! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see .
!
!##############################################################
!* $Id$
!***************************************
!* Module: CRYSTALLITE *
!***************************************
!* contains: *
!* - _init *
!* - materialpoint_stressAndItsTangent *
!* - _partitionDeformation *
!* - _updateState *
!* - _stressAndItsTangent *
!* - _postResults *
!***************************************
MODULE crystallite
use prec, only: pReal, pInt
implicit none
! ****************************************************************
! *** General variables for the crystallite calculation ***
! ****************************************************************
integer(pInt) crystallite_maxSizePostResults
integer(pInt), dimension(:), allocatable :: crystallite_sizePostResults
integer(pInt), dimension(:,:), allocatable :: crystallite_sizePostResult
character(len=64), dimension(:,:), allocatable :: crystallite_output ! name of each post result output
integer(pInt), dimension (:,:,:), allocatable :: &
crystallite_symmetryID ! crystallographic symmetry 1=cubic 2=hexagonal, needed in all orientation calcs
real(pReal), dimension (:,:,:), allocatable :: &
crystallite_dt, & ! requested time increment of each grain
crystallite_subdt, & ! substepped time increment of each grain
crystallite_subFrac, & ! already calculated fraction of increment
crystallite_subStep, & ! size of next integration step
crystallite_statedamper, & ! damping for state update
crystallite_Temperature, & ! Temp of each grain
crystallite_partionedTemperature0, & ! Temp of each grain at start of homog inc
crystallite_subTemperature0, & ! Temp of each grain at start of crystallite inc
crystallite_dotTemperature ! evolution of Temperature of each grain
real(pReal), dimension (:,:,:,:), allocatable :: &
crystallite_Tstar_v, & ! current 2nd Piola-Kirchhoff stress vector (end of converged time step)
crystallite_Tstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of FE inc
crystallite_partionedTstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of homog inc
crystallite_subTstar0_v, & ! 2nd Piola-Kirchhoff stress vector at start of crystallite inc
crystallite_orientation, & ! orientation as quaternion
crystallite_orientation0, & ! initial orientation as quaternion
crystallite_rotation ! grain rotation away from initial orientation as axis-angle (in degrees)
real(pReal), dimension (:,:,:,:,:), allocatable :: &
crystallite_Fe, & ! current "elastic" def grad (end of converged time step)
crystallite_subFe0,& ! "elastic" def grad at start of crystallite inc
crystallite_Fp, & ! current plastic def grad (end of converged time step)
crystallite_invFp, & ! inverse of current plastic def grad (end of converged time step)
crystallite_Fp0, & ! plastic def grad at start of FE inc
crystallite_partionedFp0,& ! plastic def grad at start of homog inc
crystallite_subFp0,& ! plastic def grad at start of crystallite inc
crystallite_F0, & ! def grad at start of FE inc
crystallite_partionedF, & ! def grad to be reached at end of homog inc
crystallite_partionedF0, & ! def grad at start of homog inc
crystallite_subF, & ! def grad to be reached at end of crystallite inc
crystallite_subF0, & ! def grad at start of crystallite inc
crystallite_Lp, & ! current plastic velocitiy grad (end of converged time step)
crystallite_Lp0, & ! plastic velocitiy grad at start of FE inc
crystallite_partionedLp0,& ! plastic velocity grad at start of homog inc
crystallite_subLp0,& ! plastic velocity grad at start of crystallite inc
crystallite_P, & ! 1st Piola-Kirchhoff stress per grain
crystallite_disorientation ! disorientation between two neighboring ips (only calculated for single grain IPs)
real(pReal), dimension (:,:,:,:,:,:,:), allocatable :: &
crystallite_dPdF, & ! current individual dPdF per grain (end of converged time step)
crystallite_dPdF0, & ! individual dPdF per grain at start of FE inc
crystallite_partioneddPdF0, & ! individual dPdF per grain at start of homog inc
crystallite_fallbackdPdF ! dPdF fallback for non-converged grains (elastic prediction)
logical, dimension (:,:,:), allocatable :: &
crystallite_localConstitution, & ! indicates this grain to have purely local constitutive law
crystallite_requested, & ! flag to request crystallite calculation
crystallite_todo, & ! flag to indicate need for further computation
crystallite_converged ! convergence flag
CONTAINS
!********************************************************************
! allocate and initialize per grain variables
!********************************************************************
subroutine crystallite_init(Temperature)
!*** variables and functions from other modules ***!
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use prec, only: pInt, &
pReal
use debug, only: debug_info, &
debug_reset, &
debug_verbosity
use math, only: math_I3, &
math_EulerToR, &
math_inv33, &
math_transpose33, &
math_mul33xx33, &
math_mul33x33
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems, &
mesh_maxNips, &
mesh_maxNipNeighbors
use IO
use material
use lattice, only: lattice_symmetryType
use constitutive, only: constitutive_microstructure
use constitutive_phenopowerlaw, only: constitutive_phenopowerlaw_label, &
constitutive_phenopowerlaw_structure
use constitutive_titanmod, only: constitutive_titanmod_label, &
constitutive_titanmod_structure
use constitutive_dislotwin, only: constitutive_dislotwin_label, &
constitutive_dislotwin_structure
use constitutive_nonlocal, only: constitutive_nonlocal_label, &
constitutive_nonlocal_structure
implicit none
integer(pInt), parameter :: myFile = 200_pInt, &
maxNchunks = 2_pInt
!*** input variables ***!
real(pReal) Temperature
!*** output variables ***!
!*** local variables ***!
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) g, & ! grain number
i, & ! integration point number
e, & ! element number
gMax, & ! maximum number of grains
iMax, & ! maximum number of integration points
eMax, & ! maximum number of elements
nMax, & ! maximum number of ip neighbors
myNgrains, & ! number of grains in current IP
section, &
j, &
p, &
output, &
mySize, &
myStructure, & ! lattice structure
myPhase, &
myMat
character(len=64) tag
character(len=1024) line
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '<<<+- crystallite init -+>>>'
write(6,*) '$Id$'
#include "compilation_info.f90"
!$OMP END CRITICAL (write2out)
gMax = homogenization_maxNgrains
iMax = mesh_maxNips
eMax = mesh_NcpElems
nMax = mesh_maxNipNeighbors
allocate(crystallite_Temperature(gMax,iMax,eMax)); crystallite_Temperature = Temperature
allocate(crystallite_partionedTemperature0(gMax,iMax,eMax)); crystallite_partionedTemperature0 = 0.0_pReal
allocate(crystallite_subTemperature0(gMax,iMax,eMax)); crystallite_subTemperature0 = 0.0_pReal
allocate(crystallite_dotTemperature(gMax,iMax,eMax)); crystallite_dotTemperature = 0.0_pReal
allocate(crystallite_Tstar0_v(6,gMax,iMax,eMax)); crystallite_Tstar0_v = 0.0_pReal
allocate(crystallite_partionedTstar0_v(6,gMax,iMax,eMax)); crystallite_partionedTstar0_v = 0.0_pReal
allocate(crystallite_subTstar0_v(6,gMax,iMax,eMax)); crystallite_subTstar0_v = 0.0_pReal
allocate(crystallite_Tstar_v(6,gMax,iMax,eMax)); crystallite_Tstar_v = 0.0_pReal
allocate(crystallite_P(3,3,gMax,iMax,eMax)); crystallite_P = 0.0_pReal
allocate(crystallite_F0(3,3,gMax,iMax,eMax)); crystallite_F0 = 0.0_pReal
allocate(crystallite_partionedF0(3,3,gMax,iMax,eMax)); crystallite_partionedF0 = 0.0_pReal
allocate(crystallite_partionedF(3,3,gMax,iMax,eMax)); crystallite_partionedF = 0.0_pReal
allocate(crystallite_subF0(3,3,gMax,iMax,eMax)); crystallite_subF0 = 0.0_pReal
allocate(crystallite_subF(3,3,gMax,iMax,eMax)); crystallite_subF = 0.0_pReal
allocate(crystallite_Fp0(3,3,gMax,iMax,eMax)); crystallite_Fp0 = 0.0_pReal
allocate(crystallite_partionedFp0(3,3,gMax,iMax,eMax)); crystallite_partionedFp0 = 0.0_pReal
allocate(crystallite_subFp0(3,3,gMax,iMax,eMax)); crystallite_subFp0 = 0.0_pReal
allocate(crystallite_Fp(3,3,gMax,iMax,eMax)); crystallite_Fp = 0.0_pReal
allocate(crystallite_invFp(3,3,gMax,iMax,eMax)); crystallite_invFp = 0.0_pReal
allocate(crystallite_Fe(3,3,gMax,iMax,eMax)); crystallite_Fe = 0.0_pReal
allocate(crystallite_subFe0(3,3,gMax,iMax,eMax)); crystallite_subFe0 = 0.0_pReal
allocate(crystallite_Lp0(3,3,gMax,iMax,eMax)); crystallite_Lp0 = 0.0_pReal
allocate(crystallite_partionedLp0(3,3,gMax,iMax,eMax)); crystallite_partionedLp0 = 0.0_pReal
allocate(crystallite_subLp0(3,3,gMax,iMax,eMax)); crystallite_subLp0 = 0.0_pReal
allocate(crystallite_Lp(3,3,gMax,iMax,eMax)); crystallite_Lp = 0.0_pReal
allocate(crystallite_dPdF(3,3,3,3,gMax,iMax,eMax)); crystallite_dPdF = 0.0_pReal
allocate(crystallite_dPdF0(3,3,3,3,gMax,iMax,eMax)); crystallite_dPdF0 = 0.0_pReal
allocate(crystallite_partioneddPdF0(3,3,3,3,gMax,iMax,eMax)); crystallite_partioneddPdF0 = 0.0_pReal
allocate(crystallite_fallbackdPdF(3,3,3,3,gMax,iMax,eMax)); crystallite_fallbackdPdF = 0.0_pReal
allocate(crystallite_dt(gMax,iMax,eMax)); crystallite_dt = 0.0_pReal
allocate(crystallite_subdt(gMax,iMax,eMax)); crystallite_subdt = 0.0_pReal
allocate(crystallite_subFrac(gMax,iMax,eMax)); crystallite_subFrac = 0.0_pReal
allocate(crystallite_subStep(gMax,iMax,eMax)); crystallite_subStep = 0.0_pReal
allocate(crystallite_statedamper(gMax,iMax,eMax)); crystallite_statedamper = 1.0_pReal
allocate(crystallite_orientation(4,gMax,iMax,eMax)); crystallite_orientation = 0.0_pReal
allocate(crystallite_orientation0(4,gMax,iMax,eMax)); crystallite_orientation0 = 0.0_pReal
allocate(crystallite_rotation(4,gMax,iMax,eMax)); crystallite_rotation = 0.0_pReal
allocate(crystallite_disorientation(4,nMax,gMax,iMax,eMax)); crystallite_disorientation = 0.0_pReal
allocate(crystallite_symmetryID(gMax,iMax,eMax)); crystallite_symmetryID = 0_pInt
allocate(crystallite_localConstitution(gMax,iMax,eMax)); crystallite_localConstitution = .true.
allocate(crystallite_requested(gMax,iMax,eMax)); crystallite_requested = .false.
allocate(crystallite_todo(gMax,iMax,eMax)); crystallite_todo = .false.
allocate(crystallite_converged(gMax,iMax,eMax)); crystallite_converged = .true.
allocate(crystallite_output(maxval(crystallite_Noutput), &
material_Ncrystallite)) ; crystallite_output = ''
allocate(crystallite_sizePostResults(material_Ncrystallite)) ; crystallite_sizePostResults = 0_pInt
allocate(crystallite_sizePostResult(maxval(crystallite_Noutput), &
material_Ncrystallite)) ; crystallite_sizePostResult = 0_pInt
if (.not. IO_open_jobFile_stat(myFile,material_localFileExt)) then ! no local material configuration present...
call IO_open_file(myFile,material_configFile) ! ...open material.config file
endif
line = ''
section = 0_pInt
do while (IO_lc(IO_getTag(line,'<','>')) /= material_partCrystallite) ! wind forward to
read(myFile,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(myFile,'(a1024)',END=100) line
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1_pInt
output = 0_pInt ! reset output counter
endif
if (section > 0_pInt) then
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('(output)')
output = output + 1_pInt
crystallite_output(output,section) = IO_lc(IO_stringValue(line,positions,2_pInt))
end select
endif
enddo
100 close(myFile)
do i = 1_pInt,material_Ncrystallite ! sanity checks
enddo
do i = 1_pInt,material_Ncrystallite
do j = 1_pInt,crystallite_Noutput(i)
select case(crystallite_output(j,i))
case('phase','texture','volume')
mySize = 1_pInt
case('orientation','grainrotation') ! orientation as quaternion, or deviation from initial grain orientation in axis-angle form (angle in degrees)
mySize = 4_pInt
case('eulerangles') ! Bunge (3-1-3) Euler angles
mySize = 3_pInt
case('defgrad','f','fe','fp','lp','e','ee','p','firstpiola','1stpiola','s','tstar','secondpiola','2ndpiola')
mySize = 9_pInt
case default
mySize = 0_pInt
end select
if (mySize > 0_pInt) then ! any meaningful output found
crystallite_sizePostResult(j,i) = mySize
crystallite_sizePostResults(i) = crystallite_sizePostResults(i) + mySize
endif
enddo
enddo
crystallite_maxSizePostResults = 0_pInt
do j = 1_pInt,material_Nmicrostructure
if (microstructure_active(j)) &
crystallite_maxSizePostResults = max(crystallite_maxSizePostResults,&
crystallite_sizePostResults(microstructure_crystallite(j)))
enddo
! write description file for crystallite output
call IO_write_jobFile(myFile,'outputCrystallite')
do p = 1_pInt,material_Ncrystallite
write(myFile,*)
write(myFile,'(a)') '['//trim(crystallite_name(p))//']'
write(myFile,*)
do e = 1_pInt,crystallite_Noutput(p)
write(myFile,'(a,i4)') trim(crystallite_output(e,p))//char(9),crystallite_sizePostResult(e,p)
enddo
enddo
close(myFile)
!$OMP PARALLEL PRIVATE(myNgrains,myPhase,myMat,myStructure)
!$OMP DO
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over all cp elements
myNgrains = homogenization_Ngrains(mesh_element(3,e)) ! look up homogenization-->grainCount
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element
do g = 1_pInt,myNgrains
crystallite_Fp0(1:3,1:3,g,i,e) = math_EulerToR(material_EulerAngles(1:3,g,i,e)) ! plastic def gradient reflects init orientation
crystallite_F0(1:3,1:3,g,i,e) = math_I3
crystallite_localConstitution(g,i,e) = phase_localConstitution(material_phase(g,i,e))
!$OMP FLUSH(crystallite_Fp0)
crystallite_Fe(1:3,1:3,g,i,e) = math_transpose33(crystallite_Fp0(1:3,1:3,g,i,e))
crystallite_Fp(1:3,1:3,g,i,e) = crystallite_Fp0(1:3,1:3,g,i,e)
enddo
enddo
enddo
!$OMP ENDDO
crystallite_partionedTemperature0 = Temperature ! isothermal assumption
crystallite_partionedFp0 = crystallite_Fp0
crystallite_partionedF0 = crystallite_F0
crystallite_partionedF = crystallite_F0
crystallite_requested = .true.
