!*****************************************************
!* Module: HOMOGENIZATION_RGC *
!*****************************************************
!* contains: *
!*****************************************************
! [rgc]
! type rgc
! Ngrains p x q x r (cluster)
! (output) Ngrains
MODULE homogenization_RGC
!*** Include other modules ***
use prec, only: pReal,pInt
implicit none
character (len=*), parameter :: homogenization_RGC_label = 'rgc'
integer(pInt), dimension(:), allocatable :: homogenization_RGC_sizeState, &
homogenization_RGC_sizePostResults
integer(pInt), dimension(:,:), allocatable,target :: homogenization_RGC_sizePostResult
integer(pInt), dimension(:,:), allocatable :: homogenization_RGC_Ngrains
real(pReal), dimension(:,:), allocatable :: homogenization_RGC_dAlpha, &
homogenization_RGC_angles
real(pReal), dimension(:,:,:,:), allocatable :: homogenization_RGC_orientation
real(pReal), dimension(:), allocatable :: homogenization_RGC_xiAlpha, &
homogenization_RGC_ciAlpha
character(len=64), dimension(:,:), allocatable,target :: homogenization_RGC_output ! name of each post result output
CONTAINS
!****************************************
!* - homogenization_RGC_init
!* - homogenization_RGC_stateInit
!* - homogenization_RGC_deformationPartition
!* - homogenization_RGC_stateUpdate
!* - homogenization_RGC_averageStressAndItsTangent
!* - homogenization_RGC_postResults
!****************************************
!**************************************
!* Module initialization *
!**************************************
subroutine homogenization_RGC_init(&
file & ! file pointer to material configuration
)
use prec, only: pInt, pReal
use math, only: math_Mandel3333to66, math_Voigt66to3333,math_I3,math_sampleRandomOri,math_EulerToR,inRad
use mesh, only: mesh_maxNips,mesh_NcpElems,mesh_element,FE_Nips
use IO
use material
integer(pInt), intent(in) :: file
integer(pInt), parameter :: maxNchunks = 4
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section, maxNinstance, i,j,k,l,e, output, mySize, myInstance
character(len=64) tag
character(len=1024) line
write(6,*)
write(6,'(a21,a20,a12)') '<<<+- homogenization',homogenization_RGC_label,' init -+>>>'
write(6,*) '$Id$'
write(6,*)
maxNinstance = count(homogenization_type == homogenization_RGC_label)
if (maxNinstance == 0) return
allocate(homogenization_RGC_sizeState(maxNinstance)); homogenization_RGC_sizeState = 0_pInt
allocate(homogenization_RGC_sizePostResults(maxNinstance)); homogenization_RGC_sizePostResults = 0_pInt
allocate(homogenization_RGC_Ngrains(3,maxNinstance)); homogenization_RGC_Ngrains = 0_pInt
allocate(homogenization_RGC_ciAlpha(maxNinstance)); homogenization_RGC_ciAlpha = 0.0_pReal
allocate(homogenization_RGC_xiAlpha(maxNinstance)); homogenization_RGC_xiAlpha = 0.0_pReal
allocate(homogenization_RGC_dAlpha(3,maxNinstance)); homogenization_RGC_dAlpha = 0.0_pReal
allocate(homogenization_RGC_angles(3,maxNinstance)); homogenization_RGC_angles = 400.0_pReal
allocate(homogenization_RGC_output(maxval(homogenization_Noutput),maxNinstance)); homogenization_RGC_output = ''
allocate(homogenization_RGC_sizePostResult(maxval(homogenization_Noutput),maxNinstance))
homogenization_RGC_sizePostResult = 0_pInt
allocate(homogenization_RGC_orientation(3,3,mesh_maxNips,mesh_NcpElems))
forall (i = 1:mesh_maxNips,e = 1:mesh_NcpElems)
homogenization_RGC_orientation(:,:,i,e) = math_I3
end forall
rewind(file)
line = ''
section = 0
do while (IO_lc(IO_getTag(line,'<','>')) /= material_partHomogenization) ! wind forward to <homogenization>
read(file,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(file,'(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
output = 0 ! reset output counter
endif
if (section > 0 .and. homogenization_type(section) == homogenization_RGC_label) then ! one of my sections
i = homogenization_typeInstance(section) ! which instance of my type is present homogenization
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
select case(tag)
case ('(output)')
output = output + 1
homogenization_RGC_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
case ('clustersize')
