785 lines
41 KiB
Fortran
785 lines
41 KiB
Fortran
! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!##############################################################
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!* $Id$
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!********************************************************************
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! Material subroutine for BVP solution using spectral method
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!
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! written by P. Eisenlohr,
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! F. Roters,
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! L. Hantcherli,
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! W.A. Counts,
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! D.D. Tjahjanto,
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! C. Kords,
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! M. Diehl,
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! R. Lebensohn
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!
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! MPI fuer Eisenforschung, Duesseldorf
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!
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!********************************************************************
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! Usage:
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! - start program with DAMASK_spectral PathToGeomFile/NameOfGeom.geom
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! PathToLoadFile/NameOfLoadFile.load
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! - PathToGeomFile will be the working directory
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! - make sure the file "material.config" exists in the working
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! directory. For further configuration use "numerics.config"
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!********************************************************************
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program DAMASK_spectral
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!********************************************************************
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use DAMASK_interface
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use prec, only: pInt, pReal
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use IO
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use math
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use mesh, only: mesh_ipCenterOfGravity
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use CPFEM, only: CPFEM_general, CPFEM_initAll
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use numerics, only: err_div_tol, err_stress_tol, err_stress_tolrel, err_defgrad_tol,&
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relevantStrain,itmax, memory_efficient, DAMASK_NumThreadsInt
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use homogenization, only: materialpoint_sizeResults, materialpoint_results
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!$ use OMP_LIB ! the openMP function library
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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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! 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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integer(pInt), dimension (1+maxNchunksInput*2) :: posInput
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integer(pInt), parameter :: maxNchunksGeom = 7 ! 4 identifiers, 3 values
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integer(pInt), dimension (1+2*maxNchunksGeom) :: posGeom
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integer(pInt) unit, N_l, N_s, N_t, N_n, N_freq, N_Fdot, N_temperature ! numbers of identifiers
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character(len=1024) path, line
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logical gotResolution,gotDimension,gotHomogenization
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logical, dimension(9) :: bc_maskvector
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! variables storing information from loadcase file
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real(pReal) time, time0, timeinc ! elapsed time, begin of interval, time interval
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real(pReal), dimension (:,:,:), allocatable :: bc_deformation, & ! applied velocity gradient or time derivative of deformation gradient
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bc_stress ! stress BC (if applicable)
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real(pReal), dimension(:), allocatable :: bc_timeIncrement, & ! length of increment
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bc_temperature ! isothermal starting conditions
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integer(pInt) N_Loadcases, step ! ToDo: rename?
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integer(pInt), dimension(:), allocatable :: bc_steps, & ! number of steps
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bc_frequency, & ! frequency of result writes
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bc_logscale ! linear/logaritmic time step flag
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logical, dimension(:), allocatable :: followFormerTrajectory,& ! follow trajectory of former loadcase
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velGradApplied ! decide wether velocity gradient or fdot is given
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logical, dimension(:,:,:,:), allocatable :: bc_mask ! mask of boundary conditions
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! variables storing information from geom file
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real(pReal) wgt
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real(pReal), dimension(3) :: geomdimension
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integer(pInt) homog
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integer(pInt), dimension(3) :: resolution
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! stress etc.
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real(pReal), dimension(3,3) :: ones, zeroes, temp33_Real, damper,&
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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, deltaF
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real(pReal), dimension(3,3,3,3) :: dPdF, c_current, s_current, c0_reference ! ToDo
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real(pReal), dimension(6) :: cstress, stress_res, delta_defgrad ! cauchy stress, residuum_stress, change of defgrad in Mandel notation
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real(pReal), dimension(6,6) :: dsde, c_current66, s_current66 ! Mandel notation of 4th order tensors
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real(pReal), dimension(9,9) :: s_current99, c_current99
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real(pReal), dimension(:,:,:,:,:), allocatable :: workfft, defgrad, defgradold
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real(pReal), dimension(:,:,:,:), allocatable :: coordinates
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real(pReal), dimension(:,:,:), allocatable :: temperature
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real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced
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logical, dimension(6) :: mask_stress6
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logical, dimension(9) :: mask_stress9
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integer(pInt) size_reduced
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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) :: xiDyad
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat
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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, p_hat_avg
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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, not_converged_counter
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logical errmatinv
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!Initializing
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!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
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bc_maskvector = .false.
