1100 lines
69 KiB
Fortran
1100 lines
69 KiB
Fortran
! Copyright 2012 Max-Planck-Institut fuer Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Duesseldorf 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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! Run 'DAMASK_spectral.exe --help' to get usage hints
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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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! used modules
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!##################################################################################################
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program DAMASK_spectral
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
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use DAMASK_interface
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use prec, only: pInt, pReal, DAMASK_NaN
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use IO
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use debug, only: debug_spectral, &
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debug_spectralGeneral, &
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debug_spectralDivergence, &
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debug_spectralRestart, &
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debug_spectralFFTW
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use math
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use kdtree2_module
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use CPFEM, only: CPFEM_general, CPFEM_initAll
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use FEsolving, only: restartWrite, restartInc
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use numerics, only: err_div_tol, err_stress_tolrel, rotation_tol, itmax, itmin, &
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memory_efficient, update_gamma, divergence_correction, &
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DAMASK_NumThreadsInt, &
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fftw_planner_flag, fftw_timelimit
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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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!##################################################################################################
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! variable declaration
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!##################################################################################################
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implicit none
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!--------------------------------------------------------------------------------------------------
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! variables to read from load case and geom file
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real(pReal), dimension(9) :: temp_valueVector ! stores information temporarily from loadcase file
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logical, dimension(9) :: temp_maskVector
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integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
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(1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
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1_pInt, & ! dropguessing
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maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
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myUnit = 234_pInt
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integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
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integer(pInt) :: headerLength,&
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N_l = 0_pInt,&
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N_t = 0_pInt,&
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N_n = 0_pInt,&
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N_Fdot = 0_pInt
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character(len=1024) :: path, line, keyword
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logical :: gotResolution = .false.,&
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gotDimension = .false.,&
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gotHomogenization = .false.
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!--------------------------------------------------------------------------------------------------
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! variable storing information from load case file
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type bc_type
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real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
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stress = 0.0_pReal, & ! stress BC (if applicable)
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rotation = math_I3 ! rotation of BC (if applicable)
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real(pReal) :: time = 0.0_pReal, & ! length of increment
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temperature = 300.0_pReal ! isothermal starting conditions
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integer(pInt) :: incs = 0_pInt, & ! number of increments
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outputfrequency = 1_pInt, & ! frequency of result writes
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restartfrequency = 0_pInt, & ! frequency of restart writes
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logscale = 0_pInt ! linear/logaritmic time inc flag
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logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
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velGradApplied = .false. ! decide wether velocity gradient or fdot is given
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logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
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maskStress = .false. ! mask of stress boundary conditions
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logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
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end type
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type(bc_type), allocatable, dimension(:) :: bc
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!--------------------------------------------------------------------------------------------------
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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) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal ! physical dimension of volume element per direction
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integer(pInt) :: Npoints,& ! number of Fourier points
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homog ! homogenization scheme used
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integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
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integer(pInt) :: res1_red ! to store res(1)/2 +1
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!--------------------------------------------------------------------------------------------------
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! stress, stiffness and compliance average etc.
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real(pReal), dimension(3,3) :: pstress, pstress_av, &
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defgradAim = math_I3, defgradAimOld = math_I3,&
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mask_stress, mask_defgrad, deltaF, &
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pstress_av_lab, defgradAim_lab, defgradAim_lab_old ! quantities rotated to other coordinate system
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real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current=0.0_pReal, s_prev, c_prev,& ! stiffness and compliance
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s0_reference
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real(pReal), dimension(6) :: cstress ! cauchy stress
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real(pReal), dimension(6,6) :: dsde, c0_66, s0_66 ! small strain stiffness
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real(pReal), dimension(9,9) :: s_prev99, c_prev99 ! compliance and stiffness in matrix notation
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real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
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integer(pInt) :: size_reduced = 0_pInt ! number of stress BCs
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!--------------------------------------------------------------------------------------------------
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! pointwise data
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type(C_PTR) :: tensorField ! field in real an fourier space
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real(pReal), dimension(:,:,:,:,:), pointer :: tensorField_real ! field in real space (pointer)
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complex(pReal), dimension(:,:,:,:,:), pointer :: tensorField_fourier ! field in fourier space (pointer)
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real(pReal), dimension(:,:,:,:,:), allocatable :: defgrad, defgradold
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real(pReal), dimension(:,:,:,:), allocatable :: coordinates
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real(pReal), dimension(:,:,:), allocatable :: temperature
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
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real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
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real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
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integer(pInt), dimension(3) :: k_s
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!--------------------------------------------------------------------------------------------------
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! loop variables, convergence etc.