! Initialize crystallite_symmetryID(g,i,e)
!$OMP DO
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
myPhase = material_phase(g,i,e)
myMat = phase_constitutionInstance(myPhase)
select case (phase_constitution(myPhase))
case (constitutive_phenopowerlaw_label)
myStructure = constitutive_phenopowerlaw_structure(myMat)
case (constitutive_titanmod_label)
myStructure = constitutive_titanmod_structure(myMat)
case (constitutive_dislotwin_label)
myStructure = constitutive_dislotwin_structure(myMat)
case (constitutive_nonlocal_label)
myStructure = constitutive_nonlocal_structure(myMat)
case default
myStructure = -1_pInt ! does this happen for j2 material?
end select
if (myStructure > 0_pInt) then
crystallite_symmetryID(g,i,e) = lattice_symmetryType(myStructure) ! structure = 1(fcc) or 2(bcc) => 1; 3(hex)=>2
endif
enddo
enddo
enddo
!$OMP ENDDO
!$OMP END PARALLEL
call crystallite_orientations()
crystallite_orientation0 = crystallite_orientation ! Store initial orientations for calculation of grain rotations
!$OMP PARALLEL DO PRIVATE(myNgrains)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
enddo
enddo
enddo
!$OMP END PARALLEL DO
call crystallite_stressAndItsTangent(.true.) ! request elastic answers
crystallite_fallbackdPdF = crystallite_dPdF ! use initial elastic stiffness as fallback
! *** Output to MARC output file ***
if (debug_verbosity > 0) then
!$OMP CRITICAL (write2out)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Temperature: ', shape(crystallite_Temperature)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_dotTemperature: ', shape(crystallite_dotTemperature)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Fe: ', shape(crystallite_Fe)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Fp: ', shape(crystallite_Fp)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Lp: ', shape(crystallite_Lp)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_F0: ', shape(crystallite_F0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Fp0: ', shape(crystallite_Fp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Lp0: ', shape(crystallite_Lp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedF: ', shape(crystallite_partionedF)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedTemp0: ', shape(crystallite_partionedTemperature0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedF0: ', shape(crystallite_partionedF0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedFp0: ', shape(crystallite_partionedFp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedLp0: ', shape(crystallite_partionedLp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subF: ', shape(crystallite_subF)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subTemperature0: ', shape(crystallite_subTemperature0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_symmetryID: ', shape(crystallite_symmetryID)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subF0: ', shape(crystallite_subF0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subFe0: ', shape(crystallite_subFe0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subFp0: ', shape(crystallite_subFp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subLp0: ', shape(crystallite_subLp0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_P: ', shape(crystallite_P)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Tstar_v: ', shape(crystallite_Tstar_v)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_Tstar0_v: ', shape(crystallite_Tstar0_v)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partionedTstar0_v: ', shape(crystallite_partionedTstar0_v)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subTstar0_v: ', shape(crystallite_subTstar0_v)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_dPdF: ', shape(crystallite_dPdF)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_dPdF0: ', shape(crystallite_dPdF0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_partioneddPdF0: ', shape(crystallite_partioneddPdF0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_fallbackdPdF: ', shape(crystallite_fallbackdPdF)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_orientation: ', shape(crystallite_orientation)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_orientation0: ', shape(crystallite_orientation0)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_rotation: ', shape(crystallite_rotation)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_disorientation: ', shape(crystallite_disorientation)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_dt: ', shape(crystallite_dt)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subdt: ', shape(crystallite_subdt)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subFrac: ', shape(crystallite_subFrac)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_subStep: ', shape(crystallite_subStep)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_stateDamper: ', shape(crystallite_stateDamper)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_localConstitution: ', shape(crystallite_localConstitution)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_requested: ', shape(crystallite_requested)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_todo: ', shape(crystallite_todo)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_converged: ', shape(crystallite_converged)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_sizePostResults: ', shape(crystallite_sizePostResults)
write(6,'(a35,1x,7(i8,1x))') 'crystallite_sizePostResult: ', shape(crystallite_sizePostResult)
write(6,*)
write(6,*) 'Number of nonlocal grains: ',count(.not. crystallite_localConstitution)
call flush(6)
!$OMP END CRITICAL (write2out)
endif
call debug_info()
call debug_reset()
endsubroutine
!********************************************************************
! calculate stress (P) and tangent (dPdF) for crystallites
!********************************************************************
subroutine crystallite_stressAndItsTangent(updateJaco)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use numerics, only: subStepMinCryst, &
subStepSizeCryst, &
stepIncreaseCryst, &
pert_Fg, &
pert_method, &
nCryst, &
numerics_integrator, &
numerics_integrationMode, &
relevantStrain, &
Lp_frac, &
analyticJaco
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_CrystalliteLoopDistribution
use IO, only: IO_warning
use math, only: math_inv33, &
math_identity2nd, &
math_transpose33, &
math_mul33x33, &
math_mul66x6, &
math_Mandel6to33, &
math_Mandel33to6, &
math_I3, &
math_Plain3333to99, &
math_Plain99to3333, &
math_mul99x99, &
math_Mandel66to3333, &
math_mul3333xx33, &
math_invert, &
math_mul3333xx3333, &
math_spectralDecompositionSym33
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_Ngrains, &
homogenization_maxNgrains
use constitutive, only: constitutive_sizeState, &
constitutive_sizeDotState, &
constitutive_state, &
constitutive_state_backup, &
constitutive_subState0, &
constitutive_partionedState0, &
constitutive_homogenizedC, &
constitutive_dotState, &
constitutive_dotState_backup, &
constitutive_LpAndItsTangent
implicit none
!*** input variables ***!
logical, intent(in) :: updateJaco ! flag indicating wehther we want to update the Jacobian (stiffness) or not
!*** output variables ***!
!*** local variables ***!
real(pReal) myPert, & ! perturbation with correct sign
formerSubStep
real(pReal), dimension(3,3) :: invFp, & ! inverse of the plastic deformation gradient
Fe_guess, & ! guess for elastic deformation gradient
Tstar ! 2nd Piola-Kirchhoff stress tensor
real(pReal), dimension(3,3,3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
dPdF_perturbation1, &
dPdF_perturbation2
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
F_backup, &
Fp_backup, &
InvFp_backup, &
Fe_backup, &
Lp_backup, &
P_backup
real(pReal), dimension(6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
Tstar_v_backup
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
Temperature_backup
integer(pInt) NiterationCrystallite, & ! number of iterations in crystallite loop
e, & ! element index
i, & ! integration point index
g, & ! grain index
k, &
l, &
h, &
o, &
p, &
j, &
perturbation , & ! loop counter for forward,backward perturbation mode
myNgrains, &
mySizeState, &
mySizeDotState
logical, dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
convergenceFlag_backup
! local variables used for calculating analytic Jacobian
real(pReal), dimension(3,3):: Fp_exp1, &
Fp_exp2, &
Fp_inv_current, &
dSdFe_mat1, &
dSdFe_mat2, &
Lp_constitutive, &
Eigvec, &
V_dir, &
phi_mat, &
Fpinv_rate, &
FDot_temp, &
Rot_mat, &
Fp0, &
Fp_inv_0, &
Lp0, &
Lp_current, &
Fe0
real(pReal), dimension(3,3,3,3) :: C, &
dSdFe, &
dLp_dT, &
Tensor1, &
Tensor2, &
Tensor3, &
Tensor4, &
Tensor5, &
dFedF, &
dSdF
real(pReal), dimension(9,9) :: dLp_dT_constitutive, &
A99, &
A_inv99, &
C99, &
dFedF99, &
dFedF_old99
real(pReal), dimension(3):: Eigval
real(pReal) :: dt, &
fixedpt_error, &
counter
integer(pInt) :: AnzNegEW, &
fixedpt_iter
logical :: error
! --+>> INITIALIZE TO STARTING CONDITION <<+--
if (debug_verbosity > 4 .and. debug_e > 0 .and. debug_e <= mesh_NcpElems &
.and. debug_i > 0 .and. debug_i <= mesh_maxNips &
.and. debug_g > 0 .and. debug_g <= homogenization_maxNgrains) then
!$OMP CRITICAL (write2out)
write (6,*)
write (6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> crystallite start at el ip g ', debug_e, debug_i, debug_g
write (6,'(a,/,12x,f14.9)') '<< CRYST >> Temp0', crystallite_partionedTemperature0(debug_g,debug_i,debug_e)
write (6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST >> F0 ', &
math_transpose33(crystallite_partionedF0(1:3,1:3,debug_g,debug_i,debug_e))
write (6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST >> Fp0', &
math_transpose33(crystallite_partionedFp0(1:3,1:3,debug_g,debug_i,debug_e))
write (6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST >> Lp0', &
math_transpose33(crystallite_partionedLp0(1:3,1:3,debug_g,debug_i,debug_e))
!$OMP END CRITICAL (write2out)
endif
crystallite_subStep = 0.0_pReal
!$OMP PARALLEL DO PRIVATE(myNgrains)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1_pInt,myNgrains
if (crystallite_requested(g,i,e)) then ! initialize restoration point of ...
crystallite_subTemperature0(g,i,e) = crystallite_partionedTemperature0(g,i,e) ! ...temperature
constitutive_subState0(g,i,e)%p = constitutive_partionedState0(g,i,e)%p ! ...microstructure
crystallite_subFp0(1:3,1:3,g,i,e) = crystallite_partionedFp0(1:3,1:3,g,i,e) ! ...plastic def grad
crystallite_subLp0(1:3,1:3,g,i,e) = crystallite_partionedLp0(1:3,1:3,g,i,e) ! ...plastic velocity grad
crystallite_dPdF0(1:3,1:3,1:3,1:3,g,i,e) = crystallite_partioneddPdF0(1:3,1:3,1:3,1:3,g,i,e) ! ...stiffness
crystallite_subF0(1:3,1:3,g,i,e) = crystallite_partionedF0(1:3,1:3,g,i,e) ! ...def grad
crystallite_subTstar0_v(1:6,g,i,e) = crystallite_partionedTstar0_v(1:6,g,i,e) !...2nd PK stress
crystallite_subFe0(1:3,1:3,g,i,e) = math_mul33x33(crystallite_subF0(1:3,1:3,g,i,e), &
math_inv33(crystallite_subFp0(1:3,1:3,g,i,e))) ! only needed later on for stiffness calculation
crystallite_subFrac(g,i,e) = 0.0_pReal
crystallite_subStep(g,i,e) = 1.0_pReal/subStepSizeCryst
crystallite_todo(g,i,e) = .true.
crystallite_converged(g,i,e) = .false. ! pretend failed step of twice the required size
endif
enddo
enddo
enddo
!$OMP END PARALLEL DO
! --+>> CRYSTALLITE CUTBACK LOOP <<+--
NiterationCrystallite = 0_pInt
numerics_integrationMode = 1_pInt
do while (any(crystallite_subStep(:,:,FEsolving_execELem(1):FEsolving_execElem(2)) > subStepMinCryst)) ! cutback loop for crystallites
!$OMP PARALLEL DO PRIVATE(myNgrains,formerSubStep)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1,myNgrains
! --- wind forward ---
if (crystallite_converged(g,i,e)) then
#ifndef _OPENMP
if (debug_verbosity > 4 &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,f12.8,a,f12.8,a)') '<< CRYST >> winding forward from ', &
crystallite_subFrac(g,i,e),' to current crystallite_subfrac ', &
crystallite_subFrac(g,i,e)+crystallite_subStep(g,i,e),' in crystallite_stressAndItsTangent'
write(6,*)
endif
#endif
crystallite_subFrac(g,i,e) = crystallite_subFrac(g,i,e) + crystallite_subStep(g,i,e)
formerSubStep = crystallite_subStep(g,i,e)
!$OMP FLUSH(crystallite_subFrac)
crystallite_subStep(g,i,e) = min( 1.0_pReal - crystallite_subFrac(g,i,e), &
stepIncreaseCryst * crystallite_subStep(g,i,e) )
!$OMP FLUSH(crystallite_subStep)
if (crystallite_subStep(g,i,e) > subStepMinCryst) then
crystallite_subTemperature0(g,i,e) = crystallite_Temperature(g,i,e) ! wind forward...
crystallite_subF0(1:3,1:3,g,i,e) = crystallite_subF(1:3,1:3,g,i,e) ! ...def grad
crystallite_subFp0(1:3,1:3,g,i,e) = crystallite_Fp(1:3,1:3,g,i,e) ! ...plastic def grad
crystallite_subFe0(1:3,1:3,g,i,e) = math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), crystallite_invFp(1:3,1:3,g,i,e)) ! only needed later on for stiffness calculation
crystallite_subLp0(1:3,1:3,g,i,e) = crystallite_Lp(1:3,1:3,g,i,e) ! ...plastic velocity gradient
constitutive_subState0(g,i,e)%p = constitutive_state(g,i,e)%p ! ...microstructure
crystallite_subTstar0_v(1:6,g,i,e) = crystallite_Tstar_v(1:6,g,i,e) ! ...2nd PK stress
!$OMP FLUSH(crystallite_subF0)
elseif (formerSubStep > subStepMinCryst) then ! this crystallite just converged
if (debug_verbosity > 4_pInt) then
!$OMP CRITICAL (distributionCrystallite)
debug_CrystalliteLoopDistribution(min(nCryst+1_pInt,NiterationCrystallite)) = &
debug_CrystalliteLoopDistribution(min(nCryst+1_pInt,NiterationCrystallite)) + 1_pInt
!$OMP END CRITICAL (distributionCrystallite)
endif
endif
! --- cutback ---
else
crystallite_subStep(g,i,e) = subStepSizeCryst * crystallite_subStep(g,i,e) ! cut step in half and restore...