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unit = 234_pInt
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ones = 1.0_pReal; zeroes = 0.0_pReal
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img = cmplx(0.0,1.0)
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N_l = 0_pInt
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N_s = 0_pInt
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N_t = 0_pInt
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N_temperature = 0_pInt
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time = 0.0_pReal
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N_n = 0_pInt
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N_freq = 0_pInt
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N_Fdot = 0_pInt
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not_converged_counter = 0_pInt
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gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false.
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resolution = 1_pInt
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geomdimension = 0.0_pReal
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if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments
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! Reading the loadcase file and assign variables
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path = getLoadcaseName()
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print '(a,/,a)', 'Loadcase: ',trim(path)
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print '(a,/,a)', 'Workingdir: ',trim(getSolverWorkingDirectoryName())
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print '(a,/,a)', 'SolverJobName: ',trim(getSolverJobName())
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if (.not. IO_open_file(unit,path)) call IO_error(30,ext_msg = path)
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rewind(unit)
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do
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read(unit,'(a1024)',END = 101) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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posInput = IO_stringPos(line,maxNchunksInput)
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do i = 1, maxNchunksInput, 1
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select case (IO_lc(IO_stringValue(line,posInput,i)))
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case('l', 'velocitygrad')
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N_l = N_l+1
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case('fdot')
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N_Fdot = N_Fdot+1
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case('s', 'stress', 'pk1', 'piolakirchhoff')
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N_s = N_s+1
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case('t', 'time', 'delta')
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N_t = N_t+1
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case('n', 'incs', 'increments', 'steps', 'logincs', 'logsteps')
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N_n = N_n+1
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case('f', 'freq', 'frequency')
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N_freq = N_freq+1
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case('temp','temperature')
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N_temperature = N_temperature+1
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end select
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enddo ! count all identifiers to allocate memory and do sanity check
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enddo
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101 N_Loadcases = N_n
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if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
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call IO_error(31,ext_msg = path) ! error message for incomplete inp !ToDo:change message
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! allocate memory depending on lines in input file
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allocate (bc_deformation(3,3,N_Loadcases)); bc_deformation = 0.0_pReal
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allocate (bc_stress(3,3,N_Loadcases)); bc_stress = 0.0_pReal
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allocate (bc_mask(3,3,2,N_Loadcases)); bc_mask = .false.
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allocate (velGradApplied(N_Loadcases)); velGradApplied = .false.
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allocate (bc_timeIncrement(N_Loadcases)); bc_timeIncrement = 0.0_pReal
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allocate (bc_temperature(N_Loadcases)); bc_temperature = 300.0_pReal
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allocate (bc_steps(N_Loadcases)); bc_steps = 0_pInt
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allocate (bc_logscale(N_Loadcases)); bc_logscale = 0_pInt
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allocate (bc_frequency(N_Loadcases)); bc_frequency = 1_pInt
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allocate (followFormerTrajectory(N_Loadcases)); followFormerTrajectory = .true.
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rewind(unit)
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loadcase = 0_pInt
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do
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read(unit,'(a1024)',END = 200) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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loadcase = loadcase + 1
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posInput = IO_stringPos(line,maxNchunksInput)
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do j = 1,maxNchunksInput,2
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select case (IO_lc(IO_stringValue(line,posInput,j)))
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case('fdot') ! assign values for the deformation BC matrix (in case of given fdot)
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valuevector = 0.0_pReal
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forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '*'
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do k = 1,9
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if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k)
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enddo
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bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector,(/3,3/)))
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bc_deformation(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/)))
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case('l','velocitygrad') ! assign values for the deformation BC matrix (in case of given L)
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velGradApplied(loadcase) = .true. ! in case of given L, set flag to true
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valuevector = 0.0_pReal
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forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '*'
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do k = 1,9
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if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k)
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enddo
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bc_mask(:,:,1,loadcase) = transpose(reshape(bc_maskvector,(/3,3/)))
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bc_deformation(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/)))
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case('s', 'stress', 'pk1', 'piolakirchhoff')
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valuevector = 0.0_pReal
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forall (k = 1:9) bc_maskvector(k) = IO_stringValue(line,posInput,j+k) /= '*'
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do k = 1,9
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if (bc_maskvector(k)) valuevector(k) = IO_floatValue(line,posInput,j+k) ! assign values for the bc_stress matrix
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enddo
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bc_mask(:,:,2,loadcase) = transpose(reshape(bc_maskvector,(/3,3/)))
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bc_stress(:,:,loadcase) = math_transpose3x3(reshape(valuevector,(/3,3/)))
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case('t','time','delta') ! increment time
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bc_timeIncrement(loadcase) = IO_floatValue(line,posInput,j+1)
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case('temp','temperature') ! starting temperature
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bc_temperature(loadcase) = IO_floatValue(line,posInput,j+1)
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case('n','incs','increments','steps') ! bc_steps
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bc_steps(loadcase) = IO_intValue(line,posInput,j+1)
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case('logincs','logsteps') ! true, if log scale
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bc_steps(loadcase) = IO_intValue(line,posInput,j+1)
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bc_logscale(loadcase) = 1_pInt
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case('f','freq','frequency') ! frequency of result writings
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bc_frequency(loadcase) = IO_intValue(line,posInput,j+1)
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case('guessreset','dropguessing')
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followFormerTrajectory(loadcase) = .false. ! do not continue to predict deformation along former trajectory
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end select
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enddo; enddo
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200 close(unit)
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if (followFormerTrajectory(1)) then
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call IO_warning(33) ! cannot guess along trajectory for first step of first loadcase
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followFormerTrajectory(1) = .false.
