!##############################################################
MODULE CPFEM
!##############################################################
! *** CPFEM engine ***
!
use prec, only: pReal,pInt
implicit none
!
! ****************************************************************
! *** General variables for the material behaviour calculation ***
! ****************************************************************
real(pReal), dimension (:,:), allocatable :: CPFEM_Temperature
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_bar
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_bar
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar
real(pReal), dimension (:,:,:,:,:,:),allocatable :: CPFEM_dPdF_bar
real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_bar
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_bar
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_knownGood
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction
logical :: CPFEM_init_done = .false. ! remember if init has been done already
logical :: CPFEM_calc_done = .false. ! remember if first IP has already calced the results
!
real(pReal), dimension (:,:,:,:), allocatable :: GIA_rVect_new ! boundary relaxation vectors
real(pReal), dimension (:,:,:,:), allocatable :: GIA_rVect_old ! boundary relaxation vectors
real(pReal), dimension (:,:), allocatable :: GIA_bNorm ! grain boundary normals
!
CONTAINS
!
!*********************************************************
!*** allocate the arrays defined in module CPFEM ***
!*** and initialize them ***
!*********************************************************
SUBROUTINE CPFEM_init(Temperature)
!
use prec
use math, only: math_EulertoR, math_I3, math_identity2nd
use mesh
use constitutive
!
implicit none
!
real(pReal) Temperature
integer(pInt) e,i,g,b
!
! *** mpie.marc parameters ***
allocate(CPFEM_Temperature (mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = Temperature
allocate(CPFEM_ffn_bar (3,3,mesh_maxNips,mesh_NcpElems))
forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_bar(:,:,i,e) = math_I3
allocate(CPFEM_ffn1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_bar = CPFEM_ffn_bar
allocate(CPFEM_PK1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_bar = 0.0_pReal
allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal
allocate(CPFEM_stress_bar(6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_bar = 0.0_pReal
allocate(CPFEM_jaco_bar(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_bar = 0.0_pReal
allocate(CPFEM_jaco_knownGood(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_knownGood = 0.0_pReal
!
! *** User defined results !!! MISSING incorporate consti_Nresults ***
allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
CPFEM_results = 0.0_pReal
!
! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal
allocate(CPFEM_Fp_old(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:constitutive_maxNgrains) &
CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(constitutive_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation
!
allocate(GIA_rVect_new(3,12,mesh_maxNips,mesh_NcpElems)) ; GIA_rVect_new = 0.0_pReal
allocate(GIA_rVect_old(3,12,mesh_maxNips,mesh_NcpElems)) ; GIA_rVect_old = 0.0_pReal
allocate(GIA_bNorm(3,12)) ; GIA_bNorm = 0.0_pReal
do b = 1,4
GIA_bNorm(1,b) = 1.0_pReal
GIA_bNorm(2,b+4) = 1.0_pReal
GIA_bNorm(3,b+8) = 1.0_pReal
enddo
!
! *** Output to MARC output file ***
write(6,*)
write(6,*) 'CPFEM Initialization'
write(6,*)
write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature)
write(6,*) 'CPFEM_ffn_bar: ', shape(CPFEM_ffn_bar)
write(6,*) 'CPFEM_ffn1_bar: ', shape(CPFEM_ffn1_bar)
write(6,*) 'CPFEM_PK1_bar: ', shape(CPFEM_PK1_bar)
write(6,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar)
write(6,*) 'CPFEM_stress_bar: ', shape(CPFEM_stress_bar)
write(6,*) 'CPFEM_jaco_bar: ', shape(CPFEM_jaco_bar)
write(6,*) 'CPFEM_jaco_knownGood: ', shape(CPFEM_jaco_knownGood)
write(6,*) 'CPFEM_results: ', shape(CPFEM_results)
write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old)
write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new)
!
write(6,*) 'GIA_rVect_new: ', shape(GIA_rVect_new)
write(6,*) 'GIA_rVect_old: ', shape(GIA_rVect_old)
write(6,*) 'GIA_bNorm: ', shape(GIA_bNorm)
write(6,*)
call flush(6)
return
!
END SUBROUTINE
!
!
!***********************************************************************
!*** perform initialization at first call, update variables and ***
!*** call the actual material model ***
!
! CPFEM_mode computation mode (regular, collection, recycle)
! ffn deformation gradient for t=t0
! ffn1 deformation gradient for t=t1
! Temperature temperature
! CPFEM_dt time increment
! CPFEM_en element number
! CPFEM_in intergration point number
! CPFEM_stress stress vector in Mandel notation
! CPFEM_updateJaco flag to initiate computation of Jacobian
! CPFEM_jaco jacobian in Mandel notation
! CPFEM_ngens size of stress strain law
!***********************************************************************
SUBROUTINE CPFEM_general(CPFEM_mode, ffn, ffn1, Temperature, CPFEM_dt,&
CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_updateJaco, CPFEM_jaco, CPFEM_ngens)
! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de
!
use prec, only: pReal,pInt
use FEsolving
use debug
use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33,math_det3x3,math_I3
use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element
use lattice, only: lattice_init
use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new,material_Cslip_66
implicit none
!
integer(pInt) CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n, e
real(pReal), dimension (3,3) :: ffn,ffn1,Kirchhoff_bar
real(pReal), dimension (3,3,3,3) :: H_bar
real(pReal), dimension(CPFEM_ngens) :: CPFEM_stress
real(pReal), dimension(CPFEM_ngens,CPFEM_ngens) :: CPFEM_jaco
real(pReal) Temperature,CPFEM_dt,J_inverse
integer(pInt) CPFEM_mode ! 1: regular computation with aged results&
! 2: regular computation&
! 3: collection of FEM data&
! 4: recycling of former results (MARC speciality)&
! 5: record tangent from former converged inc&
! 6: restore tangent from former converged inc
logical CPFEM_updateJaco
!
