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CPFEM: 

time integration scheme changed to start from guessing of Lp.
Newton-Raphson algorithm now accelerates as long as residuum improves.

IO:
added error 650 for polar decomposition problems

prec:
some cleanup. Introduced "relevantStrain" for convergence checking in CPFEM
This commit is contained in:
Philip Eisenlohr 2008-02-15 10:04:49 +00:00
parent f39c68dded
commit a41a4a75ef
3 changed files with 223 additions and 197 deletions
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342
trunk/CPFEM.f90
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@ -22,15 +22,13 @@
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_old real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_old
real(pReal), dimension(6,6) :: CPFEM_dummy_jacobian real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
real(pReal) CPFEM_dummy_stress
integer(pInt) :: CPFEM_inc_old = 0_pInt integer(pInt) :: CPFEM_inc_old = 0_pInt
integer(pInt) :: CPFEM_subinc_old = 1_pInt integer(pInt) :: CPFEM_subinc_old = 1_pInt
integer(pInt) :: CPFEM_cycle_old = -1_pInt integer(pInt) :: CPFEM_cycle_old = -1_pInt
integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction
logical :: CPFEM_first_call = .true. logical :: CPFEM_first_call = .true.
CONTAINS CONTAINS
!********************************************************* !*********************************************************
@ -73,9 +71,6 @@
! *** Old jacobian (consistent tangent) *** ! *** Old jacobian (consistent tangent) ***
allocate(CPFEM_jaco_old(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_old = 0.0_pReal allocate(CPFEM_jaco_old(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_old = 0.0_pReal
! !
! *** dummy Jacobian and stress returned in odd cycles
CPFEM_dummy_jacobian=1.0e50_pReal*math_identity2nd(6)
CPFEM_dummy_stress = 1e5_pReal
! !
! *** Output to MARC output file *** ! *** Output to MARC output file ***
write(6,*) write(6,*)
@ -107,23 +102,31 @@
! !
use prec, only: pReal,pInt use prec, only: pReal,pInt
use debug use debug
use math, only: math_init, invnrmMandel use math, only: math_init, invnrmMandel, math_identity2nd
use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element
use crystal, only: crystal_Init use crystal, only: crystal_Init
use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new,material_Cslip_66
implicit none implicit none
!
integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i, e integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j, e
real(pReal) ffn(3,3), ffn1(3,3), Temperature, CPFEM_dt, CPFEM_stress(CPFEM_ngens), CPFEM_jaco(CPFEM_ngens,CPFEM_ngens) 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 logical CPFEM_stress_recovery
!
! calculate only every second cycle ! calculate only every second cycle
if(mod(CPFEM_cn,2)==0) then
! really calculate only in first call of new cycle and when in stress recovery if(mod(CPFEM_cn,2) /= 0) then ! odd cycle: record data for use in even cycle and return stiff result for this odd cycle
if(CPFEM_cn/=CPFEM_cycle_old .and. (CPFEM_stress_recovery .or. CPFEM_cn==0)) then cp_en = mesh_FEasCP('elem',CPFEM_en)
! initialization step CPFEM_Temperature(CPFEM_in, cp_en) = Temperature
if (CPFEM_first_call) then CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn
! three dimensional stress state ? 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)
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 math_init()
call mesh_init() call mesh_init()
call crystal_Init() call crystal_Init()
@ -132,47 +135,47 @@ if(mod(CPFEM_cn,2)==0) then
CPFEM_Temperature = Temperature CPFEM_Temperature = Temperature
CPFEM_first_call = .false. CPFEM_first_call = .false.