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endif
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do loadcase = 1, N_Loadcases ! consistency checks and output
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print *, '------------------------------------------------------'
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print '(a,i5)', 'Loadcase:', loadcase
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if (.not. followFormerTrajectory(loadcase)) &
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print '(a)', 'drop guessing along trajectory'
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if (any(bc_mask(:,:,1,loadcase) .eqv. bc_mask(:,:,2,loadcase)))& ! exclusive or masking only
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call IO_error(31,loadcase)
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if (velGradApplied(loadcase)) then
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do j = 1, 3
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if (any(bc_mask(j,:,1,loadcase) .eqv. .true.) .and.&
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any(bc_mask(j,:,1,loadcase) .eqv. .false.)) call IO_error(32,loadcase) ! each line should be either fully or not at all defined
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enddo
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print '(a,/,3(3(f12.6,x)/))','L:' ,math_transpose3x3(bc_deformation(:,:,loadcase))
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print '(a,/,3(3(l,x)/))', 'bc_mask for L:',transpose(bc_mask(:,:,1,loadcase))
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else
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print '(a,/,3(3(f12.6,x)/))','Fdot:' ,math_transpose3x3(bc_deformation(:,:,loadcase))
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print '(a,/,3(3(l,x)/))', 'bc_mask for Fdot:',transpose(bc_mask(:,:,1,loadcase))
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endif
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print '(a,/,3(3(f12.6,x)/))','bc_stress/MPa:',math_transpose3x3(bc_stress(:,:,loadcase))*1e-6
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print '(a,/,3(3(l,x)/))', 'bc_mask for stress:' ,transpose(bc_mask(:,:,2,loadcase))
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if (bc_timeIncrement(loadcase) < 0.0_pReal) call IO_error(34,loadcase) ! negative time increment
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print '(a,f12.6)','temperature: ',bc_temperature(loadcase)
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print '(a,f12.6)','time: ',bc_timeIncrement(loadcase)
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if (bc_steps(loadcase) < 1_pInt) call IO_error(35,loadcase) ! non-positive increment count
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print '(a,i6)','incs: ',bc_steps(loadcase)
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if (bc_frequency(loadcase) < 1_pInt) call IO_error(36,loadcase) ! non-positive result frequency
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print '(a,i6)','freq: ',bc_frequency(loadcase)
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enddo
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!read header of geom file to get the information needed before the complete geom file is intepretated by mesh.f90
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path = getModelName()
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print *, '------------------------------------------------------'
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print '(a,a)', 'GeomName: ',trim(path)
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if (.not. IO_open_file(unit,trim(path)//InputFileExtension)) call IO_error(101,ext_msg = trim(path)//InputFileExtension)
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rewind(unit)
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do
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read(unit,'(a1024)',END = 100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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posGeom = IO_stringPos(line,maxNchunksGeom)
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select case ( IO_lc(IO_StringValue(line,posGeom,1)) )
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case ('dimension')
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gotDimension = .true.