homogenization_RGC_Ngrains(1,i) = IO_intValue(line,positions,2)
homogenization_RGC_Ngrains(2,i) = IO_intValue(line,positions,3)
homogenization_RGC_Ngrains(3,i) = IO_intValue(line,positions,4)
case ('scalingparameter')
homogenization_RGC_xiAlpha(i) = IO_floatValue(line,positions,2)
case ('overproportionality')
homogenization_RGC_ciAlpha(i) = IO_floatValue(line,positions,2)
case ('grainsize')
homogenization_RGC_dAlpha(1,i) = IO_floatValue(line,positions,2)
homogenization_RGC_dAlpha(2,i) = IO_floatValue(line,positions,3)
homogenization_RGC_dAlpha(3,i) = IO_floatValue(line,positions,4)
case ('clusterorientation')
homogenization_RGC_angles(1,i) = IO_floatValue(line,positions,2)
homogenization_RGC_angles(2,i) = IO_floatValue(line,positions,3)
homogenization_RGC_angles(3,i) = IO_floatValue(line,positions,4)
end select
endif
enddo
!*** assigning cluster orientations
do e = 1,mesh_NcpElems
if (homogenization_type(mesh_element(3,e)) == homogenization_RGC_label) then
myInstance = homogenization_typeInstance(mesh_element(3,e))
if (all (homogenization_RGC_angles(:,myInstance) >= 399.9_pReal)) then
homogenization_RGC_orientation(:,:,1,e) = math_EulerToR(math_sampleRandomOri())
do i = 1,FE_Nips(mesh_element(2,e))
if (microstructure_elemhomo(mesh_element(4,e))) then
homogenization_RGC_orientation(:,:,i,e) = homogenization_RGC_orientation(:,:,1,e)
else
homogenization_RGC_orientation(:,:,i,e) = math_EulerToR(math_sampleRandomOri())
endif
enddo
else
do i = 1,FE_Nips(mesh_element(2,e))
homogenization_RGC_orientation(:,:,i,e) = math_EulerToR(homogenization_RGC_angles(:,myInstance)*inRad)
enddo
endif
endif
enddo
100 do i = 1,maxNinstance ! sanity checks
write(6,'(a15,x,i4)') 'instance: ', i
write(6,*)
write(6,'(a25,3(x,i8))') 'cluster size: ',(homogenization_RGC_Ngrains(j,i),j=1,3)
write(6,'(a25,x,e10.3)') 'scaling parameter: ', homogenization_RGC_xiAlpha(i)
write(6,'(a25,x,e10.3)') 'over-proportionality: ', homogenization_RGC_ciAlpha(i)
write(6,'(a25,3(x,e10.3))') 'grain size: ',(homogenization_RGC_dAlpha(j,i),j=1,3)
write(6,'(a25,3(x,e10.3))') 'cluster orientation: ',(homogenization_RGC_angles(j,i),j=1,3)
enddo
do i = 1,maxNinstance
do j = 1,maxval(homogenization_Noutput)
select case(homogenization_RGC_output(j,i))
case('constitutivework')
mySize = 1
case('magnitudemismatch')
mySize = 3
case('penaltyenergy')
mySize = 1
case('volumediscrepancy')
mySize = 1
case default
mySize = 0
case('averagerelaxrate')
mySize = 1
case('maximumrelaxrate')
mySize = 1
end select
if (mySize > 0_pInt) then ! any meaningful output found
homogenization_RGC_sizePostResult(j,i) = mySize
homogenization_RGC_sizePostResults(i) = &
homogenization_RGC_sizePostResults(i) + mySize
endif
enddo
homogenization_RGC_sizeState(i) &
= 3*(homogenization_RGC_Ngrains(1,i)-1)*homogenization_RGC_Ngrains(2,i)*homogenization_RGC_Ngrains(3,i) &
+ 3*homogenization_RGC_Ngrains(1,i)*(homogenization_RGC_Ngrains(2,i)-1)*homogenization_RGC_Ngrains(3,i) &
+ 3*homogenization_RGC_Ngrains(1,i)*homogenization_RGC_Ngrains(2,i)*(homogenization_RGC_Ngrains(3,i)-1) &
+ 8_pInt ! (1) Average constitutive work, (2-4) Overall mismatch, (5) Average penalty energy,
! (6) Volume discrepancy, (7) Avg relaxation rate component, (8) Max relaxation rate component
enddo
return
endsubroutine
!*********************************************************************
!* initial homogenization state *
!*********************************************************************
function homogenization_RGC_stateInit(myInstance)
use prec, only: pReal,pInt
implicit none
!* Definition of variables
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(homogenization_RGC_sizeState(myInstance)) :: homogenization_RGC_stateInit
!* Open a debugging file
! open(1978,file='homogenization_RGC_debugging.out',status='unknown')
homogenization_RGC_stateInit = 0.0_pReal
return
endfunction
!********************************************************************
! partition material point def grad onto constituents
!********************************************************************
subroutine homogenization_RGC_partitionDeformation(&
F, & ! partioned def grad per grain
!
