1502 lines
66 KiB
Fortran
1502 lines
66 KiB
Fortran
! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!##############################################################
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! $Id$
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!*****************************************************
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!* Module: HOMOGENIZATION_RGC *
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!*****************************************************
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!* contains: *
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!*****************************************************
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! [rgc]
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! type rgc
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! Ngrains p x q x r (cluster)
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! (output) Ngrains
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MODULE homogenization_RGC
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!*** Include other modules ***
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use prec, only: pReal,pInt
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implicit none
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character (len=*), parameter :: homogenization_RGC_label = 'rgc'
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integer(pInt), dimension(:), allocatable :: homogenization_RGC_sizeState, &
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homogenization_RGC_sizePostResults
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integer(pInt), dimension(:,:), allocatable,target :: homogenization_RGC_sizePostResult
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integer(pInt), dimension(:,:), allocatable :: homogenization_RGC_Ngrains
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real(pReal), dimension(:,:), allocatable :: homogenization_RGC_dAlpha, &
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homogenization_RGC_angles
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real(pReal), dimension(:,:,:,:), allocatable :: homogenization_RGC_orientation
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real(pReal), dimension(:), allocatable :: homogenization_RGC_xiAlpha, &
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homogenization_RGC_ciAlpha
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character(len=64), dimension(:,:), allocatable,target :: homogenization_RGC_output ! name of each post result output
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CONTAINS
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!****************************************
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!* - homogenization_RGC_init
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!* - homogenization_RGC_stateInit
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!* - homogenization_RGC_deformationPartition
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!* - homogenization_RGC_stateUpdate
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!* - homogenization_RGC_averageStressAndItsTangent
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!* - homogenization_RGC_postResults
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!****************************************
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!**************************************
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!* Module initialization *
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!**************************************
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subroutine homogenization_RGC_init(&
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file & ! file pointer to material configuration
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)
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use prec, only: pInt, pReal
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use math, only: math_Mandel3333to66, math_Voigt66to3333,math_I3,math_sampleRandomOri,math_EulerToR,inRad
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use mesh, only: mesh_maxNips,mesh_NcpElems,mesh_element,FE_Nips
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use IO
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use material
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integer(pInt), intent(in) :: file
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integer(pInt), parameter :: maxNchunks = 4
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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integer(pInt) section, maxNinstance, i,j,k,l,e, output, mySize, myInstance
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character(len=64) tag
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character(len=1024) line
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!$OMP CRITICAL (write2out)
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write(6,*)
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write(6,'(a21,a20,a12)') '<<<+- homogenization',homogenization_RGC_label,' init -+>>>'
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write(6,*) '$Id$'
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write(6,*)
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!$OMP END CRITICAL (write2out)
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maxNinstance = count(homogenization_type == homogenization_RGC_label)
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if (maxNinstance == 0) return
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allocate(homogenization_RGC_sizeState(maxNinstance)); homogenization_RGC_sizeState = 0_pInt
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allocate(homogenization_RGC_sizePostResults(maxNinstance)); homogenization_RGC_sizePostResults = 0_pInt
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allocate(homogenization_RGC_Ngrains(3,maxNinstance)); homogenization_RGC_Ngrains = 0_pInt
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allocate(homogenization_RGC_ciAlpha(maxNinstance)); homogenization_RGC_ciAlpha = 0.0_pReal
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allocate(homogenization_RGC_xiAlpha(maxNinstance)); homogenization_RGC_xiAlpha = 0.0_pReal
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allocate(homogenization_RGC_dAlpha(3,maxNinstance)); homogenization_RGC_dAlpha = 0.0_pReal
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allocate(homogenization_RGC_angles(3,maxNinstance)); homogenization_RGC_angles = 400.0_pReal
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allocate(homogenization_RGC_output(maxval(homogenization_Noutput),maxNinstance)); homogenization_RGC_output = ''
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allocate(homogenization_RGC_sizePostResult(maxval(homogenization_Noutput),maxNinstance))
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homogenization_RGC_sizePostResult = 0_pInt
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allocate(homogenization_RGC_orientation(3,3,mesh_maxNips,mesh_NcpElems))
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forall (i = 1:mesh_maxNips,e = 1:mesh_NcpElems)
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homogenization_RGC_orientation(:,:,i,e) = math_I3
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end forall
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rewind(file)
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line = ''
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section = 0
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do while (IO_lc(IO_getTag(line,'<','>')) /= material_partHomogenization) ! wind forward to <homogenization>
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read(file,'(a1024)',END=100) line
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enddo
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do ! read thru sections of phase part
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read(file,'(a1024)',END=100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
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if (IO_getTag(line,'[',']') /= '') then ! next section
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section = section + 1
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output = 0 ! reset output counter
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endif
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if (section > 0 .and. homogenization_type(section) == homogenization_RGC_label) then ! one of my sections
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i = homogenization_typeInstance(section) ! which instance of my type is present homogenization
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positions = IO_stringPos(line,maxNchunks)
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tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
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select case(tag)
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case ('(output)')
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output = output + 1
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homogenization_RGC_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
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case ('clustersize')
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homogenization_RGC_Ngrains(1,i) = IO_intValue(line,positions,2)
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homogenization_RGC_Ngrains(2,i) = IO_intValue(line,positions,3)
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homogenization_RGC_Ngrains(3,i) = IO_intValue(line,positions,4)
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case ('scalingparameter')
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homogenization_RGC_xiAlpha(i) = IO_floatValue(line,positions,2)
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case ('overproportionality')
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homogenization_RGC_ciAlpha(i) = IO_floatValue(line,positions,2)
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case ('grainsize')
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homogenization_RGC_dAlpha(1,i) = IO_floatValue(line,positions,2)
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homogenization_RGC_dAlpha(2,i) = IO_floatValue(line,positions,3)
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homogenization_RGC_dAlpha(3,i) = IO_floatValue(line,positions,4)
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case ('clusterorientation')
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homogenization_RGC_angles(1,i) = IO_floatValue(line,positions,2)
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homogenization_RGC_angles(2,i) = IO_floatValue(line,positions,3)
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homogenization_RGC_angles(3,i) = IO_floatValue(line,positions,4)
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end select
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endif
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enddo
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!*** assigning cluster orientations
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do e = 1,mesh_NcpElems
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if (homogenization_type(mesh_element(3,e)) == homogenization_RGC_label) then
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myInstance = homogenization_typeInstance(mesh_element(3,e))
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if (all (homogenization_RGC_angles(:,myInstance) >= 399.9_pReal)) then
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homogenization_RGC_orientation(:,:,1,e) = math_EulerToR(math_sampleRandomOri())
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do i = 1,FE_Nips(mesh_element(2,e))
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if (microstructure_elemhomo(mesh_element(4,e))) then
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homogenization_RGC_orientation(:,:,i,e) = homogenization_RGC_orientation(:,:,1,e)
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else
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homogenization_RGC_orientation(:,:,i,e) = math_EulerToR(math_sampleRandomOri())
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endif
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enddo
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else
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do i = 1,FE_Nips(mesh_element(2,e))
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homogenization_RGC_orientation(:,:,i,e) = math_EulerToR(homogenization_RGC_angles(:,myInstance)*inRad)
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enddo
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endif
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endif
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enddo
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100 do i = 1,maxNinstance ! sanity checks
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!$OMP CRITICAL (write2out)
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write(6,'(a15,x,i4)') 'instance: ', i
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write(6,*)
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write(6,'(a25,3(x,i8))') 'cluster size: ',(homogenization_RGC_Ngrains(j,i),j=1,3)
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write(6,'(a25,x,e10.3)') 'scaling parameter: ', homogenization_RGC_xiAlpha(i)
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write(6,'(a25,x,e10.3)') 'over-proportionality: ', homogenization_RGC_ciAlpha(i)
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write(6,'(a25,3(x,e10.3))') 'grain size: ',(homogenization_RGC_dAlpha(j,i),j=1,3)
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write(6,'(a25,3(x,e10.3))') 'cluster orientation: ',(homogenization_RGC_angles(j,i),j=1,3)
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!$OMP END CRITICAL (write2out)
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enddo
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do i = 1,maxNinstance
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do j = 1,maxval(homogenization_Noutput)
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select case(homogenization_RGC_output(j,i))
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case('constitutivework')
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mySize = 1
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case('magnitudemismatch')
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mySize = 3
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case('penaltyenergy')
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mySize = 1
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case('volumediscrepancy')
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mySize = 1
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case('averagerelaxrate')
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mySize = 1
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case('maximumrelaxrate')
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mySize = 1
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case default
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mySize = 0
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end select
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if (mySize > 0_pInt) then ! any meaningful output found
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homogenization_RGC_sizePostResult(j,i) = mySize
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homogenization_RGC_sizePostResults(i) = &
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homogenization_RGC_sizePostResults(i) + mySize
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endif
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enddo
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homogenization_RGC_sizeState(i) &
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= 3*(homogenization_RGC_Ngrains(1,i)-1)*homogenization_RGC_Ngrains(2,i)*homogenization_RGC_Ngrains(3,i) &
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+ 3*homogenization_RGC_Ngrains(1,i)*(homogenization_RGC_Ngrains(2,i)-1)*homogenization_RGC_Ngrains(3,i) &
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+ 3*homogenization_RGC_Ngrains(1,i)*homogenization_RGC_Ngrains(2,i)*(homogenization_RGC_Ngrains(3,i)-1) &
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+ 8_pInt ! (1) Average constitutive work, (2-4) Overall mismatch, (5) Average penalty energy,
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! (6) Volume discrepancy, (7) Avg relaxation rate component, (8) Max relaxation rate component
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enddo
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return
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endsubroutine
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!*********************************************************************
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!* initial homogenization state *
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!*********************************************************************
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function homogenization_RGC_stateInit(myInstance)
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use prec, only: pReal,pInt
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implicit none
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!* Definition of variables
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integer(pInt), intent(in) :: myInstance
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real(pReal), dimension(homogenization_RGC_sizeState(myInstance)) :: homogenization_RGC_stateInit
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!* Open a debugging file
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! open(1978,file='homogenization_RGC_debugging.out',status='unknown')
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homogenization_RGC_stateInit = 0.0_pReal
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return
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endfunction
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!********************************************************************
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! partition material point def grad onto constituents
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!********************************************************************
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subroutine homogenization_RGC_partitionDeformation(&
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F, & ! partioned def grad per grain
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!