if (.not. CPFEM_init_done) then ! initialization step (three dimensional stress state check missing?)
call math_init()
call mesh_init()
call lattice_init()
call constitutive_init()
call CPFEM_init(Temperature)
CPFEM_init_done = .true.
endif
!
cp_en = mesh_FEasCP('elem',CPFEM_en)
if (cp_en == 1 .and. CPFEM_in == 1) &
write(6,'(a6,x,i4,x,a4,x,i4,x,a10,x,f8.4,x,a10,x,i2,x,a10,x,i2,x,a10,x,i2,x,a10,x,i2)') &
'elem',cp_en,'IP',CPFEM_in,&
'theTime',theTime,'theInc',theInc,'theCycle',theCycle,'theLovl',theLovl,&
'mode',CPFEM_mode
!
select case (CPFEM_mode)
case (2,1) ! regular computation (with aging of results)
if (.not. CPFEM_calc_done) then ! puuh, me needs doing all the work...
write (6,*) 'puuh me needs doing all the work', cp_en
if (CPFEM_mode == 1) then ! age results at start of new increment
CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new
GIA_rVect_old = GIA_rVect_new
write (6,*) '#### aged results'
endif
debug_cutbackDistribution = 0_pInt ! initialize debugging data
debug_InnerLoopDistribution = 0_pInt
debug_OuterLoopDistribution = 0_pInt
!
do e=1,mesh_NcpElems ! ## this shall be done in a parallel loop in the future ##
do i=1,FE_Nips(mesh_element(2,e)) ! iterate over all IPs of this element's type
debugger = (e==1 .and. i==1) ! switch on debugging for first IP in first element
call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt, i, e)
enddo
enddo
call debug_info() ! output of debugging/performance statistics
CPFEM_calc_done = .true. ! now calc is done
endif
! translate from P and dP/dF to CS and dCS/dE
Kirchhoff_bar = matmul(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en)))
J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en))
CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel33to6(J_inverse*Kirchhoff_bar)
!
H_bar = 0.0_pReal
forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
H_bar(i,j,k,l) = H_bar(i,j,k,l) + &
(CPFEM_ffn1_bar(j,m,CPFEM_in,cp_en)*CPFEM_ffn1_bar(l,n,CPFEM_in,cp_en)*CPFEM_dPdF_bar(i,m,k,n,CPFEM_in,cp_en) - &
math_I3(j,l)*CPFEM_ffn1_bar(i,m,CPFEM_in,cp_en)*CPFEM_PK1_bar(k,m,CPFEM_in,cp_en)) + &
0.5_pReal*(math_I3(i,k)*Kirchhoff_bar(j,l) + math_I3(j,l)*Kirchhoff_bar(i,k) + &
math_I3(i,l)*Kirchhoff_bar(j,k) + math_I3(j,k)*Kirchhoff_bar(i,l))
CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel3333to66(J_inverse*H_bar)
!
case (3) ! collect and return odd result
CPFEM_Temperature(CPFEM_in,cp_en) = Temperature
CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) = ffn
CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) = ffn1
CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress
CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens)
CPFEM_calc_done = .false.
case (4) ! do nothing since we can recycle the former results (MARC specialty)
case (5) ! record consistent tangent at beginning of new increment
CPFEM_jaco_knownGood = CPFEM_jaco_bar
case (6) ! restore consistent tangent after cutback
CPFEM_jaco_bar = CPFEM_jaco_knownGood
end select
!
! return the local stress and the jacobian from storage
CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en)
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en)
! if (cp_en == 1 .and. CPFEM_in == 1) write (6,*) 'stress',CPFEM_stress
! if (cp_en == 1 .and. CPFEM_in == 1 .and. CPFEM_updateJaco) write (6,*) 'stiffness',CPFEM_jaco
! if (cp_en == 1 .and. CPFEM_in == 1) write (6,*) 'vector',GIA_rVect_new(:,:,1,1)
!
return
!
END SUBROUTINE
!
!**********************************************************
!*** calculate the material point behaviour ***
!**********************************************************
SUBROUTINE CPFEM_MaterialPoint(&
updateJaco,& ! flag to initiate Jacobian updating
CPFEM_dt,& ! Time increment (dt)
CPFEM_in,& ! Integration point number
cp_en) ! Element number
!
use prec
use FEsolving, only: theCycle
use debug
use math, only: math_pDecomposition,math_RtoEuler,inDeg,math_I3,math_invert3x3,math_permut,math_invert,math_delta
use IO, only: IO_error
use mesh, only: mesh_element
use crystallite
use constitutive
implicit none
!
character(len=128) msg
integer(pInt) cp_en,CPFEM_in,grain,max_cutbacks,i,j,k,l,m,n,iBoun,NRiter,dummy,ii,jj,kk,ll,ip,jp
logical updateJaco,error,NRconvergent,failed
real(pReal) CPFEM_dt,volfrac,dTime,shMod,C_kb,resNorm,resMax,subStep,subFrac,temp1,temp2
real(pReal), dimension(3,3) :: F0_bar,F1_bar,dF_bar,PK1_per,F1_per
real(pReal), dimension(3,3) :: U,R
real(pReal), dimension(3,3,8) :: PK1,Fp0,Fp1,Fe1,F1,F0
real(pReal), dimension(3,3,12) :: GPK1,GF1,Nye,GRB1
real(pReal), dimension(3,3,3,3,8) :: dPdF
real(pReal), dimension(3,3,3,3,12) :: dRdX1
real(pReal), dimension(36) :: var,res
real(pReal), dimension(36,36) :: dresdvar,dvardres
real(pReal), dimension(3,12) :: rx,rVect
real(pReal), dimension(12) :: NyeNorm
real(pReal), dimension(constitutive_maxNstatevars,8) :: state0,state1
!
if (texture_Ngrains(mesh_element(4,cp_en)) /= 8_pInt) then
call IO_error(800)
return
endif
!
CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average first PK stress
if (updateJaco) CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average consistent tangent
!
! ------------- GIA loop --------------------
!
! collect information
shMod = 0.2_pReal*(material_C11(1) - material_C12(1)) + 0.3_pReal*material_C44(1) ! equivalent shear modulus
C_kb = material_bg(1)*shMod/material_GrainSize(1) ! equivalent boundary stiffness
!
F0_bar = CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) ! effective deformation gradient at t_n
state0 = constitutive_state_old(:,:,CPFEM_in,cp_en) ! state variables at t_n
Fp0 = CPFEM_Fp_old(:,:,:,CPFEM_in,cp_en) ! grain plastic def. gradient at t_n
rVect = GIA_rVect_old(:,:,CPFEM_in,cp_en) ! relaxation vectors from previous convergent step
!
dF_bar = CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) - CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) ! deformation gradient increment
subFrac = 0.0_pReal
subStep = 1.0_pReal
!
! Substepping procedure to improve N-R iteration
SubStepping: do
dTime = subStep*CPFEM_dt
call GIA_RelaxedDeformation(F0,F0_bar,rVect) ! def. gradient of indiv. grains at t_n
F1_bar = F0_bar + subStep*dF_bar ! effective def. gradient at t_n+1
forall (iBoun=1:12,i=1:3) var(3_pInt*(iBoun-1_pInt)+i) = rVect(i,iBoun) ! primary variable: relaxation vector
!
! Newton-Raphson iteration block
NRiter = 1_pInt
NRIteration: do
forall (iBoun=1:12,i=1:3) rx(i,iBoun) = var(3_pInt*(iBoun-1_pInt)+i) ! relaxation vectors (guess)
!
! deformation gradients of grains at t_n+1 (guess)
call GIA_RelaxedDeformation(F1,F1_bar,rx)
!
! -------------- grain loop -----------------
do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
call SingleCrystallite(msg,PK1(:,:,grain),dPdF(:,:,:,:,grain),&
CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en),&
Fp1(:,:,grain),Fe1(:,:,grain),state1(:,grain),& ! output up to here
dTime,cp_en,CPFEM_in,grain,.true.,&
CPFEM_Temperature(CPFEM_in,cp_en),F1(:,:,grain),F0(:,:,grain),Fp0(:,:,grain),state0(:,grain))
if (msg /= 'ok') then ! solution not reached --> exit NRIteration
write(6,*) 'GIA: grain loop failed to converge @ EL:',cp_en,' IP:',CPFEM_in
NRconvergent = .false.
exit NRiteration
endif
enddo ! grain loop
!
! calculate the deformation jump and stress jump across the boundaries
call GIA_BoundaryJump(GF1,F1)
call GIA_BoundaryJump(GPK1,PK1)
!
! compute the Nye tensor at the boundary
Nye = 0.0_pReal
NyeNorm = 0.0_pReal
do iBoun = 1,12
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
Nye(i,j,iBoun) = Nye(i,j,iBoun) - 0.5_pReal*math_permut(j,k,l)*GIA_bNorm(k,iBoun)*GF1(i,l,iBoun)
enddo
enddo
NyeNorm(iBoun) = NyeNorm(iBoun) + Nye(i,j,iBoun)*Nye(i,j,iBoun)
enddo
enddo
NyeNorm(iBoun) = sqrt(NyeNorm(iBoun))
if (NyeNorm(iBoun) > 1.0e-8_pReal) Nye(:,:,iBoun) = Nye(:,:,iBoun)/NyeNorm(iBoun)
enddo
!
! compute the stress-like penalty at the boundary
GRB1 = 0.0_pReal
do iBoun = 1,12
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
GRB1(i,j,iBoun) = GRB1(i,j,iBoun) + Nye(i,k,iBoun)*GIA_bNorm(l,iBoun)*math_permut(k,l,j)
enddo
enddo
enddo
enddo
GRB1(:,:,iBoun) = 0.5_pReal*(C_kb + C_kb)*GRB1(:,:,iBoun)
enddo
!
! compute the resiudal of stress at the boundary
res = 0.0_pReal
resNorm = 0.0_pReal
do iBoun = 1,12
do j = 1,3
do i = 1,3
res(3_pInt*(iBoun-1_pInt)+j) = res(3_pInt*(iBoun-1_pInt)+j) - &
GIA_bNorm(i,iBoun)*(GPK1(i,j,iBoun) - GRB1(i,j,iBoun))
enddo
resNorm = resNorm + res(3_pInt*(iBoun-1_pInt)+j)*res(3_pInt*(iBoun-1_pInt)+j)
enddo
enddo
resNorm = sqrt(resNorm)
!
if (debugger) write(6,'(x,a,i3,a,i3,a,i3,a,e10.4)')'EL:',cp_en,' IP:',CPFEM_in,' Iter:',NRiter,' RNorm:',resNorm
if (NRiter == 1_pInt) resMax = resNorm
if ((resNorm < resToler*resMax) .or. (resNorm < resAbsol)) then ! resNorm < tolerance ===> convergent
NRconvergent = .true.