endif endif
if (CPFEM_inc==CPFEM_inc_old) then ! not a new increment
! case of a new subincrement:update starting with subinc 2 if (CPFEM_inc == CPFEM_inc_old) then ! not a new increment
if (CPFEM_subinc > CPFEM_subinc_old) then if (CPFEM_subinc > CPFEM_subinc_old) then ! new subincrement: update starting with subinc 2
CPFEM_sigma_old = CPFEM_sigma_new CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new constitutive_state_old = constitutive_state_new
CPFEM_subinc_old = CPFEM_subinc CPFEM_subinc_old = CPFEM_subinc
endif endif
else ! new increment else ! new increment
CPFEM_sigma_old = CPFEM_sigma_new CPFEM_sigma_old = CPFEM_sigma_new
CPFEM_Fp_old = CPFEM_Fp_new CPFEM_Fp_old = CPFEM_Fp_new
constitutive_state_old = constitutive_state_new constitutive_state_old = constitutive_state_new
CPFEM_inc_old = CPFEM_inc CPFEM_inc_old = CPFEM_inc
CPFEM_subinc_old = 1_pInt CPFEM_subinc_old = 1_pInt
endif endif
CPFEM_cycle_old=CPFEM_cn 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 ! this shall be done in a parallel loop in the future
debug_cutbackDistribution = 0_pInt
debug_stressLoopDistribution = 0_pInt
debug_stateLoopDistribution = 0_pInt
do e=1,mesh_NcpElems do e=1,mesh_NcpElems
do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e))) 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) call CPFEM_stressIP(CPFEM_cn, CPFEM_dt, i, e)
enddo enddo
enddo enddo
call debug_info() ! output of debugging/performance statistics
end if end if
! return stress and jacobi ! return stress and jacobi
! Mandel: 11, 22, 33, SQRT(2)*12, SQRT(2)*23, SQRT(2)*13 ! Mandel: 11, 22, 33, SQRT(2)*12, SQRT(2)*23, SQRT(2)*13
! Marc: 11, 22, 33, 12, 23, 13 ! Marc: 11, 22, 33, 12, 23, 13
cp_en = mesh_FEasCP('elem', CPFEM_en) cp_en = mesh_FEasCP('elem', CPFEM_en)
CPFEM_stress(1:CPFEM_ngens)=invnrmMandel(1:CPFEM_ngens)*CPFEM_stress_all(1:CPFEM_ngens, CPFEM_in, cp_en) CPFEM_stress(1:CPFEM_ngens) = invnrmMandel(1:CPFEM_ngens)*CPFEM_stress_all(1:CPFEM_ngens, CPFEM_in, cp_en)
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens)=CPFEM_jaco_old(1:CPFEM_ngens,1:CPFEM_ngens, CPFEM_in, cp_en) CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jaco_old(1:CPFEM_ngens,1:CPFEM_ngens, CPFEM_in, cp_en)
forall(i=1:CPFEM_ngens) CPFEM_jaco(1:CPFEM_ngens,i)=CPFEM_jaco(1:CPFEM_ngens,i)*invnrmMandel(1:CPFEM_ngens) forall(i=1:CPFEM_ngens) &
else CPFEM_jaco(1:CPFEM_ngens,i) = CPFEM_jaco(1:CPFEM_ngens,i)*invnrmMandel(1:CPFEM_ngens)
! record data for use in second cycle and return fixed result
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_dummy_stress
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens)=CPFEM_dummy_jacobian(1:CPFEM_ngens,1:CPFEM_ngens)
end if end if
return return
@ -190,21 +193,21 @@ if(mod(CPFEM_cn,2)==0) then
use prec, only: pReal,pInt,ijaco,nCutback use prec, only: pReal,pInt,ijaco,nCutback
use debug use debug
use math, only: math_pDecomposition,math_RtoEuler, inDeg use math, only: math_pDecomposition,math_RtoEuler, inDeg, math_I3, math_invert3x3
use IO, only: IO_error use IO, only: IO_error
use mesh, only: mesh_element use mesh, only: mesh_element
use constitutive use constitutive
!
implicit none implicit none
integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt
character(len=128) msg character(len=128) msg
integer(pInt) CPFEM_cn,cp_en,CPFEM_in,grain,i integer(pInt) CPFEM_cn,cp_en,CPFEM_in,grain,i
logical updateJaco,error logical updateJaco,error
real(pReal) CPFEM_dt,dt,t,volfrac real(pReal) CPFEM_dt,dt,t,volfrac,det
real(pReal), dimension(6) :: cs,Tstar_v real(pReal), dimension(6) :: cs,Tstar_v
real(pReal), dimension(6,6) :: cd real(pReal), dimension(6,6) :: cd
real(pReal), dimension(3,3) :: Fe,U,R,deltaFg real(pReal), dimension(3,3) :: Fe,U,R,deltaFg,invFgthen,invFpnow,Lp
real(pReal), dimension(3,3,2) :: Fg,Fp real(pReal), dimension(3,3,2) :: Fg,Fp
real(pReal), dimension(constitutive_maxNstatevars,2) :: state real(pReal), dimension(constitutive_maxNstatevars,2) :: state
@ -218,16 +221,26 @@ if(mod(CPFEM_cn,2)==0) then
! ------------------------------------------- ! -------------------------------------------
i = 0_pInt ! cutback counter i = 0_pInt ! cutback counter
dt = CPFEM_dt
state(:,i_now) = constitutive_state_old(:,grain,CPFEM_in,cp_en) state(:,i_now) = constitutive_state_old(:,grain,CPFEM_in,cp_en)
Fg(:,:,i_now) = CPFEM_ffn_all(:,:,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) 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) deltaFg = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
dt = CPFEM_dt
Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess
Fg(:,:,i_then) = Fg(:,:,i_now) Fg(:,:,i_then) = Fg(:,:,i_now)
state(:,i_then) = 0.0_pReal ! state_old as initial guess Fp(:,:,i_then) = Fp(:,:,i_now)
state(:,i_then) = 0.0_pReal ! state_old as initial guess
t = 0.0_pReal t = 0.0_pReal
! ------- crystallite integration ----------- ! ------- crystallite integration -----------
@ -241,24 +254,22 @@ if(mod(CPFEM_cn,2)==0) then
Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg
endif endif
call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Fp(:,:,i_then),Fe,state(:,i_then),& 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,& t,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,&
Fg(:,:,i_now),Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now)) Fg(:,:,i_now),Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now))
if (msg == 'ok') then ! solution converged if (msg == 'ok') then ! solution converged
if (t == CPFEM_dt) then if (t == CPFEM_dt) then
debug_cutbackDistribution(i) = debug_cutbackDistribution(i)+1 debug_cutbackDistribution(i+1) = debug_cutbackDistribution(i+1)+1
exit ! reached final "then" exit ! reached final "then"
endif endif
else ! solution not found else ! solution not found
i = i+1_pInt ! inc cutback counter i = i+1_pInt ! inc cutback counter
! write(6,*) 'ncut:', i
if (i > nCutback) then ! limit exceeded? if (i > nCutback) then ! limit exceeded?
debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1
write(6,*)
write(6,*) 'cutback limit --> '//msg write(6,*) 'cutback limit --> '//msg
write(6,*) 'Grain: ',grain
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',mesh_element(1,cp_en)
call IO_error(600) call IO_error(600)
return ! byebye return ! byebye
else else
t = t-dt ! rewind time t = t-dt ! rewind time
Fg(:,:,i_then) = Fg(:,:,i_then)-deltaFg ! rewind Fg Fg(:,:,i_then) = Fg(:,:,i_then)-deltaFg ! rewind Fg
@ -283,7 +294,7 @@ if(mod(CPFEM_cn,2)==0) then
write(6,*) 'Grain: ',grain write(6,*) 'Grain: ',grain
write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',mesh_element(1,cp_en) write(6,*) 'Element: ',mesh_element(1,cp_en)
call IO_error(600) call IO_error(650)
return return
endif endif
CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R))*inDeg ! orientation CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R))*inDeg ! orientation
@ -299,15 +310,13 @@ if(mod(CPFEM_cn,2)==0) then
!******************************************************************** !********************************************************************
! Calculates the stress for a single component ! Calculates the stress for a single component
! it is based on the paper by Kalidindi et al.:
! J. Mech. Phys, Solids Vol. 40, No. 3, pp. 537-569, 1992
! it is modified to use anisotropic elasticity matrix
!******************************************************************** !********************************************************************
subroutine CPFEM_stressCrystallite(& subroutine CPFEM_stressCrystallite(&
msg,& ! return message msg,& ! return message
cs,& ! Cauchy stress vector cs,& ! Cauchy stress vector
dcs_de,& ! consistent tangent dcs_de,& ! consistent tangent
Tstar_v,& ! second Piola-Kirchoff stress tensor Tstar_v,& ! second Piola-Kirchoff stress tensor
Lp,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient Fe_new,& ! new "elastic" deformation gradient
state_new,& ! new state variable array state_new,& ! new state variable array
@ -323,7 +332,9 @@ if(mod(CPFEM_cn,2)==0) then
state_old) ! old state variable array state_old) ! old state variable array
use prec, only: pReal,pInt,pert_e use prec, only: pReal,pInt,pert_e
use debug
use constitutive, only: constitutive_Nstatevars use constitutive, only: constitutive_Nstatevars
use mesh, only: mesh_element
use math, only: math_Mandel6to33,mapMandel use math, only: math_Mandel6to33,mapMandel
implicit none implicit none
@ -331,17 +342,15 @@ if(mod(CPFEM_cn,2)==0) then
logical updateJaco logical updateJaco
integer(pInt) cp_en,CPFEM_in,grain,i integer(pInt) cp_en,CPFEM_in,grain,i
real(pReal) dt real(pReal) dt
real(pReal), dimension(3,3) :: Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,Fp_pert,Fe_new,Fe_pert,E_pert real(pReal), dimension(3,3) :: Lp,Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,Fp_pert,Fe_new,Fe_pert,E_pert
real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert
real(pReal), dimension(6,6) :: dcs_de real(pReal), dimension(6,6) :: dcs_de
real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert
call CPFEM_timeIntegration(msg,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step 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,Fp_old,state_old) dt,cp_en,CPFEM_in,grain,Fg_new,Fg_old,Fp_old,state_old)
if (msg /= 'ok') return ! solution not reached --> report back
if (msg /= 'ok') return
cs = CPFEM_CauchyStress(Tstar_v,Fe_new) ! Cauchy stress cs = CPFEM_CauchyStress(Tstar_v,Fe_new) ! Cauchy stress
if (updateJaco) then ! consistent tangent using numerical perturbation of Fg if (updateJaco) then ! consistent tangent using numerical perturbation of Fg
do i = 1,6 ! Fg component do i = 1,6 ! Fg component
E_pert = 0.0_pReal E_pert = 0.0_pReal
@ -351,8 +360,8 @@ if(mod(CPFEM_cn,2)==0) then
Fg_pert = Fg_new+matmul(E_pert,Fg_old) ! perturbated Fg Fg_pert = Fg_new+matmul(E_pert,Fg_old) ! perturbated Fg
Tstar_v_pert = Tstar_v ! initial guess from end of time step Tstar_v_pert = Tstar_v ! initial guess from end of time step