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F0, & ! initial partioned def grad per grain
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avgF, & ! my average def grad
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state, & ! my state
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ip, & ! my integration point
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el & ! my element
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)
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use prec, only: pReal,pInt,p_vec
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use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,homogenization_Ngrains,homogenization_typeInstance
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use FEsolving, only: theInc,cycleCounter,theTime
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implicit none
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!* Definition of variables
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: F0
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real(pReal), dimension (3,3), intent(in) :: avgF
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type(p_vec), intent(in) :: state
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integer(pInt), intent(in) :: ip,el
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!
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real(pReal), dimension (3) :: aVect,nVect
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integer(pInt), dimension (4) :: intFace
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integer(pInt), dimension (3) :: iGrain3
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integer(pInt) homID, iGrain,iFace,i,j
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logical RGCdebug
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!
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integer(pInt), parameter :: nFace = 6
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RGCdebug = .false.
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!* Debugging the overall deformation gradient
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if (RGCdebug) then
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!$OMP CRITICAL (write2out)
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write(6,'(x,a,i3,a,i3,a)')'========== Increment: ',theInc,' Cycle: ',cycleCounter,' =========='
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write(6,'(x,a32)')'Overall deformation gradient: '
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do i = 1,3
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write(6,'(x,3(e14.8,x))')(avgF(i,j), j = 1,3)
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enddo
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write(6,*)' '
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call flush(6)
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!$OMP END CRITICAL (write2out)
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endif
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!* Compute the deformation gradient of individual grains due to relaxations
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homID = homogenization_typeInstance(mesh_element(3,el))
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F = 0.0_pReal
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do iGrain = 1,homogenization_Ngrains(mesh_element(3,el))
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iGrain3 = homogenization_RGC_grain1to3(iGrain,homID)
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do iFace = 1,nFace
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intFace = homogenization_RGC_getInterface(iFace,iGrain3) ! identifying 6 interfaces of each grain
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aVect = homogenization_RGC_relaxationVector(intFace,state,homID)! get the relaxation vectors for each interface from global relaxation vector array
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nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the normal of each interface
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forall (i=1:3,j=1:3) &
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F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! calculating deformation relaxations due to interface relaxation
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enddo
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F(:,:,iGrain) = F(:,:,iGrain) + avgF(:,:) ! resulting relaxed deformation gradient
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!* Debugging the grain deformation gradients
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if (RGCdebug) then
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!$OMP CRITICAL (write2out)
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write(6,'(x,a32,x,i3)')'Deformation gradient of grain: ',iGrain
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do i = 1,3
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write(6,'(x,3(e14.8,x))')(F(i,j,iGrain), j = 1,3)
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enddo
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write(6,*)' '
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call flush(6)
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!$OMP END CRITICAL (write2out)
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endif
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enddo
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return
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endsubroutine
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!********************************************************************
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! update the internal state of the homogenization scheme
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! and tell whether "done" and "happy" with result
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!********************************************************************
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function homogenization_RGC_updateState(&
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state, & ! my state
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state0, & ! my state at the beginning of increment
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!
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P, & ! array of current grain stresses
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F, & ! array of current grain deformation gradients
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F0, & ! array of initial grain deformation gradients
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avgF, & ! average deformation gradient
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dt, & ! time increment
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dPdF, & ! array of current grain stiffnesses
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ip, & ! my integration point
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el & ! my element
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)
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use prec, only: pReal,pInt,p_vec
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use math, only: math_invert
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use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,homogenization_typeInstance, &
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homogenization_Ngrains
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use numerics, only: absTol_RGC,relTol_RGC,absMax_RGC,relMax_RGC,pPert_RGC, &
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maxdRelax_RGC,viscPower_RGC,viscModus_RGC,refRelaxRate_RGC
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use FEsolving, only: theInc,cycleCounter,theTime
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implicit none
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!* Definition of variables
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type(p_vec), intent(inout) :: state
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type(p_vec), intent(in) :: state0
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real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: P,F,F0
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real(pReal), dimension (3,3,3,3,homogenization_maxNgrains), intent(in) :: dPdF
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real(pReal), dimension (3,3), intent(in) :: avgF
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real(pReal), intent(in) :: dt
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integer(pInt), intent(in) :: ip,el
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!
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logical, dimension(2) :: homogenization_RGC_updateState
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integer(pInt), dimension (4) :: intFaceN,intFaceP,faceID
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integer(pInt), dimension (3) :: nGDim,iGr3N,iGr3P,stresLoc
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integer(pInt), dimension (2) :: residLoc
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integer(pInt) homID,i1,i2,i3,iNum,i,j,nIntFaceTot,iGrN,iGrP,iMun,iFace,k,l,ival,ipert,iGrain,nGrain
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real(pReal), dimension (3,3,homogenization_maxNgrains) :: R,pF,pR,D,pD
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real(pReal), dimension (3,homogenization_maxNgrains) :: NN,pNN
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real(pReal), dimension (3) :: normP,normN,mornP,mornN
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real(pReal) residMax,stresMax,constitutiveWork,penaltyEnergy,volDiscrep,penDiscrep
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logical error,RGCdebug,RGCdebugJacobi,RGCcheck
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!
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integer(pInt), parameter :: nFace = 6
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!
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real(pReal), dimension(:,:), allocatable :: tract,jmatrix,jnverse,smatrix,pmatrix,rmatrix
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real(pReal), dimension(:), allocatable :: resid,relax,p_relax,p_resid,drelax
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RGCcheck = (el == 1 .and. ip == 1)
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RGCdebug = .false.
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RGCdebugJacobi = .false.