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real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
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real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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complex(pReal), dimension(3) :: temp3_Complex
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complex(pReal), dimension(3,3) :: temp33_Complex
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real(pReal), dimension(3,3) :: temp33_Real
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integer(pInt) :: i, j, k, l, m, n, p, errorID
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integer(pInt) :: N_Loadcases, loadcase, inc, iter, ielem, CPFEM_mode, &
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ierr, totalIncsCounter = 0_pInt,&
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notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
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logical :: errmatinv
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real(pReal) :: defgradDet
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character(len=6) :: loadcase_string
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!--------------------------------------------------------------------------------------------------
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!variables controlling debugging
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logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
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!--------------------------------------------------------------------------------------------------
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!variables for additional output due to general debugging
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real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
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!--------------------------------------------------------------------------------------------------
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! variables for additional output of divergence calculations
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type(C_PTR) :: divergence, plan_divergence
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real(pReal), dimension(:,:,:,:), pointer :: divergence_real
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complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
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real(pReal), dimension(:,:,:,:), allocatable :: divergence_postProc
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real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS,&
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err_div_max, err_real_div_max,&
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max_div_error
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!--------------------------------------------------------------------------------------------------
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! variables for debugging fft using a scalar field
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type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
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plan_scalarField_forth, plan_scalarField_back
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complex(pReal), dimension(:,:,:), pointer :: scalarField_real
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complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
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integer(pInt) :: row, column
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!##################################################################################################
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! reading of information from load case file and geometry file
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!##################################################################################################
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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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open (output_unit, encoding='UTF-8')
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call DAMASK_interface_init()
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print '(a)', ''
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print '(a)', ' <<<+- DAMASK_spectral init -+>>>'
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print '(a)', ' $Id$'
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#include "compilation_info.f90"
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print '(a,a)', ' Working Directory: ',trim(getSolverWorkingDirectoryName())
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print '(a,a)', ' Solver Job Name: ',trim(getSolverJobName())
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print '(a)', ''
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!--------------------------------------------------------------------------------------------------
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! reading the load case file and allocate data structure containing load cases
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path = getLoadcaseName()
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call IO_open_file(myUnit,path)
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rewind(myUnit)
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do
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read(myUnit,'(a1024)',END = 100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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positions = IO_stringPos(line,maxNchunksLoadcase)
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do i = 1_pInt, maxNchunksLoadcase, 1_pInt ! reading compulsory parameters for loadcase
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select case (IO_lc(IO_stringValue(line,positions,i)))
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case('l','velocitygrad','velgrad','velocitygradient')
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N_l = N_l + 1_pInt
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case('fdot','dotf')
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N_Fdot = N_Fdot + 1_pInt
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case('t','time','delta')
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N_t = N_t + 1_pInt
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case('n','incs','increments','steps','logincs','logsteps')
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N_n = N_n + 1_pInt
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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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100 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(error_ID=837_pInt,ext_msg = trim(path)) ! error message for incomplete loadcase
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allocate (bc(N_Loadcases))
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!--------------------------------------------------------------------------------------------------
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! reading the load case and assign values to the allocated data structure
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rewind(myUnit)
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loadcase = 0_pInt
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do
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read(myUnit,'(a1024)',END = 101) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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loadcase = loadcase + 1_pInt
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positions = IO_stringPos(line,maxNchunksLoadcase)
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do j = 1_pInt,maxNchunksLoadcase
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select case (IO_lc(IO_stringValue(line,positions,j)))
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case('fdot','dotf','l','velocitygrad','velgrad','velocitygradient') ! assign values for the deformation BC matrix
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bc(loadcase)%velGradApplied = &