F0, & ! initial partioned def grad per grain
avgF, & ! my average def grad
state, & ! my state
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 FEsolving, only: theInc,cycleCounter,theTime
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) :: ip,el
!
real(pReal), dimension (3) :: aVect,nVect
integer(pInt), dimension (4) :: intFace
integer(pInt), dimension (3) :: iGrain3
integer(pInt) homID, iGrain,iFace,i,j
logical RGCdebug
!
integer(pInt), parameter :: nFace = 6
RGCdebug = .false.
!* Debugging the overall deformation gradient
if (RGCdebug) then
write(6,'(x,a,i3,a,i3,a)')'========== Increment: ',theInc,' Cycle: ',cycleCounter,' =========='
write(6,'(x,a32)')'Overall deformation gradient: '
do i = 1,3
write(6,'(x,3(e14.8,x))')(avgF(i,j), j = 1,3)
enddo
write(6,*)' '
call flush(6)
endif
!* 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))
call homogenization_RGC_grain1to3(iGrain3,iGrain,homID)
do iFace = 1,nFace
call homogenization_RGC_getInterface(intFace,iFace,iGrain3)
call homogenization_RGC_relaxationVector(aVect,intFace,state,homID)
call homogenization_RGC_interfaceNormal(nVect,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
!* Debugging the grain deformation gradients
if (RGCdebug) then
write(6,'(x,a32,x,i3)')'Deformation gradient of grain: ',iGrain
do i = 1,3
write(6,'(x,3(e14.8,x))')(F(i,j,iGrain), j = 1,3)
enddo
write(6,*)' '
call flush(6)
endif
enddo
return
endsubroutine
!********************************************************************
! update the internal state of the homogenization scheme
! and tell whether "done" and "happy" with result
!********************************************************************
function homogenization_RGC_updateState(&
state, & ! my state
state0, & ! my state at the beginning of increment
!
P, & ! array of current grain stresses
F, & ! array of current grain deformation gradients
F0, & ! array of initial grain deformation gradients
avgF, & ! average deformation gradient
dt, & ! time increment
dPdF, & ! array of current grain stiffnesses
ip, & ! my integration point
el & ! my element
)
use prec, only: pReal,pInt,p_vec
use math, only: math_invert
use mesh, only: mesh_element,mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,homogenization_typeInstance, &
homogenization_Ngrains
use numerics, only: absTol_RGC,relTol_RGC,absMax_RGC,relMax_RGC,pPert_RGC, &
maxdRelax_RGC,viscPower_RGC,viscModus_RGC,refRelaxRate_RGC
use FEsolving, only: theInc,cycleCounter,theTime
implicit none
!* Definition of variables
type(p_vec), intent(inout) :: state
type(p_vec), intent(in) :: state0
real(pReal), dimension (3,3,homogenization_maxNgrains), intent(in) :: P,F,F0
real(pReal), dimension (3,3,3,3,homogenization_maxNgrains), intent(in) :: dPdF
real(pReal), dimension (3,3), intent(in) :: avgF
real(pReal), intent(in) :: dt
integer(pInt), intent(in) :: ip,el
!
logical, dimension(2) :: homogenization_RGC_updateState
integer(pInt), dimension (4) :: intFaceN,intFaceP,faceID
integer(pInt), dimension (3) :: nGDim,iGr3N,iGr3P,stresLoc
integer(pInt), dimension (2) :: residLoc
integer(pInt) homID,i1,i2,i3,iNum,i,j,nIntFaceTot,iGrN,iGrP,iMun,iFace,k,l,ival,ipert,iGrain,nGrain
real(pReal), dimension (3,3,homogenization_maxNgrains) :: R,pF,pR,D,pD
real(pReal), dimension (3,homogenization_maxNgrains) :: NN,pNN
real(pReal), dimension (3) :: normP,normN,mornP,mornN
real(pReal) residMax,stresMax,constitutiveWork,penaltyEnergy,volDiscrep,penDiscrep
logical error,RGCdebug,RGCdebugJacobi,RGCcheck
!
integer(pInt), parameter :: nFace = 6
!
real(pReal), dimension(:,:), allocatable :: tract,jmatrix,jnverse,smatrix,pmatrix,rmatrix
real(pReal), dimension(:), allocatable :: resid,relax,p_relax,p_resid,drelax
RGCcheck = (el == 1 .and. ip == 1)
RGCdebug = .false.