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!* -------------------------------------------------------------------------------------------------------------
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!*** Initialization of RGC update state calculation
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!* Get the dimension of the cluster (grains and interfaces)
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homID = homogenization_typeInstance(mesh_element(3,el))
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nGDim = homogenization_RGC_Ngrains(:,homID)
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nGrain = homogenization_Ngrains(mesh_element(3,el))
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nIntFaceTot = (nGDim(1)-1)*nGDim(2)*nGDim(3) + nGDim(1)*(nGDim(2)-1)*nGDim(3) &
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+ nGDim(1)*nGDim(2)*(nGDim(3)-1)
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!* Allocate the size of the global relaxation arrays/jacobian matrices depending on the size of the cluster
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allocate(resid(3*nIntFaceTot)); resid = 0.0_pReal
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allocate(tract(nIntFaceTot,3)); tract = 0.0_pReal
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allocate(relax(3*nIntFaceTot)); relax = state%p(1:3*nIntFaceTot)
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allocate(drelax(3*nIntFaceTot))
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drelax = state%p(1:3*nIntFaceTot) - state0%p(1:3*nIntFaceTot)
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!* Debugging the obtained state
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if (RGCdebug) then
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!$OMP CRITICAL (write2out)
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write(6,'(x,a30)')'Obtained state: '
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do i = 1,3*nIntFaceTot
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write(6,'(x,2(e14.8,x))')state%p(i)
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enddo
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write(6,*)' '
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!$OMP END CRITICAL (write2out)
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endif
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!* Computing interface mismatch and stress penalty tensor for all interfaces of all grains
|
|
call homogenization_RGC_stressPenalty(R,NN,avgF,F,ip,el,homID)
|
|
|
|
!* Calculating volume discrepancy and stress penalty related to overall volume discrepancy
|
|
call homogenization_RGC_volumePenalty(D,volDiscrep,F,avgF,ip,el,homID)
|
|
|
|
!* Debugging the mismatch, stress and penalties of grains
|
|
if (RGCdebug) then
|
|
!$OMP CRITICAL (write2out)
|
|
do iGrain = 1,nGrain
|
|
write(6,'(x,a30,x,i3,x,a4,3(x,e14.8))')'Mismatch magnitude of grain(',iGrain,') :',NN(1,iGrain),NN(2,iGrain),NN(3,iGrain)
|
|
write(6,*)' '
|
|
write(6,'(x,a30,x,i3)')'Stress and penalties of grain: ',iGrain
|
|
do i = 1,3
|
|
write(6,'(x,3(e14.8,x),x,3(e14.8,x),x,3(e14.8,x))')(P(i,j,iGrain), j = 1,3), &
|
|
(R(i,j,iGrain), j = 1,3), &
|
|
(D(i,j,iGrain), j = 1,3)
|
|
enddo
|
|
write(6,*)' '
|
|
enddo
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
!* End of initialization
|
|
|
|
!* -------------------------------------------------------------------------------------------------------------
|
|
!*** Computing the residual stress from the balance of traction at all (interior) interfaces
|
|
do iNum = 1,nIntFaceTot
|
|
faceID = homogenization_RGC_interface1to4(iNum,homID) ! identifying the interface ID in local coordinate system (4-dimensional index)
|
|
|
|
!* Identify the left/bottom/back grain (-|N)
|
|
iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate system (3-dimensional index)
|
|
iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate the local grain ID into global coordinate system (1-dimensional index)
|
|
intFaceN = homogenization_RGC_getInterface(2*faceID(1),iGr3N)
|
|
normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the interface normal
|
|
|
|
!* Identify the right/up/front grain (+|P)
|
|
iGr3P = iGr3N
|
|
iGr3P(faceID(1)) = iGr3N(faceID(1))+1 ! identifying the grain ID in local coordinate system (3-dimensional index)
|
|
iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate the local grain ID into global coordinate system (1-dimensional index)
|
|
intFaceP = homogenization_RGC_getInterface(2*faceID(1)-1,iGr3P)
|
|
normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the interface normal
|
|
|
|
!* Compute the residual of traction at the interface (in local system, 4-dimensional index)
|
|
do i = 1,3
|
|
tract(iNum,i) = sign(viscModus_RGC*(abs(drelax(i+3*(iNum-1)))/(refRelaxRate_RGC*dt))**viscPower_RGC, &
|
|
drelax(i+3*(iNum-1))) ! contribution from the relaxation viscosity
|
|
do j = 1,3
|
|
tract(iNum,i) = tract(iNum,i) + (P(i,j,iGrP) + R(i,j,iGrP) + D(i,j,iGrP))*normP(j) &
|
|
+ (P(i,j,iGrN) + R(i,j,iGrN) + D(i,j,iGrN))*normN(j)
|
|
! contribution from material stress P, mismatch penalty R, and volume penalty D
|
|
! projected into the interface
|
|
resid(i+3*(iNum-1)) = tract(iNum,i) ! translate the local residual into global 1-dimensional residual array
|
|
enddo
|
|
enddo
|
|
|
|
!* Debugging the residual stress
|
|
if (RGCdebug) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30,x,i3)')'Traction at interface: ',iNum
|
|
write(6,'(x,3(e14.8,x))')(tract(iNum,j), j = 1,3)
|
|
write(6,*)' '
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
enddo
|
|
!* End of residual stress calculation
|
|
|
|
!* -------------------------------------------------------------------------------------------------------------
|
|
!*** Convergence check for stress residual
|
|
stresMax = maxval(abs(P)) ! get the maximum of first Piola-Kirchhoff (material) stress
|
|
stresLoc = maxloc(abs(P)) ! get the location of the maximum stress
|
|
residMax = maxval(abs(tract)) ! get the maximum of the residual
|
|
residLoc = maxloc(abs(tract)) ! get the position of the maximum residual
|
|
|
|
!* Debugging the convergent criteria
|
|
if (RGCcheck) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a)')' '
|
|
write(6,'(x,a,x,i2,x,i4)')'RGC residual check ...',ip,el
|
|
write(6,'(x,a15,x,e14.8,x,a7,i3,x,a12,i2,i2)')'Max stress: ',stresMax, &
|
|
'@ grain',stresLoc(3),'in component',stresLoc(1),stresLoc(2)
|
|
write(6,'(x,a15,x,e14.8,x,a7,i3,x,a12,i2)')'Max residual: ',residMax, &
|
|
'@ iface',residLoc(1),'in direction',residLoc(2)
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
homogenization_RGC_updateState = .false.
|
|
!* If convergence reached => done and happy
|
|
if (residMax < relTol_RGC*stresMax .or. residMax < absTol_RGC) then
|
|
homogenization_RGC_updateState = .true.
|
|
|
|
if (RGCcheck) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a55)')'... done and happy'
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
! write(6,'(x,a,x,i3,x,a6,x,i3,x,a12)')'RGC_updateState: ip',ip,'| el',el,'converged :)'
|
|
|
|
!* Then compute/update the state for postResult, i.e., ...
|
|
!* ... all energy densities computed by time-integration
|
|
constitutiveWork = state%p(3*nIntFaceTot+1)
|
|
penaltyEnergy = state%p(3*nIntFaceTot+5)
|
|
do iGrain = 1,homogenization_Ngrains(mesh_element(3,el)) ! time-integration loop for the calculating the work and energy
|
|
do i = 1,3
|
|
do j = 1,3
|
|
constitutiveWork = constitutiveWork + P(i,j,iGrain)*(F(i,j,iGrain) - F0(i,j,iGrain))/dble(nGrain)
|
|
penaltyEnergy = penaltyEnergy + R(i,j,iGrain)*(F(i,j,iGrain) - F0(i,j,iGrain))/dble(nGrain)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
state%p(3*nIntFaceTot+1) = constitutiveWork ! the bulk mechanical/constitutive work
|
|
state%p(3*nIntFaceTot+2) = sum(NN(1,:))/dble(nGrain) ! the overall mismatch of all interface normal to e1-direction
|
|
state%p(3*nIntFaceTot+3) = sum(NN(2,:))/dble(nGrain) ! the overall mismatch of all interface normal to e2-direction
|
|
state%p(3*nIntFaceTot+4) = sum(NN(3,:))/dble(nGrain) ! the overall mismatch of all interface normal to e3-direction
|
|
state%p(3*nIntFaceTot+5) = penaltyEnergy ! the overall penalty energy
|
|
state%p(3*nIntFaceTot+6) = volDiscrep ! the overall volume discrepancy
|
|
state%p(3*nIntFaceTot+7) = sum(abs(drelax))/dt/dble(3*nIntFaceTot) ! the average rate of relaxation vectors
|
|
state%p(3*nIntFaceTot+8) = maxval(abs(drelax))/dt ! the maximum rate of relaxation vectors
|
|
|
|
if (RGCcheck) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30,x,e14.8)')'Constitutive work: ',constitutiveWork
|
|
write(6,'(x,a30,3(x,e14.8))')'Magnitude mismatch: ',sum(NN(1,:))/dble(nGrain), &
|
|
sum(NN(2,:))/dble(nGrain), &
|
|
sum(NN(3,:))/dble(nGrain)
|
|
write(6,'(x,a30,x,e14.8)')'Penalty energy: ',penaltyEnergy
|
|
write(6,'(x,a30,x,e14.8)')'Volume discrepancy: ',volDiscrep
|
|
write(6,*)''
|
|
write(6,'(x,a30,x,e14.8)')'Maximum relaxation rate: ',maxval(abs(drelax))/dt
|
|
write(6,'(x,a30,x,e14.8)')'Average relaxation rate: ',sum(abs(drelax))/dt/dble(3*nIntFaceTot)
|
|
write(6,*)''
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
deallocate(tract,resid,relax,drelax)
|
|
return
|
|
|
|
!* If residual blows-up => done but unhappy
|
|
elseif (residMax > relMax_RGC*stresMax .or. residMax > absMax_RGC) then
|
|
!* Try to restart when residual blows up exceeding maximum bound
|
|
homogenization_RGC_updateState = (/.true.,.false./) ! with direct cut-back
|
|
|
|
if (RGCcheck) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a55)')'... broken'
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
deallocate(tract,resid,relax,drelax)
|
|
return
|
|
|
|
!* Otherwise, proceed with computing the Jacobian and state update
|
|
else
|
|
|
|
if (RGCcheck) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a55)')'... not yet done'
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
endif
|
|
!*** End of convergence check for residual stress
|
|
|
|
!* -------------------------------------------------------------------------------------------------------------
|
|
!*** Construct the global Jacobian matrix for updating the global relaxation vector array when convergence is not yet reached ...