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(IO_lc(IO_stringValue(line,positions,j)) == 'l'.or. & ! in case of given L, set flag to true
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IO_lc(IO_stringValue(line,positions,j)) == 'velocitygrad'.or.&
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IO_lc(IO_stringValue(line,positions,j)) == 'velgrad'.or.&
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IO_lc(IO_stringValue(line,positions,j)) == 'velocitygradient')
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temp_valueVector = 0.0_pReal
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temp_maskVector = .false.
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forall (k = 1_pInt:9_pInt) temp_maskVector(k) = IO_stringValue(line,positions,j+k) /= '*'
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do k = 1_pInt,9_pInt
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if (temp_maskVector(k)) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
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enddo
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bc(loadcase)%maskDeformation = transpose(reshape(temp_maskVector,[ 3,3]))
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bc(loadcase)%deformation = math_plain9to33(temp_valueVector)
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case('p','pk1','piolakirchhoff','stress')
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temp_valueVector = 0.0_pReal
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forall (k = 1_pInt:9_pInt) bc(loadcase)%maskStressVector(k) =&
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IO_stringValue(line,positions,j+k) /= '*'
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do k = 1_pInt,9_pInt
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if (bc(loadcase)%maskStressVector(k)) temp_valueVector(k) =&
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IO_floatValue(line,positions,j+k) ! assign values for the bc(loadcase)%stress matrix
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enddo
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bc(loadcase)%maskStress = transpose(reshape(bc(loadcase)%maskStressVector,[ 3,3]))
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bc(loadcase)%stress = math_plain9to33(temp_valueVector)
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case('t','time','delta') ! increment time
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bc(loadcase)%time = IO_floatValue(line,positions,j+1_pInt)
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case('temp','temperature') ! starting temperature
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bc(loadcase)%temperature = IO_floatValue(line,positions,j+1_pInt)
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case('n','incs','increments','steps') ! number of increments
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bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
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case('logincs','logincrements','logsteps') ! number of increments (switch to log time scaling)
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bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
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bc(loadcase)%logscale = 1_pInt
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case('f','freq','frequency','outputfreq') ! frequency of result writings
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bc(loadcase)%outputfrequency = IO_intValue(line,positions,j+1_pInt)
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case('r','restart','restartwrite') ! frequency of writing restart information
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bc(loadcase)%restartfrequency = max(0_pInt,IO_intValue(line,positions,j+1_pInt))
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case('guessreset','dropguessing')
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bc(loadcase)%followFormerTrajectory = .false. ! do not continue to predict deformation along former trajectory
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case('euler') ! rotation of loadcase given in euler angles
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p = 0_pInt ! assuming values given in radians
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l = 1_pInt ! assuming keyword indicating degree/radians
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select case (IO_lc(IO_stringValue(line,positions,j+1_pInt)))
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case('deg','degree')
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p = 1_pInt ! for conversion from degree to radian
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case('rad','radian')
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case default
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l = 0_pInt ! immediately reading in angles, assuming radians
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end select
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forall(k = 1_pInt:3_pInt) temp33_Real(k,1) = &
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IO_floatValue(line,positions,j+l+k) * real(p,pReal) * inRad
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bc(loadcase)%rotation = math_EulerToR(temp33_Real(:,1))
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case('rotation','rot') ! assign values for the rotation of loadcase matrix
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temp_valueVector = 0.0_pReal
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forall (k = 1_pInt:9_pInt) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
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bc(loadcase)%rotation = math_plain9to33(temp_valueVector)
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end select
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enddo; enddo
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101 close(myUnit)
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if (sum(bc(1:N_Loadcases)%incs)>9000_pInt) stop !discuss with Philip, stop code trouble. suggesting warning
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!-------------------------------------------------------------------------------------------------- ToDo: if temperature at CPFEM is treated properly, move this up immediately after interface init
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! initialization of all related DAMASK modules (e.g. mesh.f90 reads in geometry)
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call CPFEM_initAll(bc(1)%temperature,1_pInt,1_pInt)
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if (update_gamma .and. .not. memory_efficient) call IO_error(error_ID = 847_pInt)
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!--------------------------------------------------------------------------------------------------
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! read header of geom file to get size information. complete geom file is intepretated by mesh.f90
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path = getModelName()
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call IO_open_file(myUnit,trim(path)//InputFileExtension)
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rewind(myUnit)
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read(myUnit,'(a1024)') line
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positions = IO_stringPos(line,2_pInt)
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keyword = IO_lc(IO_StringValue(line,positions,2_pInt))
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if (keyword(1:4) == 'head') then
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headerLength = IO_intValue(line,positions,1_pInt) + 1_pInt
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else
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call IO_error(error_ID=842_pInt)
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endif
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rewind(myUnit)
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do i = 1_pInt, headerLength
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read(myUnit,'(a1024)') line
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positions = IO_stringPos(line,maxNchunksGeom)