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) ! ...temperature
crystallite_Fp(1:3,1:3,g,i,e) = crystallite_subFp0(1:3,1:3,g,i,e) ! ...plastic def grad
crystallite_invFp(1:3,1:3,g,i,e) = math_inv33(crystallite_Fp(1:3,1:3,g,i,e))
crystallite_Lp(1:3,1:3,g,i,e) = crystallite_subLp0(1:3,1:3,g,i,e) ! ...plastic velocity grad
constitutive_state(g,i,e)%p = constitutive_subState0(g,i,e)%p ! ...microstructure
crystallite_Tstar_v(1:6,g,i,e) = crystallite_subTstar0_v(1:6,g,i,e) ! ...2nd PK stress
! cant restore dotState here, since not yet calculated in first cutback after initialization
!$OMP FLUSH(crystallite_invFp)
#ifndef _OPENMP
if (debug_verbosity > 4_pInt &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,f12.8)') '<< CRYST >> cutback step in crystallite_stressAndItsTangent with new crystallite_subStep: ',&
crystallite_subStep(g,i,e)
write(6,*)
endif
#endif
endif
! --- prepare for integration ---
!$OMP FLUSH(crystallite_subStep)
crystallite_todo(g,i,e) = crystallite_subStep(g,i,e) > subStepMinCryst ! still on track or already done (beyond repair)
if (crystallite_todo(g,i,e)) then
crystallite_subF(1:3,1:3,g,i,e) = crystallite_subF0(1:3,1:3,g,i,e) &
+ crystallite_subStep(g,i,e) &
* (crystallite_partionedF(1:3,1:3,g,i,e) - crystallite_partionedF0(1:3,1:3,g,i,e))
!$OMP FLUSH(crystallite_subF)
crystallite_Fe(1:3,1:3,g,i,e) = math_mul33x33(crystallite_subF(1:3,1:3,g,i,e), crystallite_invFp(1:3,1:3,g,i,e))
crystallite_subdt(g,i,e) = crystallite_subStep(g,i,e) * crystallite_dt(g,i,e)
crystallite_converged(g,i,e) = .false. ! start out non-converged
endif
enddo
enddo
enddo
!$OMP END PARALLEL DO
! --- integrate --- requires fully defined state array (basic + dependent state)
if (any(crystallite_todo)) then
select case(numerics_integrator(numerics_integrationMode))
case(1_pInt)
call crystallite_integrateStateFPI()
case(2_pInt)
call crystallite_integrateStateEuler()
case(3_pInt)
call crystallite_integrateStateAdaptiveEuler()
case(4_pInt)
call crystallite_integrateStateRK4()
case(5_pInt)
call crystallite_integrateStateRKCK45()
endselect
endif
NiterationCrystallite = NiterationCrystallite + 1_pInt
enddo ! cutback loop
! --+>> CHECK FOR NON-CONVERGED CRYSTALLITES <<+--
!$OMP PARALLEL DO PRIVATE(myNgrains,invFp,Fe_guess,Tstar)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1,myNgrains
if (.not. crystallite_converged(g,i,e)) then ! respond fully elastically (might be not required due to becoming terminally ill anyway)
invFp = math_inv33(crystallite_partionedFp0(1:3,1:3,g,i,e))
Fe_guess = math_mul33x33(crystallite_partionedF(1:3,1:3,g,i,e), invFp)
Tstar = math_Mandel6to33( math_mul66x6( 0.5_pReal*constitutive_homogenizedC(g,i,e), &
math_Mandel33to6( math_mul33x33(transpose(Fe_guess),Fe_guess) - math_I3 ) ) )
crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(Fe_guess,math_mul33x33(Tstar,transpose(invFp)))
endif
#ifndef _OPENMP
if (debug_verbosity > 4 &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write (6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> central solution of cryst_StressAndTangent at el ip g ',e,i,g
write (6,*)
write (6,'(a,/,3(12x,3(f12.4,1x)/))') '<< CRYST >> P / MPa', math_transpose33(crystallite_P(1:3,1:3,g,i,e))/1.0e6_pReal
write (6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST >> Fp', math_transpose33(crystallite_Fp(1:3,1:3,g,i,e))
write (6,'(a,/,3(12x,3(f14.9,1x)/))') '<< CRYST >> Lp', math_transpose33(crystallite_Lp(1:3,1:3,g,i,e))
write (6,*)
endif
#endif
enddo
enddo
enddo
!$OMP END PARALLEL DO
! --+>> STIFFNESS CALCULATION <<+--
if(updateJaco) then ! Jacobian required
if (.not. analyticJaco) then ! Calculate Jacobian using perturbations
numerics_integrationMode = 2_pInt
! --- BACKUP ---
!$OMP PARALLEL DO PRIVATE(myNgrains,mySizeState,mySizeDotState)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1,myNgrains
mySizeState = constitutive_sizeState(g,i,e) ! number of state variables for this grain
mySizeDotState = constitutive_sizeDotState(g,i,e) ! number of dotStates for this grain
constitutive_state_backup(g,i,e)%p(1:mySizeState) = &
constitutive_state(g,i,e)%p(1:mySizeState) ! remember unperturbed, converged state, ...
constitutive_dotState_backup(g,i,e)%p(1:mySizeDotState) = &
constitutive_dotState(g,i,e)%p(1:mySizeDotState) ! ... dotStates, ...
enddo; enddo; enddo
!$OMP END PARALLEL DO
Temperature_backup = crystallite_Temperature ! ... Temperature, ...
F_backup = crystallite_subF ! ... and kinematics
Fp_backup = crystallite_Fp
InvFp_backup = crystallite_invFp
Fe_backup = crystallite_Fe
Lp_backup = crystallite_Lp
Tstar_v_backup = crystallite_Tstar_v
P_backup = crystallite_P
convergenceFlag_backup = crystallite_converged
! --- CALCULATE STATE AND STRESS FOR PERTURBATION ---
dPdF_perturbation1 = crystallite_dPdF0 ! initialize stiffness with known good values from last increment
dPdF_perturbation2 = crystallite_dPdF0 ! initialize stiffness with known good values from last increment
do perturbation = 1,2 ! forward and backward perturbation
if (iand(pert_method,perturbation) > 0) then ! mask for desired direction
myPert = -pert_Fg * (-1.0_pReal)**perturbation ! set perturbation step
do k = 1,3; do l = 1,3 ! ...alter individual components
#ifndef _OPENMP
if (debug_verbosity> 5) then
!$OMP CRITICAL (write2out)
write(6,'(a,2(1x,i1),1x,a)') '<< CRYST >> [[[[[[ Stiffness perturbation',k,l,']]]]]]'
write(6,*)
!$OMP END CRITICAL (write2out)
endif
#endif
! --- INITIALIZE UNPERTURBED STATE ---
select case(numerics_integrator(numerics_integrationMode))
case(1_pInt) ! Fix-point method: restore to last converged state at end of subinc, since this is probably closest to perturbed state
!$OMP PARALLEL DO PRIVATE(myNgrains,mySizeState,mySizeDotState)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
mySizeState = constitutive_sizeState(g,i,e)
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeState) = constitutive_state_backup(g,i,e)%p(1:mySizeState)
constitutive_dotState(g,i,e)%p(1:mySizeDotState) = constitutive_dotState_backup(g,i,e)%p(1:mySizeDotState)
enddo; enddo; enddo
!OMP END PARALLEL DO
crystallite_Temperature = Temperature_backup
crystallite_Fp = Fp_backup
crystallite_invFp = InvFp_backup
crystallite_Fe = Fe_backup
crystallite_Lp = Lp_backup
crystallite_Tstar_v = Tstar_v_backup
case(2_pInt,3_pInt) ! explicit Euler methods: nothing to restore (except for F), since we are only doing a stress integration step
case(4_pInt,5_pInt) ! explicit Runge-Kutta methods: restore to start of subinc, since we are doing a full integration of state and stress
!$OMP PARALLEL DO PRIVATE(myNgrains,mySizeState,mySizeDotState)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
mySizeState = constitutive_sizeState(g,i,e)
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeState) = constitutive_subState0(g,i,e)%p(1:mySizeState)
constitutive_dotState(g,i,e)%p(1:mySizeDotState) = constitutive_dotState_backup(g,i,e)%p(1:mySizeDotState)
enddo; enddo; enddo
!OMP END PARALLEL DO
crystallite_Temperature = crystallite_subTemperature0
crystallite_Fp = crystallite_subFp0
crystallite_Fe = crystallite_subFe0
crystallite_Tstar_v = crystallite_subTstar0_v
end select
! --- PERTURB EITHER FORWARD OR BACKWARD ---
crystallite_subF = F_backup
crystallite_subF(k,l,:,:,:) = crystallite_subF(k,l,:,:,:) + myPert
crystallite_converged = convergenceFlag_backup
crystallite_todo = crystallite_requested .and. crystallite_converged
where (crystallite_todo) crystallite_converged = .false. ! start out non-converged
select case(numerics_integrator(numerics_integrationMode))
case(1_pInt)
call crystallite_integrateStateFPI()
case(2_pInt)
call crystallite_integrateStateEuler()
case(3_pInt)
call crystallite_integrateStateAdaptiveEuler()
case(4_pInt)
call crystallite_integrateStateRK4()
case(5_pInt)
call crystallite_integrateStateRKCK45()
end select
!OMP PARALLEL DO PRIVATE(myNgrains)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
if (crystallite_requested(g,i,e) .and. crystallite_converged(g,i,e)) then ! converged state warrants stiffness update
select case(perturbation)
case(1_pInt)
dPdF_perturbation1(1:3,1:3,k,l,g,i,e) = (crystallite_P(1:3,1:3,g,i,e) - P_backup(1:3,1:3,g,i,e)) / myPert ! tangent dP_ij/dFg_kl
case(2_pInt)
dPdF_perturbation2(1:3,1:3,k,l,g,i,e) = (crystallite_P(1:3,1:3,g,i,e) - P_backup(1:3,1:3,g,i,e)) / myPert ! tangent dP_ij/dFg_kl
end select
endif
enddo; enddo; enddo
!OMP END PARALLEL DO
enddo; enddo ! k,l loop
endif
enddo ! perturbation direction
! --- STIFFNESS ACCORDING TO PERTURBATION METHOD AND CONVERGENCE ---
!$OMP PARALLEL DO PRIVATE(myNgrains)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
if (crystallite_requested(g,i,e) .and. convergenceFlag_backup(g,i,e)) then ! central solution converged
select case(pert_method)
case(1_pInt)
crystallite_dPdF(1:3,1:3,1:3,1:3,g,i,e) = dPdF_perturbation1(1:3,1:3,1:3,1:3,g,i,e)
case(2_pInt)
crystallite_dPdF(1:3,1:3,1:3,1:3,g,i,e) = dPdF_perturbation2(1:3,1:3,1:3,1:3,g,i,e)
case(3_pInt)
crystallite_dPdF(1:3,1:3,1:3,1:3,g,i,e) = 0.5_pReal* ( dPdF_perturbation1(1:3,1:3,1:3,1:3,g,i,e) &
+ dPdF_perturbation2(1:3,1:3,1:3,1:3,g,i,e))
end select
elseif (crystallite_requested(g,i,e) .and. .not. convergenceFlag_backup(g,i,e)) then ! central solution did not converge
crystallite_dPdF(1:3,1:3,1:3,1:3,g,i,e) = crystallite_fallbackdPdF(1:3,1:3,1:3,1:3,g,i,e) ! use (elastic) fallback
endif
enddo
enddo
enddo
!$OMP END PARALLEL DO
! --- RESTORE ---
!$OMP PARALLEL DO PRIVATE(myNgrains,mySizeState,mySizeDotState)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,myNgrains
mySizeState = constitutive_sizeState(g,i,e)
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeState) = constitutive_state_backup(g,i,e)%p(1:mySizeState)
constitutive_dotState(g,i,e)%p(1:mySizeDotState) = constitutive_dotState_backup(g,i,e)%p(1:mySizeDotState)
enddo; enddo; enddo
!OMP END PARALLEL DO
crystallite_Temperature = Temperature_backup
crystallite_subF = F_backup
crystallite_Fp = Fp_backup
crystallite_invFp = InvFp_backup
crystallite_Fe = Fe_backup
crystallite_Lp = Lp_backup
crystallite_Tstar_v = Tstar_v_backup
crystallite_P = P_backup
crystallite_converged = convergenceFlag_backup
else ! Calculate Jacobian using analytical expression
! --- CALCULATE ANALYTIC dPdF ---
!$OMP PARALLEL DO PRIVATE(myNgrains,Fp_inv_0,C,Eigval,Eigvec,Fp_exp1,Fp_exp2,Fp_inv_current,&
!$OMP dSdFe_mat1,dSdFe_mat2,Fpinv_rate,FDot_temp,counter,phi_mat,Tensor1,Tensor2,Tensor3,Tensor4,&
!$OMP Tensor5,V_dir,dLp_dT_constitutive,dLp_dT,C99,A99,A_inv99,AnzNegEW,error,&
!$OMP dFedF99,dFedF_old99,dFedF,fixedpt_iter,fixedpt_error,dSdF)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1_pInt,myNgrains
Fp_inv_0 = math_inv33(crystallite_subFp0(1:3,1:3,g,i,e))
C = math_Mandel66to3333(constitutive_homogenizedC(g,i,e))
call math_spectralDecompositionSym33(-(1.0_pReal-Lp_frac)*crystallite_dt(g,i,e)*0.5_pReal&
*crystallite_subLp0(1:3,1:3,g,i,e),Eigval,Eigvec,error)
Fp_exp1 = 0.0_pReal
Fp_exp1(1,1) = exp(Eigval(1))
Fp_exp1(2,2) = exp(Eigval(2))
Fp_exp1(3,3) = exp(Eigval(3))
Fp_exp1 = math_mul33x33(math_mul33x33(Eigvec,Fp_exp1),math_transpose33(Eigvec)) ! exp(-(1-Lp_frac)*Lp old*dt/2)
call math_spectralDecompositionSym33(-(Lp_frac)*crystallite_dt(g,i,e)*0.5_pReal*&
crystallite_Lp(1:3,1:3,g,i,e),Eigval,Eigvec,error)
Fp_exp2 = 0.0_pReal
Fp_exp2(1,1) = exp(Eigval(1))
Fp_exp2(2,2) = exp(Eigval(2))
Fp_exp2(3,3) = exp(Eigval(3))
Fp_exp2 = math_mul33x33(math_mul33x33(Eigvec,Fp_exp2),math_transpose33(Eigvec)) ! exp(-(Lp_frac)*Lp current*dt/2)
Fp_inv_current = math_mul33x33(math_mul33x33(math_mul33x33(math_mul33x33(Fp_inv_0, &
Fp_exp1),Fp_exp2),Fp_exp2),Fp_exp1) ! Fp current^-1 = Fp old^-1 * exp(-(1-Lp_frac)*Lp old*dt/2) * exp(-(Lp_frac)*Lp current*dt) * exp(-(1-Lp_frac)*Lp old*dt/2)
dSdFe_mat2 = math_mul33x33(math_mul33x33(Fp_exp1,Fp_exp2),Eigvec)
dSdFe_mat1 = math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),Fp_inv_0),dSdFe_mat2)
dSdFe_mat2 = math_transpose33(dSdFe_mat2)
Fpinv_rate = -math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),math_mul33x33(Fp_inv_current,&
(1.0_pReal-Lp_frac)*crystallite_subLp0(1:3,1:3,g,i,e)+ Lp_frac*crystallite_Lp(1:3,1:3,g,i,e))) ! F * dFp^-1 = F * dFp^-1/dt *dt... dFp may overshoot dF by small ammount as
FDot_temp = crystallite_subF(1:3,1:3,g,i,e) - crystallite_F0(1:3,1:3,g,i,e) ! dF = dFe + dFp is not strictly enforced (can result in small oscillations in dP/dF)
counter = 0.0_pReal
phi_mat = 0.0_pReal
do h=1_pInt,3_pInt; do j=1_pInt,3_pInt
if (Eigval(h) == Eigval(j)) then
phi_mat(h,j) = 1.0_pReal
else
phi_mat(h,j) = sinh(Eigval(h) - Eigval(j))/(Eigval(h) - Eigval(j))
endif
if (abs(FDot_temp(h,j)) .lt. relevantStrain) then
counter = counter + 1.0_pReal
FDot_temp(h,j) = 0.0_pReal
else
FDot_temp(h,j) = crystallite_dt(g,i,e)/FDot_temp(h,j)
endif
enddo; enddo
if (counter .lt. 9.0_pReal) then
FDot_temp = FDot_temp/(9.0_pReal - counter)
endif
Tensor1 = 0.0_pReal
Tensor2 = 0.0_pReal
Tensor3 = 0.0_pReal
Tensor4 = 0.0_pReal