RGCdebugJacobi = .false.
!* Get the dimension of the cluster (grains and interfaces)
homID = homogenization_typeInstance(mesh_element(3,el))
nGDim = homogenization_RGC_Ngrains(:,homID)
nGrain = homogenization_Ngrains(mesh_element(3,el))
nIntFaceTot = (nGDim(1)-1)*nGDim(2)*nGDim(3) + nGDim(1)*(nGDim(2)-1)*nGDim(3) &
+ nGDim(1)*nGDim(2)*(nGDim(3)-1)
!* Allocate the size of the arrays/matrices depending on the size of the cluster
allocate(resid(3*nIntFaceTot)); resid = 0.0_pReal
allocate(tract(nIntFaceTot,3)); tract = 0.0_pReal
allocate(relax(3*nIntFaceTot)); relax = state%p(1:3*nIntFaceTot)
allocate(drelax(3*nIntFaceTot))
drelax = state%p(1:3*nIntFaceTot) - state0%p(1:3*nIntFaceTot)
!* Debugging the obtained state
if (RGCdebug) then
write(6,'(x,a30)')'Obtained state: '
do i = 1,3*nIntFaceTot
write(6,'(x,2(e14.8,x))')state%p(i)
enddo
write(6,*)' '
endif
!* Stress-like penalty related to mismatch or incompatibility at interfaces
call homogenization_RGC_stressPenalty(R,NN,avgF,F,ip,el,homID)
!* Stress-like 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
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
endif
!* Compute the residual stress from the balance of traction at all (interior) interfaces
do iNum = 1,nIntFaceTot
call homogenization_RGC_interface1to4(faceID,iNum,homID)
!* Identify the left/bottom/back grain (-|N)
iGr3N = faceID(2:4)
call homogenization_RGC_grain3to1(iGrN,iGr3N,homID)
call homogenization_RGC_getInterface(intFaceN,2*faceID(1),iGr3N)
call homogenization_RGC_interfaceNormal(normN,intFaceN,ip,el) ! get the interface normal
!* Identify the right/up/front grain (+|P)
iGr3P = iGr3N
iGr3P(faceID(1)) = iGr3N(faceID(1))+1
call homogenization_RGC_grain3to1(iGrP,iGr3P,homID)
call homogenization_RGC_getInterface(intFaceP,2*faceID(1)-1,iGr3P)
call homogenization_RGC_interfaceNormal(normP,intFaceP,ip,el) ! get the interface normal
do i = 1,3 ! compute the traction balance at the interface
tract(iNum,i) = sign(viscModus_RGC*(abs(drelax(i+3*(iNum-1)))/(refRelaxRate_RGC*dt))**viscPower_RGC, &
drelax(i+3*(iNum-1)))
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)
resid(i+3*(iNum-1)) = tract(iNum,i) ! map into 1D residual array
enddo
enddo
!* Debugging the residual stress
if (RGCdebug) then
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,*)' '
endif
enddo
!* Convergence check for stress residual
stresMax = maxval(abs(P))
stresLoc = maxloc(abs(P))
residMax = maxval(abs(tract))
residLoc = maxloc(abs(tract))
!* Debugging the convergent criteria
if (RGCcheck) then
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)
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
write(6,'(x,a55)')'... done and happy'
write(6,*)' '
call flush(6)
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))
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
!* ... the bulk mechanical/constitutive work
state%p(3*nIntFaceTot+1) = constitutiveWork
!* ... the overall mismatch
state%p(3*nIntFaceTot+2) = sum(NN(1,:))/dble(nGrain)
state%p(3*nIntFaceTot+3) = sum(NN(2,:))/dble(nGrain)
state%p(3*nIntFaceTot+4) = sum(NN(3,:))/dble(nGrain)
state%p(3*nIntFaceTot+5) = penaltyEnergy
!* ... the volume discrepancy
state%p(3*nIntFaceTot+6) = volDiscrep
state%p(3*nIntFaceTot+7) = sum(abs(drelax))/dt/dble(3*nIntFaceTot)
state%p(3*nIntFaceTot+8) = maxval(abs(drelax))/dt
if (el == 1 .and. ip == 1) then
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)
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
! 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,x,a,x,e14.8)')'due to high residual =',residMax,'for stress =',stresMax
! state%p(1:3*nIntFaceTot) = 0.0_pReal ! ... with full Taylor assumption
! write(6,'(x,a,x,i3,x,a,x,i3,x,a)')'RGC_updateState: ip',ip,'| el',el,'relaxation vectors reset to zero'