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select case ( IO_lc(IO_StringValue(line,positions,1)) )
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case ('dimension')
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gotDimension = .true.
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do j = 2_pInt,6_pInt,2_pInt
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select case (IO_lc(IO_stringValue(line,positions,j)))
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case('x')
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geomdim(1) = IO_floatValue(line,positions,j+1_pInt)
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case('y')
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geomdim(2) = IO_floatValue(line,positions,j+1_pInt)
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case('z')
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geomdim(3) = IO_floatValue(line,positions,j+1_pInt)
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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,positions,2_pInt)
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case ('resolution')
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gotResolution = .true.
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do j = 2_pInt,6_pInt,2_pInt
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select case (IO_lc(IO_stringValue(line,positions,j)))
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case('a')
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res(1) = IO_intValue(line,positions,j+1_pInt)
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case('b')
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res(2) = IO_intValue(line,positions,j+1_pInt)
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case('c')
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res(3) = IO_intValue(line,positions,j+1_pInt)
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end select
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enddo
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end select
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enddo
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close(myUnit)
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!--------------------------------------------------------------------------------------------------
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! sanity checks of geometry parameters
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if (.not.(gotDimension .and. gotHomogenization .and. gotResolution))&
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call IO_error(error_ID = 845_pInt)
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if (any(geomdim<=0.0_pReal)) call IO_error(error_ID = 802_pInt)
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if(mod(res(1),2_pInt)/=0_pInt .or.&
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mod(res(2),2_pInt)/=0_pInt .or.&
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(mod(res(3),2_pInt)/=0_pInt .and. res(3)/= 1_pInt)) call IO_error(error_ID = 803_pInt)
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!--------------------------------------------------------------------------------------------------
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! variables derived from resolution
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res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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Npoints = res(1)*res(2)*res(3)
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wgt = 1.0_pReal/real(Npoints, pReal)
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!--------------------------------------------------------------------------------------------------
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! output of geometry
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print '(a)', ''
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print '(a)', '#############################################################'
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print '(a)', 'DAMASK spectral:'
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print '(a)', 'The spectral method boundary value problem solver for'
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print '(a)', 'the Duesseldorf Advanced Material Simulation Kit'
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print '(a)', '#############################################################'
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print '(a,a)', 'geometry file: ',trim(path)//'.geom'
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print '(a)', '============================================================='
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print '(a,3(i12 ))','resolution a b c:', res
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print '(a,3(f12.5))','dimension x y z:', geomdim
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print '(a,i5)','homogenization: ',homog
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print '(a)', '#############################################################'
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print '(a,a)', 'loadcase file: ',trim(getLoadcaseName())
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! consistency checks and output of load case
|
|
bc(1)%followFormerTrajectory = .false. ! cannot guess along trajectory for first inc of first loadcase
|
|
errorID = 0_pInt
|
|
do loadcase = 1_pInt, N_Loadcases
|
|
write (loadcase_string, '(i6)' ) loadcase
|
|
|
|
print '(a)', '============================================================='
|
|
print '(a,i6)', 'loadcase: ', loadcase
|
|
|
|
if (.not. bc(loadcase)%followFormerTrajectory) print '(a)', 'drop guessing along trajectory'
|
|
if (bc(loadcase)%velGradApplied) then
|
|
do j = 1_pInt, 3_pInt
|
|
if (any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .true.) .and. &
|
|
any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .false.)) errorID = 832_pInt ! each row should be either fully or not at all defined
|
|
enddo
|
|
print '(a)','velocity gradient:'
|
|
else
|
|
print '(a)','deformation gradient rate:'
|
|
endif
|
|
write (*,'(3(3(f12.7,1x)/))',advance='no') merge(math_transpose33(bc(loadcase)%deformation),&
|
|
reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskDeformation))
|
|
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' stress / GPa:',&
|
|
1e-9_pReal*merge(math_transpose33(bc(loadcase)%stress),&
|
|
reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskStress))
|
|
if (any(bc(loadcase)%rotation /= math_I3)) &
|
|
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',&
|
|
math_transpose33(bc(loadcase)%rotation)
|
|
print '(a,f12.6)','temperature:',bc(loadcase)%temperature
|
|
print '(a,f12.6)','time: ',bc(loadcase)%time
|
|
print '(a,i5)' ,'increments: ',bc(loadcase)%incs
|
|
print '(a,i5)','output frequency: ',bc(loadcase)%outputfrequency
|
|
print '(a,i5)','restart frequency: ',bc(loadcase)%restartfrequency
|
|
|
|
if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 831_pInt ! exclusive or masking only
|
|
if (any(bc(loadcase)%maskStress .and. transpose(bc(loadcase)%maskStress) .and. &
|
|
reshape([ .false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false.],[ 3,3]))) &
|
|
errorID = 838_pInt ! no rotation is allowed by stress BC
|
|
if (any(abs(math_mul33x33(bc(loadcase)%rotation,math_transpose33(bc(loadcase)%rotation))&
|
|
-math_I3) > reshape(spread(rotation_tol,1,9),[ 3,3]))&
|
|
.or. abs(math_det33(bc(loadcase)%rotation)) > 1.0_pReal + rotation_tol)&
|
|
errorID = 846_pInt ! given rotation matrix contains strain
|
|
if (bc(loadcase)%time < 0.0_pReal) errorID = 834_pInt ! negative time increment
|
|
if (bc(loadcase)%incs < 1_pInt) errorID = 835_pInt ! non-positive incs count
|
|
if (bc(loadcase)%outputfrequency < 1_pInt) errorID = 836_pInt ! non-positive result frequency
|
|
if (errorID > 0_pInt) call IO_error(error_ID = errorID, ext_msg = loadcase_string)
|
|
enddo
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! debugging parameters
|
|
debugGeneral = iand(debug_spectral,debug_spectralGeneral) > 0_pInt
|
|
debugDivergence = iand(debug_spectral,debug_spectralDivergence) > 0_pInt
|
|