|
|
!* ... of the constitutive stress tangent,
|
|
!* assembled from dPdF or material constitutive model "smatrix"
|
|
allocate(smatrix(3*nIntFaceTot,3*nIntFaceTot)); smatrix = 0.0_pReal
|
|
do iNum = 1,nIntFaceTot
|
|
faceID = homogenization_RGC_interface1to4(iNum,homID) ! assembling of local dPdF into global Jacobian matrix
|
|
|
|
!* Identify the left/bottom/back grain (-|N)
|
|
iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate sytem
|
|
iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate into global grain ID
|
|
intFaceN = homogenization_RGC_getInterface(2*faceID(1),iGr3N) ! identifying the connecting interface in local coordinate system
|
|
normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the interface normal
|
|
do iFace = 1,nFace
|
|
intFaceN = homogenization_RGC_getInterface(iFace,iGr3N) ! identifying all interfaces that influence relaxation of the above interface
|
|
mornN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get normal of the interfaces
|
|
iMun = homogenization_RGC_interface4to1(intFaceN,homID) ! translate the interfaces ID into local 4-dimensional index
|
|
if (iMun .gt. 0) then ! get the corresponding tangent
|
|
forall(i=1:3,j=1:3,k=1:3,l=1:3) &
|
|
smatrix(3*(iNum-1)+i,3*(iMun-1)+j) = smatrix(3*(iNum-1)+i,3*(iMun-1)+j) + dPdF(i,k,j,l,iGrN)*normN(k)*mornN(l)
|
|
! projecting the material tangent dPdF into the interface
|
|
! to obtain the Jacobian matrix contribution of dPdF
|
|
endif
|
|
enddo
|
|
|
|
!* Identify the right/up/front grain (+|P)
|
|
iGr3P = iGr3N
|
|
iGr3P(faceID(1)) = iGr3N(faceID(1))+1 ! identifying the grain ID in local coordinate sytem
|
|
iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate into global grain ID
|
|
intFaceP = homogenization_RGC_getInterface(2*faceID(1)-1,iGr3P) ! identifying the connecting interface in local coordinate system
|
|
normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the interface normal
|
|
do iFace = 1,nFace
|
|
intFaceP = homogenization_RGC_getInterface(iFace,iGr3P) ! identifying all interfaces that influence relaxation of the above interface
|
|
mornP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get normal of the interfaces
|
|
iMun = homogenization_RGC_interface4to1(intFaceP,homID) ! translate the interfaces ID into local 4-dimensional index
|
|
if (iMun .gt. 0) then ! get the corresponding tangent
|
|
forall(i=1:3,j=1:3,k=1:3,l=1:3) &
|
|
smatrix(3*(iNum-1)+i,3*(iMun-1)+j) = smatrix(3*(iNum-1)+i,3*(iMun-1)+j) + dPdF(i,k,j,l,iGrP)*normP(k)*mornP(l)
|
|
endif
|
|
enddo
|
|
enddo
|
|
|
|
!* Debugging the global Jacobian matrix of stress tangent
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Jacobian matrix of stress'
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,100(e10.4,x))')(smatrix(i,j), j = 1,3*nIntFaceTot)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* ... of the stress penalty tangent (mismatch penalty and volume penalty,
|
|
!* computed using numerical perturbation method) "pmatrix"
|
|
allocate(pmatrix(3*nIntFaceTot,3*nIntFaceTot)); pmatrix = 0.0_pReal
|
|
allocate(p_relax(3*nIntFaceTot)); p_relax = 0.0_pReal
|
|
allocate(p_resid(3*nIntFaceTot)); p_resid = 0.0_pReal
|
|
do ipert = 1,3*nIntFaceTot
|
|
p_relax = relax
|
|
p_relax(ipert) = relax(ipert) + pPert_RGC ! perturb the relaxation vector
|
|
state%p(1:3*nIntFaceTot) = p_relax
|
|
call homogenization_RGC_grainDeformation(pF,F0,avgF,state,ip,el) ! compute the grains deformation from perturbed state
|
|
call homogenization_RGC_stressPenalty(pR,pNN,avgF,pF,ip,el,homID) ! compute stress penalty due to interface mismatch from perturbed state
|
|
call homogenization_RGC_volumePenalty(pD,volDiscrep,pF,avgF,ip,el,homID)! compute stress penalty due to volume discrepancy from perturbed state
|
|
|
|
!* Computing the global stress residual array from the perturbed state
|
|
p_resid = 0.0_pReal
|
|
do iNum = 1,nIntFaceTot
|
|
faceID = homogenization_RGC_interface1to4(iNum,homID) ! identifying the interface ID in local coordinate system (4-dimensional index)
|
|
|
|
!* Identify the left/bottom/back grain (-|N)
|
|
iGr3N = faceID(2:4) ! identifying the grain ID in local coordinate system (3-dimensional index)
|
|
iGrN = homogenization_RGC_grain3to1(iGr3N,homID) ! translate the local grain ID into global coordinate system (1-dimensional index)
|
|
intFaceN = homogenization_RGC_getInterface(2*faceID(1),iGr3N) ! identifying the interface ID of the grain
|
|
normN = homogenization_RGC_interfaceNormal(intFaceN,ip,el) ! get the corresponding interface normal
|
|
|
|
!* Identify the right/up/front grain (+|P)
|
|
iGr3P = iGr3N
|
|
iGr3P(faceID(1)) = iGr3N(faceID(1))+1 ! identifying the grain ID in local coordinate system (3-dimensional index)
|
|
iGrP = homogenization_RGC_grain3to1(iGr3P,homID) ! translate the local grain ID into global coordinate system (1-dimensional index)
|
|
intFaceP = homogenization_RGC_getInterface(2*faceID(1)-1,iGr3P) ! identifying the interface ID of the grain
|
|
normP = homogenization_RGC_interfaceNormal(intFaceP,ip,el) ! get the corresponding normal
|
|
|
|
!* Compute the residual stress (contribution of mismatch and volume penalties) from perturbed state at all interfaces
|
|
do i = 1,3
|
|
do j = 1,3
|
|
p_resid(i+3*(iNum-1)) = p_resid(i+3*(iNum-1)) + (pR(i,j,iGrP) - R(i,j,iGrP))*normP(j) &
|
|
+ (pR(i,j,iGrN) - R(i,j,iGrN))*normN(j) &
|
|
+ (pD(i,j,iGrP) - D(i,j,iGrP))*normP(j) &
|
|
+ (pD(i,j,iGrN) - D(i,j,iGrN))*normN(j)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
pmatrix(:,ipert) = p_resid/pPert_RGC
|
|
enddo
|
|
|
|
!* Debugging the global Jacobian matrix of penalty tangent
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Jacobian matrix of penalty'
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,100(e10.4,x))')(pmatrix(i,j), j = 1,3*nIntFaceTot)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* ... of the numerical viscosity traction "rmatrix"
|
|
allocate(rmatrix(3*nIntFaceTot,3*nIntFaceTot)); rmatrix = 0.0_pReal
|
|
forall (i=1:3*nIntFaceTot) &
|
|
rmatrix(i,i) = viscModus_RGC*viscPower_RGC/(refRelaxRate_RGC*dt)* &
|
|
(abs(drelax(i))/(refRelaxRate_RGC*dt))**(viscPower_RGC - 1.0_pReal)
|
|
! tangent due to numerical viscosity traction appears
|
|
! only in the main diagonal term
|
|
|
|
!* Debugging the global Jacobian matrix of numerical viscosity tangent
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Jacobian matrix of penalty'
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,100(e10.4,x))')(rmatrix(i,j), j = 1,3*nIntFaceTot)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* The overall Jacobian matrix summarizing contributions of smatrix, pmatrix, rmatrix
|
|
allocate(jmatrix(3*nIntFaceTot,3*nIntFaceTot)); jmatrix = smatrix + pmatrix + rmatrix
|
|
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Jacobian matrix (total)'
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,100(e10.4,x))')(jmatrix(i,j), j = 1,3*nIntFaceTot)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!*** End of construction and assembly of Jacobian matrix
|
|
|
|
!* -------------------------------------------------------------------------------------------------------------
|
|
!*** Computing the update of the state variable (relaxation vectors) using the Jacobian matrix
|
|
allocate(jnverse(3*nIntFaceTot,3*nIntFaceTot)); jnverse = 0.0_pReal
|
|
call math_invert(3*nIntFaceTot,jmatrix,jnverse,ival,error) ! Compute the inverse of the overall Jacobian matrix
|
|
|
|
!* Debugging the inverse Jacobian matrix
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Jacobian inverse'
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,100(e10.4,x))')(jnverse(i,j), j = 1,3*nIntFaceTot)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* Calculate the state update (global relaxation vectors) for the next Newton-Raphson iteration
|
|
drelax = 0.0_pReal
|
|
do i = 1,3*nIntFaceTot
|
|
do j = 1,3*nIntFaceTot
|
|
drelax(i) = drelax(i) - jnverse(i,j)*resid(j) ! Calculate the correction for the state variable
|
|
enddo
|
|
enddo
|
|
relax = relax + drelax ! Updateing the state variable for the next iteration
|
|
state%p(1:3*nIntFaceTot) = relax
|
|
if (any(abs(drelax(:)) > maxdRelax_RGC)) then ! Forcing cutback when the incremental change of relaxation vector becomes too large
|
|
homogenization_RGC_updateState = (/.true.,.false./)
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a,x,i3,x,a,x,i3,x,a)')'RGC_updateState: ip',ip,'| el',el,'enforces cutback'
|
|
write(6,'(x,a,x,e14.8)')'due to large relaxation change =',maxval(abs(drelax))
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* Debugging the return state
|
|
if (RGCdebugJacobi) then
|
|
!$OMP CRITICAL (write2out)
|
|
write(6,'(x,a30)')'Returned state: '
|
|
do i = 1,3*nIntFaceTot
|
|
write(6,'(x,2(e14.8,x))')state%p(i)
|
|
enddo
|
|
write(6,*)' '
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
deallocate(tract,resid,jmatrix,jnverse,relax,drelax,pmatrix,smatrix,p_relax,p_resid)
|
|
!*** End of calculation of state update
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! derive average stress and stiffness from constituent quantities
|
|
!********************************************************************
|
|
subroutine homogenization_RGC_averageStressAndItsTangent(&
|
|
avgP, & ! average stress at material point
|
|
dAvgPdAvgF, & ! average stiffness at material point
|
|
!