Tensor5 = 0.0_pReal
do h=1_pInt,3_pInt; do j=1_pInt,3_pInt
V_dir = 0.0_pReal
V_dir(h,j) = -Lp_frac*crystallite_dt(g,i,e)
V_dir = math_mul33x33(math_mul33x33(math_transpose33(Eigvec),V_dir),Eigvec)
Tensor2(1:3,1:3,h,j) = math_mul33x33(math_mul33x33(dSdFe_mat1,V_dir*phi_mat),dSdFe_mat2)
Tensor1(h,j,1:3,1:3) = Fpinv_rate(h,j)*FDot_temp ! assuming dF_old = dF_new... need full-rank Tensor1 otherwise. good only for unidirectional loading
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
Tensor1(h,j,o,p) = math_I3(h,o)*Fp_inv_current(p,j) + Tensor1(h,j,o,p) ! dF_im/dF_kl * (Fp current^-1)_mj + d(Fp current^-1)_ij/dt * dt/Fdot_kl
Tensor3(h,j,1:3,1:3) = 0.5_pReal*(math_mul33x33(C(h,j,1:3,1:3),math_transpose33(&
crystallite_subFe0(1:3,1:3,g,i,e))) + math_mul33x33(C(h,j,1:3,1:3),&
math_transpose33(crystallite_subFe0(1:3,1:3,g,i,e)))) ! dS_ij/dFe_kl
Tensor5(h,j,o,p) = math_I3(h,o)*math_I3(j,p) - math_I3(h,j)*math_I3(o,p)/3.0_pReal ! tensor to strip away volumetric components of Lp added due to numerical error
enddo; enddo; enddo; enddo
call constitutive_LpAndItsTangent(Lp_constitutive, dLp_dT_constitutive, &
crystallite_Tstar_v(1:6,g,i,e), crystallite_Temperature(g,i,e), g, i, e)
dLp_dT = math_Plain99to3333(dLp_dT_constitutive)
Tensor4 = math_mul3333xx3333(math_mul3333xx3333(math_mul3333xx3333(Tensor2,dLp_dT),&
Tensor5),Tensor3) ! applying chain rule to get F_im * dFp^-1_mj/dFe_kl
A99 = math_identity2nd(9_pInt) - math_Plain3333to99(Tensor4)
C99 = math_Plain3333to99(Tensor1) ! [I - F_im * dFp^-1_mj/dFe_op]*dFe_op/dF_kl = dF_im/dF_kl * (Fp current^-1)_mj + d(Fp current^-1)_ij/dt * dt/Fdot_kl
call math_invert(9_pInt,A99, A_inv99, AnzNegEW, error)
dFedF99 = math_mul99x99(A_inv99,C99) ! solve for dFe_ij/dF_kl
dFedF = math_Plain99to3333(dFedF99)
fixedpt_iter = 1_pInt
fixedpt_error = 1.0_pReal
do while ((fixedpt_iter .lt. 10_pInt) .and. (fixedpt_error .gt. 1e-20_pReal)) ! if solution is not accurate, use as estimate for better solution
dFedF_old99 = dFedF99
A99 = math_mul99x99(A_inv99,A99)
C99 = dFedF_old99
call math_invert(9_pInt,A99, A_inv99, AnzNegEW, error)
dFedF99 = math_mul99x99(A_inv99,C99)
fixedpt_error = maxval(abs(dFedF99 - dFedF_old99))
fixedpt_iter = fixedpt_iter + 1_pInt
enddo
dFedF = math_Plain99to3333(dFedF99)
Tensor4 = math_mul3333xx3333(Tensor4,dFedF)
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
dFedF(1:3,1:3,o,p) = math_transpose33(dFedF(1:3,1:3,o,p))
enddo; enddo
dSdF = math_mul3333xx3333(Tensor3,dFedF) ! dS/dF = dS/dFe * dFe/dF
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
crystallite_dPdF(1:3,1:3,o,p,g,i,e) = math_mul33x33(math_mul33x33(math_transpose33(&
dFedF(1:3,1:3,o,p)),math_Mandel6to33(crystallite_Tstar_v)),math_transpose33(&
Fp_inv_current)) + & ! dP/dF = dFe/dF * S * Fp^-T...
math_mul33x33(math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),&
Fp_inv_current),math_Mandel6to33(crystallite_Tstar_v)),math_mul33x33(math_inv33&
(crystallite_subF(1:3,1:3,g,i,e)),Tensor4(1:3,1:3,o,p))+Fpinv_rate*FDot_temp(o,p))& ! + Fe * S * dFp^-T/dF...
+ math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),Fp_inv_current),&
math_mul33x33(dSdF(1:3,1:3,o,p),math_transpose33(Fp_inv_current))) ! + Fe * dS/dF * Fp^-T
enddo; enddo
enddo; enddo; enddo
!$OMP END PARALLEL DO
endif
endif ! jacobian calculation
endsubroutine
!********************************************************************
! integrate stress, state and Temperature with
! 4h order explicit Runge Kutta method
!********************************************************************
subroutine crystallite_integrateStateRK4(gg,ii,ee)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use numerics, only: numerics_integrationMode
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_StateLoopDistribution
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_Ngrains, &
homogenization_maxNgrains
use constitutive, only: constitutive_sizeDotState, &
constitutive_state, &
constitutive_subState0, &
constitutive_dotState, &
constitutive_RK4dotState, &
constitutive_collectDotState, &
constitutive_dotTemperature, &
constitutive_microstructure
implicit none
real(pReal), dimension(4), parameter :: timeStepFraction = (/0.5_pReal, 0.5_pReal, 1.0_pReal, 1.0_pReal/) ! factor giving the fraction of the original timestep used for Runge Kutta Integration
real(pReal), dimension(4), parameter :: weight = (/1.0_pReal, 2.0_pReal, 2.0_pReal, 1.0_pReal/) ! weight of slope used for Runge Kutta integration
!*** input variables ***!
integer(pInt), optional, intent(in):: ee, & ! element index
ii, & ! integration point index
gg ! grain index
!*** output variables ***!
!*** local variables ***!
integer(pInt) e, & ! element index in element loop
i, & ! integration point index in ip loop
g, & ! grain index in grain loop
n, &
mySizeDotState
integer(pInt), dimension(2) :: eIter ! bounds for element iteration
integer(pInt), dimension(2,mesh_NcpElems) :: iIter, & ! bounds for ip iteration
gIter ! bounds for grain iteration
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
RK4dotTemperature ! evolution of Temperature of each grain for Runge Kutta integration
logical singleRun ! flag indicating computation for single (g,i,e) triple
if (present(ee) .and. present(ii) .and. present(gg)) then
eIter = ee
iIter(1:2,ee) = ii
gIter(1:2,ee) = gg
singleRun = .true.
else
eIter = FEsolving_execElem(1:2)
do e = eIter(1),eIter(2)
iIter(1:2,e) = FEsolving_execIP(1:2,e)
gIter(1:2,e) = [ 1_pInt,homogenization_Ngrains(mesh_element(3,e))]
enddo
singleRun = .false.
endif
! --- RESET DOTSTATE ---
!$OMP PARALLEL PRIVATE(mySizeDotState)
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- FIRST RUNGE KUTTA STEP ---
RK4dotTemperature = 0.0_pReal ! initialize Runge-Kutta dotTemperature
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_RK4dotState(g,i,e)%p = 0.0_pReal ! initialize Runge-Kutta dotState
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p /= constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e) /= crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- SECOND TO FOURTH RUNGE KUTTA STEP PLUS FINAL INTEGRATION ---
do n = 1_pInt,4_pInt
! --- state update ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
if (n < 4) then
constitutive_RK4dotState(g,i,e)%p = constitutive_RK4dotState(g,i,e)%p + weight(n)*constitutive_dotState(g,i,e)%p
RK4dotTemperature(g,i,e) = RK4dotTemperature(g,i,e) + weight(n)*crystallite_dotTemperature(g,i,e)
elseif (n == 4) then
constitutive_dotState(g,i,e)%p = (constitutive_RK4dotState(g,i,e)%p + &
weight(n)*constitutive_dotState(g,i,e)%p) / 6.0_pReal ! use weighted RKdotState for final integration
crystallite_dotTemperature(g,i,e) = (RK4dotTemperature(g,i,e) + weight(n)*crystallite_dotTemperature(g,i,e)) / 6.0_pReal
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeDotState) = constitutive_subState0(g,i,e)%p(1:mySizeDotState) &
+ constitutive_dotState(g,i,e)%p(1:mySizeDotState) * crystallite_subdt(g,i,e) * timeStepFraction(n)
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) &
+ crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e) * timeStepFraction(n)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- update dependent states ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- stress integration ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (crystallite_integrateStress(g,i,e,timeStepFraction(n))) then ! fraction of original times step
if (n == 4) then ! final integration step
#ifndef _OPENMP
if (debug_verbosity > 5 &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState at el ip g ',e,i,g
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> dotState', constitutive_dotState(g,i,e)%p(1:mySizeDotState)
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> new state', constitutive_state(g,i,e)%p(1:mySizeDotState)
write(6,*)
endif
#endif
crystallite_converged(g,i,e) = .true. ! ... converged per definition
crystallite_todo(g,i,e) = .false. ! ... integration done
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(n,numerics_integrationMode) = &
debug_StateLoopDistribution(n,numerics_integrationMode) + 1
!$OMP END CRITICAL (distributionState)
endif
endif
else ! broken stress integration
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- dot state and RK dot state---
if (n < 4) then
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), timeStepFraction(n)*crystallite_subdt(g,i,e), & ! fraction of original timestep
crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p /= constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e) /= crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
endif
enddo
!$OMP END PARALLEL
! --- CHECK CONVERGENCE ---
crystallite_todo = .false. ! done with integration
if (.not. singleRun) then ! if not requesting Integration of just a single IP
if (any(.not. crystallite_converged .and. .not. crystallite_localConstitution)) then ! any non-local not yet converged (or broken)...
crystallite_converged = crystallite_converged .and. crystallite_localConstitution ! ...restart all non-local as not converged
endif
endif
endsubroutine
!********************************************************************
! integrate stress, state and Temperature with
! 5th order Runge-Kutta Cash-Karp method with adaptive step size
! (use 5th order solution to advance = "local extrapolation")
!********************************************************************
subroutine crystallite_integrateStateRKCK45(gg,ii,ee)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_StateLoopDistribution
use numerics, only: rTol_crystalliteState, &
rTol_crystalliteTemperature, &
numerics_integrationMode
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_Ngrains, &
homogenization_maxNgrains
use constitutive, only: constitutive_sizeDotState, &
constitutive_maxSizeDotState, &
constitutive_state, &
constitutive_aTolState, &
constitutive_subState0, &
constitutive_dotState, &
constitutive_RKCK45dotState, &
constitutive_collectDotState, &
constitutive_dotTemperature, &
constitutive_microstructure
implicit none
!*** input variables ***!
integer(pInt), optional, intent(in):: ee, & ! element index
ii, & ! integration point index
gg ! grain index
!*** output variables ***!
!*** local variables ***!
integer(pInt) e, & ! element index in element loop
i, & ! integration point index in ip loop
g, & ! grain index in grain loop
n, & ! stage index in integration stage loop
mySizeDotState, & ! size of dot State
s ! state index
integer(pInt), dimension(2) :: eIter ! bounds for element iteration
integer(pInt), dimension(2,mesh_NcpElems) :: iIter, & ! bounds for ip iteration
gIter ! bounds for grain iteration
real(pReal), dimension(6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
RKCK45dotTemperature ! evolution of Temperature of each grain for Runge Kutta Cash Karp integration
real(pReal), dimension(5,5) :: a ! coefficients in Butcher tableau (used for preliminary integration in stages 2 to 6)
real(pReal), dimension(6) :: b, db ! coefficients in Butcher tableau (used for final integration and error estimate)
real(pReal), dimension(5) :: c ! coefficients in Butcher tableau (fractions of original time step in stages 2 to 6)
real(pReal), dimension(constitutive_maxSizeDotState,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
stateResiduum, & ! residuum from evolution in micrstructure
relStateResiduum ! relative residuum from evolution in microstructure
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
temperatureResiduum, & ! residuum from evolution in temperature
relTemperatureResiduum ! relative residuum from evolution in temperature
logical singleRun ! flag indicating computation for single (g,i,e) triple
! --- FILL BUTCHER TABLEAU ---
a = 0.0_pReal
b = 0.0_pReal
db = 0.0_pReal
c = 0.0_pReal
a(1,1) = 0.2_pReal
a(1,2) = 0.075_pReal
a(2,2) = 0.225_pReal
a(1,3) = 0.3_pReal
a(2,3) = -0.9_pReal
a(3,3) = 1.2_pReal
a(1,4) = -11.0_pReal / 54.0_pReal
a(2,4) = 2.5_pReal
a(3,4) = -70.0_pReal / 27.0_pReal
a(4,4) = 35.0_pReal / 27.0_pReal
a(1,5) = 1631.0_pReal / 55296.0_pReal
a(2,5) = 175.0_pReal / 512.0_pReal
a(3,5) = 575.0_pReal / 13824.0_pReal
a(4,5) = 44275.0_pReal / 110592.0_pReal
a(5,5) = 253.0_pReal / 4096.0_pReal
b(1) = 37.0_pReal / 378.0_pReal
b(3) = 250.0_pReal / 621.0_pReal
b(4) = 125.0_pReal / 594.0_pReal
b(6) = 512.0_pReal / 1771.0_pReal
db(1) = b(1) - 2825.0_pReal / 27648.0_pReal
db(3) = b(3) - 18575.0_pReal / 48384.0_pReal
db(4) = b(4) - 13525.0_pReal / 55296.0_pReal
db(5) = - 277.0_pReal / 14336.0_pReal
db(6) = b(6) - 0.25_pReal
c(1) = 0.2_pReal
c(2) = 0.3_pReal
c(3) = 0.6_pReal
c(4) = 1.0_pReal
c(5) = 0.875_pReal
! --- LOOP ITERATOR FOR ELEMENT, GRAIN, IP ---
if (present(ee) .and. present(ii) .and. present(gg)) then
eIter = ee
iIter(1:2,ee) = ii
gIter(1:2,ee) = gg
singleRun = .true.
else
eIter = FEsolving_execElem(1:2)
do e = eIter(1),eIter(2)
iIter(1:2,e) = FEsolving_execIP(1:2,e)
gIter(1:2,e) = [1_pInt,homogenization_Ngrains(mesh_element(3,e))]
enddo
singleRun = .false.