debugRestart = iand(debug_spectral,debug_spectralRestart) > 0_pInt
|
|
debugFFTW = iand(debug_spectral,debug_spectralFFTW) > 0_pInt
|
|
|
|
!##################################################################################################
|
|
! initialization
|
|
!##################################################################################################
|
|
|
|
allocate (defgrad ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
|
|
allocate (defgradold ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
|
|
allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
|
|
allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
|
|
allocate (temperature( res(1), res(2),res(3)), source = bc(1)%temperature) ! start out isothermally
|
|
tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
|
|
call c_f_pointer(tensorField, tensorField_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation
|
|
call c_f_pointer(tensorField, tensorField_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! init fields to no deformation
|
|
ielem = 0_pInt
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
defgrad(i,j,k,1:3,1:3) = math_I3
|
|
defgradold(i,j,k,1:3,1:3) = math_I3
|
|
coordinates(i,j,k,1:3) = geomdim/real(res * [i,j,k], pReal) - geomdim/real(2_pInt*res,pReal)
|
|
call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
|
|
0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
|
|
c_current = c_current + dPdF
|
|
enddo; enddo; enddo
|
|
|
|
c0_reference = c_current * wgt ! linear reference material stiffness
|
|
c0_66 = math_Mandel3333to66(c0_reference)
|
|
call math_invert(6_pInt, c0_66, s0_66, i, errmatinv) ! invert in mandel notation
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
s0_reference = math_Mandel66to3333(s0_66)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! possible restore deformation gradient from saved state
|
|
if (restartInc > 1_pInt) then ! using old values from file
|
|
if (debugRestart) print '(a,i6,a)' , 'Reading values of increment ',&
|
|
restartInc - 1_pInt,' from file'
|
|
call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
|
|
trim(getSolverJobName()),size(defgrad))
|
|
read (777,rec=1) defgrad
|
|
close (777)
|
|
defgradold = defgrad
|
|
defgradAim = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
defgradAim = defgradAim + defgrad(i,j,k,1:3,1:3) ! calculating old average deformation
|
|
enddo; enddo; enddo
|
|
defgradAim = defgradAim * wgt
|
|
defgradAimOld = defgradAim
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) and remove the given highest frequencies
|
|
if (divergence_correction) then
|
|
virt_dim = 1.0_pReal
|
|
else
|
|
virt_dim = geomdim
|
|
endif
|
|
|
|
do k = 1_pInt, res(3)
|
|
k_s(3) = k - 1_pInt
|
|
if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
|
|
do j = 1_pInt, res(2)
|
|
k_s(2) = j - 1_pInt
|
|
if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
|
|
do i = 1_pInt, res1_red
|
|
k_s(1) = i - 1_pInt
|
|
xi(1:3,i,j,k) = real(k_s, pReal)/virt_dim
|
|
enddo; enddo; enddo
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate the gamma operator
|
|
if(memory_efficient) then ! allocate just single fourth order tensor
|
|
allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
|
|
else ! precalculation of gamma_hat field
|
|
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source =0.0_pReal)
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
! if(k==res(3)/2 .or. k==res(3)/2+2 .or.&
|
|
! j==res(2)/2 .or. j==res(2)/2+2 .or.&
|
|
! i==res(1)/2 .or. i==res(1)/2+2) then
|
|
! gamma_hat(i,j,k,1:3,1:3,1:3,1:3) = s0_reference
|
|
! else
|
|
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Real(l,m) = sum(c0_reference(l,m,1:3,1:3)*xiDyad)
|
|
temp33_Real = math_inv33(temp33_Real)
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
|
|
gamma_hat(i,j,k, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
|
|
endif
|
|
enddo; enddo; enddo
|
|
gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! general initialization of fftw (see manual on fftw.org for more details)
|
|
if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=808_pInt) ! check for correct precision in C
|
|
#ifdef _OPENMP
|
|
if(DAMASK_NumThreadsInt > 0_pInt) then
|
|
ierr = fftw_init_threads()
|
|
if (ierr == 0_pInt) call IO_error(error_ID = 809_pInt)
|
|
call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
|
|
endif
|
|
#endif
|
|
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! creating plans
|
|
plan_stress = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
|
|
tensorField_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
|
|
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
|
|
tensorField_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,fftw_planner_flag)
|
|
|
|
plan_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
|
|
tensorField_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,&
|
|
tensorField_real,[ res(3),res(2) ,res(1)+2_pInt],&
|
|
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! depending on (debug) options, allocate more memory and create additional plans
|
|
if (debugDivergence) then
|
|
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
|
|
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
|
|
call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
|
|
allocate (divergence_postProc(res(1),res(2),res(3),3)); divergence_postProc= 0.0_pReal
|
|
plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
|
|
divergence_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,&
|
|
divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
|
|
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
|
|
endif
|
|
|
|
if (debugFFTW) then
|
|
scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
|
|
scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T))
|
|
call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)])
|
|
call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)])
|
|
plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
|
|
scalarField_real,scalarField_fourier,-1,fftw_planner_flag)
|
|
plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
|
|
scalarField_fourier,scalarField_real,+1,fftw_planner_flag)
|
|
endif
|
|
|
|
if (debugGeneral) print '(a)' , 'FFTW initialized'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! write header of output file
|
|
open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
|
|
//'.spectralOut',form='UNFORMATTED',status='REPLACE')
|
|
write(538) 'load', trim(getLoadcaseName())
|
|
write(538) 'workingdir', trim(getSolverWorkingDirectoryName())
|
|
write(538) 'geometry', trim(getSolverJobName())//InputFileExtension
|
|
write(538) 'resolution', res
|
|
write(538) 'dimension', geomdim
|
|
write(538) 'materialpoint_sizeResults', materialpoint_sizeResults
|
|
write(538) 'loadcases', N_Loadcases
|
|
write(538) 'frequencies', bc(1:N_Loadcases)%outputfrequency ! one entry per loadcase
|
|
write(538) 'times', bc(1:N_Loadcases)%time ! one entry per loadcase
|
|
write(538) 'logscales', bc(1:N_Loadcases)%logscale
|
|
write(538) 'increments', bc(1:N_Loadcases)%incs ! one entry per loadcase
|
|
write(538) 'startingIncrement', restartInc - 1_pInt ! start with writing out the previous inc
|
|
write(538) 'eoh' ! end of header
|
|
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! initial (non-deformed or read-in) results
|
|
if (debugGeneral) print '(a)' , 'Header of result file written out'
|
|
|
|
!##################################################################################################
|
|
! Loop over loadcases defined in the loadcase file
|
|
!##################################################################################################
|
|
do loadcase = 1_pInt, N_Loadcases
|
|
time0 = time ! loadcase start time
|
|
if (bc(loadcase)%followFormerTrajectory .and. &
|
|
(restartInc < totalIncsCounter .or. &
|
|
restartInc > totalIncsCounter+bc(loadcase)%incs) ) then ! continue to guess along former trajectory where applicable
|
|
guessmode = 1.0_pReal
|
|
else
|
|
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! arrays for mixed boundary conditions
|
|
mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
|
|
mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
|
|
size_reduced = int(count(bc(loadcase)%maskStressVector), pInt)
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