|
|
P, & ! array of current grain stresses
|
|
dPdF, & ! array of current grain stiffnesses
|
|
ip, & ! my integration point
|
|
el & ! my element
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,homogenization_Ngrains,homogenization_typeInstance
|
|
use math, only: math_Plain3333to99
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3,3), intent(out) :: avgP
|
|
real(pReal), dimension (3,3,3,3), intent(out) :: dAvgPdAvgF
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: P
|
|
real(pReal), dimension (3,3,3,3,homogenization_maxNgrains), intent(in) :: dPdF
|
|
real(pReal), dimension (9,9) :: dPdF99
|
|
integer(pInt), intent(in) :: ip,el
|
|
!
|
|
logical homogenization_RGC_stateUpdate,RGCdebug
|
|
integer(pInt) homID, i, j, Ngrains, iGrain
|
|
|
|
RGCdebug = .false. !(ip == 1 .and. el == 1)
|
|
|
|
homID = homogenization_typeInstance(mesh_element(3,el))
|
|
Ngrains = homogenization_Ngrains(mesh_element(3,el))
|
|
|
|
!* Debugging the grain tangent
|
|
if (RGCdebug) then
|
|
!$OMP CRITICAL (write2out)
|
|
do iGrain = 1,Ngrains
|
|
dPdF99 = math_Plain3333to99(dPdF(:,:,:,:,iGrain))
|
|
write(6,'(x,a30,x,i3)')'Stress tangent of grain: ',iGrain
|
|
do i = 1,9
|
|
write(6,'(x,(e14.8,x))') (dPdF99(i,j), j = 1,9)
|
|
enddo
|
|
write(6,*)' '
|
|
enddo
|
|
call flush(6)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
!* Computing the average first Piola-Kirchhoff stress P and the average tangent dPdF
|
|
avgP = sum(P,3)/dble(Ngrains)
|
|
dAvgPdAvgF = sum(dPdF,5)/dble(Ngrains)
|
|
|
|
return
|
|
|
|
endsubroutine
|
|
|
|
!********************************************************************
|
|
! derive average stress and stiffness from constituent quantities
|
|
!********************************************************************
|
|
function homogenization_RGC_averageTemperature(&
|
|
Temperature, & ! temperature
|
|
ip, & ! my integration point
|
|
el & ! my element
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains, homogenization_Ngrains
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (homogenization_maxNgrains), intent(in) :: Temperature
|
|
integer(pInt), intent(in) :: ip,el
|
|
real(pReal) homogenization_RGC_averageTemperature
|
|
integer(pInt) homID, i, Ngrains
|
|
|
|
!* Computing the average temperature
|
|
Ngrains = homogenization_Ngrains(mesh_element(3,el))
|
|
homogenization_RGC_averageTemperature = sum(Temperature(1:Ngrains))/dble(Ngrains)
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! return array of homogenization results for post file inclusion
|
|
!********************************************************************
|
|
pure function homogenization_RGC_postResults(&
|
|
state, & ! my state
|
|
ip, & ! my integration point
|
|
el & ! my element
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element
|
|
use material, only: homogenization_typeInstance,homogenization_Noutput,homogenization_Ngrains
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
type(p_vec), intent(in) :: state
|
|
integer(pInt), intent(in) :: ip,el
|
|
!
|
|
integer(pInt) homID,o,c,nIntFaceTot
|
|
real(pReal), dimension(homogenization_RGC_sizePostResults(homogenization_typeInstance(mesh_element(3,el)))) :: &
|
|
homogenization_RGC_postResults
|
|
|
|
homID = homogenization_typeInstance(mesh_element(3,el))
|
|
nIntFaceTot = (homogenization_RGC_Ngrains(1,homID)-1)*homogenization_RGC_Ngrains(2,homID)*homogenization_RGC_Ngrains(3,homID) + &
|
|
homogenization_RGC_Ngrains(1,homID)*(homogenization_RGC_Ngrains(2,homID)-1)*homogenization_RGC_Ngrains(3,homID) + &
|
|
homogenization_RGC_Ngrains(1,homID)*homogenization_RGC_Ngrains(2,homID)*(homogenization_RGC_Ngrains(3,homID)-1)
|
|
|
|
c = 0_pInt
|
|
homogenization_RGC_postResults = 0.0_pReal
|
|
do o = 1,homogenization_Noutput(mesh_element(3,el))
|
|
select case(homogenization_RGC_output(o,homID))
|
|
case('constitutivework')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+1)
|
|
c = c + 1
|
|
case('magnitudemismatch')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+2)
|
|
homogenization_RGC_postResults(c+2) = state%p(3*nIntFaceTot+3)
|
|
homogenization_RGC_postResults(c+3) = state%p(3*nIntFaceTot+4)
|
|
c = c + 3
|
|
case('penaltyenergy')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+5)
|
|
c = c + 1
|
|
case('volumediscrepancy')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+6)
|
|
c = c + 1
|
|
case('averagerelaxrate')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+7)
|
|
c = c + 1
|
|
case('maximumrelaxrate')
|
|
homogenization_RGC_postResults(c+1) = state%p(3*nIntFaceTot+8)
|
|
c = c + 1
|
|
end select
|
|
enddo
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to calculate stress-like penalty due to deformation mismatch
|
|
!********************************************************************
|
|
subroutine homogenization_RGC_stressPenalty(&
|
|
rPen, & ! stress-like penalty
|
|
nMis, & ! total amount of mismatch
|
|
!
|
|
avgF, & ! initial effective stretch tensor
|
|
fDef, & ! deformation gradients
|
|
ip, & ! integration point
|
|
el, & ! element
|
|
homID & ! homogenization ID
|
|
)
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element
|
|
use constitutive, only: constitutive_homogenizedC
|
|
use math, only: math_civita,math_invert3x3
|
|
use material, only: homogenization_maxNgrains,homogenization_Ngrains
|
|
use numerics, only: xSmoo_RGC
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: rPen
|
|
real(pReal), dimension (3,homogenization_maxNgrains), intent(out) :: nMis
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef
|
|
real(pReal), dimension (3,3), intent(in) :: avgF
|
|
integer(pInt), intent(in) :: ip,el
|
|
integer(pInt), dimension (4) :: intFace
|
|
integer(pInt), dimension (3) :: iGrain3,iGNghb3,nGDim
|
|
real(pReal), dimension (3,3) :: gDef,nDef,avgC
|
|
real(pReal), dimension (3) :: nVect,surfCorr
|
|
real(pReal), dimension (2) :: Gmoduli
|
|
integer(pInt) homID,iGrain,iGNghb,iFace,i,j,k,l,m
|
|
real(pReal) muGrain,muGNghb,nDefNorm,xiAlpha,ciAlpha,bgGrain,bgGNghb,detF
|
|
!
