DAMASK_EICMD/trunk/CPFEM.f90

573 lines
26 KiB
Fortran

!##############################################################
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_stress_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobi_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_all
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ini_ori
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_old
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobian
real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
integer(pInt) :: CPFEM_inc_old = 0_pInt
integer(pInt) :: CPFEM_subinc_old = 1_pInt
integer(pInt) :: CPFEM_cycle_old = -1_pInt
integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction
logical :: CPFEM_first_call = .true.
CONTAINS
!*********************************************************
!*** allocate the arrays defined in module CPFEM ***
!*** and initialize them ***
!*********************************************************
SUBROUTINE CPFEM_init()
!
use prec
use math, only: math_EulertoR, math_I3, math_identity2nd
use mesh
use constitutive
!
implicit none
integer(pInt) e,i,g
!
! *** mpie.marc parameters ***
allocate(CPFEM_Temperature (mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = 0.0_pReal
allocate(CPFEM_ffn_all (3,3,mesh_maxNips,mesh_NcpElems))
forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_all(:,:,i,e) = math_I3
allocate(CPFEM_ffn1_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_all = CPFEM_ffn_all
allocate(CPFEM_stress_all( 6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_all = 0.0_pReal
allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobi_all = 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
!
! *** Second Piola-Kirchoff stress tensor at (t=t0) and (t=t1) ***
allocate(CPFEM_sigma_old(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_old = 0.0_pReal
allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_new = 0.0_pReal
!
! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
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(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal
!
! *** FEM jacobian (consistent tangent) ***
allocate(CPFEM_jacobian(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobian = 0.0_pReal
!
!
! *** Output to MARC output file ***
write(6,*)
write(6,*) 'Arrays allocated:'
write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature)
write(6,*) 'CPFEM_ffn_all: ', shape(CPFEM_ffn_all)
write(6,*) 'CPFEM_ffn1_all: ', shape(CPFEM_ffn1_all)
write(6,*) 'CPFEM_stress_all: ', shape(CPFEM_stress_all)
write(6,*) 'CPFEM_jacobi_all: ', shape(CPFEM_jacobi_all)
write(6,*) 'CPFEM_results: ', shape(CPFEM_results)
write(6,*) 'CPFEM_sigma_old: ', shape(CPFEM_sigma_old)
write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new)
write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old)
write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new)
write(6,*) 'CPFEM_jacobian: ', shape(CPFEM_jacobian)
write(6,*)
call flush(6)
return
END SUBROUTINE
!***********************************************************************
!*** perform initialization at first call, update variables and ***
!*** call the actual material model ***
!***********************************************************************
SUBROUTINE CPFEM_general(ffn, ffn1, Temperature, CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_stress_recovery, CPFEM_dt,&
CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_jaco, CPFEM_ngens)
!
use prec, only: pReal,pInt
use debug
use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33
use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element
use crystal, only: crystal_Init
use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new,material_Cslip_66
implicit none
integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l, e
real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens)
logical CPFEM_stress_recovery
! calculate only every second cycle
if (mod(CPFEM_cn,2) /= 0) then ! odd cycle: record data for use in even cycle and return stiff result for this odd cycle
cp_en = mesh_FEasCP('elem',CPFEM_en)
CPFEM_Temperature(CPFEM_in, cp_en) = Temperature
CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn
CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1
CPFEM_stress(1:CPFEM_ngens) = CPFEM_odd_stress
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens)
CPFEM_cycle_old = CPFEM_cn
else ! even cycle: really calculate only in first call of new cycle and when in stress recovery
if (CPFEM_cn /= CPFEM_cycle_old .and. CPFEM_stress_recovery) then
if (CPFEM_first_call) then ! initialization step
! three dimensional stress state ?
call math_init()
call mesh_init()
call crystal_Init()
call constitutive_init()
call CPFEM_init()
CPFEM_Temperature = Temperature
CPFEM_first_call = .false.