|
|
!##################################################################################################
|
|
! loop oper incs defined in input file for current loadcase
|
|
!##################################################################################################
|
|
do inc = 1_pInt, bc(loadcase)%incs
|
|
totalIncsCounter = totalIncsCounter + 1_pInt
|
|
if(totalIncsCounter >= restartInc) then ! do calculations (otherwise just forwarding)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! forwarding time
|
|
timeinc_old = timeinc
|
|
if (bc(loadcase)%logscale == 0_pInt) then ! linear scale
|
|
timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
|
|
else
|
|
if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
|
|
if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
|
|
timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
|
|
else ! not-1st inc of 1st loadcase of logarithmic scale
|
|
timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
|
|
endif
|
|
else ! not-1st loadcase of logarithmic scale
|
|
timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
|
|
real(bc(loadcase)%incs ,pReal))&
|
|
-(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
|
|
real(bc(loadcase)%incs ,pReal)) )
|
|
endif
|
|
endif
|
|
time = time + timeinc
|
|
|
|
if (bc(loadcase)%velGradApplied) then ! calculate deltaF from given L and current F
|
|
deltaF = timeinc * mask_defgrad * math_mul33x33(bc(loadcase)%deformation, defgradAim)
|
|
else ! deltaF = fDot *timeinc where applicable
|
|
deltaF = timeinc * mask_defgrad * bc(loadcase)%deformation
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! winding forward of deformation aim in loadcase system
|
|
temp33_Real = defgradAim
|
|
defgradAim = defgradAim &
|
|
+ guessmode * mask_stress * (defgradAim - defgradAimOld)*timeinc/timeinc_old &
|
|
+ deltaF
|
|
defgradAimOld = temp33_Real
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! update local deformation gradient
|
|
deltaF = math_rotate_backward33(deltaF,bc(loadcase)%rotation)
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
temp33_Real = defgrad(i,j,k,1:3,1:3)
|
|
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
|
|
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
|
|
*timeinc/timeinc_old &
|
|
+ (1.0_pReal-guessmode) * deltaF ! if not guessing, use prescribed average deformation where applicable
|
|
defgradold(i,j,k,1:3,1:3) = temp33_Real
|
|
enddo; enddo; enddo
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate reduced compliance
|
|
|
|
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
|
|
c_prev = math_rotate_forward3333(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former inc
|
|
c_prev99 = math_Plain3333to99(c_prev)
|
|
k = 0_pInt ! build reduced stiffness
|
|
do n = 1_pInt,9_pInt
|
|
if(bc(loadcase)%maskStressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(bc(loadcase)%maskStressVector(m)) then
|
|
j = j + 1_pInt
|
|
c_reduced(k,j) = c_prev99(n,m)
|
|
endif; enddo; endif; enddo
|
|
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
s_prev99 = 0.0_pReal ! build full compliance
|
|
k = 0_pInt
|
|
do n = 1_pInt,9_pInt
|
|
if(bc(loadcase)%maskStressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(bc(loadcase)%maskStressVector(m)) then
|
|
j = j + 1_pInt
|
|
s_prev99(n,m) = s_reduced(k,j)
|
|
endif; enddo; endif; enddo
|
|
s_prev = (math_Plain99to3333(s_prev99))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! report begin of new increment
|
|
print '(a)', '##################################################################'
|
|
print '(A,I5.5,A,es12.5)', 'Increment ', totalIncsCounter, ' Time ',time
|
|
|
|
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
|
|
CPFEM_mode = 1_pInt ! winding forward
|
|
iter = 0_pInt
|
|
err_div = 2.0_pReal * err_div_tol ! go into loop
|
|
|
|
!##################################################################################################
|
|
! convergence loop (looping over iterations)
|
|
!##################################################################################################
|
|
do while((iter < itmax .and. (err_div > err_div_tol .or. err_stress > err_stress_tol))&
|
|
.or. iter < itmin)
|
|
iter = iter + 1_pInt
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! report begin of new iteration
|
|
print '(a)', ''
|
|
print '(a)', '=================================================================='
|
|
print '(5(a,i6.6))', 'Loadcase ',loadcase,' Increment ',inc,'/',bc(loadcase)%incs,&
|
|
' @ Iteration ',iter,'/',itmax
|
|
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
|
|
math_transpose33(defgradAim)
|
|
print '(a)', ''
|
|
print '(a)', '... update stress field P(F) .....................................'
|
|
defgradAim_lab_old = math_rotate_backward33(defgradAim,bc(loadcase)%rotation)
|
|
!--------------------------------------------------------------------------------------------------
|
|
! evaluate constitutive response
|
|
call deformed_fft(res,geomdim,defgradAim_lab_old,1.0_pReal,defgrad,coordinates) ! calculate current coordinates
|
|
ielem = 0_pInt
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
call CPFEM_general(3_pInt,& ! collect cycle
|
|
coordinates(i,j,k,1:3), defgradold(i,j,k,1:3,1:3),&
|
|
defgrad(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
|
|
cstress,dsde, pstress, dPdF)
|
|
enddo; enddo; enddo
|
|
|
|
tensorField_real = 0.0_pReal ! needed because of the padding for FFTW
|
|
c_current = 0.0_pReal
|
|
ielem = 0_pInt
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
|
|
coordinates(i,j,k,1:3),&
|
|
defgradold(i,j,k,1:3,1:3), defgrad(i,j,k,1:3,1:3),& ! others get 2 (saves winding forward effort)
|
|
temperature(i,j,k),timeinc,ielem,1_pInt,&
|
|
cstress,dsde, pstress,dPdF)
|
|
CPFEM_mode = 2_pInt
|
|
tensorField_real(i,j,k,1:3,1:3) = pstress
|
|
c_current = c_current + dPdF
|
|
enddo; enddo; enddo
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! copy one component of the stress field to to a single FT and check for mismatch
|
|
if (debugFFTW) then
|
|
row = (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
|
|
column = (mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
|
|
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
|
|
cmplx(tensorField_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! call function to calculate divergence from math (for post processing) to check results
|
|
if (debugDivergence) &
|
|
call divergence_fft(res,geomdim,3_pInt,&
|
|
tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_postProc) !padding
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the FT because it simplifies calculation of average stress in real space also
|
|
call fftw_execute_dft_r2c(plan_stress,tensorField_real,tensorField_fourier)
|
|
|
|
pstress_av_lab = real(tensorField_fourier(1,1,1,1:3,1:3),pReal)*wgt
|
|
pstress_av = math_rotate_forward33(pstress_av_lab,bc(loadcase)%rotation)
|
|
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
|
|
math_transpose33(pstress_av)/1.e6_pReal
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 FT results
|
|
if (debugFFTW) then
|
|
call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
|
|
print '(a,i1,1x,i1)', 'checking FT results of compontent ', row, column
|
|
print '(a,2(es11.4,1x))', 'max FT relative error = ',&
|
|
maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
|
|
tensorField_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
|
|
scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
|
|
maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
|
|
tensorField_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
|
|
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! removing highest frequencies
|
|
tensorField_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
tensorField_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
if(res(3)>1_pInt) &
|
|
tensorField_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress BC handling
|
|
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
|
|
err_stress = maxval(abs(mask_stress * (pstress_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable)
|
|
err_stress_tol = maxval(abs(pstress_av)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
|
|
print '(a)', ''
|
|
print '(a)', '... correcting deformation gradient to fulfill BCs ...............'