|
|
integer(pInt), parameter :: nFace = 6
|
|
real(pReal), parameter :: nDefToler = 1.0e-10
|
|
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
|
|
rPen = 0.0_pReal
|
|
nMis = 0.0_pReal
|
|
|
|
!* Get the correction factor the modulus of penalty stress representing the evolution of area of the interfaces due to deformations
|
|
surfCorr = homogenization_RGC_surfaceCorrection(avgF,ip,el)
|
|
|
|
!* Debugging the surface correction factor
|
|
! if (ip == 1 .and. el == 1) then
|
|
! write(6,'(x,a20,2(x,i3))')'Correction factor: ',ip,el
|
|
! write(6,'(x,3(e10.4,x))')(surfCorr(i), i = 1,3)
|
|
! endif
|
|
|
|
!* -------------------------------------------------------------------------------------------------------------
|
|
!*** Computing the mismatch and penalty stress tensor of all grains
|
|
do iGrain = 1,homogenization_Ngrains(mesh_element(3,el))
|
|
Gmoduli = homogenization_RGC_equivalentModuli(iGrain,ip,el)
|
|
muGrain = Gmoduli(1) ! collecting the equivalent shear modulus of grain
|
|
bgGrain = Gmoduli(2) ! and the lengthh of Burgers vector
|
|
iGrain3 = homogenization_RGC_grain1to3(iGrain,homID) ! get the grain ID in local 3-dimensional index (x,y,z)-position
|
|
|
|
!* Looping over all six interfaces of each grain
|
|
do iFace = 1,nFace
|
|
intFace = homogenization_RGC_getInterface(iFace,iGrain3) ! get the 4-dimensional index of the interface in local numbering system of the grain
|
|
nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the interface normal
|
|
iGNghb3 = iGrain3 ! identify the neighboring grain across the interface
|
|
iGNghb3(abs(intFace(1))) = iGNghb3(abs(intFace(1))) + int(dble(intFace(1))/dble(abs(intFace(1))))
|
|
if (iGNghb3(1) < 1) iGNghb3(1) = nGDim(1) ! with periodicity along e1 direction
|
|
if (iGNghb3(1) > nGDim(1)) iGNghb3(1) = 1
|
|
if (iGNghb3(2) < 1) iGNghb3(2) = nGDim(2) ! with periodicity along e2 direction
|
|
if (iGNghb3(2) > nGDim(2)) iGNghb3(2) = 1
|
|
if (iGNghb3(3) < 1) iGNghb3(3) = nGDim(3) ! with periodicity along e3 direction
|
|
if (iGNghb3(3) > nGDim(3)) iGNghb3(3) = 1
|
|
iGNghb = homogenization_RGC_grain3to1(iGNghb3,homID) ! get the ID of the neighboring grain
|
|
Gmoduli = homogenization_RGC_equivalentModuli(iGNghb,ip,el) ! collecting the shear modulus and Burgers vector of the neighbor
|
|
muGNghb = Gmoduli(1)
|
|
bgGNghb = Gmoduli(2)
|
|
gDef = 0.5_pReal*(fDef(:,:,iGNghb) - fDef(:,:,iGrain)) ! compute the difference/jump in deformation gradeint across the neighbor
|
|
|
|
!* Compute the mismatch tensor of all interfaces
|
|
nDefNorm = 0.0_pReal
|
|
nDef = 0.0_pReal
|
|
do i = 1,3
|
|
do j = 1,3
|
|
do k = 1,3
|
|
do l = 1,3
|
|
nDef(i,j) = nDef(i,j) - nVect(k)*gDef(i,l)*math_civita(j,k,l)! compute the interface mismatch tensor from the jump of deformation gradient
|
|
enddo
|
|
enddo
|
|
nDefNorm = nDefNorm + nDef(i,j)*nDef(i,j) ! compute the norm of the mismatch tensor
|
|
enddo
|
|
enddo
|
|
nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! approximation to zero mismatch if mismatch is zero (singularity)
|
|
nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm
|
|
! total amount of mismatch experienced by the grain (at all six interfaces)
|
|
|
|
!* Debugging the mismatch tensor
|
|
! if (ip == 1 .and. el == 1) then
|
|
! write(6,'(x,a20,i2,x,a20,x,i3)')'Mismatch to face: ',intFace(1),'neighbor grain: ',iGNghb
|
|
! do i = 1,3
|
|
! write(6,'(x,3(e10.4,x))')(nDef(i,j), j = 1,3)
|
|
! enddo
|
|
! write(6,'(x,a20,e10.4))')'with magnitude: ',nDefNorm
|
|
! endif
|
|
|
|
!* Compute the stress penalty of all interfaces
|
|
do i = 1,3
|
|
do j = 1,3
|
|
do k = 1,3
|
|
do l = 1,3
|
|
rPen(i,j,iGrain) = rPen(i,j,iGrain) + 0.5_pReal*(muGrain*bgGrain + muGNghb*bgGNghb)*homogenization_RGC_xiAlpha(homID) &
|
|
*surfCorr(abs(intFace(1)))/homogenization_RGC_dAlpha(abs(intFace(1)),homID) &
|
|
*cosh(homogenization_RGC_ciAlpha(homID)*nDefNorm) &
|
|
*0.5_pReal*nVect(l)*nDef(i,k)/nDefNorm*math_civita(k,l,j) &
|
|
*tanh(nDefNorm/xSmoo_RGC)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
!* Debugging the stress-like penalty
|
|
! if (ip == 1 .and. el == 1) then
|
|
! write(6,'(x,a20,i2)')'Penalty of grain: ',iGrain
|
|
! do i = 1,3
|
|
! write(6,'(x,3(e10.4,x))')(rPen(i,j,iGrain), j = 1,3)
|
|
! enddo
|
|
! endif
|
|
|
|
enddo
|
|
!*** End of mismatch and penalty stress tensor calculation
|
|
|
|
return
|
|
|
|
endsubroutine
|
|
|
|
!********************************************************************
|
|
! subroutine to calculate stress-like penalty due to volume discrepancy
|
|
!********************************************************************
|
|
subroutine homogenization_RGC_volumePenalty(&
|
|
vPen, & ! stress-like penalty due to volume
|
|
vDiscrep, & ! total volume discrepancy
|
|
!
|
|
fDef, & ! deformation gradients
|
|
fAvg, & ! overall deformation gradient
|
|
ip, & ! integration point
|
|
el, & ! element
|
|
homID & ! homogenization ID
|
|
)
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element
|
|
use math, only: math_det3x3,math_inv3x3
|
|
use material, only: homogenization_maxNgrains,homogenization_Ngrains
|
|
use numerics, only: maxVolDiscr_RGC,volDiscrMod_RGC,volDiscrPow_RGC
|
|
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: vPen
|
|
real(pReal), intent(out) :: vDiscrep
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: fDef
|
|
real(pReal), dimension (3,3), intent(in) :: fAvg
|
|
integer(pInt), intent(in) :: ip,el
|
|
real(pReal), dimension (homogenization_maxNgrains) :: gVol
|
|
integer(pInt) homID,iGrain,nGrain,i,j
|
|
!