exit NRiteration
elseif ((NRiter > NRiterMax) .or. (resNorm > resBound*resMax)) then ! resNorm > up. bound ===> substepping
NRconvergent = .false.
exit NRiteration
else ! update the residual
dRdX1 = 0.0_pReal
do iBoun = 1,12
if (NyeNorm(iBoun) < 1.0e-8_pReal) NyeNorm(iBoun) = 1.0e-8_pReal
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
temp1 = 0.0_pReal
temp2 = 0.0_pReal
do ii = 1,3
do jj = 1,3
do kk = 1,3
temp1 = temp1 + GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)*math_delta(i,k)* &
GIA_bNorm(kk,iBoun)*math_permut(ii,kk,l)
do ll = 1,3
temp2 = temp2 + Nye(i,ii,iBoun)*GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)* &
Nye(k,kk,iBoun)*GIA_bNorm(ll,iBoun)*math_permut(kk,ll,l)
enddo
enddo
enddo
enddo
dRdX1(i,j,k,l,iBoun) = 0.25_pReal*(C_kb + C_kb)*(temp1 - temp2)/NyeNorm(iBoun)
enddo
enddo
enddo
enddo
enddo
call GIA_JacobianMatrix(dresdvar,dPdF,dRdX1)
dvardres = 0.0_pReal
call math_invert(36,dresdvar,dvardres,dummy,failed)
if (failed) then
write(6,*) 'GIA: failed to invert the Jacobian @ EL:',cp_en,' IP:',CPFEM_in
NRconvergent = .false.
exit NRiteration
endif
forall (i=1:36,j=1:36) var(i) = var(i) - dvardres(i,j)*res(j)
endif
!
NRiter = NRiter + 1_pInt
enddo NRIteration ! End of N-R iteration blok
!
if (.not. NRconvergent) then
subStep = 0.5_pReal*subStep
else
subFrac = subFrac + subStep
subStep = 1.0_pReal - subFrac
Fp0 = Fp1
F0_bar = F1_bar
state0 = state1
rVect = rx
endif
!
if (subStep < subStepMin) exit SubStepping
enddo SubStepping ! End of substepping blok
!
! ------------- GIA loop (end) --------------
!
! return to the general subroutine when convergence is not reached
if (.not. NRconvergent) then
write(6,'(x,a)') 'GIA: convergence is not reached @ EL:',cp_en,' IP:',CPFEM_in
call IO_error(600)
return
endif
!
! updates all variables, deformation gradients, and vectors
GIA_rVect_new(:,:,CPFEM_in,cp_en) = rVect
CPFEM_Fp_new(:,:,:,CPFEM_in,cp_en) = Fp1
constitutive_state_new(:,:,CPFEM_in,cp_en) = state1
!
! compute the effective stress and consistent tangent
do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en)
CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) + &
volfrac*PK1(:,:,grain) ! average Cauchy stress
!
! update results plotted in MENTAT
call math_pDecomposition(Fe1(:,:,grain),U,R,error) ! polar decomposition
if (error) then
write(6,*) Fe1(:,:,grain)
write(6,*) 'polar decomposition'
write(6,*) 'Grain: ',grain
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',mesh_element(1,cp_en)
call IO_error(650)
return
endif
CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R))*inDeg ! orientation
CPFEM_results(4 ,grain,CPFEM_in,cp_en) = volfrac ! volume fraction of orientation
enddo
!
if (theCycle >= 0_pInt) then
forall (grain=1:texture_Ngrains(mesh_element(4,cp_en))) &
CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) + volfrac*dPdF(:,:,:,:,grain)
else
do ip = 1,3
do jp = 1,3
F1_per = F1_bar
F1_per(ip,jp) = F1_per(ip,jp) + 1.0e-5_pReal
forall (iBoun=1:12,i=1:3) var(3_pInt*(iBoun-1_pInt)+i) = rVect(i,iBoun)
NRiter = 1_pInt
!
NRPerturbation: do
forall (iBoun=1:12,i=1:3) rx(i,iBoun) = var(3_pInt*(iBoun-1_pInt)+i) ! relaxation vectors (guess)
call GIA_RelaxedDeformation(F1,F1_bar,rx)
do grain = 1,8
call SingleCrystallite(msg,PK1(:,:,grain),dPdF(:,:,:,:,grain),&
CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en),&
Fp1(:,:,grain),Fe1(:,:,grain),state1(:,grain),& ! output up to here
dTime,cp_en,CPFEM_in,grain,.true.,&
CPFEM_Temperature(CPFEM_in,cp_en),F1(:,:,grain),F0(:,:,grain),Fp0(:,:,grain),state0(:,grain))
if (msg /= 'ok') then ! solution not reached --> exit NRIteration
write(6,*) 'GIA: perturbation grain loop failed to converge within allowable step-size'
NRconvergent = .false.
exit NRPerturbation
endif
enddo
call GIA_BoundaryJump(GF1,F1)
call GIA_BoundaryJump(GPK1,PK1)
!
Nye = 0.0_pReal
NyeNorm = 0.0_pReal
do iBoun = 1,12
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
Nye(i,j,iBoun) = Nye(i,j,iBoun) - 0.5_pReal*math_permut(j,k,l)*GIA_bNorm(k,iBoun)*GF1(i,l,iBoun)
enddo
enddo
NyeNorm(iBoun) = NyeNorm(iBoun) + Nye(i,j,iBoun)*Nye(i,j,iBoun)
enddo
enddo
NyeNorm(iBoun) = sqrt(NyeNorm(iBoun))
if (NyeNorm(iBoun) > 1.0e-8_pReal) Nye(:,:,iBoun) = Nye(:,:,iBoun)/NyeNorm(iBoun)
enddo
!