endif
if (CPFEM_inc == CPFEM_inc_old) then ! not a new increment
if (CPFEM_subinc > CPFEM_subinc_old) then ! new subincrement: update starting with subinc 2
CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new
CPFEM_subinc_old = CPFEM_subinc
endif
else ! new increment
CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new
CPFEM_inc_old = CPFEM_inc
CPFEM_subinc_old = 1_pInt
endif
CPFEM_cycle_old = CPFEM_cn
debug_cutbackDistribution = 0_pInt ! initialize debugging data
debug_InnerLoopDistribution = 0_pInt
debug_OuterLoopDistribution = 0_pInt
! this shall be done in a parallel loop in the future
do e=1,mesh_NcpElems
do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e)))
debugger = (e==1 .and. i==1)
call CPFEM_stressIP(CPFEM_cn, CPFEM_dt, i, e)
enddo
enddo
call debug_info() ! output of debugging/performance statistics
end if
! return stress and jacobi
cp_en = mesh_FEasCP('elem', CPFEM_en)
CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_all(1:CPFEM_ngens, CPFEM_in, cp_en)
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jacobian(1:CPFEM_ngens,1:CPFEM_ngens, CPFEM_in, cp_en)
end if
return
END SUBROUTINE
!**********************************************************
!*** calculate the material behaviour at IP level ***
!**********************************************************
SUBROUTINE CPFEM_stressIP(&
CPFEM_cn,& ! Cycle number
CPFEM_dt,& ! Time increment (dt)
CPFEM_in,& ! Integration point number
cp_en) ! Element number
use prec, only: pReal,pInt,ijaco,nCutback
use debug
use math, only: math_pDecomposition,math_RtoEuler, inDeg, math_I3, math_invert3x3
use IO, only: IO_error
use mesh, only: mesh_element
use constitutive
implicit none
integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt
character(len=128) msg
integer(pInt) CPFEM_cn,cp_en,CPFEM_in,grain,i
logical updateJaco,error
real(pReal) CPFEM_dt,dt,t,volfrac,det
real(pReal), dimension(6) :: cs,Tstar_v
real(pReal), dimension(6,6) :: cd
real(pReal), dimension(3,3) :: Fe,U,R,deltaFg,invFgthen,invFpnow,Lp
real(pReal), dimension(3,3,2) :: Fg,Fp
real(pReal), dimension(constitutive_maxNstatevars,2) :: state
updateJaco = (mod(CPFEM_cn,2_pInt*ijaco)==0) ! update consistent tangent every ijaco'th iteration
CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress
if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent
! -------------- grain loop -----------------
do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
! -------------------------------------------
i = 0_pInt ! cutback counter
dt = CPFEM_dt
state(:,i_now) = constitutive_state_old(:,grain,CPFEM_in,cp_en)
Fg(:,:,i_now) = CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
Fp(:,:,i_now) = CPFEM_Fp_old(:,:,grain,CPFEM_in,cp_en)
invFgthen = 0.0_pReal
invFpnow = 0.0_pReal
call math_invert3x3(CPFEM_ffn1_all(:,:,CPFEM_in,cp_en),invFgthen,det,error)
call math_invert3x3(Fp(:,:,i_now),invFpnow,det,error)
if (dt /= 0.0_pReal) then
Lp = (math_I3-matmul(Fp(:,:,i_now),matmul(invFgthen,matmul(Fg(:,:,i_now),invFpnow))))/dt ! fully plastic initial guess
else
Lp = 0.0_pReal ! fully elastic guess
endif
deltaFg = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess
Fg(:,:,i_then) = Fg(:,:,i_now)
Fp(:,:,i_then) = Fp(:,:,i_now)
state(:,i_then) = 0.0_pReal ! state_old as initial guess
t = 0.0_pReal
! ------- crystallite integration -----------
do
! -------------------------------------------
if (t+dt < CPFEM_dt) then ! intermediate solution
t = t+dt ! next time inc
Fg(:,:,i_then) = Fg(:,:,i_then)+deltaFg ! corresponding Fg
else ! full step solution
t = CPFEM_dt ! final time
Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg
endif
call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Lp,Fp(:,:,i_then),Fe,state(:,i_then),&
t,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,&
Fg(:,:,i_now),Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now))
if (msg == 'ok') then ! solution converged
if (t == CPFEM_dt) then
debug_cutbackDistribution(i+1) = debug_cutbackDistribution(i+1)+1
exit ! reached final "then"
endif
else ! solution not found
i = i+1_pInt ! inc cutback counter
if (i > nCutback) then ! limit exceeded?
debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1
write(6,'(x,a,x,i6,x,a,x,i2,x,a,x,i2)') 'element:',cp_en,'IP:',CPFEM_in,'grain:',grain
write(6,*) 'cutback limit --> '//msg
call IO_error(600)
return ! byebye
else
t = t-dt ! rewind time
Fg(:,:,i_then) = Fg(:,:,i_then)-deltaFg ! rewind Fg
dt = 0.5_pReal*dt ! cut time-step in half
deltaFg = 0.5_pReal*deltaFg ! cut Fg-step in half
endif
endif
enddo ! crystallite integration (cutback loop)
! ---- update crystallite matrices at t = t1 ----
CPFEM_Fp_new(:,:,grain,CPFEM_in,cp_en) = Fp(:,:,i_then)
constitutive_state_new(:,grain,CPFEM_in,cp_en) = state(:,i_then)
CPFEM_sigma_new(:,grain,CPFEM_in,cp_en) = Tstar_v
! ---- contribute to IP result ----
volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en)
CPFEM_stress_all(:,CPFEM_in,cp_en) = CPFEM_stress_all(:,CPFEM_in,cp_en)+volfrac*cs ! average Cauchy stress
if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = CPFEM_jacobian(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent
! ---- update results plotted in MENTAT ----
call math_pDecomposition(Fe,U,R,error) ! polar decomposition
if (error) then
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
CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = &
constitutive_post_results(Tstar_v,state(:,i_then),CPFEM_dt,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
enddo ! grain loop
return
END SUBROUTINE
!********************************************************************
! Calculates the stress for a single component
!********************************************************************
subroutine CPFEM_stressCrystallite(&
msg,& ! return message
cs,& ! Cauchy stress vector
dcs_de,& ! consistent tangent
Tstar_v,& ! second Piola-Kirchhoff stress tensor
Lp,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
state_new,& ! new state variable array
!
dt,& ! time increment
cp_en,& ! element number
CPFEM_in,& ! integration point number
grain,& ! grain number
updateJaco,& ! boolean to calculate Jacobi matrix
Fg_old,& ! old global deformation gradient
Fg_new,& ! new global deformation gradient
Fp_old,& ! old plastic deformation gradient
state_old) ! old state variable array
use prec, only: pReal,pInt,pert_Fg
use debug
use constitutive, only: constitutive_Nstatevars
use mesh, only: mesh_element
use math, only: math_Mandel6to33,math_Mandel33to6,math_Mandel3333to66,math_I3,math_det3x3,math_invert3x3
implicit none
character(len=*) msg
logical updateJaco,error
integer(pInt) cp_en,CPFEM_in,grain,i,j,k,l,m,n
real(pReal) dt,invJ,det
real(pReal), dimension(3,3,3,3) :: A,H
real(pReal), dimension(3,3) :: Lp,Lp_pert,Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,invFp_new,Fp_pert,invFp_pert
real(pReal), dimension(3,3) :: Fe_new,Fe_pert,Tstar,tau,P,P_pert,E_pert
real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert
real(pReal), dimension(6,6) :: dcs_de
real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert
call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step
dt,cp_en,CPFEM_in,grain,Fg_new,Fg_old,Fp_old,state_old)
if (msg /= 'ok') return ! solution not reached --> report back
Tstar = math_Mandel6to33(Tstar_v) ! second PK in intermediate
tau = matmul(Fe_new,matmul(Tstar,transpose(Fe_new))) ! Kirchhoff stress
invJ = 1.0_pReal/math_det3x3(Fe_new) ! inverse dilatation of Fe
cs = math_Mandel33to6(invJ*tau) ! Cauchy stress
if (updateJaco) then ! consistent tangent using numerical perturbation of Fg (D.Tjahjanto Diss p.106)