if (RGCcheck) then
write(6,'(x,a55)')'... broken'
write(6,*)' '
call flush(6)
endif
! write(6,'(x,a,x,i3,x,a6,x,i3,x,a9)')'RGC_updateState: ip',ip,'| el',el,'broken :('
deallocate(tract,resid,relax,drelax)
return
!*** Otherwise, proceed with computing the Jacobian and state update
else
if (RGCcheck) then
write(6,'(x,a55)')'... not yet done'
write(6,*)' '
call flush(6)
endif
endif
!* Construct the Jacobian matrix of the constitutive stress tangent from dPdF
allocate(smatrix(3*nIntFaceTot,3*nIntFaceTot)); smatrix = 0.0_pReal
do iNum = 1,nIntFaceTot
call homogenization_RGC_interface1to4(faceID,iNum,homID)
!* Identify the left/bottom/back grain (-|N)
iGr3N = faceID(2:4)
call homogenization_RGC_grain3to1(iGrN,iGr3N,homID)
call homogenization_RGC_getInterface(intFaceN,2*faceID(1),iGr3N)
call homogenization_RGC_interfaceNormal(normN,intFaceN,ip,el) ! get the interface normal
do iFace = 1,nFace
call homogenization_RGC_getInterface(intFaceN,iFace,iGr3N)
call homogenization_RGC_interfaceNormal(mornN,intFaceN,ip,el) ! get influencing interfaces normal
call homogenization_RGC_interface4to1(iMun,intFaceN,homID)
if (iMun .gt. 0) then ! get the 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)
endif
enddo
!* Identify the right/up/front grain (+|P)
iGr3P = iGr3N
iGr3P(faceID(1)) = iGr3N(faceID(1))+1
call homogenization_RGC_grain3to1(iGrP,iGr3P,homID)
call homogenization_RGC_getInterface(intFaceP,2*faceID(1)-1,iGr3P)
call homogenization_RGC_interfaceNormal(normP,intFaceP,ip,el) ! get the interface normal
do iFace = 1,nFace
call homogenization_RGC_getInterface(intFaceP,iFace,iGr3P)
call homogenization_RGC_interfaceNormal(mornP,intFaceP,ip,el) ! get influencing interfaces normal
call homogenization_RGC_interface4to1(iMun,intFaceP,homID)
if (iMun .gt. 0) then ! get the 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
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)
endif
!* Compute the Jacobian of the stress-like penalty (penalty tangent)
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)
call homogenization_RGC_stressPenalty(pR,pNN,avgF,pF,ip,el,homID)
call homogenization_RGC_volumePenalty(pD,volDiscrep,pF,avgF,ip,el,homID)
p_resid = 0.0_pReal
do iNum = 1,nIntFaceTot
call homogenization_RGC_interface1to4(faceID,iNum,homID)
!* Identify the left/bottom/back grain (-|N)
iGr3N = faceID(2:4)
call homogenization_RGC_grain3to1(iGrN,iGr3N,homID)
call homogenization_RGC_getInterface(intFaceN,2*faceID(1),iGr3N)
call homogenization_RGC_interfaceNormal(normN,intFaceN,ip,el) ! get the corresponding normal
!* Identify the right/up/front grain (+|P)
iGr3P = iGr3N
iGr3P(faceID(1)) = iGr3N(faceID(1))+1
call homogenization_RGC_grain3to1(iGrP,iGr3P,homID)
call homogenization_RGC_getInterface(intFaceP,2*faceID(1)-1,iGr3P)
call homogenization_RGC_interfaceNormal(normP,intFaceP,ip,el) ! get the corresponding normal
!* Compute the perturbed traction at interface
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
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)
endif
!* Construct the Jacobian matrix of the numerical viscosity tangent
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)
!* Debugging the global Jacobian matrix of numerical viscosity tangent
if (RGCdebugJacobi) then
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)
endif
!* The overall Jacobian matrix (due to constitutive and penalty tangents)
allocate(jmatrix(3*nIntFaceTot,3*nIntFaceTot)); jmatrix = smatrix + pmatrix + rmatrix
if (RGCdebugJacobi) then
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)
endif
allocate(jnverse(3*nIntFaceTot,3*nIntFaceTot)); jnverse = 0.0_pReal
call math_invert(3*nIntFaceTot,jmatrix,jnverse,ival,error)