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do i = 2,6,2
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select case (IO_lc(IO_stringValue(line,posGeom,i)))
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case('x')
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geomdimension(1) = IO_floatValue(line,posGeom,i+1)
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case('y')
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geomdimension(2) = IO_floatValue(line,posGeom,i+1)
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case('z')
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geomdimension(3) = IO_floatValue(line,posGeom,i+1)
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end select
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enddo
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case ('homogenization')
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gotHomogenization = .true.
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homog = IO_intValue(line,posGeom,2)
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case ('resolution')
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gotResolution = .true.
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do i = 2,6,2
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select case (IO_lc(IO_stringValue(line,posGeom,i)))
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case('a')
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resolution(1) = IO_intValue(line,posGeom,i+1)
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case('b')
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resolution(2) = IO_intValue(line,posGeom,i+1)
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case('c')
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resolution(3) = IO_intValue(line,posGeom,i+1)
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end select
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enddo
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end select
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if (gotDimension .and. gotHomogenization .and. gotResolution) exit
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enddo
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100 close(unit)
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if(mod(resolution(1),2_pInt)/=0_pInt .or.&
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mod(resolution(2),2_pInt)/=0_pInt .or.&
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(mod(resolution(3),2_pInt)/=0_pInt .and. resolution(3)/= 1_pInt)) call IO_error(103)
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print '(a,/,i4,i4,i4)','resolution a b c:', resolution
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print '(a,/,f8.4,f8.5,f8.5)','dimension x y z:', geomdimension
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print '(a,i4)','homogenization: ',homog
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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 (temperature( resolution(1),resolution(2),resolution(3))); temperature = bc_temperature(1) ! start out isothermally
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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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defgradAimOld = math_I3
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defgrad_av = math_I3
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! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field
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call CPFEM_initAll(bc_temperature(1),1_pInt,1_pInt)
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ielem = 0_pInt
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c_current = 0.0_pReal
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do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
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defgradold(i,j,k,:,:) = math_I3 ! no deformation at the beginning
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defgrad(i,j,k,:,:) = math_I3
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ielem = ielem +1
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coordinates(1:3,i,j,k) = mesh_ipCenterOfGravity(1:3,1,ielem) ! set to initial coordinates ToDo: SHOULD BE UPDATED TO CURRENT POSITION IN FUTURE REVISIONS!!!
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call CPFEM_general(2,coordinates(1:3,i,j,k),math_I3,math_I3,temperature(i,j,k),0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
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c_current = c_current + dPdF
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enddo; enddo; enddo
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c0_reference = c_current * wgt ! linear reference material stiffness
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do k = 1, resolution(3) ! calculation of discrete angular frequencies, ordered 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)/geomdimension(3) ! 3D case
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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
|
|
|
|
if(memory_efficient) then ! allocate just single fourth order tensor
