539,'(f12.6,a,f12.6)'),defgrad_av(3,3)-1,' ',pstress_av(3,3)
write(*,*) 'U11 U22 U33'
write(*,*) defgrad_av(1,1)-1,defgrad_av(2,2)-1,defgrad_av(3,3)-1
write(*,*) 'U11/U33'
write(*,*) (defgrad_av(1,1)-1)/(defgrad_av(3,3)-1)
write(*,*) 'S11 S22 S33'
write(*,*) pstress_av(1,1),pstress_av(2,2),pstress_av(3,3)
write(539,'(E12.6,a,E12.6)',defgrad_av(3,3)-1,' ',pstress_av(3,3)
print '(A,3(E10.4,tr2))' ' ', defgrad_av(1,:)
print '(A,3(E10.4,tr2))' ' Deformation Gradient: ', defgrad_av(2,:)
print '(A,3(E10.4,tr2))' ' ', defgrad_av(3,:)
print *, ''
print '(A,3(E10.4,tr2))' ' ', pstress_av(1,:)
print '(A,3(E10.4,tr2))' ' Piola-Kirchhoff Stress: ', pstress_av(2,:)
print '(A,3(E10.4,tr2))' ' ', pstress_av(3,:)
print '(A)' '************************************************************'
!gsmh output
temp33_Real(1,:) = 0.0_pReal
temp33_Real(1,3) = -1.0_pReal
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
nrstep = 'stress'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'
@ -468,7 +466,7 @@ program mpie_spectral
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(I10,f16.8,tr2,f16.8,tr2,f16.8)'), ielem,math_mul33x3(defgrad(i,j,k,:,:),real((/i, j, k/), pReal))
write(589, '(I10,tr2,E12.6,tr2,E12.6,tr2,E12.6)'), ielem, real(i), real(j), real(k) !displacement(i,j,k,:)
enddo; enddo; enddo
write(589, '(A, /, A, /, I10)'), '$EndNodes', '$Elements', prodnn
do i = 1, prodnn
@ -480,8 +478,35 @@ program mpie_spectral
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(i10,f16.8,tr2,f16.8,tr2,f16.8,tr2,f16.8,tr2,f16.8,tr2,f16.8,&
tr2,f16.8,tr2,f16.8,tr2,f16.8,tr2)'), ielem, pstress_field(i,j,k,:,:)
write(589, '(i10,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,&
tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2)'), ielem, pstress_field(i,j,k,:,:)
enddo; enddo; enddo
write(nriter, *) iter
write(nrstep, *) steps
write(589, *), '$EndNodeData'
close(589)
nrstep = 'defgrad'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'
open(589,file = nrstep)
write(589, '(A, /, A, /, A, /, A, /, I10)'), '$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,tr2,E12.6,tr2,E12.6,tr2,E12.6)'), ielem, real(i), real(j), real(k) !displacement(i,j,k,:)
enddo; enddo; enddo
write(589, '(A, /, A, /, I10)'), '$EndNodes', '$Elements', prodnn
do i = 1, prodnn
write(589, '(I10, A, I10)'), i, ' 15 2 1 2', i
enddo
write(589, '(A)'), '$EndElements'
write(589, '(A, /, A, /, A, /, A, /, A, /, A, /, A, /, A, /, I10)'), '$NodeData', '1',&
'"'//trim(adjustl(nrstep))//'"', '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,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,&
tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2)'), ielem, defgrad(i,j,k,:,:) - math_I3
enddo; enddo; enddo
write(589, *), '$EndNodeData'
close(589)