GRB1 = 0.0_pReal
do iBoun = 1,12
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
GRB1(i,j,iBoun) = GRB1(i,j,iBoun) + Nye(i,k,iBoun)*GIA_bNorm(l,iBoun)*math_permut(k,l,j)
enddo
enddo
enddo
enddo
GRB1(:,:,iBoun) = 0.5_pReal*(C_kb + C_kb)*GRB1(:,:,iBoun)
enddo
!
res = 0.0_pReal
resNorm = 0.0_pReal
do iBoun = 1,12
do j = 1,3
do i = 1,3
res(3_pInt*(iBoun-1_pInt)+j) = res(3_pInt*(iBoun-1_pInt)+j) - &
GIA_bNorm(i,iBoun)*(GPK1(i,j,iBoun) - GRB1(i,j,iBoun))
enddo
resNorm = resNorm + res(3_pInt*(iBoun-1_pInt)+j)*res(3_pInt*(iBoun-1_pInt)+j)
enddo
enddo
resNorm = sqrt(resNorm)
!
! if (debugger) write(6,'(x,a,i3,a,i3,a,i3,a,i3,a,e10.4)')'EL = ',cp_en,':IP = ',CPFEM_in,':pert = ',3*(ip-1)+jp,':Iter = ',NRiter,':RNorm = ',resNorm
if (NRiter == 1_pInt) resMax = resNorm
if ((resNorm < resToler*resMax) .or. (resNorm < resAbsol)) then ! resNorm < tolerance ===> convergent
NRconvergent = .true.
exit NRPerturbation
elseif ((NRiter > NRiterMax) .or. (resNorm > resBound*resMax)) then ! resNorm > up. bound ===> substepping
NRconvergent = .false.
exit NRPerturbation
else ! update the residual
dRdX1 = 0.0_pReal
do iBoun = 1,12
if (NyeNorm(iBoun) < 1.0e-8_pReal) NyeNorm(iBoun) = 1.0e-8_pReal
do i = 1,3
do j = 1,3
do k = 1,3
do l = 1,3
temp1 = 0.0_pReal
temp2 = 0.0_pReal
do ii = 1,3
do jj = 1,3
do kk = 1,3
temp1 = temp1 + GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)*math_delta(i,k)* &
GIA_bNorm(kk,iBoun)*math_permut(ii,kk,l)
do ll = 1,3
temp2 = temp2 + Nye(i,ii,iBoun)*GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)* &
Nye(k,kk,iBoun)*GIA_bNorm(ll,iBoun)*math_permut(kk,ll,l)
enddo
enddo
enddo
enddo
dRdX1(i,j,k,l,iBoun) = 0.25_pReal*(C_kb + C_kb)*(temp1 - temp2)/NyeNorm(iBoun)
enddo
enddo
enddo
enddo
enddo
call GIA_JacobianMatrix(dresdvar,dPdF,dRdX1)
dvardres = 0.0_pReal
call math_invert(36,dresdvar,dvardres,dummy,failed)
if (failed) then
write(6,*) 'GIA: perturbation failed to invert the Jacobian'
NRconvergent = .false.
exit NRPerturbation
endif
forall (i=1:36,j=1:36) var(i) = var(i) - dvardres(i,j)*res(j)
endif
NRiter = NRiter + 1_pInt
enddo NRPerturbation ! End of N-R iteration blok
!
PK1_per = 0.0_pReal
do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en)
PK1_per = PK1_per + volfrac*PK1(:,:,grain)
enddo
CPFEM_dPdF_bar(:,:,ip,jp,CPFEM_in,cp_en) = (PK1_per - CPFEM_PK1_bar(:,:,CPFEM_in,cp_en))/1.0e-5_pReal
enddo
enddo
endif
!
return
!
END SUBROUTINE
!
!
!********************************************************************
! Calculates the relaxed deformation gradients of grains
!********************************************************************
subroutine GIA_RelaxedDeformation(&
F,& ! relaxed deformation gradient of grains
F_bar,& ! effective deformation gradient
r) ! relaxation vectors at boundary
!
implicit none
!
real(pReal), dimension(3,3) :: F_bar
real(pReal), dimension(3,3,8) :: F
real(pReal), dimension(3,12) :: r,n
integer(pInt) i,j,iBoun,grain
!
n = GIA_bNorm
do i = 1,3
do j = 1,3
F(i,j,1) = F_bar(i,j) + n(i, 1)*r(j, 1) + n(i, 5)*r(j, 5) + n(i, 9)*r(j, 9)
F(i,j,2) = F_bar(i,j) - n(i, 1)*r(j, 1) + n(i, 6)*r(j, 6) + n(i,10)*r(j,10)
F(i,j,3) = F_bar(i,j) + n(i, 2)*r(j, 2) - n(i, 5)*r(j, 5) + n(i,11)*r(j,11)
F(i,j,4) = F_bar(i,j) - n(i, 2)*r(j, 2) - n(i, 6)*r(j, 6) + n(i,12)*r(j,12)
F(i,j,5) = F_bar(i,j) + n(i, 3)*r(j, 3) + n(i, 7)*r(j, 7) - n(i, 9)*r(j, 9)
F(i,j,6) = F_bar(i,j) - n(i, 3)*r(j, 3) + n(i, 8)*r(j, 8) - n(i,10)*r(j,10)
F(i,j,7) = F_bar(i,j) + n(i, 4)*r(j, 4) - n(i, 7)*r(j, 7) - n(i,11)*r(j,11)
F(i,j,8) = F_bar(i,j) - n(i, 4)*r(j, 4) - n(i, 8)*r(j, 8) - n(i,12)*r(j,12)
enddo
enddo
!
return
!