!* Debugging the inverse Jacobian matrix
if (RGCdebugJacobi) then
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)
endif
!* Calculate the state update (i.e., new relaxation vectors)
drelax = 0.0_pReal
do i = 1,3*nIntFaceTot
do j = 1,3*nIntFaceTot
drelax(i) = drelax(i) - jnverse(i,j)*resid(j)
enddo
enddo
relax = relax + drelax
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
! state%p(1:3*nIntFaceTot) = 0.0_pReal
! write(6,'(x,a,x,i3,x,a,x,i3,x,a)')'RGC_updateState: ip',ip,'| el',el,'relaxation vectors reset to zero'
homogenization_RGC_updateState = (/.true.,.false./)
! 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)
endif
!* Debugging the return state
if (RGCdebugJacobi) then
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)
endif
deallocate(tract,resid,jmatrix,jnverse,relax,drelax,pmatrix,smatrix,p_relax,p_resid)
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))
!* Debugging the grain tangent
if (RGCdebug) then
do iGrain = 1,homogenization_Ngrains(mesh_element(3,el))
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)
endif
Ngrains = homogenization_Ngrains(mesh_element(3,el))
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
! homID = homogenization_typeInstance(mesh_element(3,el)) ! <<not required at the moment>>
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
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 penalty correction factor representing surface evolution
call homogenization_RGC_surfaceCorrection(surfCorr,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
do iGrain = 1,homogenization_Ngrains(mesh_element(3,el))
call homogenization_RGC_equivalentModuli(muGrain,bgGrain,iGrain,ip,el)
call homogenization_RGC_grain1to3(iGrain3,iGrain,homID)
!* Compute the mismatch tensor at all six interfaces
do iFace = 1,nFace
call homogenization_RGC_getInterface(intFace,iFace,iGrain3)
call homogenization_RGC_interfaceNormal(nVect,intFace,ip,el) ! get the interface normal
iGNghb3 = iGrain3 ! identify the grain neighbor
iGNghb3(abs(intFace(1))) = iGNghb3(abs(intFace(1))) + int(dble(intFace(1))/dble(abs(intFace(1))))
!* The grain periodicity along e1
if (iGNghb3(1) < 1) iGNghb3(1) = nGDim(1)
if (iGNghb3(1) > nGDim(1)) iGNghb3(1) = 1
!* The grain periodicity along e2
if (iGNghb3(2) < 1) iGNghb3(2) = nGDim(2)
if (iGNghb3(2) > nGDim(2)) iGNghb3(2) = 1
!* The grain periodicity along e3
if (iGNghb3(3) < 1) iGNghb3(3) = nGDim(3)
if (iGNghb3(3) > nGDim(3)) iGNghb3(3) = 1
call homogenization_RGC_grain3to1(iGNghb,iGNghb3,homID) ! get the grain neighbor
call homogenization_RGC_equivalentModuli(muGNghb,bgGNghb,iGNghb,ip,el)
gDef = 0.5_pReal*(fDef(:,:,iGNghb) - fDef(:,:,iGrain)) ! difference in F with the neighbor
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
enddo
enddo
nDefNorm = nDefNorm + nDef(i,j)*nDef(i,j)
enddo
enddo
nDefNorm = max(nDefToler,sqrt(nDefNorm)) ! zero mismatch approximation if too small
!* 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-like penalty from all six 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
!* Total amount of mismatch experienced by the grain (at all six interfaces)
nMis(abs(intFace(1)),iGrain) = nMis(abs(intFace(1)),iGrain) + nDefNorm
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
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 volumes of grain and the effective volume and the total volume discrepancy
vDiscrep = math_det3x3(fAvg)
do iGrain = 1,nGrain
gVol(iGrain) = math_det3x3(fDef(:,:,iGrain))
vDiscrep = vDiscrep - gVol(iGrain)/dble(nGrain)
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
!********************************************************************
subroutine homogenization_RGC_surfaceCorrection(&
vSurf, & ! surface correction factor
!