|
|
nGrain = homogenization_Ngrains(mesh_element(3,el))
|
|
|
|
!* Compute the volumes of grains and of cluster
|
|
vDiscrep = math_det3x3(fAvg) ! compute the volume of the cluster
|
|
do iGrain = 1,nGrain
|
|
gVol(iGrain) = math_det3x3(fDef(:,:,iGrain)) ! compute the volume of individual grains
|
|
vDiscrep = vDiscrep - gVol(iGrain)/dble(nGrain) ! calculate the difference/dicrepancy between
|
|
! the volume of the cluster and the the total volume of grains
|
|
enddo
|
|
|
|
!* Calculate the stress and penalty due to volume discrepancy
|
|
vPen = 0.0_pReal
|
|
do iGrain = 1,nGrain
|
|
vPen(:,:,iGrain) = -1.0_pReal/dble(nGrain)*volDiscrMod_RGC*volDiscrPow_RGC/maxVolDiscr_RGC* &
|
|
sign((abs(vDiscrep)/maxVolDiscr_RGC)**(volDiscrPow_RGC - 1.0),vDiscrep)* &
|
|
gVol(iGrain)*transpose(math_inv3x3(fDef(:,:,iGrain)))
|
|
|
|
!* Debugging the stress-like penalty of volume discrepancy
|
|
! if (ip == 1 .and. el == 1) then
|
|
! write(6,'(x,a30,i2)')'Volume penalty of grain: ',iGrain
|
|
! do i = 1,3
|
|
! write(6,'(x,3(e10.4,x))')(vPen(i,j,iGrain), j = 1,3)
|
|
! enddo
|
|
! endif
|
|
|
|
enddo
|
|
|
|
return
|
|
|
|
endsubroutine
|
|
|
|
!********************************************************************
|
|
! subroutine to compute the correction factor due to surface area evolution
|
|
!********************************************************************
|
|
function homogenization_RGC_surfaceCorrection(&
|
|
avgF, & ! average deformation gradient
|
|
ip, & ! my IP
|
|
el & ! my element
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use math, only: math_invert3x3,math_mul33x33
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension(3,3), intent(in) :: avgF
|
|
real(pReal), dimension(3) :: homogenization_RGC_surfaceCorrection
|
|
integer(pInt), intent(in) :: ip,el
|
|
real(pReal), dimension(3,3) :: invC,avgC
|
|
real(pReal), dimension(3) :: nVect
|
|
real(pReal) detF
|
|
integer(pInt), dimension(4) :: intFace
|
|
integer(pInt) i,j,iBase
|
|
logical error
|
|
|
|
!* Compute the correction factor accouted for surface evolution (area change) due to deformation
|
|
avgC = 0.0_pReal
|
|
avgC = math_mul33x33(transpose(avgF),avgF)
|
|
invC = 0.0_pReal
|
|
call math_invert3x3(avgC,invC,detF,error)
|
|
homogenization_RGC_surfaceCorrection = 0.0_pReal
|
|
do iBase = 1,3
|
|
intFace = (/iBase,1_pInt,1_pInt,1_pInt/)
|
|
nVect = homogenization_RGC_interfaceNormal(intFace,ip,el) ! get the normal of the interface
|
|
do i = 1,3
|
|
do j = 1,3
|
|
homogenization_RGC_surfaceCorrection(iBase) = & ! compute the component of (the inverse of) the stretch in the direction of the normal
|
|
homogenization_RGC_surfaceCorrection(iBase) + invC(i,j)*nVect(i)*nVect(j)
|
|
enddo
|
|
enddo
|
|
homogenization_RGC_surfaceCorrection(iBase) = & ! get the surface correction factor (area contraction/enlargement)
|
|
sqrt(homogenization_RGC_surfaceCorrection(iBase))*detF
|
|
enddo
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to compute the equivalent shear and bulk moduli from the elasticity tensor
|
|
!********************************************************************
|
|
function homogenization_RGC_equivalentModuli(&
|
|
grainID, & ! grain ID
|
|
ip, & ! IP number
|
|
el & ! element number
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use constitutive, only: constitutive_homogenizedC,constitutive_averageBurgers
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_typeInstance
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), intent(in) :: grainID,ip,el
|
|
real(pReal), dimension (6,6) :: elasTens
|
|
real(pReal), dimension(2) :: homogenization_RGC_equivalentModuli
|
|
real(pReal) cEquiv_11,cEquiv_12,cEquiv_44
|
|
|
|
elasTens = constitutive_homogenizedC(grainID,ip,el)
|
|
|
|
!* Compute the equivalent shear modulus after Turterltaub and Suiker, JMPS (2005)
|
|
cEquiv_11 = (elasTens(1,1) + elasTens(2,2) + elasTens(3,3))/3.0_pReal
|
|
cEquiv_12 = (elasTens(1,2) + elasTens(2,3) + elasTens(3,1) + &
|
|
elasTens(1,3) + elasTens(2,1) + elasTens(3,2))/6.0_pReal
|
|
cEquiv_44 = (elasTens(4,4) + elasTens(5,5) + elasTens(6,6))/3.0_pReal
|
|
homogenization_RGC_equivalentModuli(1) = 0.2_pReal*(cEquiv_11 - cEquiv_12) + 0.6_pReal*cEquiv_44
|
|
|
|
!* Obtain the length of Burgers vector
|
|
homogenization_RGC_equivalentModuli(2) = constitutive_averageBurgers(grainID,ip,el)
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to collect relaxation vectors of an interface
|
|
!********************************************************************
|
|
function homogenization_RGC_relaxationVector(&
|
|
intFace, & ! set of interface ID in 4D array (normal and position)
|
|
state, & ! set of global relaxation vectors
|
|
homID & ! homogenization ID
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_typeInstance
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3) :: homogenization_RGC_relaxationVector
|
|
integer(pInt), dimension (4), intent(in) :: intFace
|
|
type(p_vec), intent(in) :: state
|
|
integer(pInt), dimension (3) :: nGDim
|
|
integer(pInt) iNum,homID
|
|
|
|
!* Collect the interface relaxation vector from the global state array
|
|
homogenization_RGC_relaxationVector = 0.0_pReal
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
iNum = homogenization_RGC_interface4to1(intFace,homID) ! identify the position of the interface in global state array
|
|
if (iNum .gt. 0_pInt) homogenization_RGC_relaxationVector = state%p((3*iNum-2):(3*iNum))
|
|
! get the corresponding entries
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to identify the normal of an interface
|
|
!********************************************************************
|
|
function homogenization_RGC_interfaceNormal(&
|
|
intFace, & ! interface ID in 4D array (normal and position)
|
|
ip, & ! my IP
|
|
el & ! my element
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use math, only: math_mul33x3
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3) :: homogenization_RGC_interfaceNormal
|
|
integer(pInt), dimension (4), intent(in) :: intFace
|
|
integer(pInt), intent(in) :: ip,el
|
|
integer(pInt) nPos,i
|
|
|
|
!* Get the normal of the interface, identified from the value of intFace(1)
|
|
homogenization_RGC_interfaceNormal = 0.0_pReal
|
|
nPos = abs(intFace(1)) ! identify the position of the interface in global state array
|
|
homogenization_RGC_interfaceNormal(nPos) = intFace(1)/abs(intFace(1)) ! get the normal vector w.r.t. cluster axis
|
|
|
|
homogenization_RGC_interfaceNormal = &
|
|
math_mul33x3(homogenization_RGC_orientation(:,:,ip,el),homogenization_RGC_interfaceNormal)
|
|
! map the normal vector into sample coordinate system (basis)
|
|
|
|
! if (ip == 1 .and. el == 1) then
|
|
! write(6,'(x,a32,3(x,i3))')'Interface normal: ',intFace(1)
|
|
! write(6,'(x,3(e14.8,x))')(nVect(i), i = 1,3)
|
|
! write(6,*)' '
|
|
! call flush(6)
|
|
! endif
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to collect six faces of a grain in 4D (normal and position)
|
|
!********************************************************************
|
|
function homogenization_RGC_getInterface(&
|
|
iFace, & ! face index (1..6) mapped like (-e1,-e2,-e3,+e1,+e2,+e3) or iDir = (-1,-2,-3,1,2,3)
|
|
iGrain3 & ! grain ID in 3D array
|
|
)
|
|
use prec, only: pReal,pInt,p_vec
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), dimension (4) :: homogenization_RGC_getInterface
|
|
integer(pInt), dimension (3), intent(in) :: iGrain3
|
|
integer(pInt), intent(in) :: iFace
|
|
integer(pInt) iDir
|
|
|
|
!* Direction of interface normal
|
|
iDir = (int(dble(iFace-1)/2.0_pReal)+1)*(-1_pInt)**iFace
|
|
homogenization_RGC_getInterface(1) = iDir
|
|
|
|
!* Identify the interface position by the direction of its normal
|
|
homogenization_RGC_getInterface(2:4) = iGrain3(:)
|
|
if (iDir < 0_pInt) & ! to have a correlation with coordinate/position in real space
|
|
homogenization_RGC_getInterface(1_pInt-iDir) = homogenization_RGC_getInterface(1_pInt-iDir)-1_pInt
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to map grain ID from in 1D (global array) to in 3D (local position)
|
|
!********************************************************************
|
|
function homogenization_RGC_grain1to3(&
|
|
grain1, & ! grain ID in 1D array
|
|
homID & ! homogenization ID
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), dimension (3) :: homogenization_RGC_grain1to3
|
|
integer(pInt), intent(in) :: grain1,homID
|
|
integer(pInt), dimension (3) :: nGDim
|
|
|
|
!* Get the grain position
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
homogenization_RGC_grain1to3(3) = 1+(grain1-1)/(nGDim(1)*nGDim(2))
|
|
homogenization_RGC_grain1to3(2) = 1+mod((grain1-1)/nGDim(1),nGDim(2))
|
|
homogenization_RGC_grain1to3(1) = 1+mod((grain1-1),nGDim(1))
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to map grain ID from in 3D (local position) to in 1D (global array)
|
|
!********************************************************************
|
|
function homogenization_RGC_grain3to1(&
|
|
grain3, & ! grain ID in 3D array (pos.x,pos.y,pos.z)
|
|
homID & ! homogenization ID
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), dimension (3), intent(in) :: grain3
|
|
integer(pInt) :: homogenization_RGC_grain3to1
|
|
integer(pInt), dimension (3) :: nGDim
|
|
integer(pInt) homID
|
|
|
|
!* Get the grain ID
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
homogenization_RGC_grain3to1 = grain3(1) + nGDim(1)*(grain3(2)-1) + nGDim(1)*nGDim(2)*(grain3(3)-1)
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to map interface ID from 4D (normal and local position) into 1D (global array)
|
|
!********************************************************************
|
|
function homogenization_RGC_interface4to1(&
|
|
iFace4D, & ! interface ID in 4D array (n.dir,pos.x,pos.y,pos.z)
|
|
homID & ! homogenization ID
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), dimension (4), intent(in) :: iFace4D
|
|
integer(pInt) :: homogenization_RGC_interface4to1
|
|
integer(pInt), dimension (3) :: nGDim,nIntFace
|
|
integer(pInt) homID,dir
|
|
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
!* Compute the total number of interfaces, which ...