END SUBROUTINE
!
!
!********************************************************************
! Calculates the jump of tensors across the grain boundary
!********************************************************************
subroutine GIA_BoundaryJump(&
F_boun,& ! tensor jump across the boundary
F_bulk) ! bulk tensor
!
implicit none
!
real(pReal), dimension(3,3,12) :: F_boun
real(pReal), dimension(3,3,8) :: F_bulk
integer(pInt) i,j,iBoun,grain
!
F_boun(:,:, 1) = F_bulk(:,:,2) - F_bulk(:,:,1)
F_boun(:,:, 2) = F_bulk(:,:,4) - F_bulk(:,:,3)
F_boun(:,:, 3) = F_bulk(:,:,6) - F_bulk(:,:,5)
F_boun(:,:, 4) = F_bulk(:,:,8) - F_bulk(:,:,7)
F_boun(:,:, 5) = F_bulk(:,:,3) - F_bulk(:,:,1)
F_boun(:,:, 6) = F_bulk(:,:,4) - F_bulk(:,:,2)
F_boun(:,:, 7) = F_bulk(:,:,7) - F_bulk(:,:,5)
F_boun(:,:, 8) = F_bulk(:,:,8) - F_bulk(:,:,6)
F_boun(:,:, 9) = F_bulk(:,:,5) - F_bulk(:,:,1)
F_boun(:,:,10) = F_bulk(:,:,6) - F_bulk(:,:,2)
F_boun(:,:,11) = F_bulk(:,:,7) - F_bulk(:,:,3)
F_boun(:,:,12) = F_bulk(:,:,8) - F_bulk(:,:,4)
!
return
!
END SUBROUTINE
!
!
!********************************************************************
! Calculates the jump of tensors across the grain boundary
!********************************************************************
subroutine GIA_JacobianMatrix(&
dresdvar,& ! Jacobian matrix
dPdF,& ! stress consistent tangent of bulk
dRdX) ! stress-like penalty tangent at boundary
!
implicit none
!
real(pReal), dimension(3,3,3,3,8) :: dPdF
real(pReal), dimension(3,3,3,3,12) :: dRdX
real(pReal), dimension(36,36) :: dresdvar
real(pReal), dimension(3,12) :: n
integer(pInt) i,j,k,l
!
n = GIA_bNorm
dresdvar = 0.0_pReal
do i = 1,3
do k = 1,3
do l = 1,3
do j = 1,3
!
! at boundary 1, influenced by boundary +5, -6, +9, -10
dresdvar(( 1-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 1-1)*3 + l) &
+ (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 2))*n(i, 1)*n(k, 1) &
+ (dRdX(i,j,k,l, 1) + dRdX(i,j,k,l, 1))*n(i, 1)*n(k, 1)
dresdvar(( 1-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 5-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 1)*n(k, 5) &
+ dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 5)
dresdvar(( 1-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 6-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 1)*n(k, 6) &
- dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 6)
dresdvar(( 1-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 9-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 1)*n(k, 9) &
+ dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 9)
dresdvar(( 1-1)*3 + j,(10-1)*3 + l) = dresdvar(( 1-1)*3 + j,(10-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 1)*n(k,10) &
- dRdX(i,j,k,l, 1)*n(i, 1)*n(k,10)
!
! at boundary 2, influenced by boundary -5, +6, +11, -12
dresdvar(( 2-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 2-1)*3 + l) &
+ (dPdF(i,j,k,l, 3) + dPdF(i,j,k,l, 4))*n(i, 2)*n(k, 2) &
+ (dRdX(i,j,k,l, 2) + dRdX(i,j,k,l, 2))*n(i, 2)*n(k, 2)
dresdvar(( 2-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 5-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 2)*n(k, 5) &
- dRdX(i,j,k,l, 2)*n(i, 2)*n(k, 5)
dresdvar(( 2-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 6-1)*3 + l) + dPdF(i,j,k,l, 4)*n(i, 2)*n(k, 6) &
+ dRdX(i,j,k,l, 2)*n(i, 2)*n(k, 6)
dresdvar(( 2-1)*3 + j,(11-1)*3 + l) = dresdvar(( 2-1)*3 + j,(11-1)*3 + l) + dPdF(i,j,k,l, 3)*n(i, 2)*n(k,11) &
+ dRdX(i,j,k,l, 2)*n(i, 2)*n(k,11)
dresdvar(( 2-1)*3 + j,(12-1)*3 + l) = dresdvar(( 2-1)*3 + j,(12-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i, 2)*n(k,12) &
- dRdX(i,j,k,l, 2)*n(i, 2)*n(k,12)
!
! at boundary 3, influenced by boundary +7, -8, -9, +10
dresdvar(( 3-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 3-1)*3 + l) &
+ (dPdF(i,j,k,l, 5) + dPdF(i,j,k,l, 6))*n(i, 3)*n(k, 3) &
+ (dRdX(i,j,k,l, 3) + dRdX(i,j,k,l, 3))*n(i, 3)*n(k, 3)
dresdvar(( 3-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 7-1)*3 + l) + dPdF(i,j,k,l, 5)*n(i, 3)*n(k, 7) &
+ dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 7)
dresdvar(( 3-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 8-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 3)*n(k, 8) &
- dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 8)
dresdvar(( 3-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 9-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 3)*n(k, 9) &
- dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 9)
dresdvar(( 3-1)*3 + j,(10-1)*3 + l) = dresdvar(( 3-1)*3 + j,(10-1)*3 + l) + dPdF(i,j,k,l, 6)*n(i, 3)*n(k,10) &
+ dRdX(i,j,k,l, 3)*n(i, 3)*n(k,10)
!