endif
! --- RESET DOTSTATE ---
!$OMP PARALLEL PRIVATE(mySizeDotState)
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- FIRST RUNGE KUTTA STEP ---
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,1x,i1)') '<< CRYST >> RUNGE KUTTA STEP',1
endif
#endif
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p /= constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e) /= crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- SECOND TO SIXTH RUNGE KUTTA STEP ---
do n = 1_pInt,5_pInt
! --- state update ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_RKCK45dotState(n,g,i,e)%p = constitutive_dotState(g,i,e)%p ! store Runge-Kutta dotState
RKCK45dotTemperature(n,g,i,e) = crystallite_dotTemperature(g,i,e) ! store Runge-Kutta dotTemperature
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (n == 1) then ! NEED TO DO THE ADDITION IN THIS LENGTHY WAY BECAUSE OF PARALLELIZATION (CAN'T USE A REDUCTION CLAUSE ON A POINTER OR USER DEFINED TYPE)
constitutive_dotState(g,i,e)%p = a(1,1) * constitutive_RKCK45dotState(1,g,i,e)%p
crystallite_dotTemperature(g,i,e) = a(1,1) * RKCK45dotTemperature(1,g,i,e)
elseif (n == 2) then
constitutive_dotState(g,i,e)%p = a(1,2) * constitutive_RKCK45dotState(1,g,i,e)%p &
+ a(2,2) * constitutive_RKCK45dotState(2,g,i,e)%p
crystallite_dotTemperature(g,i,e) = a(1,2) * RKCK45dotTemperature(1,g,i,e) &
+ a(2,2) * RKCK45dotTemperature(2,g,i,e)
elseif (n == 3) then
constitutive_dotState(g,i,e)%p = a(1,3) * constitutive_RKCK45dotState(1,g,i,e)%p &
+ a(2,3) * constitutive_RKCK45dotState(2,g,i,e)%p &
+ a(3,3) * constitutive_RKCK45dotState(3,g,i,e)%p
crystallite_dotTemperature(g,i,e) = a(1,3) * RKCK45dotTemperature(1,g,i,e) &
+ a(2,3) * RKCK45dotTemperature(2,g,i,e) &
+ a(3,3) * RKCK45dotTemperature(3,g,i,e)
elseif (n == 4) then
constitutive_dotState(g,i,e)%p = a(1,4) * constitutive_RKCK45dotState(1,g,i,e)%p &
+ a(2,4) * constitutive_RKCK45dotState(2,g,i,e)%p &
+ a(3,4) * constitutive_RKCK45dotState(3,g,i,e)%p &
+ a(4,4) * constitutive_RKCK45dotState(4,g,i,e)%p
crystallite_dotTemperature(g,i,e) = a(1,4) * RKCK45dotTemperature(1,g,i,e) &
+ a(2,4) * RKCK45dotTemperature(2,g,i,e) &
+ a(3,4) * RKCK45dotTemperature(3,g,i,e) &
+ a(4,4) * RKCK45dotTemperature(4,g,i,e)
elseif (n == 5) then
constitutive_dotState(g,i,e)%p = a(1,5) * constitutive_RKCK45dotState(1,g,i,e)%p &
+ a(2,5) * constitutive_RKCK45dotState(2,g,i,e)%p &
+ a(3,5) * constitutive_RKCK45dotState(3,g,i,e)%p &
+ a(4,5) * constitutive_RKCK45dotState(4,g,i,e)%p &
+ a(5,5) * constitutive_RKCK45dotState(5,g,i,e)%p
crystallite_dotTemperature(g,i,e) = a(1,5) * RKCK45dotTemperature(1,g,i,e) &
+ a(2,5) * RKCK45dotTemperature(2,g,i,e) &
+ a(3,5) * RKCK45dotTemperature(3,g,i,e) &
+ a(4,5) * RKCK45dotTemperature(4,g,i,e) &
+ a(5,5) * RKCK45dotTemperature(5,g,i,e)
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeDotState) = constitutive_subState0(g,i,e)%p(1:mySizeDotState) &
+ constitutive_dotState(g,i,e)%p(1:mySizeDotState) * crystallite_subdt(g,i,e)
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) &
+ crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- update dependent states ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- stress integration ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (.not. crystallite_integrateStress(g,i,e,c(n))) then ! fraction of original time step
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- dot state and RK dot state---
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,1x,i1)') '<< CRYST >> RUNGE KUTTA STEP',n+1
endif
#endif
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), c(n)*crystallite_subdt(g,i,e), & ! fraction of original timestep
crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p/=constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e)/=crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
enddo
! --- STATE UPDATE WITH ERROR ESTIMATE FOR STATE AND TEMPERATURE ---
relStateResiduum = 0.0_pReal
relTemperatureResiduum = 0.0_pReal
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_RKCK45dotState(6,g,i,e)%p = constitutive_dotState(g,i,e)%p ! store Runge-Kutta dotState
RKCK45dotTemperature(6,g,i,e) = crystallite_dotTemperature(g,i,e) ! store Runge-Kutta dotTemperature
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
! --- absolute residuum in state and temperature ---
! NEED TO DO THE ADDITION IN THIS LENGTHY WAY BECAUSE OF PARALLELIZATION
! CAN'T USE A REDUCTION CLAUSE ON A POINTER OR USER DEFINED TYPE
stateResiduum(1:mySizeDotState,g,i,e) = ( db(1) * constitutive_RKCK45dotState(1,g,i,e)%p(1:mySizeDotState) &
+ db(2) * constitutive_RKCK45dotState(2,g,i,e)%p(1:mySizeDotState) &
+ db(3) * constitutive_RKCK45dotState(3,g,i,e)%p(1:mySizeDotState) &
+ db(4) * constitutive_RKCK45dotState(4,g,i,e)%p(1:mySizeDotState) &
+ db(5) * constitutive_RKCK45dotState(5,g,i,e)%p(1:mySizeDotState) &
+ db(6) * constitutive_RKCK45dotState(6,g,i,e)%p(1:mySizeDotState)) &
* crystallite_subdt(g,i,e)
temperatureResiduum(g,i,e) = ( db(1) * RKCK45dotTemperature(1,g,i,e) &
+ db(2) * RKCK45dotTemperature(2,g,i,e) &
+ db(3) * RKCK45dotTemperature(3,g,i,e) &
+ db(4) * RKCK45dotTemperature(4,g,i,e) &
+ db(5) * RKCK45dotTemperature(5,g,i,e) &
+ db(6) * RKCK45dotTemperature(6,g,i,e)) &
* crystallite_subdt(g,i,e)
! --- dot state and dot temperature ---
constitutive_dotState(g,i,e)%p = b(1) * constitutive_RKCK45dotState(1,g,i,e)%p &
+ b(2) * constitutive_RKCK45dotState(2,g,i,e)%p &
+ b(3) * constitutive_RKCK45dotState(3,g,i,e)%p &
+ b(4) * constitutive_RKCK45dotState(4,g,i,e)%p &
+ b(5) * constitutive_RKCK45dotState(5,g,i,e)%p &
+ b(6) * constitutive_RKCK45dotState(6,g,i,e)%p
crystallite_dotTemperature(g,i,e) = b(1) * RKCK45dotTemperature(1,g,i,e) &
+ b(2) * RKCK45dotTemperature(2,g,i,e) &
+ b(3) * RKCK45dotTemperature(3,g,i,e) &
+ b(4) * RKCK45dotTemperature(4,g,i,e) &
+ b(5) * RKCK45dotTemperature(5,g,i,e) &
+ b(6) * RKCK45dotTemperature(6,g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- state and temperature update ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeDotState) = constitutive_subState0(g,i,e)%p(1:mySizeDotState) &
+ constitutive_dotState(g,i,e)%p(1:mySizeDotState) * crystallite_subdt(g,i,e)
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) &
+ crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- relative residui and state convergence ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
forall (s = 1_pInt:mySizeDotState, abs(constitutive_state(g,i,e)%p(s)) > 0.0_pReal) &
relStateResiduum(s,g,i,e) = stateResiduum(s,g,i,e) / constitutive_state(g,i,e)%p(s)
if (crystallite_Temperature(g,i,e) > 0) &
relTemperatureResiduum(g,i,e) = temperatureResiduum(g,i,e) / crystallite_Temperature(g,i,e)
!$OMP FLUSH(relStateResiduum,relTemperatureResiduum)
crystallite_todo(g,i,e) = &
( all( abs(relStateResiduum(:,g,i,e)) < rTol_crystalliteState &
.or. abs(stateResiduum(1:mySizeDotState,g,i,e)) < constitutive_aTolState(g,i,e)%p(1:mySizeDotState) ) &
.and. abs(relTemperatureResiduum(g,i,e)) < rTol_crystalliteTemperature )
#ifndef _OPENMP
if (debug_verbosity > 5_pInt &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,i8,1x,i3,1x,i3)') '<< CRYST >> updateState at el ip g ',e,i,g
write(6,*)
write(6,'(a,/,(12x,12(f12.1,1x)))') '<< CRYST >> absolute residuum tolerance', &
stateResiduum(1:mySizeDotState,g,i,e) / constitutive_aTolState(g,i,e)%p(1:mySizeDotState)
write(6,*)
write(6,'(a,/,(12x,12(f12.1,1x)))') '<< CRYST >> relative residuum tolerance', &
relStateResiduum(1:mySizeDotState,g,i,e) / rTol_crystalliteState
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> dotState', constitutive_dotState(g,i,e)%p(1:mySizeDotState)
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> new state', constitutive_state(g,i,e)%p(1:mySizeDotState)
write(6,*)
endif
#endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE DEPENDENT STATES IF RESIDUUM BELOW TOLERANCE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- FINAL STRESS INTEGRATION STEP IF RESIDUUM BELOW TOLERANCE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (crystallite_integrateStress(g,i,e)) then
crystallite_converged(g,i,e) = .true. ! ... converged per definitionem
crystallite_todo(g,i,e) = .false. ! ... integration done
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(6,numerics_integrationMode) =&
debug_StateLoopDistribution(6,numerics_integrationMode) + 1_pInt
!$OMP END CRITICAL (distributionState)
endif
else
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP END PARALLEL
! --- nonlocal convergence check ---
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,a,i2)') '<< CRYST >> ', count(crystallite_converged(:,:,:)), ' grains converged'
write(6,*)
endif
#endif
if (.not. singleRun) then ! if not requesting Integration of just a single IP
if ( any(.not. crystallite_converged .and. .not. crystallite_localConstitution)) then ! any non-local not yet converged (or broken)...
crystallite_converged = crystallite_converged .and. crystallite_localConstitution ! ...restart all non-local as not converged
endif
endif
endsubroutine
!********************************************************************
! integrate stress, state and Temperature with
! 1nd order Euler method with adaptive step size
!********************************************************************
subroutine crystallite_integrateStateAdaptiveEuler(gg,ii,ee)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_StateLoopDistribution
use numerics, only: rTol_crystalliteState, &
rTol_crystalliteTemperature, &
numerics_integrationMode
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_Ngrains, &
homogenization_maxNgrains
use constitutive, only: constitutive_sizeDotState, &
constitutive_maxSizeDotState, &
constitutive_state, &
constitutive_aTolState, &
constitutive_subState0, &
constitutive_dotState, &
constitutive_collectDotState, &
constitutive_dotTemperature, &
constitutive_microstructure
implicit none
!*** input variables ***!
integer(pInt), optional, intent(in):: ee, & ! element index
ii, & ! integration point index
gg ! grain index
!*** output variables ***!
!*** local variables ***!
integer(pInt) e, & ! element index in element loop
i, & ! integration point index in ip loop
g, & ! grain index in grain loop
mySizeDotState, & ! size of dot State
s ! state index
integer(pInt), dimension(2) :: eIter ! bounds for element iteration
integer(pInt), dimension(2,mesh_NcpElems) :: iIter, & ! bounds for ip iteration
gIter ! bounds for grain iteration
real(pReal), dimension(constitutive_maxSizeDotState,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
stateResiduum, & ! residuum from evolution in micrstructure
relStateResiduum ! relative residuum from evolution in microstructure
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
temperatureResiduum, & ! residuum from evolution in temperature
relTemperatureResiduum ! relative residuum from evolution in temperature
logical singleRun ! flag indicating computation for single (g,i,e) triple
! --- LOOP ITERATOR FOR ELEMENT, GRAIN, IP ---
if (present(ee) .and. present(ii) .and. present(gg)) then
eIter = ee
iIter(1:2,ee) = ii
gIter(1:2,ee) = gg
singleRun = .true.
else
eIter = FEsolving_execElem(1:2)
do e = eIter(1),eIter(2)
iIter(1:2,e) = FEsolving_execIP(1:2,e)
gIter(1:2,e) = [1_pInt,homogenization_Ngrains(mesh_element(3,e))]
enddo
singleRun = .false.
endif
!$OMP PARALLEL PRIVATE(mySizeDotState)
if (numerics_integrationMode < 2) then
! --- RESET DOTSTATE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- DOT STATE AND TEMPERATURE (EULER INTEGRATION) ---
stateResiduum = 0.0_pReal
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p /= constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e) /= crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- STATE UPDATE (EULER INTEGRATION) ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
stateResiduum(1:mySizeDotState,g,i,e) = - 0.5_pReal * constitutive_dotState(g,i,e)%p * crystallite_subdt(g,i,e) ! contribution to absolute residuum in state and temperature
temperatureResiduum(g,i,e) = - 0.5_pReal * crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeDotState) = constitutive_subState0(g,i,e)%p(1:mySizeDotState) &
+ constitutive_dotState(g,i,e)%p(1:mySizeDotState) * crystallite_subdt(g,i,e)
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) &
+ crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE DEPENDENT STATES (EULER INTEGRATION) ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
endif
! --- STRESS INTEGRATION (EULER INTEGRATION) ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (.not. crystallite_integrateStress(g,i,e)) then
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- DOT STATE AND TEMPERATURE (HEUN METHOD) ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p /= constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e) /= crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- ERROR ESTIMATE FOR STATE AND TEMPERATURE (HEUN METHOD) ---
relStateResiduum = 0.0_pReal
relTemperatureResiduum = 0.0_pReal
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
! --- contribution of heun step to absolute residui ---
stateResiduum(1:mySizeDotState,g,i,e) = stateResiduum(1:mySizeDotState,g,i,e) &
+ 0.5_pReal * constitutive_dotState(g,i,e)%p * crystallite_subdt(g,i,e) ! contribution to absolute residuum in state and temperature
temperatureResiduum(g,i,e) = temperatureResiduum(g,i,e) &
+ 0.5_pReal * crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
!$OMP FLUSH(stateResiduum,temperatureResiduum)
! --- relative residui ---
forall (s = 1_pInt:mySizeDotState, abs(constitutive_state(g,i,e)%p(s)) > 0.0_pReal) &
relStateResiduum(s,g,i,e) = stateResiduum(s,g,i,e) / constitutive_state(g,i,e)%p(s)
if (crystallite_Temperature(g,i,e) > 0_pInt) &
relTemperatureResiduum(g,i,e) = temperatureResiduum(g,i,e) / crystallite_Temperature(g,i,e)
!$OMP FLUSH(relStateResiduum,relTemperatureResiduum)
#ifndef _OPENMP
if (debug_verbosity > 5 &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState at el ip g ',e,i,g
write(6,*)
write(6,'(a,/,(12x,12(f12.1,1x)))') '<< CRYST >> absolute residuum tolerance', &
stateResiduum(1:mySizeDotState,g,i,e) / constitutive_aTolState(g,i,e)%p(1:mySizeDotState)
write(6,*)
write(6,'(a,/,(12x,12(f12.1,1x)))') '<< CRYST >> relative residuum tolerance', &
relStateResiduum(1:mySizeDotState,g,i,e) / rTol_crystalliteState
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> dotState', constitutive_dotState(g,i,e)%p(1:mySizeDotState) &
- 2.0_pReal * stateResiduum(1:mySizeDotState,g,i,e) / crystallite_subdt(g,i,e) ! calculate former dotstate from higher order solution and state residuum
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> new state', constitutive_state(g,i,e)%p(1:mySizeDotState)
write(6,*)
endif
#endif
! --- converged ? ---
if ( all( abs(relStateResiduum(:,g,i,e)) < rTol_crystalliteState &
.or. abs(stateResiduum(1:mySizeDotState,g,i,e)) < constitutive_aTolState(g,i,e)%p(1:mySizeDotState)) &
.and. abs(relTemperatureResiduum(g,i,e)) < rTol_crystalliteTemperature ) then
crystallite_converged(g,i,e) = .true. ! ... converged per definitionem
crystallite_todo(g,i,e) = .false. ! ... integration done
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(2,numerics_integrationMode) = debug_StateLoopDistribution(2,numerics_integrationMode) + 1
!$OMP END CRITICAL (distributionState)
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP END PARALLEL
! --- NONLOCAL CONVERGENCE CHECK ---
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,a,i2)') '<< CRYST >> ', count(crystallite_converged(:,:,:)), ' grains converged'
write(6,*)
endif
#endif
if (.not. singleRun) then ! if not requesting Integration of just a single IP
if ( any(.not. crystallite_converged .and. .not. crystallite_localConstitution)) then ! any non-local not yet converged (or broken)...