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), intent(out) :: vSurf
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)
avgC = 0.0_pReal
avgC = math_mul33x33(transpose(avgF),avgF)
invC = 0.0_pReal
call math_invert3x3(avgC,invC,detF,error)
vSurf = 0.0_pReal
do iBase = 1,3
intFace = (/iBase,1_pInt,1_pInt,1_pInt/)
call homogenization_RGC_interfaceNormal(nVect,intFace,ip,el)
do i = 1,3
do j = 1,3
vSurf(iBase) = vSurf(iBase) + invC(i,j)*nVect(i)*nVect(j)
enddo
enddo
vSurf(iBase) = sqrt(vSurf(iBase))*detF
enddo
return
endsubroutine
!********************************************************************
! subroutine to compute the equivalent shear and bulk moduli from the elasticity tensor
!********************************************************************
subroutine homogenization_RGC_equivalentModuli(&
shearMod, & ! equivalent (isotropic) shear modulus
vBurgers, & ! length of burgers vector
!
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), intent(out) :: shearMod,vBurgers
real(pReal) cEquiv_11,cEquiv_12,cEquiv_44
elasTens = constitutive_homogenizedC(grainID,ip,el)
!* Compute the equivalent shear modulus using 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
shearMod = 0.2_pReal*(cEquiv_11 - cEquiv_12) + 0.6_pReal*cEquiv_44
vBurgers = constitutive_averageBurgers(grainID,ip,el)
return
endsubroutine
!********************************************************************
! subroutine to collect relaxation vectors of an interface
!********************************************************************
subroutine homogenization_RGC_relaxationVector(&
aVect, & ! relaxation vector of the interface
!
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), intent(out) :: aVect
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
aVect = 0.0_pReal
nGDim = homogenization_RGC_Ngrains(:,homID)
call homogenization_RGC_interface4to1(iNum,intFace,homID) ! Get the position in global state array
if (iNum .gt. 0_pInt) aVect = state%p((3*iNum-2):(3*iNum)) ! Collect the corresponding entries
return
endsubroutine
!********************************************************************
! subroutine to identify the normal of an interface
!********************************************************************
subroutine homogenization_RGC_interfaceNormal(&
nVect, & ! interface normal
!
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), intent(out) :: nVect
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)
nVect = 0.0_pReal
nPos = abs(intFace(1))
nVect(nPos) = intFace(1)/abs(intFace(1))
nVect = math_mul33x3(homogenization_RGC_orientation(:,:,ip,el),nVect)
! 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
endsubroutine
!********************************************************************
! subroutine to collect six faces of a grain in 4D (normal and position)
!********************************************************************
subroutine homogenization_RGC_getInterface(&
intFace, & ! interface ID in 4D (normal and position)
!
iFace, & ! number of faces of grain
iGrain3 & ! grain ID in 3D array
)
use prec, only: pReal,pInt,p_vec
implicit none
!* Definition of variables
integer(pInt), dimension (4), intent(out) :: intFace
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
intFace(1) = iDir
!* Identify the interface position by the direction of its normal
intFace(2:4) = iGrain3(:)
if (iDir .eq. -1_pInt) intFace(2) = intFace(2)-1
if (iDir .eq. -2_pInt) intFace(3) = intFace(3)-1
if (iDir .eq. -3_pInt) intFace(4) = intFace(4)-1
return
endsubroutine
!********************************************************************
! subroutine to map grain ID from in 1D (array) to in 3D (position)
!********************************************************************
subroutine homogenization_RGC_grain1to3(&
grain3, & ! grain ID in 3D array (pos.x,pos.y,pos.z)
!
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), intent(out) :: grain3
integer(pInt), intent(in) :: grain1,homID
integer(pInt), dimension (3) :: nGDim
!* Get the grain position
nGDim = homogenization_RGC_Ngrains(:,homID)
grain3(3) = int(dble(grain1-1)/dble(nGDim(1))/dble(nGDim(2)))+1
grain3(2) = mod(int(dble(grain1-1)/dble(nGDim(1))),nGDim(2))+1
grain3(1) = mod((grain1-1),nGDim(1))+1
return
endsubroutine
!********************************************************************
! subroutine to map grain ID from in 3D (position) to in 1D (array)
!********************************************************************
subroutine homogenization_RGC_grain3to1(&
grain1, & ! grain ID in 1D array
!