! at boundary 4, influenced by boundary -7, +8, -11, +12
dresdvar(( 4-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 4-1)*3 + l) &
+ (dPdF(i,j,k,l, 7) + dPdF(i,j,k,l, 8))*n(i, 4)*n(k, 4) &
+ (dRdX(i,j,k,l, 4) + dRdX(i,j,k,l, 4))*n(i, 4)*n(k, 4)
dresdvar(( 4-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 7-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 4)*n(k, 7) &
- dRdX(i,j,k,l, 4)*n(i, 4)*n(k, 7)
dresdvar(( 4-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 8-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 4)*n(k, 8) &
+ dRdX(i,j,k,l, 4)*n(i, 4)*n(k, 8)
dresdvar(( 4-1)*3 + j,(11-1)*3 + l) = dresdvar(( 4-1)*3 + j,(11-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 4)*n(k,11) &
- dRdX(i,j,k,l, 4)*n(i, 4)*n(k,11)
dresdvar(( 4-1)*3 + j,(12-1)*3 + l) = dresdvar(( 4-1)*3 + j,(12-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 4)*n(k,12) &
+ dRdX(i,j,k,l, 4)*n(i, 4)*n(k,12)
!
! at boundary 5, influenced by boundary +1, -2, +9, -11
dresdvar(( 5-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 5-1)*3 + l) &
+ (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 3))*n(i, 5)*n(k, 5) &
+ (dRdX(i,j,k,l, 5) + dRdX(i,j,k,l, 5))*n(i, 5)*n(k, 5)
dresdvar(( 5-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 1-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 5)*n(k, 1) &
+ dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 1)
dresdvar(( 5-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 2-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 5)*n(k, 2) &
- dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 2)
dresdvar(( 5-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 9-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 5)*n(k, 9) &
+ dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 9)
dresdvar(( 5-1)*3 + j,(11-1)*3 + l) = dresdvar(( 5-1)*3 + j,(11-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 5)*n(k,11) &
- dRdX(i,j,k,l, 5)*n(i, 5)*n(k,11)
!
! at boundary 6, influenced by boundary -1, +2, +10, -12
dresdvar(( 6-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 6-1)*3 + l) &
+ (dPdF(i,j,k,l, 2) + dPdF(i,j,k,l, 4))*n(i, 6)*n(k, 6) &
+ (dRdX(i,j,k,l, 6) + dRdX(i,j,k,l, 6))*n(i, 6)*n(k, 6)
dresdvar(( 6-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 1-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 6)*n(k, 1) &
- dRdX(i,j,k,l, 6)*n(i, 6)*n(k, 1)
dresdvar(( 6-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 2-1)*3 + l) + dPdF(i,j,k,l, 4)*n(i, 6)*n(k, 2) &
+ dRdX(i,j,k,l, 6)*n(i, 6)*n(k, 2)
dresdvar(( 6-1)*3 + j,(10-1)*3 + l) = dresdvar(( 6-1)*3 + j,(10-1)*3 + l) + dPdF(i,j,k,l, 2)*n(i, 6)*n(k,10) &
+ dRdX(i,j,k,l, 6)*n(i, 6)*n(k,10)
dresdvar(( 6-1)*3 + j,(12-1)*3 + l) = dresdvar(( 6-1)*3 + j,(12-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i, 6)*n(k,12) &
- dRdX(i,j,k,l, 6)*n(i, 6)*n(k,12)
!
! at boundary 7, influenced by boundary +3, -4, -9, +11
dresdvar(( 7-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 7-1)*3 + l) &
+ (dPdF(i,j,k,l, 5) + dPdF(i,j,k,l, 7))*n(i, 7)*n(k, 7) &
+ (dRdX(i,j,k,l, 7) + dRdX(i,j,k,l, 7))*n(i, 7)*n(k, 7)
dresdvar(( 7-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 3-1)*3 + l) + dPdF(i,j,k,l, 5)*n(i, 7)*n(k, 3) &
+ dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 3)
dresdvar(( 7-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 4-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 7)*n(k, 4) &
- dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 4)
dresdvar(( 7-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 9-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 7)*n(k, 9) &
- dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 9)
dresdvar(( 7-1)*3 + j,(11-1)*3 + l) = dresdvar(( 7-1)*3 + j,(11-1)*3 + l) + dPdF(i,j,k,l, 7)*n(i, 7)*n(k,11) &
+ dRdX(i,j,k,l, 7)*n(i, 7)*n(k,11)
!
! at boundary 8, influenced by boundary -3, +4, -10, +12
dresdvar(( 8-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 8-1)*3 + l) &
+ (dPdF(i,j,k,l, 6) + dPdF(i,j,k,l, 8))*n(i, 8)*n(k, 8) &
+ (dRdX(i,j,k,l, 8) + dRdX(i,j,k,l, 8))*n(i, 8)*n(k, 8)
dresdvar(( 8-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 3-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 8)*n(k, 3) &
- dRdX(i,j,k,l, 8)*n(i, 8)*n(k, 3)
dresdvar(( 8-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 4-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 8)*n(k, 4) &
+ dRdX(i,j,k,l, 8)*n(i, 8)*n(k, 4)
dresdvar(( 8-1)*3 + j,(10-1)*3 + l) = dresdvar(( 8-1)*3 + j,(10-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 8)*n(k,10) &
- dRdX(i,j,k,l, 8)*n(i, 8)*n(k,10)
dresdvar(( 8-1)*3 + j,(12-1)*3 + l) = dresdvar(( 8-1)*3 + j,(12-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 8)*n(k,12) &
+ dRdX(i,j,k,l, 8)*n(i, 8)*n(k,12)
!