|
|
print '(a,f6.2,a,es11.4,a)', 'error stress = ', err_stress/err_stress_tol, &
|
|
' (',err_stress,' Pa)'
|
|
defgradAim = defgradAim - math_mul3333xx33(s_prev, ((pstress_av - bc(loadcase)%stress))) ! residual on given stress components
|
|
print '(a,1x,es11.4)' ,'determinant of new deformation = ',math_det33(defgradAim)
|
|
else
|
|
err_stress_tol = +huge(1.0_pReal)
|
|
endif
|
|
|
|
defgradAim_lab = math_rotate_backward33(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! actual spectral method
|
|
print '(a)', ''
|
|
print '(a)', '... calculating equilibrium with spectral method .................'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
pstress_av_L2 = sqrt(maxval (math_eigenvalues33(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress
|
|
math_transpose33(pstress_av_lab)))))
|
|
err_div_RMS = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2)
|
|
do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
|
err_div_RMS = err_div_RMS &
|
|
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
|
|
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
|
+sum(aimag(math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),&
|
|
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal))
|
|
enddo
|
|
err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
|
|
+ sum(real(math_mul33x3_complex(tensorField_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
|
|
+ sum(real(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),&
|
|
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),&
|
|
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)
|
|
enddo; enddo
|
|
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
|
|
if(err_div_RMS/pstress_av_L2*sqrt(wgt) >err_div&
|
|
.and.iter >2_pInt&
|
|
.and.err_stress < err_stress_tol) then
|
|
print*, 'Increasing divergence, stopping iterations'
|
|
iter = itmax
|
|
endif
|
|
err_div = err_div_RMS/pstress_av_L2*sqrt(wgt) ! criterion to stop iterations
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate additional divergence criteria and report
|
|
if(debugDivergence) then ! calculate divergence again
|
|
err_div_max = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
temp3_Complex = math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),&
|
|
xi(1:3,i,j,k))*two_pi_img
|
|
err_div_max = max(err_div_max,sqrt(sum(abs(temp3_Complex)**2.0_pReal)))
|
|
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
|
|
enddo; enddo; enddo
|
|
|
|
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real)
|
|
divergence_real = divergence_real*wgt
|
|
err_real_div_RMS = 0.0_pReal
|
|
err_real_div_max = 0.0_pReal
|
|
max_div_error = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
max_div_error= max(max_div_error,maxval((divergence_real(i,j,k,1:3)&
|
|
-divergence_postProc(i,j,k,1:3))/divergence_real(i,j,k,1:3)))
|
|
err_real_div_RMS=err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of L_2 norm of div(stress) in real space
|
|
err_real_div_max=max(err_real_div_max,sqrt(sum(divergence_real(i,j,k,1:3)**2.0_pReal)))! maximum of L two norm of div(stress) in real space
|
|
enddo; enddo; enddo
|
|
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
|
|
err_div_max = err_div_max*sqrt(wgt)
|
|
|
|
print '(a,es11.4)', 'error divergence FT RMS = ',err_div_RMS
|
|
print '(a,es11.4)', 'error divergence FT max = ',err_div_max
|
|
print '(a,es11.4)', 'error divergence Real RMS = ',err_real_div_RMS
|
|
print '(a,es11.4)', 'error divergence Real max = ',err_real_div_max
|
|
print '(a,es11.4)', 'max deviat. from postProc = ',max_div_error
|
|
endif
|
|
print '(a,f6.2,a,es11.4,a)','error divergence = ', err_div/err_div_tol,&
|
|
' (',err_div_RMS,' N/m³)'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! to the actual spectral method calculation (mechanical equilibrium)
|
|
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
|
|
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
|
|
! if(k==res(3)/2 .or. k==res(3)/2+2 .or.&
|
|
! j==res(2)/2 .or. j==res(2)/2+2 .or.&
|
|
! i==res(1)/2 .or. i==res(1)/2+2) then
|
|
! forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt)&
|
|
! temp33_Complex(m,n) = sum(s0_reference(m,n, 1:3,1:3)* tensorField_fourier(i,j,k,1:3,1:3))
|
|
! else
|
|
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Real(l,m) = sum(c0_reference(l,m,1:3,1:3)*xiDyad)
|
|
temp33_Real = math_inv33(temp33_Real)
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
|
|
gamma_hat(1,1,1, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
|
|
tensorField_fourier(i,j,k,1:3,1:3))
|
|
tensorField_fourier(i,j,k,1:3,1:3) = temp33_Complex
|
|
endif
|
|
enddo; enddo; enddo
|
|
|
|
else ! use precalculated gamma-operator
|
|
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
|
|
forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
|
|
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
|
|
tensorField_fourier(i,j,k,1:3,1:3))
|
|
tensorField_fourier(i,j,k, 1:3,1:3) = temp33_Complex
|
|
enddo; enddo; enddo
|
|
|
|
endif
|
|
|
|
tensorField_fourier(1,1,1,1:3,1:3) = cmplx((defgradAim_lab_old - defgradAim_lab) & ! assign (negative) average deformation gradient change to zero frequency (real part)
|
|
* real(Npoints,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
scalarField_fourier(i,j,k) = tensorField_fourier(i,j,k,row,column)
|
|
enddo; enddo; enddo
|
|
do i = 0_pInt, res(1)/2_pInt-2_pInt !unpack fft data for conj complex symmetric part
|
|
m = 1_pInt
|
|
do k = 1_pInt, res(3)
|
|
n = 1_pInt
|
|
do j = 1_pInt, res(2)
|
|
scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
|
|
if(n == 1_pInt) n = res(2) + 1_pInt
|
|
n = n-1_pInt
|
|
enddo
|
|
if(m == 1_pInt) m = res(3) + 1_pInt
|
|
m = m -1_pInt
|
|
enddo; enddo
|
|
endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the inverse FT
|
|
call fftw_execute_dft_c2r(plan_correction,tensorField_fourier,tensorField_real) ! back transform of fluct deformation gradient