crystallite_converged = crystallite_converged .and. crystallite_localConstitution ! ...restart all non-local as not converged
endif
endif
endsubroutine
!********************************************************************
! integrate stress, state and Temperature with
! 1st order explicit Euler method
!********************************************************************
subroutine crystallite_integrateStateEuler(gg,ii,ee)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use numerics, only: numerics_integrationMode
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_StateLoopDistribution
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems
use material, only: homogenization_Ngrains
use constitutive, only: constitutive_sizeDotState, &
constitutive_state, &
constitutive_subState0, &
constitutive_dotState, &
constitutive_collectDotState, &
constitutive_dotTemperature, &
constitutive_microstructure
implicit none
!*** input variables ***!
integer(pInt), optional, intent(in):: ee, & ! element index
ii, & ! integration point index
gg ! grain index
!*** output variables ***!
!*** local variables ***!
integer(pInt) e, & ! element index in element loop
i, & ! integration point index in ip loop
g, & ! grain index in grain loop
mySizeDotState
integer(pInt), dimension(2) :: eIter ! bounds for element iteration
integer(pInt), dimension(2,mesh_NcpElems) :: iIter, & ! bounds for ip iteration
gIter ! bounds for grain iteration
logical singleRun ! flag indicating computation for single (g,i,e) triple
if (present(ee) .and. present(ii) .and. present(gg)) then
eIter = ee
iIter(1:2,ee) = ii
gIter(1:2,ee) = gg
singleRun = .true.
else
eIter = FEsolving_execElem(1:2)
do e = eIter(1),eIter(2)
iIter(1:2,e) = FEsolving_execIP(1:2,e)
gIter(1:2,e) = [1_pInt,homogenization_Ngrains(mesh_element(3,e))]
enddo
singleRun = .false.
endif
!$OMP PARALLEL PRIVATE(mySizeDotState)
if (numerics_integrationMode < 2) then
! --- RESET DOTSTATE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
! --- DOT STATE AND TEMPERATURE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
crystallite_dotTemperature(g,i,e) = constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Temperature(g,i,e),g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if ( any(constitutive_dotState(g,i,e)%p/=constitutive_dotState(g,i,e)%p) & ! NaN occured in dotState
.or. crystallite_dotTemperature(g,i,e)/=crystallite_dotTemperature(g,i,e) ) then ! NaN occured in dotTemperature
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! if broken local...
crystallite_todo(g,i,e) = .false. ! ... skip this one next time
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE STATE AND TEMPERATURE ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
mySizeDotState = constitutive_sizeDotState(g,i,e)
constitutive_state(g,i,e)%p(1:mySizeDotState) = constitutive_subState0(g,i,e)%p(1:mySizeDotState) &
+ constitutive_dotState(g,i,e)%p(1:mySizeDotState) * crystallite_subdt(g,i,e)
crystallite_Temperature(g,i,e) = crystallite_subTemperature0(g,i,e) &
+ crystallite_dotTemperature(g,i,e) * crystallite_subdt(g,i,e)
#ifndef _OPENMP
if (debug_verbosity > 5 &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState at el ip g ',e,i,g
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> dotState', constitutive_dotState(g,i,e)%p(1:mySizeDotState)
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> new state', constitutive_state(g,i,e)%p(1:mySizeDotState)
write(6,*)
endif
#endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE DEPENDENT STATES ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
enddo; enddo; enddo
!$OMP ENDDO
endif
! --- STRESS INTEGRATION ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (crystallite_integrateStress(g,i,e)) then
crystallite_converged(g,i,e) = .true.
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(1,numerics_integrationMode) = debug_StateLoopDistribution(1,numerics_integrationMode) + 1
!$OMP END CRITICAL (distributionState)
endif
else ! broken stress integration
if (.not. crystallite_localConstitution(g,i,e)) then ! if broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
!$OMP END PARALLEL
! --- CHECK NON-LOCAL CONVERGENCE ---
crystallite_todo = .false. ! done with integration
if (.not. singleRun) then ! if not requesting Integration of just a single IP
if (any(.not. crystallite_converged .and. .not. crystallite_localConstitution)) then ! any non-local not yet converged (or broken)...
crystallite_converged = crystallite_converged .and. crystallite_localConstitution ! ...restart all non-local as not converged
endif
endif
endsubroutine
!********************************************************************
! integrate stress, state and Temperature with
! adaptive 1st order explicit Euler method
! using Fixed Point Iteration to adapt the stepsize
!********************************************************************
subroutine crystallite_integrateStateFPI(gg,ii,ee)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use debug, only: debug_verbosity, &
debug_StateLoopDistribution
use numerics, only: nState, &
numerics_integrationMode
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
mesh_NcpElems
use material, only: homogenization_Ngrains
use constitutive, only: constitutive_dotState, &
constitutive_collectDotState, &
constitutive_dotTemperature, &
constitutive_microstructure, &
constitutive_previousDotState, &
constitutive_previousDotState2
implicit none
!*** input variables ***!
integer(pInt), optional, intent(in):: ee, & ! element index
ii, & ! integration point index
gg ! grain index
!*** output variables ***!
!*** local variables ***!
integer(pInt) NiterationState, & ! number of iterations in state loop
e, & ! element index in element loop
i, & ! integration point index in ip loop
g ! grain index in grain loop
integer(pInt), dimension(2) :: eIter ! bounds for element iteration
integer(pInt), dimension(2,mesh_NcpElems) :: iIter, & ! bounds for ip iteration
gIter ! bounds for grain iteration
real(pReal) dot_prod12, &
dot_prod22
logical singleRun, & ! flag indicating computation for single (g,i,e) triple
stateConverged, & ! flag indicating convergence of state integration
temperatureConverged, & ! flag indicating convergence of temperature integration
stateUpdateDone, & ! flag indicating successfull state update
temperatureUpdateDone ! flag indicating successfull temperature update
if (present(ee) .and. present(ii) .and. present(gg)) then
eIter = ee
iIter(1:2,ee) = ii
gIter(1:2,ee) = gg
singleRun = .true.
else
eIter = FEsolving_execElem(1:2)
do e = eIter(1),eIter(2)
iIter(1:2,e) = FEsolving_execIP(1:2,e)
gIter(1:2,e) = [1_pInt,homogenization_Ngrains(mesh_element(3,e))]
enddo
singleRun = .false.
endif
! --+>> PREGUESS FOR STATE <<+--
! --- RESET DOTSTATE ---
!$OMP PARALLEL
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
constitutive_previousDotState(g,i,e)%p = 0.0_pReal
constitutive_previousDotState2(g,i,e)%p = 0.0_pReal
enddo; enddo; enddo
!$OMP ENDDO
! --- DOT STATES ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- STATE & TEMPERATURE UPDATE ---
!$OMP SINGLE
crystallite_statedamper = 1.0_pReal
!$OMP END SINGLE
!$OMP DO PRIVATE(stateUpdateDone,temperatureUpdateDone,stateConverged,temperatureConverged)
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call crystallite_updateState(stateUpdateDone, stateConverged, g,i,e) ! update state
call crystallite_updateTemperature(temperatureUpdateDone, temperatureConverged, g,i,e) ! update temperature
crystallite_todo(g,i,e) = stateUpdateDone .and. temperatureUpdateDone
if ( (.not. stateUpdateDone .or. .not. temperatureUpdateDone) &
.and. .not. crystallite_localConstitution(g,i,e) ) then ! if updateState or updateTemperature signals broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE DEPENDENT STATES ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
constitutive_previousDotState2(g,i,e)%p = constitutive_previousDotState(g,i,e)%p ! age previous dotState
constitutive_previousDotState(g,i,e)%p = constitutive_dotState(g,i,e)%p ! age previous dotState
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
!$OMP END PARALLEL
! --+>> STATE LOOP <<+--
NiterationState = 0_pInt
do while (any(crystallite_todo) .and. NiterationState < nState ) ! convergence loop for crystallite
NiterationState = NiterationState + 1_pInt
!$OMP PARALLEL
! --- STRESS INTEGRATION ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
if (.not. crystallite_integrateStress(g,i,e)) then ! if broken ...
if (.not. crystallite_localConstitution(g,i,e)) then ! ... and non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ... then all non-locals skipped
!$OMP END CRITICAL (checkTodo)
else ! ... and local...
crystallite_todo(g,i,e) = .false. ! ... then skip only me
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,a)') '<< CRYST >> ', count(crystallite_todo(:,:,:)),' grains todo after stress integration'
endif
#endif
! --- DOT STATES ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_collectDotState(crystallite_Tstar_v(1:6,g,i,e), crystallite_Fe, crystallite_Fp, &
crystallite_Temperature(g,i,e), crystallite_subdt(g,i,e), crystallite_orientation, g,i,e)
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- STATE & TEMPERATURE UPDATE ---
!$OMP SINGLE
crystallite_statedamper = 1.0_pReal
!$OMP END SINGLE
!$OMP DO PRIVATE(dot_prod12,dot_prod22,stateUpdateDone,temperatureUpdateDone,stateConverged,temperatureConverged)
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
! --- state damper ---
dot_prod12 = dot_product( constitutive_dotState(g,i,e)%p - constitutive_previousDotState(g,i,e)%p, &
constitutive_previousDotState(g,i,e)%p - constitutive_previousDotState2(g,i,e)%p )
dot_prod22 = dot_product( constitutive_previousDotState(g,i,e)%p - constitutive_previousDotState2(g,i,e)%p, &
constitutive_previousDotState(g,i,e)%p - constitutive_previousDotState2(g,i,e)%p )
if ( dot_prod22 > 0.0_pReal &
.and. ( dot_prod12 < 0.0_pReal &
.or. dot_product(constitutive_dotState(g,i,e)%p, constitutive_previousDotState(g,i,e)%p) < 0.0_pReal) ) then
crystallite_statedamper(g,i,e) = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22)
!$OMP FLUSH(crystallite_statedamper)
endif
! --- updates ---
call crystallite_updateState(stateUpdateDone, stateConverged, g,i,e) ! update state
call crystallite_updateTemperature(temperatureUpdateDone, temperatureConverged, g,i,e) ! update temperature
crystallite_todo(g,i,e) = stateUpdateDone .and. temperatureUpdateDone
crystallite_converged(g,i,e) = stateConverged .and. temperatureConverged
if ( (.not. stateUpdateDone .or. .not. temperatureUpdateDone) &
.and. .not. crystallite_localConstitution(g,i,e) ) then ! if updateState or updateTemperature signals broken non-local...
!$OMP CRITICAL (checkTodo)
crystallite_todo = crystallite_todo .and. crystallite_localConstitution ! ...all non-locals skipped
!$OMP END CRITICAL (checkTodo)
elseif (stateConverged .and. temperatureConverged) then ! check (private) logicals "stateConverged" and "temperatureConverged" instead of (shared) "crystallite_converged", so no need to flush the "crystallite_converged" array
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionState)
debug_StateLoopDistribution(NiterationState,numerics_integrationMode) = &
debug_StateLoopDistribution(NiterationState,numerics_integrationMode) + 1_pInt
!$OMP END CRITICAL (distributionState)
endif
endif
endif
enddo; enddo; enddo
!$OMP ENDDO
! --- UPDATE DEPENDENT STATES ---
!$OMP DO
do e = eIter(1),eIter(2); do i = iIter(1,e),iIter(2,e); do g = gIter(1,e),gIter(2,e) ! iterate over elements, ips and grains
if (crystallite_todo(g,i,e)) then
call constitutive_microstructure(crystallite_Temperature(g,i,e), crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fp(1:3,1:3,g,i,e), g, i, e) ! update dependent state variables to be consistent with basic states
endif
constitutive_previousDotState2(g,i,e)%p = constitutive_previousDotState(g,i,e)%p ! age previous dotState
constitutive_previousDotState(g,i,e)%p = constitutive_dotState(g,i,e)%p ! age previous dotState
constitutive_dotState(g,i,e)%p = 0.0_pReal ! reset dotState to zero
enddo; enddo; enddo
!$OMP ENDDO
!$OMP END PARALLEL
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,a,i2)') '<< CRYST >> ', count(crystallite_converged(:,:,:)), &
' grains converged after state integration no. ', NiterationState
write(6,*)
endif
#endif
! --- CONVERGENCE CHECK ---
if (.not. singleRun) then ! if not requesting Integration of just a single IP
if (any(.not. crystallite_converged .and. .not. crystallite_localConstitution)) then ! any non-local not yet converged (or broken)...
crystallite_converged = crystallite_converged .and. crystallite_localConstitution ! ...restart all non-local as not converged
endif
endif
crystallite_todo = crystallite_todo .and. .not. crystallite_converged ! skip all converged
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,a)') '<< CRYST >> ', count(crystallite_converged(:,:,:)),' grains converged after non-local check'
write(6,'(a,i8,a,i2)') '<< CRYST >> ', count(crystallite_todo(:,:,:)),' grains todo after state integration no. ',&
NiterationState
write(6,*)
endif
#endif
enddo ! crystallite convergence loop
endsubroutine
!********************************************************************
! update the internal state of the constitutive law
! and tell whether state has converged
!********************************************************************
subroutine crystallite_updateState(done, converged, g, i, e)
!*** variables and functions from other modules ***!