! at boundary 9, influenced by boundary +1, -3, +5, -7
dresdvar(( 9-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 9-1)*3 + l) &
+ (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 5))*n(i, 9)*n(k, 9) &
+ (dRdX(i,j,k,l, 9) + dRdX(i,j,k,l, 9))*n(i, 9)*n(k, 9)
dresdvar(( 9-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 1-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 9)*n(k, 1) &
+ dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 1)
dresdvar(( 9-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 3-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 9)*n(k, 3) &
- dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 3)
dresdvar(( 9-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 5-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 9)*n(k, 5) &
+ dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 5)
dresdvar(( 9-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 7-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 9)*n(k, 7) &
- dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 7)
!
! at boundary 10, influenced by boundary -1, +3, +6, -8
dresdvar((10-1)*3 + j,(10-1)*3 + l) = dresdvar((10-1)*3 + j,(10-1)*3 + l) &
+ (dPdF(i,j,k,l, 2) + dPdF(i,j,k,l, 6))*n(i,10)*n(k,10) &
+ (dRdX(i,j,k,l,10) + dRdX(i,j,k,l,10))*n(i,10)*n(k,10)
dresdvar((10-1)*3 + j,( 1-1)*3 + l) = dresdvar((10-1)*3 + j,( 1-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i,10)*n(k, 1) &
- dRdX(i,j,k,l,10)*n(i,10)*n(k, 1)
dresdvar((10-1)*3 + j,( 3-1)*3 + l) = dresdvar((10-1)*3 + j,( 3-1)*3 + l) + dPdF(i,j,k,l, 6)*n(i,10)*n(k, 3) &
+ dRdX(i,j,k,l,10)*n(i,10)*n(k, 3)
dresdvar((10-1)*3 + j,( 6-1)*3 + l) = dresdvar((10-1)*3 + j,( 6-1)*3 + l) + dPdF(i,j,k,l, 2)*n(i,10)*n(k, 6) &
+ dRdX(i,j,k,l,10)*n(i,10)*n(k, 6)
dresdvar((10-1)*3 + j,( 8-1)*3 + l) = dresdvar((10-1)*3 + j,( 8-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i,10)*n(k, 8) &
- dRdX(i,j,k,l,10)*n(i,10)*n(k, 8)
!
! at boundary 11, influenced by boundary +2, -4, -5, +7
dresdvar((11-1)*3 + j,(11-1)*3 + l) = dresdvar((11-1)*3 + j,(11-1)*3 + l) &
+ (dPdF(i,j,k,l, 3) + dPdF(i,j,k,l, 7))*n(i,11)*n(k,11) &
+ (dRdX(i,j,k,l,11) + dRdX(i,j,k,l,11))*n(i,11)*n(k,11)
dresdvar((11-1)*3 + j,( 2-1)*3 + l) = dresdvar((11-1)*3 + j,( 2-1)*3 + l) + dPdF(i,j,k,l, 3)*n(i,11)*n(k, 2) &
+ dRdX(i,j,k,l,11)*n(i,11)*n(k, 2)
dresdvar((11-1)*3 + j,( 4-1)*3 + l) = dresdvar((11-1)*3 + j,( 4-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i,11)*n(k, 4) &
- dRdX(i,j,k,l,11)*n(i,11)*n(k, 4)
dresdvar((11-1)*3 + j,( 5-1)*3 + l) = dresdvar((11-1)*3 + j,( 5-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i,11)*n(k, 5) &
- dRdX(i,j,k,l,11)*n(i,11)*n(k, 5)
dresdvar((11-1)*3 + j,( 7-1)*3 + l) = dresdvar((11-1)*3 + j,( 7-1)*3 + l) + dPdF(i,j,k,l, 7)*n(i,11)*n(k, 7) &
+ dRdX(i,j,k,l,11)*n(i,11)*n(k, 7)
!
! at boundary 12, influenced by boundary -2, +4, -6, +8
dresdvar((12-1)*3 + j,(12-1)*3 + l) = dresdvar((12-1)*3 + j,(12-1)*3 + l) &
+ (dPdF(i,j,k,l, 4) + dPdF(i,j,k,l, 8))*n(i,12)*n(k,12) &
+ (dRdX(i,j,k,l,12) + dRdX(i,j,k,l,12))*n(i,12)*n(k,12)
dresdvar((12-1)*3 + j,( 2-1)*3 + l) = dresdvar((12-1)*3 + j,( 2-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i,12)*n(k, 2) &
- dRdX(i,j,k,l,12)*n(i,12)*n(k, 2)
dresdvar((12-1)*3 + j,( 4-1)*3 + l) = dresdvar((12-1)*3 + j,( 4-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i,12)*n(k, 4) &
+ dRdX(i,j,k,l,12)*n(i,12)*n(k, 4)
dresdvar((12-1)*3 + j,( 6-1)*3 + l) = dresdvar((12-1)*3 + j,( 6-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i,12)*n(k, 6) &
- dRdX(i,j,k,l,12)*n(i,12)*n(k, 6)
dresdvar((12-1)*3 + j,( 8-1)*3 + l) = dresdvar((12-1)*3 + j,( 8-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i,12)*n(k, 8) &
+ dRdX(i,j,k,l,12)*n(i,12)*n(k, 8)
!
enddo
enddo
enddo
enddo
!
return
!
END SUBROUTINE
!
!
END MODULE
!##############################################################