|
|
allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal
|
|
else ! precalculation of gamma_hat field
|
|
allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal
|
|
do k = 1, resolution(3); 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
|
|
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
|
|
enddo; enddo
|
|
temp33_Real = math_inv3x3(math_mul3333xx33(c0_reference, xiDyad))
|
|
else
|
|
xiDyad = 0.0_pReal
|
|
temp33_Real = 0.0_pReal
|
|
endif
|
|
do l=1,3; do m=1,3; do n=1,3; do p=1,3
|
|
gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
|
|
(xiDyad(m,p)+xiDyad(p,m))
|
|
enddo; enddo; enddo; enddo
|
|
enddo; enddo; enddo
|
|
endif
|
|
|
|
allocate (workfft(resolution(1)+2,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal
|
|
|
|
! Initialization of fftw (see manual on fftw.org for more details)
|
|
|
|
if(DAMASK_NumThreadsInt>0_pInt) then
|
|
call dfftw_init_threads(ierr)
|
|
if(ierr == 0_pInt) call IO_error(104,ierr)
|
|
call dfftw_plan_with_nthreads(DAMASK_NumThreadsInt)
|
|
endif
|
|
|
|
call dfftw_plan_many_dft_r2c(plan_fft(1),3,(/resolution(1),resolution(2),resolution(3)/),9,&
|
|
workfft,(/resolution(1) +2,resolution(2),resolution(3)/),1,(resolution(1) +2)*resolution(2)*resolution(3),&
|
|
workfft,(/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),FFTW_PATIENT)
|
|
call dfftw_plan_many_dft_c2r(plan_fft(2),3,(/resolution(1),resolution(2),resolution(3)/),9,&
|
|
workfft,(/resolution(1)/2+1,resolution(2),resolution(3)/),1,(resolution(1)/2+1)*resolution(2)*resolution(3),&
|
|
workfft,(/resolution(1) +2,resolution(2),resolution(3)/),1,(resolution(1) +2)*resolution(2)*resolution(3),FFTW_PATIENT)
|
|
|
|
! write header of output file
|
|
open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
|
|
//'.spectralOut',form='UNFORMATTED')
|
|
write(538), 'load', trim(getLoadcaseName())
|
|
write(538), 'workingdir', trim(getSolverWorkingDirectoryName())
|
|
write(538), 'geometry', trim(getSolverJobName())//InputFileExtension
|
|
write(538), 'resolution', resolution
|
|
write(538), 'dimension', geomdimension
|
|
write(538), 'materialpoint_sizeResults', materialpoint_sizeResults
|
|
write(538), 'loadcases', N_Loadcases
|
|
write(538), 'logscale', bc_logscale ! one entry per loadcase (0: linear, 1: log)
|
|
write(538), 'frequencies', bc_frequency ! one entry per loadcase
|
|
write(538), 'times', bc_timeIncrement ! one entry per loadcase
|
|
bc_steps(1) = bc_steps(1)+1 ! +1 to store initial situation
|
|
write(538), 'increments', bc_steps ! one entry per loadcase
|
|
bc_steps(1) = bc_steps(1)-1 ! re-adjust for correct looping
|
|
write(538), 'eoh' ! end of header
|
|
|
|
write(538) materialpoint_results(:,1,:) ! initial (non-deformed) results
|
|
! Initialization done
|
|
|
|
!*************************************************************
|
|
! Loop over loadcases defined in the loadcase file
|
|
do loadcase = 1, N_Loadcases
|
|
!*************************************************************
|
|
time0 = time ! loadcase start time
|
|
|
|
if (followFormerTrajectory(loadcase)) then
|
|
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))
|
|
|
|
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
|
|
do step = 1, bc_steps(loadcase)
|
|
!*************************************************************
|
|
if (bc_logscale(loadcase) == 1_pInt) then ! loglinear scale
|
|
if (loadcase == 1_pInt) then ! 1st loadcase of loglinear scale
|
|
if (step == 1_pInt) then ! 1st step of 1st loadcase of loglinear scale
|
|
timeinc = bc_timeIncrement(1)*(2.0**(1 - bc_steps(1))) ! assume 1st step is equal to 2nd
|
|
else ! not-1st step of 1st loadcase of loglinear scale
|
|
timeinc = bc_timeIncrement(1)*(2.0**(step - (1 + bc_steps(1))))
|
|
endif
|
|
else ! not-1st loadcase of loglinear scale
|
|
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)
|
|
|
|
temp33_Real = defgradAim
|
|
defgradAim = defgradAim &
|
|
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
|
|
+ mask_defgrad * deltaF * timeinc
|
|
defgradAimOld = temp33_Real
|
|
|
|
! 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)
|
|
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
|
|
defgradold(i,j,k,:,:) = temp33_Real
|
|
enddo; enddo; enddo
|
|
|
|
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
|
|
|
|
if (all(bc_mask(:,:,1,loadcase))) then
|
|
calcmode = 1_pInt ! if no stress BC is given (calmode 0 is not needed)
|
|
else
|
|
calcmode = 0_pInt ! start calculation of BC fulfillment
|
|
endif
|
|
|
|
CPFEM_mode = 1_pInt ! winding forward
|
|
iter = 0_pInt
|
|
err_div= 2.0_pReal * err_div_tol ! go into loop
|
|
|
|
!*************************************************************
|
|
! convergence loop
|
|
do while(iter < itmax .and. &
|
|
(err_div > err_div_tol .or. &
|
|
err_stress > err_stress_tol .or. &
|
|
err_defgrad > err_defgrad_tol))
|
|
iter = iter + 1_pInt
|
|
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
|
|
!*************************************************************
|
|
|
|
! 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
|
|
|
|
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)
|
|
enddo
|
|
|
|
|
|
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
|
|