call math_invert3x3(Fp_new,invFp_new,det,error)
if (error) then
msg = 'inversion of Fp_new'
return
endif
P = matmul(Fe_new,&
matmul(Tstar,transpose(invFp_new))) ! first PK at center
do k=1,3
do l=1,3
Fg_pert = Fg_new ! initialize perturbed Fg
Fg_pert(k,l) = Fg_pert(k,l) + pert_Fg ! perturb single component
Lp_pert = Lp
state_pert = state_new ! initial guess from end of time step
call CPFEM_timeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, &
dt,cp_en,CPFEM_in,grain,Fg_pert,Fg_old,Fp_old,state_old)
if (msg /= 'ok') then
msg = 'consistent tangent --> '//msg
return
endif
call math_invert3x3(Fp_pert,invFp_pert,det,error)
if (error) then
msg = 'inversion of Fp_pert'
return
endif
P_pert = matmul(Fe_pert,&
matmul(math_mandel6to33(Tstar_v_pert),transpose(invFp_pert))) ! perturbed first PK
A(:,:,k,l) = (P_pert-P)/pert_Fg ! dP_ij/dFg_kl
enddo
enddo
H = 0.0_pReal
forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
H(i,j,k,l) = H(i,j,k,l) + &
(Fg_new(j,m)*Fg_new(l,n)*A(i,m,k,n) - math_I3(j,l)*Fg_new(i,m)*P(k,m)) + &
0.5_pReal*(math_I3(i,k)*tau(j,l) + math_I3(j,l)*tau(i,k) + &
math_I3(i,l)*tau(j,k) + math_I3(j,k)*tau(i,l))
dcs_de = math_Mandel3333to66(invJ*H) ! Mandel version of stiffness tensor
endif
return
END SUBROUTINE
!***********************************************************************
!*** fully-implicit two-level time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!***********************************************************************
SUBROUTINE CPFEM_timeIntegration(&
msg,& ! return message
Lpguess,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient
Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0)
state,& ! current microstructure at end of time inc (taken as guess if /= 0)
!
dt,& ! time increment
cp_en,& ! element number
CPFEM_in,& ! integration point number
grain,& ! grain number
Fg_new,& ! new total def gradient
Fg_old,& ! old total def gradient
Fp_old,& ! former plastic def gradient
state_old) ! former microstructure
use prec
use debug
use mesh, only: mesh_element
use constitutive, only: constitutive_Nstatevars,&
constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent,&
constitutive_Microstructure
use math
implicit none
character(len=*) msg
integer(pInt) cp_en, CPFEM_in, grain
integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n
real(pReal) dt, det, p_hydro, max_dlnLp, max_deltalnLp, leapfrog,maxleap
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(9) :: deltaLp,deltaR
real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2
real(pReal), dimension(6,6) :: C_66
real(pReal), dimension(3,3) :: Fg_new,invFg_new,Fg_old,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new,Fe_old
real(pReal), dimension(3,3) :: Tstar
real(pReal), dimension(3,3) :: Lp,Lpguess,Lpguess_old,dLpguess,Rinner,Rinner_old,A,B,BT,AB,BTA
real(pReal), dimension(3,3,3,3) :: C
real(pReal), dimension(constitutive_Nstatevars(grain, CPFEM_in, cp_en)) :: state_old,state,ROuter
logical failed
msg = 'ok' ! error-free so far
eye2 = math_identity2nd(9)
call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp_old
if (failed) then
msg = 'inversion Fp_old'
return
endif
call math_invert3x3(Fg_new,invFg_new,det,failed) ! inversion of Fg_new
if (failed) then
msg = 'inversion Fg_new'
return
endif
Fe_old = matmul(Fg_new,invFp_old)
A = matmul(transpose(Fe_old), Fe_old)