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
print '(a,i1,1x,i1)', 'checking iFT results of compontent ', row, column
|
|
call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
|
|
print '(a,es11.4)', 'max iFT relative error = ',&
|
|
maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
|
|
tensorField_real(1:res(1),1:res(2),1:res(3),row,column))/&
|
|
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate some additional output
|
|
if(debugGeneral) then
|
|
maxCorrectionSkew = 0.0_pReal
|
|
maxCorrectionSym = 0.0_pReal
|
|
temp33_Real = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
maxCorrectionSym = max(maxCorrectionSym,&
|
|
maxval(math_symmetric33(tensorField_real(i,j,k,1:3,1:3))))
|
|
maxCorrectionSkew = max(maxCorrectionSkew,&
|
|
maxval(math_skew33(tensorField_real(i,j,k,1:3,1:3))))
|
|
temp33_Real = temp33_Real + tensorField_real(i,j,k,1:3,1:3)
|
|
enddo; enddo; enddo
|
|
print '(a,1x,es11.4)' , 'max symmetrix correction of deformation =',&
|
|
maxCorrectionSym*wgt
|
|
print '(a,1x,es11.4)' , 'max skew correction of deformation =',&
|
|
maxCorrectionSkew*wgt
|
|
print '(a,1x,es11.4)' , 'max sym/skew of avg correction = ',&
|
|
maxval(math_symmetric33(temp33_real))/&
|
|
maxval(math_skew33(temp33_real))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! updated deformation gradient
|
|
defgrad = defgrad - tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate bounds of det(F) and report
|
|
if(debugGeneral) then
|
|
defgradDetMax = -huge(1.0_pReal)
|
|
defgradDetMin = +huge(1.0_pReal)
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
defgradDet = math_det33(defgrad(i,j,k,1:3,1:3))
|
|
defgradDetMax = max(defgradDetMax,defgradDet)
|
|
defgradDetMin = min(defgradDetMin,defgradDet)
|
|
enddo; enddo; enddo
|
|
|
|
print '(a,1x,es11.4)' , 'max determinant of deformation =', defgradDetMax
|
|
print '(a,1x,es11.4)' , 'min determinant of deformation =', defgradDetMin
|
|
endif
|
|
|
|
enddo ! end looping when convergency is achieved
|
|
|
|
print '(a)', ''
|
|
print '(a)', '=================================================================='
|
|
if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
|
|
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' NOT converged'
|
|
notConvergedCounter = notConvergedCounter + 1_pInt
|
|
else
|
|
convergedCounter = convergedCounter + 1_pInt
|
|
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' converged'
|
|
endif
|
|
|
|
if (mod(inc,bc(loadcase)%outputFrequency) == 0_pInt) then ! at output frequency
|
|
print '(a)', ''
|
|
print '(a)', '... writing results to file ......................................'
|
|
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
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endif
|
|
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if( bc(loadcase)%restartFrequency > 0_pInt .and. &
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mod(inc,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
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|
restartWrite = .true.
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print '(A)', 'writing converged results for restart'
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call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(defgrad)) ! writing deformation gradient field to file
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write (777,rec=1) defgrad
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close (777)
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restartInc=totalIncsCounter
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endif
|
|
|
|
if (update_gamma) then
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|
print*, 'update c0_reference '
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|
c0_reference = c_current*wgt
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|
! s0_reference = math_Plain99to3333(s0_99)
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|
|
|
!c0_99 = math_Plain3333to99(c0_reference)
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|
! call math_invert(9_pInt, s0_99, c0_99, i, errmatinv) ! invert reduced stiffness
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|
! if(errmatinv) call IO_error(error_ID=400_pInt)
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|
! print*, (c0_reference - math_Plain99to3333(c0_99))/c0_reference
|
|
! pause
|
|
endif
|
|
|
|
endif ! end calculation/forwarding
|
|
enddo ! end looping over incs in current loadcase
|
|
deallocate(c_reduced)
|
|
deallocate(s_reduced)
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|
enddo ! end looping over loadcases
|
|
print '(a)', ''
|
|
print '(a)', '##################################################################'
|
|
print '(i6.6,a,i6.6,a)', notConvergedCounter, ' out of ', &
|
|
notConvergedCounter + convergedCounter, ' increments did not converge!'
|
|
close(538)
|
|
call fftw_destroy_plan(plan_stress); call fftw_destroy_plan(plan_correction)
|
|
if (debugDivergence) call fftw_destroy_plan(plan_divergence)
|
|
if (debugFFTW) then
|
|
call fftw_destroy_plan(plan_scalarField_forth)
|
|
call fftw_destroy_plan(plan_scalarField_back)
|
|
endif
|
|
call quit(0_pInt)
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|
end program DAMASK_spectral
|
|
|
|
!********************************************************************
|
|
! quit subroutine to satisfy IO_error
|
|
!
|
|
!********************************************************************
|
|
subroutine quit(stop_id)
|
|
use prec, only: pInt
|
|
implicit none
|
|
|
|
integer(pInt), intent(in) :: stop_id
|
|
|
|
if (stop_id == 0_pInt) stop 0 ! normal termination
|
|
if (stop_id <= 9000_pInt) then ! trigger regridding
|
|
print*, stop_id
|
|
stop 1
|
|
endif
|
|
stop 'abnormal termination of DAMASK_spectral'
|
|
end subroutine
|