|
|
err_div = err_div/p_hat_avg !weigthting of error by average stress (L infinity norm)
|
|
|
|
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
|
|
xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
|
|
enddo; enddo
|
|
temp33_Real = math_inv3x3(math_mul3333xx33(c0_reference, xiDyad))
|
|
else
|
|
xiDyad = 0.0_pReal
|
|
temp33_Real = 0.0_pReal
|
|
endif
|
|
do l=1,3; do m=1,3; do n=1,3; do p=1,3
|
|
gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
|
|
(xiDyad(m,p) +xiDyad(p,m))
|
|
enddo; enddo; enddo; enddo
|
|
do m = 1,3; do n = 1,3
|
|
temp33_Complex(m,n) = sum(gamma_hat(1,1,1,m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
|
|
+workfft(i*2 ,j,k,:,:)*img))
|
|
enddo; enddo
|
|
workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of average strain
|
|
workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
|
|
enddo; enddo; enddo
|
|
else ! use precalculated gamma-operator
|
|
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
|
|
do m = 1,3; do n = 1,3
|
|
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n,:,:) *(workfft(i*2-1,j,k,:,:)&
|
|
+ workfft(i*2 ,j,k,:,:)*img))
|
|
enddo; enddo
|
|
workfft(i*2-1,j,k,:,:) = real (temp33_Complex) ! change of average strain
|
|
workfft(i*2 ,j,k,:,:) = aimag(temp33_Complex)
|
|
enddo; enddo; enddo
|
|
endif
|
|
|
|
workfft(1,1,1,:,:) = defgrad_av - math_I3 ! zero frequency (real part)
|
|
workfft(2,1,1,:,:) = 0.0_pReal ! zero frequency (imaginary part)
|
|
|
|
call dfftw_execute_dft_c2r(plan_fft(2),workfft,workfft)
|
|
defgrad = defgrad + workfft(1:resolution(1),:,:,:,:)*wgt
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do m = 1,3; do n = 1,3
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defgrad_av(m,n) = sum(defgrad(:,:,:,m,n))*wgt
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defgrad(:,:,:,m,n) = defgrad(:,:,:,m,n) + (defgradAim(m,n) - defgrad_av(m,n)) ! anticipated target minus current state
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enddo; enddo
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|
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err_stress = maxval(abs(mask_stress * (pstress_av - bc_stress(:,:,loadcase))))
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err_stress_tol = maxval(abs(pstress_av))*err_stress_tolrel ! accecpt relative error specified
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err_defgrad = maxval(abs(mask_defgrad * (defgrad_av - defgradAim)))
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print '(2(a,E13.8))', ' error divergence: ',err_div, ' Tol. = ', err_div_tol
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print '(2(a,E13.8))', ' error stress: ',err_stress, ' Tol. = ', err_stress_tol
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print '(2(a,E13.8))', ' error deformation gradient: ',err_defgrad,' Tol. = ', err_defgrad_tol
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!ToDo: usefull .and. for err_div?
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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.
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calcmode = 0_pInt
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defgradAimCorr = 0.0_pReal
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damper = 1.0_pReal
|
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endif
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end select
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enddo ! end looping when convergency is achieved
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|
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if (mod(step,bc_frequency(loadcase)) == 0_pInt) & ! at output frequency
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write(538) materialpoint_results(:,1,:) ! write result to file
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|
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print '(A)', '------------------------------------------------------------'
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print '(a,x,f12.7)' , ' Determinant of Deformation Aim: ', math_det3x3(defgradAim)
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print '(a,/,3(3(f12.7,x)/))', ' Deformation Aim: ',math_transpose3x3(defgradAim)
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print '(a,/,3(3(f12.7,x)/))', ' Deformation Gradient:',math_transpose3x3(defgrad_av)
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print '(a,/,3(3(f10.4,x)/))', ' Cauchy Stress / MPa: ',math_transpose3x3(cstress_av)/1.e6
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print '(a,/,3(3(f10.4,x)/))', ' Piola-Kirchhoff Stress / MPa: ',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!'
|
|
close(538)
|
|
call dfftw_destroy_plan(plan_fft(1)); call dfftw_destroy_plan(plan_fft(2))
|
|
|
|
end program DAMASK_spectral
|
|
|
|
!********************************************************************
|
|
! quit subroutine to satisfy IO_error
|
|
!
|
|
!********************************************************************
|
|
subroutine quit(id)
|
|
use prec
|
|
implicit none
|
|
|
|
integer(pInt) id
|
|
|
|
stop
|
|
end subroutine
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