if (all(state == 0.0_pReal)) state = state_old ! former state guessed, if none specified
iOuter = 0_pInt ! outer counter
Outer: do ! outer iteration: State
iOuter = iOuter+1
if (iOuter > nOuter) then
msg = 'limit Outer iteration'
debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1
return
endif
call constitutive_Microstructure(state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
C_66 = constitutive_HomogenizedC(state, grain, CPFEM_in, cp_en)
C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor
iInner = 0_pInt
leapfrog = 1.0_pReal ! correction as suggested by invdRdLp-step
maxleap = 1024.0_pReal ! preassign maximum acceleration level
Inner: do ! inner iteration: Lp
iInner = iInner+1
if (iInner > nInner) then ! too many loops required
msg = 'limit Inner iteration'
debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1
return
endif
B = math_i3 - dt*Lpguess
BT = transpose(B)
AB = matmul(A,B)
BTA = matmul(BT,A)
Tstar_v = 0.5_pReal*matmul(C_66,math_mandel33to6(matmul(BT,AB)-math_I3))
Tstar = math_Mandel6to33(Tstar_v)
p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal
forall(i=1:3) Tstar_v(i) = Tstar_v(i)-p_hydro ! subtract hydrostatic pressure
call constitutive_LpAndItsTangent(Lp,dLp, &
Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
Rinner = Lpguess - Lp ! update current residuum
if (( maxval(abs(Rinner)) < abstol_Inner ) .or. &
( any(abs(dt*Lpguess) > relevantStrain) .and. &
maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner )&
) exit Inner
! check for acceleration/deceleration in Newton--Raphson correction
if (leapfrog > 1.0_pReal .and. &
(sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum
sum(Rinner*Rinner_old) < 0.0_pReal)) then ! residuum changed sign (overshoot)
maxleap = 0.5_pReal * leapfrog ! limit next acceleration
leapfrog = 1.0_pReal ! grinding halt
else ! better residuum
dTdLp = 0.0_pReal ! calc dT/dLp
forall (i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
dTdLp(3*(i-1)+j,3*(k-1)+l) = dTdLp(3*(i-1)+j,3*(k-1)+l) + &
C(i,j,l,n)*AB(k,n)+C(i,j,m,l)*BTA(m,k)
dTdLp = -0.5_pReal*dt*dTdLp
dRdLp = eye2 - matmul(dLp,dTdLp) ! calc dR/dLp
invdRdLp = 0.0_pReal
call math_invert(9,dRdLp,invdRdLp,dummy,failed) ! invert dR/dLp --> dLp/dR
if (failed) then
msg = 'inversion dR/dLp'
return
endif
Rinner_old = Rinner ! remember current residuum
Lpguess_old = Lpguess ! remember current Lp guess
if (iInner > 1 .and. leapfrog < maxleap) &
leapfrog = 2.0_pReal * leapfrog ! accelerate
endif
Lpguess = Lpguess_old ! start from current guess
Rinner = Rinner_old ! use current residuum
forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess
Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l)
enddo Inner
debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
ROuter = state - state_old - &
dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),&
grain,CPFEM_in,cp_en) ! residuum from evolution of microstructure
state = state - ROuter ! update of microstructure
if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer
enddo Outer
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
invFp_new = matmul(invFp_old,B)
call math_invert3x3(invFp_new,Fp_new,det,failed)
if (failed) then
msg = 'inversion Fp_new'
return
endif
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !!
Fe_new = matmul(Fg_new,invFp_new) ! calc resulting Fe
forall (i=1:3) Tstar_v(i) = Tstar_v(i)+p_hydro ! add hydrostatic component back
return
END SUBROUTINE
END MODULE