use prec, only: pInt
use numerics, only: rTol_crystalliteState
use constitutive, only: constitutive_dotState, &
constitutive_previousDotState, &
constitutive_sizeDotState, &
constitutive_subState0, &
constitutive_state, &
constitutive_aTolState, &
constitutive_microstructure
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g
!*** input variables ***!
integer(pInt), intent(in):: e, & ! element index
i, & ! integration point index
g ! grain index
!*** output variables ***!
logical, intent(out) :: converged, & ! flag indicating if state converged
done ! flag indicating if state was updated
!*** local variables ***!
real(pReal), dimension(constitutive_sizeDotState(g,i,e)) :: &
residuum, & ! residuum from evolution of microstructure
dotState, & ! local copy of dotState
state ! local copy of relevant part of state
integer(pInt) mySize
!* start out as not done and not converged
!* and make local copies of state and dotState (needed for parallelization, since no chance of flushing a pointer)
done = .false.
converged = .false.
mySize = constitutive_sizeDotState(g,i,e)
dotState(1:mySize) = constitutive_dotState(g,i,e)%p(1:mySize)
state(1:mySize) = constitutive_state(g,i,e)%p(1:mySize)
!* correct dotState, calculate residuum and check if it is valid
dotState(1:mySize) = constitutive_dotState(g,i,e)%p(1:mySize) * crystallite_statedamper(g,i,e) &
+ constitutive_previousDotState(g,i,e)%p(1:mySize) * (1.0_pReal - crystallite_statedamper(g,i,e))
residuum = constitutive_state(g,i,e)%p(1:mySize) - constitutive_subState0(g,i,e)%p(1:mySize) &
- dotState(1:mySize) * crystallite_subdt(g,i,e)
if (any(residuum /= residuum)) then ! if NaN occured then return without changing the state
#ifndef _OPENMP
if (debug_verbosity > 4) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState encountered NaN at el ip g ',e,i,g
endif
#endif
return
endif
!* update state and set convergence flag to true if residuum is below relative/absolute tolerance, otherwise set it to false
state(1:mySize) = state(1:mySize) - residuum
done = .true.
converged = all( abs(residuum) < constitutive_aTolState(g,i,e)%p(1:mySize) &
.or. abs(residuum) < rTol_crystalliteState * abs(state(1:mySize)) )
#ifndef _OPENMP
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
if (converged) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState converged at el ip g ',e,i,g
else
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateState did not converge at el ip g ',e,i,g
endif
write(6,*)
write(6,'(a,f6.1)') '<< CRYST >> crystallite_statedamper ',crystallite_statedamper(g,i,e)
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> dotState',dotState(1:mySize)
write(6,*)
write(6,'(a,/,(12x,12(e12.5,1x)))') '<< CRYST >> new state',state(1:mySize)
write(6,*)
endif
#endif
!* sync global state and dotState with local copies
constitutive_dotState(g,i,e)%p(1:mySize) = dotState(1:mySize)
constitutive_state(g,i,e)%p(1:mySize) = state(1:mySize)
endsubroutine
!********************************************************************
! update the temperature of the grain
! and tell whether it has converged
!********************************************************************
subroutine crystallite_updateTemperature(done, converged, g, i, e)
!*** variables and functions from other modules ***!
use prec, only: pInt
use numerics, only: rTol_crystalliteTemperature
use constitutive, only: constitutive_dotTemperature
use debug, only: debug_verbosity
!*** input variables ***!
integer(pInt), intent(in):: e, & ! element index
i, & ! integration point index
g ! grain index
!*** output variables ***!
logical, intent(out) :: converged, & ! flag indicating if temperature converged
done ! flag indicating if temperature was updated
!*** local variables ***!
real(pReal) residuum ! residuum from evolution of temperature
!* start out as not done and not converged
done = .false.
converged = .false.
!* correct dotState, calculate residuum and check if it is valid
!* (if NaN occured then return without changing the temperature)
residuum = crystallite_Temperature(g,i,e) - crystallite_subTemperature0(g,i,e) &
- constitutive_dotTemperature(crystallite_Tstar_v(1:6,g,i,e),crystallite_Temperature(g,i,e),g,i,e) &
* crystallite_subdt(g,i,e)
if (residuum /= residuum) then
#ifndef _OPENMP
if (debug_verbosity > 4) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> updateTemperature encountered NaN at el ip g ',e,i,g
endif
#endif
return
endif
!* update temperature and set convergence flag to true if residuum is below relative tolerance (or zero Kelvin), otherwise set it to false
crystallite_Temperature(g,i,e) = crystallite_Temperature(g,i,e) - residuum
done = .true.
!$OMP FLUSH(crystallite_Temperature)
converged = ( crystallite_Temperature(g,i,e) == 0.0_pReal &
.or. abs(residuum) < rTol_crystalliteTemperature * crystallite_Temperature(g,i,e))
endsubroutine
!***********************************************************************
!*** calculation of stress (P) with time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
function crystallite_integrateStress(&
g,& ! grain number
i,& ! integration point number
e,& ! element number
timeFraction &
)
!*** variables and functions from other modules ***!
use prec, only: pReal, &
pInt, &
pLongInt
use numerics, only: nStress, &
aTol_crystalliteStress, &
rTol_crystalliteStress, &
iJacoLpresiduum, &
relevantStrain, &
numerics_integrationMode
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
debug_i, &
debug_g, &
debug_cumLpCalls, &
debug_cumLpTicks, &
debug_StressLoopDistribution, &
debug_LeapfrogBreakDistribution
use constitutive, only: constitutive_LpAndItsTangent, &
constitutive_homogenizedC
use math, only: math_mul33x33, &
math_mul33xx33, &
math_mul66x6, &
math_mul99x99, &
math_transpose33, &
math_inv33, &
math_invert33, &
math_invert, &
math_det33, &
math_norm33, &
math_I3, &
math_identity2nd, &
math_Mandel66to3333, &
math_Mandel6to33, &
math_mandel33to6
implicit none
!*** input variables ***!
integer(pInt), intent(in):: e, & ! element index
i, & ! integration point index
g ! grain index
real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep
!*** output variables ***!
logical crystallite_integrateStress ! flag indicating if integration suceeded
!*** local variables ***!
real(pReal), dimension(3,3):: Fg_new, & ! deformation gradient at end of timestep
Fp_current, & ! plastic deformation gradient at start of timestep
Fp_new, & ! plastic deformation gradient at end of timestep
Fe_new, & ! elastic deformation gradient at end of timestep
invFp_new, & ! inverse of Fp_new
invFp_current, & ! inverse of Fp_current
Lpguess, & ! current guess for plastic velocity gradient
Lpguess_old, & ! known last good guess for plastic velocity gradient
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
residuum, & ! current residuum of plastic velocity gradient
residuum_old, & ! last residuum of plastic velocity gradient
deltaLp, & ! direction of next guess
gradientR, & ! derivative of the residuum norm
A, &
B, &
BT, &
AB, &
BTA
real(pReal), dimension(6):: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
real(pReal), dimension(9,9):: dLp_dT_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
dT_dLp, & ! partial derivative of 2nd Piola-Kirchhoff stress
dR_dLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
inv_dR_dLp ! inverse of dRdLp
real(pReal), dimension(3,3,3,3):: C ! 4th rank elasticity tensor
real(pReal), dimension(6,6):: C_66 ! simplified 2nd rank elasticity tensor
real(pReal) p_hydro, & ! volumetric part of 2nd Piola-Kirchhoff Stress
det, & ! determinant
expectedImprovement, &
steplength0, &
steplength, &
steplength_max, &
dt ! time increment
logical error ! flag indicating an error
integer(pInt) NiterationStress, & ! number of stress integrations
dummy, &
h, &
j, &
k, &
l, &
m, &
n, &
jacoCounter ! counter to check for Jacobian update
integer(pLongInt) tick, &
tock, &
tickrate, &
maxticks
!* be pessimistic
crystallite_integrateStress = .false.
#ifndef _OPENMP
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> integrateStress at el ip g ',e,i,g
endif
#endif
!* only integrate over fraction of timestep?
if (present(timeFraction)) then
dt = crystallite_subdt(g,i,e) * timeFraction
Fg_new = crystallite_subF0(1:3,1:3,g,i,e) + (crystallite_subF(1:3,1:3,g,i,e) - crystallite_subF0(1:3,1:3,g,i,e)) * timeFraction
else
dt = crystallite_subdt(g,i,e)
Fg_new = crystallite_subF(1:3,1:3,g,i,e)
endif
!* feed local variables
Fp_current = crystallite_subFp0(1:3,1:3,g,i,e)
Lpguess_old = crystallite_Lp(1:3,1:3,g,i,e) ! consider present Lp good (i.e. worth remembering) ...
Lpguess = crystallite_Lp(1:3,1:3,g,i,e) ! ... and take it as first guess
!* inversion of Fp_current...
invFp_current = math_inv33(Fp_current)
if (all(invFp_current == 0.0_pReal)) then ! ... failed?
#ifndef _OPENMP
if (debug_verbosity > 4) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> integrateStress failed on invFp_current inversion at el ip g ',e,i,g
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,*)
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> invFp_new',math_transpose33(invFp_new(1:3,1:3))
endif
endif
#endif
return
endif
A = math_mul33x33(transpose(invFp_current), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_current)))
!* get elasticity tensor
C_66 = constitutive_homogenizedC(g,i,e)
C = math_Mandel66to3333(C_66)
!* start LpLoop with normal step length
NiterationStress = 0_pInt
steplength0 = 1.0_pReal
steplength = steplength0
steplength_max = 16.0_pReal
jacoCounter = 0_pInt
LpLoop: do
NiterationStress = NiterationStress + 1_pInt
!* too many loops required ?
if (NiterationStress > nStress) then
#ifndef _OPENMP
if (debug_verbosity > 4_pInt) then
write(6,'(a,i8,1x,i2,1x,i3)') '<< CRYST >> integrateStress reached loop limit at el ip g ',e,i,g
write(6,*)
endif
#endif
return
endif
B = math_I3 - dt*Lpguess
BT = math_transpose33(B)
AB = math_mul33x33(A,B)
BTA = math_mul33x33(BT,A)
!* calculate 2nd Piola-Kirchhoff stress tensor
Tstar_v = 0.5_pReal * math_mul66x6(C_66,math_mandel33to6(math_mul33x33(BT,AB) - math_I3))
p_hydro = sum(Tstar_v(1:3)) / 3.0_pReal
forall(n=1_pInt:3_pInt) Tstar_v(n) = Tstar_v(n) - p_hydro ! get deviatoric stress tensor
!* calculate plastic velocity gradient and its tangent according to constitutive law
if (debug_verbosity > 0) then
call system_clock(count=tick,count_rate=tickrate,count_max=maxticks)
endif
call constitutive_LpAndItsTangent(Lp_constitutive, dLp_dT_constitutive, Tstar_v, crystallite_Temperature(g,i,e), g, i, e)
if (debug_verbosity > 4) then
call system_clock(count=tock,count_rate=tickrate,count_max=maxticks)
!$OMP CRITICAL (debugTimingLpTangent)
debug_cumLpCalls = debug_cumLpCalls + 1_pInt
debug_cumLpTicks = debug_cumLpTicks + tock-tick
!$OMP FLUSH (debug_cumLpTicks)
if (tock < tick) debug_cumLpTicks = debug_cumLpTicks + maxticks
!$OMP END CRITICAL (debugTimingLpTangent)
endif
#ifndef _OPENMP
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger) &
.and. numerics_integrationMode == 1_pInt) then
write(6,'(a,i3)') '<< CRYST >> iteration ', NiterationStress
write(6,*)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lp_constitutive', math_transpose33(Lp_constitutive)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lpguess', math_transpose33(Lpguess)
endif
#endif
!* update current residuum and check for convergence of loop
residuum = Lpguess - Lp_constitutive
if (.not.(any(residuum /= residuum)) .and. & ! exclude any NaN in residuum
( maxval(abs(residuum)) < aTol_crystalliteStress .or. & ! below absolute tolerance .or.
( any(abs(dt * Lpguess) > relevantStrain) .and. & ! worth checking? .and.
maxval(abs(residuum / Lpguess), abs(dt*Lpguess) > relevantStrain) < rTol_crystalliteStress & ! below relative tolerance
) &
) &
) then
exit LpLoop
endif
!* NaN occured at regular speed -> return
if (steplength >= steplength0 .and. any(residuum /= residuum)) then
#ifndef _OPENMP
if (debug_verbosity > 4) then
write(6,'(a,i8,1x,i2,1x,i3,a,i3,a)') '<< CRYST >> integrateStress encountered NaN at el ip g ',e,i,g,&
' ; iteration ', NiterationStress,&
' >> returning..!'
endif
#endif
return
endif
if (NiterationStress > 1_pInt) then
!* not at regular speed
if (steplength <= steplength0) then
!* Armijo rule is fullfilled (norm of residuum was reduced by at least 0.01 of what was expected)
if (math_norm33(residuum) <= math_norm33(residuum_old) + 0.01_pReal * steplength * expectedImprovement) then
!* reduced step length -> return to normal step length
if (steplength < steplength0) then
steplength = steplength0
!* normal step length without change in sign of residuum -> accelerate if not yet at maximum speed
elseif (sum(residuum * residuum_old) >= 0.0_pReal .and. steplength + 1_pInt <= steplength_max) then
steplength = steplength + 1.0_pReal
endif
!* Armijo rule not fullfilled -> try smaller step size in same direction
else
steplength = 0.5_pReal * steplength
Lpguess = Lpguess_old + steplength * deltaLp
cycle LpLoop
endif
!* at high-speed
else
!* no NaN, Armijo rule fullfilled, and sign of residuum did not change -> accelerate if not yet at maximum speed
if (.not. any(residuum /= residuum) &
.and. math_norm33(residuum) <= math_norm33(residuum_old) + 0.01_pReal * steplength * expectedImprovement &
.and. sum(residuum * residuum_old) >= 0.0_pReal) then
if (steplength + 1_pInt <= steplength_max) then
steplength = steplength + 1.0_pReal
endif
!* something went wrong at accelerated speed? -> return to regular speed and try again
else
#ifndef _OPENMP
if (debug_verbosity > 5) then
write(6,'(a,i8,1x,i2,1x,i3,1x,a,i3)') '<< CRYST >> integrateStress encountered high-speed crash at el ip g ',e,i,g,&
'; iteration ', NiterationStress
endif
#endif
!* NaN occured -> use old guess and residuum
if (any(residuum /= residuum)) then
Lpguess = Lpguess_old
residuum = residuum_old
endif
steplength_max = steplength - 1.0_pReal ! limit acceleration
steplength = steplength0 ! grinding halt
jacoCounter = 0_pInt ! reset counter for Jacobian update (we want to do an update next time!)