|
|
nIntFace(1) = (nGDim(1)-1)*nGDim(2)*nGDim(3) ! ... normal //e1
|
|
nIntFace(2) = nGDim(1)*(nGDim(2)-1)*nGDim(3) ! ... normal //e2
|
|
nIntFace(3) = nGDim(1)*nGDim(2)*(nGDim(3)-1) ! ... normal //e3
|
|
|
|
!* Get the corresponding interface ID in 1D global array
|
|
if (abs(iFace4D(1)) == 1_pInt) then ! ... interface with normal //e1
|
|
homogenization_RGC_interface4to1 = iFace4D(3) + nGDim(2)*(iFace4D(4)-1) &
|
|
+ nGDim(2)*nGDim(3)*(iFace4D(2)-1)
|
|
if ((iFace4D(2) == 0_pInt) .or. (iFace4D(2) == nGDim(1))) homogenization_RGC_interface4to1 = 0_pInt
|
|
elseif (abs(iFace4D(1)) == 2_pInt) then ! ... interface with normal //e2
|
|
homogenization_RGC_interface4to1 = iFace4D(4) + nGDim(3)*(iFace4D(2)-1) &
|
|
+ nGDim(3)*nGDim(1)*(iFace4D(3)-1) + nIntFace(1)
|
|
if ((iFace4D(3) == 0_pInt) .or. (iFace4D(3) == nGDim(2))) homogenization_RGC_interface4to1 = 0_pInt
|
|
elseif (abs(iFace4D(1)) == 3_pInt) then ! ... interface with normal //e3
|
|
homogenization_RGC_interface4to1 = iFace4D(2) + nGDim(1)*(iFace4D(3)-1) &
|
|
+ nGDim(1)*nGDim(2)*(iFace4D(4)-1) + nIntFace(1) + nIntFace(2)
|
|
if ((iFace4D(4) == 0_pInt) .or. (iFace4D(4) == nGDim(3))) homogenization_RGC_interface4to1 = 0_pInt
|
|
endif
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! subroutine to map interface ID from 1D (global array) into 4D (normal and local position)
|
|
!********************************************************************
|
|
function homogenization_RGC_interface1to4(&
|
|
iFace1D, & ! interface ID in 1D array
|
|
homID & ! homogenization ID
|
|
)
|
|
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), dimension (4) :: homogenization_RGC_interface1to4
|
|
integer(pInt), intent(in) :: iFace1D
|
|
integer(pInt), dimension (3) :: nGDim,nIntFace
|
|
integer(pInt) homID
|
|
|
|
nGDim = homogenization_RGC_Ngrains(:,homID)
|
|
!* Compute the total number of interfaces, which ...
|
|
nIntFace(1) = (nGDim(1)-1)*nGDim(2)*nGDim(3) ! ... normal //e1
|
|
nIntFace(2) = nGDim(1)*(nGDim(2)-1)*nGDim(3) ! ... normal //e2
|
|
nIntFace(3) = nGDim(1)*nGDim(2)*(nGDim(3)-1) ! ... normal //e3
|
|
|
|
!* Get the corresponding interface ID in 4D (normal and local position)
|
|
if (iFace1D > 0 .and. iFace1D <= nIntFace(1)) then ! ... interface with normal //e1
|
|
homogenization_RGC_interface1to4(1) = 1
|
|
homogenization_RGC_interface1to4(3) = mod((iFace1D-1),nGDim(2))+1
|
|
homogenization_RGC_interface1to4(4) = mod(int(dble(iFace1D-1)/dble(nGDim(2))),nGDim(3))+1
|
|
homogenization_RGC_interface1to4(2) = int(dble(iFace1D-1)/dble(nGDim(2))/dble(nGDim(3)))+1
|
|
elseif (iFace1D > nIntFace(1) .and. iFace1D <= (nIntFace(2) + nIntFace(1))) then
|
|
! ... interface with normal //e2
|
|
homogenization_RGC_interface1to4(1) = 2
|
|
homogenization_RGC_interface1to4(4) = mod((iFace1D-nIntFace(1)-1),nGDim(3))+1
|
|
homogenization_RGC_interface1to4(2) = mod(int(dble(iFace1D-nIntFace(1)-1)/dble(nGDim(3))),nGDim(1))+1
|
|
homogenization_RGC_interface1to4(3) = int(dble(iFace1D-nIntFace(1)-1)/dble(nGDim(3))/dble(nGDim(1)))+1
|
|
elseif (iFace1D > nIntFace(2) + nIntFace(1) .and. iFace1D <= (nIntFace(3) + nIntFace(2) + nIntFace(1))) then
|
|
! ... interface with normal //e3
|
|
homogenization_RGC_interface1to4(1) = 3
|
|
homogenization_RGC_interface1to4(2) = mod((iFace1D-nIntFace(2)-nIntFace(1)-1),nGDim(1))+1
|
|
homogenization_RGC_interface1to4(3) = mod(int(dble(iFace1D-nIntFace(2)-nIntFace(1)-1)/dble(nGDim(1))),nGDim(2))+1
|
|
homogenization_RGC_interface1to4(4) = int(dble(iFace1D-nIntFace(2)-nIntFace(1)-1)/dble(nGDim(1))/dble(nGDim(2)))+1
|
|
endif
|
|
|
|
return
|
|
|
|
endfunction
|
|
|
|
!********************************************************************
|
|
! calculating the grain deformation gradient
|
|
! (the same with homogenization_RGC_partionDeformation,
|
|
! but used only for perturbation scheme)
|
|
!********************************************************************
|
|
subroutine homogenization_RGC_grainDeformation(&
|
|
F, & ! partioned def grad per grain
|
|
!
|
|
F0, & ! initial partioned def grad per grain
|
|
avgF, & ! my average def grad
|
|
state, & ! my state
|
|
ip, & ! my IP
|
|
el & ! my element
|
|
)
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_element
|
|
use material, only: homogenization_maxNgrains,homogenization_Ngrains,homogenization_typeInstance
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(out) :: F
|
|
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: F0
|
|
real(pReal), dimension (3,3), intent(in) :: avgF
|
|
type(p_vec), intent(in) :: state
|
|
integer(pInt), intent(in) :: el,ip
|
|
!
|
|
real(pReal), dimension (3) :: aVect,nVect
|
|
integer(pInt), dimension (4) :: intFace
|
|
integer(pInt), dimension (3) :: iGrain3
|
|
integer(pInt) homID, iGrain,iFace,i,j
|
|
!
|
|
integer(pInt), parameter :: nFace = 6
|
|
|
|
!* Compute the deformation gradient of individual grains due to relaxations
|
|
homID = homogenization_typeInstance(mesh_element(3,el))
|
|
F = 0.0_pReal
|
|
do iGrain = 1,homogenization_Ngrains(mesh_element(3,el))
|
|
iGrain3 = homogenization_RGC_grain1to3(iGrain,homID)
|
|
do iFace = 1,nFace
|
|
intFace = homogenization_RGC_getInterface(iFace,iGrain3)
|
|
aVect = homogenization_RGC_relaxationVector(intFace,state,homID)
|
|
nVect = homogenization_RGC_interfaceNormal(intFace,ip,el)
|
|
forall (i=1:3,j=1:3) &
|
|
F(i,j,iGrain) = F(i,j,iGrain) + aVect(i)*nVect(j) ! effective relaxations
|
|
enddo
|
|
F(:,:,iGrain) = F(:,:,iGrain) + avgF(:,:) ! relaxed deformation gradient
|
|
enddo
|
|
|
|
return
|
|
|
|
endsubroutine
|
|
|
|
END MODULE
|