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), intent(out) :: grain1
integer(pInt), dimension (3) :: nGDim
integer(pInt) homID
!* Get the grain ID
nGDim = homogenization_RGC_Ngrains(:,homID)
grain1 = grain3(1) + nGDim(1)*(grain3(2)-1) + nGDim(1)*nGDim(2)*(grain3(3)-1)
return
endsubroutine
!********************************************************************
! subroutine to map interface ID from 4D (normal and position) into 1D (array)
!********************************************************************
subroutine homogenization_RGC_interface4to1(&
iFace1D, & ! interface ID in 1D array
!
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), intent(out) :: iFace1D
integer(pInt), dimension (3) :: nGDim,nIntFace
integer(pInt) homID
nGDim = homogenization_RGC_Ngrains(:,homID)
!* Get the 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
!* For interface with normal //e1
if (abs(iFace4D(1)) == 1_pInt) then
iFace1D = iFace4D(3) + nGDim(2)*(iFace4D(4)-1) + nGDim(2)*nGDim(3)*(iFace4D(2)-1)
if ((iFace4D(2) == 0_pInt) .or. (iFace4D(2) == nGDim(1))) iFace1D = 0_pInt
!* For interface with normal //e2
elseif (abs(iFace4D(1)) == 2_pInt) then
iFace1D = 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))) iFace1D = 0_pInt
!* For interface with normal //e3
elseif (abs(iFace4D(1)) == 3_pInt) then
iFace1D = 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))) iFace1D = 0_pInt
endif
return
endsubroutine
!********************************************************************
! subroutine to map interface ID from 1D (array) into 4D (normal and position)
!********************************************************************
subroutine homogenization_RGC_interface1to4(&
iFace4D, & ! interface ID in 4D array (n.dir,pos.x,pos.y,pos.z)
!
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), intent(out) :: iFace4D
integer(pInt), intent(in) :: iFace1D
integer(pInt), dimension (3) :: nGDim,nIntFace
integer(pInt) homID
nGDim = homogenization_RGC_Ngrains(:,homID)
!* Get the 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
!* For interface ID between 1 and nIntFace(1)
if (iFace1D > 0 .and. iFace1D <= nIntFace(1)) then
iFace4D(1) = 1
iFace4D(3) = mod((iFace1D-1),nGDim(2))+1
iFace4D(4) = mod(int(dble(iFace1D-1)/dble(nGDim(2))),nGDim(3))+1
iFace4D(2) = int(dble(iFace1D-1)/dble(nGDim(2))/dble(nGDim(3)))+1
!* For interface ID between nIntFace(1) and nIntFace(1) + nIntFace(2)
elseif (iFace1D > nIntFace(1) .and. iFace1D <= (nIntFace(2) + nIntFace(1))) then
iFace4D(1) = 2
iFace4D(4) = mod((iFace1D-nIntFace(1)-1),nGDim(3))+1
iFace4D(2) = mod(int(dble(iFace1D-nIntFace(1)-1)/dble(nGDim(3))),nGDim(1))+1
iFace4D(3) = int(dble(iFace1D-nIntFace(1)-1)/dble(nGDim(3))/dble(nGDim(1)))+1
!* For interface ID between nIntFace(1) + nIntFace(2) and nIntFace(1) + nIntFace(2) + nIntFace(3)
elseif (iFace1D > nIntFace(2) + nIntFace(1) .and. iFace1D <= (nIntFace(3) + nIntFace(2) + nIntFace(1))) then
iFace4D(1) = 3
iFace4D(2) = mod((iFace1D-nIntFace(2)-nIntFace(1)-1),nGDim(1))+1
iFace4D(3) = mod(int(dble(iFace1D-nIntFace(2)-nIntFace(1)-1)/dble(nGDim(1))),nGDim(2))+1
iFace4D(4) = int(dble(iFace1D-nIntFace(2)-nIntFace(1)-1)/dble(nGDim(1))/dble(nGDim(2)))+1
endif
return
endsubroutine
!********************************************************************
! calculating the grain deformation gradient
!********************************************************************
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))
call homogenization_RGC_grain1to3(iGrain3,iGrain,homID)
do iFace = 1,nFace
call homogenization_RGC_getInterface(intFace,iFace,iGrain3)
call homogenization_RGC_relaxationVector(aVect,intFace,state,homID)
call homogenization_RGC_interfaceNormal(nVect,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