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionLeapfrogBreak)
debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) = &
debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) + 1_pInt
!$OMP END CRITICAL (distributionLeapfrogBreak)
endif
endif
endif
endif
!* calculate Jacobian for correction term and remember current residuum and Lpguess
if (mod(jacoCounter, iJacoLpresiduum) == 0_pInt) then
dT_dLp = 0.0_pReal
do h=1_pInt,3_pInt; do j=1_pInt,3_pInt; do k=1_pInt,3_pInt; do l=1_pInt,3_pInt; do m=1_pInt,3_pInt
dT_dLp(3*(h-1)+j,3*(k-1)+l) = dT_dLp(3*(h-1)+j,3*(k-1)+l) + C(h,j,l,m) * AB(k,m) + C(h,j,m,l) * BTA(m,k)
enddo; enddo; enddo; enddo; enddo
dT_dLp = -0.5_pReal * dt * dT_dLp
dR_dLp = math_identity2nd(9_pInt) - math_mul99x99(dLp_dT_constitutive, dT_dLp)
inv_dR_dLp = 0.0_pReal
call math_invert(9_pInt,dR_dLp,inv_dR_dLp,dummy,error) ! invert dR/dLp --> dLp/dR
if (error) then
#ifndef _OPENMP
if (debug_verbosity > 4_pInt) then
write(6,'(a,i8,1x,i2,1x,i3,a,i3)') '<< CRYST >> integrateStress failed on dR/dLp inversion at el ip g ',e,i,g
if (debug_verbosity > 5_pInt &
.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,*)
write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dR_dLp',transpose(dR_dLp)
write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dT_dLp',transpose(dT_dLp)
write(6,'(a,/,9(12x,9(e15.3,1x)/))') '<< CRYST >> dLp_dT_constitutive',transpose(dLp_dT_constitutive)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> AB',math_transpose33(AB)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> BTA',math_transpose33(BTA)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lp_constitutive',math_transpose33(Lp_constitutive)
write(6,'(a,/,3(12x,3(e20.7,1x)/))') '<< CRYST >> Lpguess',math_transpose33(Lpguess)
endif
endif
#endif
return
endif
deltaLp = 0.0_pReal
do k=1_pInt,3_pInt; do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt
deltaLp(k,l) = deltaLp(k,l) - inv_dR_dLp(3_pInt*(k-1_pInt)+l,3_pInt*(m-1_pInt)+n) * residuum(m,n)
enddo; enddo; enddo; enddo
gradientR = 0.0_pReal
do k=1_pInt,3_pInt; do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt
gradientR(k,l) = gradientR(k,l) + dR_dLp(3*(k-1)+l,3_pInt*(m-1_pInt)+n) * residuum(m,n)
enddo; enddo; enddo; enddo
gradientR = gradientR / math_norm33(gradientR)
expectedImprovement = math_mul33xx33(deltaLp, gradientR)
endif
jacoCounter = jacoCounter + 1_pInt ! increase counter for jaco update
residuum_old = residuum
Lpguess_old = Lpguess
Lpguess = Lpguess + steplength * deltaLp
enddo LpLoop
!* calculate new plastic and elastic deformation gradient
invFp_new = math_mul33x33(invFp_current,B)
invFp_new = invFp_new/math_det33(invFp_new)**(1.0_pReal/3.0_pReal) ! regularize by det
call math_invert33(invFp_new,Fp_new,det,error)
if (error) then
#ifndef _OPENMP
if (debug_verbosity > 4) then
write(6,'(a,i8,1x,i2,1x,i3,a,i3)') '<< CRYST >> integrateStress failed on invFp_new inversion at el ip g ',&
e,i,g, ' ; iteration ', NiterationStress
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
write(6,*)
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> invFp_new',math_transpose33(invFp_new)
endif
endif
#endif
return
endif
Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
!* add volumetric component to 2nd Piola-Kirchhoff stress and calculate 1st Piola-Kirchhoff stress
forall (n=1_pInt:3_pInt) Tstar_v(n) = Tstar_v(n) + p_hydro
crystallite_P(1:3,1:3,g,i,e) = math_mul33x33(Fe_new, math_mul33x33(math_Mandel6to33(Tstar_v), math_transpose33(invFp_new)))
!* store local values in global variables
crystallite_Lp(1:3,1:3,g,i,e) = Lpguess
crystallite_Tstar_v(1:6,g,i,e) = Tstar_v
crystallite_Fp(1:3,1:3,g,i,e) = Fp_new
crystallite_Fe(1:3,1:3,g,i,e) = Fe_new
crystallite_invFp(1:3,1:3,g,i,e) = invFp_new
!* set return flag to true
crystallite_integrateStress = .true.
#ifndef _OPENMP
if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger) &
.and. numerics_integrationMode == 1_pInt) then
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> P / MPa',math_transpose33(crystallite_P(1:3,1:3,g,i,e))/1.0e6_pReal
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> Cauchy / MPa', &
math_mul33x33(crystallite_P(1:3,1:3,g,i,e), math_transpose33(Fg_new)) / 1.0e6_pReal / math_det33(Fg_new)
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> Fe Lp Fe^-1', &
math_transpose33(math_mul33x33(Fe_new, math_mul33x33(crystallite_Lp(1:3,1:3,g,i,e), math_inv33(Fe_new)))) ! transpose to get correct print out order
write(6,'(a,/,3(12x,3(f12.7,1x)/))') '<< CRYST >> Fp',math_transpose33(crystallite_Fp(1:3,1:3,g,i,e))
endif
#endif
if (debug_verbosity > 4) then
!$OMP CRITICAL (distributionStress)
debug_StressLoopDistribution(NiterationStress,numerics_integrationMode) = &
debug_StressLoopDistribution(NiterationStress,numerics_integrationMode) + 1_pInt
!$OMP END CRITICAL (distributionStress)
endif
endfunction
!********************************************************************
! calculates orientations and disorientations (in case of single grain ips)
!********************************************************************
subroutine crystallite_orientations()
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use math, only: math_pDecomposition, &
math_RtoQuaternion, &
math_QuaternionDisorientation, &
math_qConj
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use IO, only: IO_warning
use material, only: material_phase, &
homogenization_Ngrains, &
phase_localConstitution, &
phase_constitutionInstance
use mesh, only: mesh_element, &
mesh_ipNeighborhood, &
FE_NipNeighbors
use constitutive_nonlocal, only: constitutive_nonlocal_structure, &
constitutive_nonlocal_updateCompatibility
implicit none
!*** input variables ***!
!*** output variables ***!
!*** local variables ***!
integer(pInt) e, & ! element index
i, & ! integration point index
g, & ! grain index
n, & ! neighbor index
neighboring_e, & ! element index of my neighbor
neighboring_i, & ! integration point index of my neighbor
myPhase, & ! phase
neighboringPhase, &
myInstance, & ! instance of constitution
neighboringInstance, &
myStructure, & ! lattice structure
neighboringStructure
real(pReal), dimension(3,3) :: U, R
real(pReal), dimension(4) :: orientation
logical error
! --- CALCULATE ORIENTATION AND LATTICE ROTATION ---
!$OMP PARALLEL DO PRIVATE(error,U,R,orientation)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
do g = 1_pInt,homogenization_Ngrains(mesh_element(3,e))
call math_pDecomposition(crystallite_Fe(1:3,1:3,g,i,e), U, R, error) ! polar decomposition of Fe
if (error) then
call IO_warning(650_pInt, e, i, g)
orientation = [1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal] ! fake orientation
else
orientation = math_RtoQuaternion(transpose(R))
endif
crystallite_rotation(1:4,g,i,e) = math_QuaternionDisorientation(crystallite_orientation0(1:4,g,i,e), & ! active rotation from ori0
orientation, & ! to current orientation
0_pInt ) ! we don't want symmetry here
crystallite_orientation(1:4,g,i,e) = orientation
enddo
enddo
enddo
!$OMP END PARALLEL DO
! --- UPDATE SOME ADDITIONAL VARIABLES THAT ARE NEEDED FOR NONLOCAL MATERIAL ---
! --- we use crystallite_orientation from above, so need a seperate loop
!$OMP PARALLEL DO PRIVATE(myPhase,myInstance,myStructure,neighboring_e,neighboring_i,neighboringPhase,&
!$OMP neighboringInstance,neighboringStructure)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e)
myPhase = material_phase(1,i,e) ! get my phase
if (.not. phase_localConstitution(myPhase)) then ! if nonlocal model
myInstance = phase_constitutionInstance(myPhase)
myStructure = constitutive_nonlocal_structure(myInstance) ! get my crystal structure
! --- calculate disorientation between me and my neighbor ---
do n = 1_pInt,FE_NipNeighbors(mesh_element(2,e)) ! loop through my neighbors
neighboring_e = mesh_ipNeighborhood(1,n,i,e)
neighboring_i = mesh_ipNeighborhood(2,n,i,e)
if ((neighboring_e > 0) .and. (neighboring_i > 0)) then ! if neighbor exists
neighboringPhase = material_phase(1,neighboring_i,neighboring_e) ! get my neighbor's phase
if (.not. phase_localConstitution(neighboringPhase)) then ! neighbor got also nonlocal constitution
neighboringInstance = phase_constitutionInstance(neighboringPhase)
neighboringStructure = constitutive_nonlocal_structure(neighboringInstance) ! get my neighbor's crystal structure
if (myStructure == neighboringStructure) then ! if my neighbor has same crystal structure like me
crystallite_disorientation(:,n,1,i,e) = &
math_QuaternionDisorientation( crystallite_orientation(1:4,1,i,e), &
crystallite_orientation(1:4,1,neighboring_i,neighboring_e), &
crystallite_symmetryID(1,i,e)) ! calculate disorientation
else ! for neighbor with different phase
crystallite_disorientation(:,n,1,i,e) = (/0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal/) ! 180 degree rotation about 100 axis
endif
else ! for neighbor with local constitution
crystallite_disorientation(:,n,1,i,e) = (/-1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal/) ! homomorphic identity
endif
else ! no existing neighbor
crystallite_disorientation(:,n,1,i,e) = (/-1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal/) ! homomorphic identity
endif
enddo
! --- calculate compatibility and transmissivity between me and my neighbor ---
call constitutive_nonlocal_updateCompatibility(crystallite_orientation,i,e)
endif
enddo
enddo
!$OMP END PARALLEL DO
endsubroutine
!********************************************************************
! return results of particular grain
!********************************************************************
function crystallite_postResults(&
dt,& ! time increment
g,& ! grain number
i,& ! integration point number
e & ! element number
)
!*** variables and functions from other modules ***!
use prec, only: pInt, &
pReal
use math, only: math_QuaternionToEuler, &
math_QuaternionToAxisAngle, &
math_mul33x33, &
math_transpose33, &
math_det33, &
math_I3, &
inDeg, &
math_Mandel6to33
use mesh, only: mesh_element, &
mesh_ipVolume
use material, only: microstructure_crystallite, &
crystallite_Noutput, &
material_phase, &
material_texture, &
homogenization_Ngrains
use constitutive, only: constitutive_sizePostResults, &
constitutive_postResults
implicit none
!*** input variables ***!
integer(pInt), intent(in):: e, & ! element index
i, & ! integration point index
g ! grain index
real(pReal), intent(in):: dt ! time increment
!*** output variables ***!
real(pReal), dimension(1+crystallite_sizePostResults(microstructure_crystallite(mesh_element(4,e)))+ &
1+constitutive_sizePostResults(g,i,e)) :: crystallite_postResults
!*** local variables ***!
real(pReal), dimension(3,3) :: Ee
real(pReal) detF
integer(pInt) o,c,crystID,mySize
crystID = microstructure_crystallite(mesh_element(4,e))
crystallite_postResults = 0.0_pReal
c = 0_pInt
crystallite_postResults(c+1) = real(crystallite_sizePostResults(crystID),pReal) ! size of results from cryst
c = c + 1_pInt
do o = 1_pInt,crystallite_Noutput(crystID)
mySize = 0_pInt
select case(crystallite_output(o,crystID))
case ('phase')
mySize = 1_pInt
crystallite_postResults(c+1) = real(material_phase(g,i,e),pReal) ! phaseID of grain
case ('texture')
mySize = 1_pInt
crystallite_postResults(c+1) = real(material_texture(g,i,e),pReal) ! textureID of grain
case ('volume')
mySize = 1_pInt
detF = math_det33(crystallite_partionedF(1:3,1:3,g,i,e)) ! V_current = det(F) * V_reference
crystallite_postResults(c+1) = detF * mesh_ipVolume(i,e) / homogenization_Ngrains(mesh_element(3,e)) ! grain volume (not fraction but absolute)
case ('orientation')
mySize = 4_pInt
crystallite_postResults(c+1:c+mySize) = crystallite_orientation(1:4,g,i,e) ! grain orientation as quaternion
case ('eulerangles')
mySize = 3_pInt
crystallite_postResults(c+1:c+mySize) = inDeg * math_QuaternionToEuler(crystallite_orientation(1:4,g,i,e)) ! grain orientation as Euler angles in degree
case ('grainrotation')
mySize = 4_pInt
crystallite_postResults(c+1:c+mySize) = math_QuaternionToAxisAngle(crystallite_rotation(1:4,g,i,e)) ! grain rotation away from initial orientation as axis-angle
crystallite_postResults(c+4) = inDeg * crystallite_postResults(c+4) ! angle in degree
! remark: tensor output is of the form 11,12,13, 21,22,23, 31,32,33
! thus row index i is slow, while column index j is fast. reminder: "row is slow"
case ('defgrad','f')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_transpose33(crystallite_partionedF(1:3,1:3,g,i,e)),[mySize])
case ('e')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = 0.5_pReal * reshape((math_mul33x33( &
math_transpose33(crystallite_partionedF(1:3,1:3,g,i,e)), &
crystallite_partionedF(1:3,1:3,g,i,e)) - math_I3),[mySize])
case ('fe')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_transpose33(crystallite_Fe(1:3,1:3,g,i,e)),[mySize])
case ('ee')
Ee = 0.5_pReal * (math_mul33x33(math_transpose33(crystallite_Fe(1:3,1:3,g,i,e)), crystallite_Fe(1:3,1:3,g,i,e)) - math_I3)
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(Ee,[mySize])
case ('fp')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_transpose33(crystallite_Fp(1:3,1:3,g,i,e)),[mySize])
case ('lp')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_transpose33(crystallite_Lp(1:3,1:3,g,i,e)),[mySize])
case ('p','firstpiola','1stpiola')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_transpose33(crystallite_P(1:3,1:3,g,i,e)),[mySize])
case ('s','tstar','secondpiola','2ndpiola')
mySize = 9_pInt
crystallite_postResults(c+1:c+mySize) = reshape(math_Mandel6to33(crystallite_Tstar_v(1:6,g,i,e)),[mySize])
end select
c = c + mySize
enddo
crystallite_postResults(c+1) = real(constitutive_sizePostResults(g,i,e),pReal) ! size of constitutive results
c = c + 1_pInt
crystallite_postResults(c+1:c+constitutive_sizePostResults(g,i,e)) = constitutive_postResults(crystallite_Tstar_v(1:6,g,i,e), &
crystallite_Fe, &
crystallite_Temperature(g,i,e), &
dt, g, i, e)
c = c + constitutive_sizePostResults(g,i,e)
endfunction
END MODULE
!##############################################################