state_pert = state_new ! initial guess from end of time step state_pert = state_new ! initial guess from end of time step
call CPFEM_timeIntegration(msg,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, & call CPFEM_timeIntegration(msg,Lp,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, &
dt,cp_en,CPFEM_in,grain,Fg_pert,Fp_old,state_old) dt,cp_en,CPFEM_in,grain,Fg_pert,Fg_old,Fp_old,state_old)
if (msg /= 'ok') then if (msg /= 'ok') then
msg = 'consistent tangent --> '//msg msg = 'consistent tangent --> '//msg
return return
@ -369,24 +378,29 @@ if(mod(CPFEM_cn,2)==0) then
!*********************************************************************** !***********************************************************************
!*** fully-implicit two-level time integration *** !*** fully-implicit two-level time integration ***
!*** based on a residuum in Lp and intermediate ***
!*** acceleration of the Newton-Raphson correction ***
!*********************************************************************** !***********************************************************************
SUBROUTINE CPFEM_timeIntegration(& SUBROUTINE CPFEM_timeIntegration(&
msg,& ! return message msg,& ! return message
Lpguess,& ! guess of plastic velocity gradient
Fp_new,& ! new plastic deformation gradient Fp_new,& ! new plastic deformation gradient
Fe_new,& ! new "elastic" deformation gradient Fe_new,& ! new "elastic" deformation gradient
Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0) Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0)
state_new,& ! current microstructure at end of time inc (taken as guess if /= 0) state,& ! current microstructure at end of time inc (taken as guess if /= 0)
! !
dt,& ! time increment dt,& ! time increment
cp_en,& ! element number cp_en,& ! element number
CPFEM_in,& ! integration point number CPFEM_in,& ! integration point number
grain,& ! grain number grain,& ! grain number
Fg_new,& ! new total def gradient Fg_new,& ! new total def gradient
Fg_old,& ! old total def gradient
Fp_old,& ! former plastic def gradient Fp_old,& ! former plastic def gradient
state_old) ! former microstructure state_old) ! former microstructure
use prec use prec
use debug use debug
use mesh, only: mesh_element
use constitutive, only: constitutive_Nstatevars,& use constitutive, only: constitutive_Nstatevars,&
constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent,& constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent,&
constitutive_Microstructure constitutive_Microstructure
@ -395,130 +409,136 @@ if(mod(CPFEM_cn,2)==0) then
character(len=*) msg character(len=*) msg
integer(pInt) cp_en, CPFEM_in, grain integer(pInt) cp_en, CPFEM_in, grain
integer(pInt) iState,iStress,dummy, i,j,k,l,m integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n
real(pReal) dt,det, p_hydro real(pReal) dt, det, p_hydro, max_dlnLp, max_deltalnLp, leapfrog,maxleap
real(pReal), dimension(6) :: Tstar_v,dTstar_v,Rstress, T_elastic, Rstress_old real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(6,6) :: C_66,Jacobi,invJacobi real(pReal), dimension(9) :: deltaLp,deltaR
real(pReal), dimension(3,3) :: Fg_new,Fp_old,Fp_new,Fe_new,invFp_old,invFp_new,Lp,A,B,AB
real(pReal), dimension(3,3,3,3) :: dLp, LTL real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2
real(pReal), dimension(constitutive_Nstatevars(grain, CPFEM_in, cp_en)) :: state_old,state_new,dstate,Rstate,RstateS 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 logical failed
msg = 'ok' ! error-free so far msg = 'ok' ! error-free so far
call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp eye2 = math_identity2nd(9)
call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp_old
if (failed) then if (failed) then
msg = 'inversion Fp_old' msg = 'inversion Fp_old'
return return
endif 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)
A = matmul(Fg_new,invFp_old) ! actually Fe if (all(state == 0.0_pReal)) state = state_old ! former state guessed, if none specified
A = matmul(transpose(A), A) iOuter = 0_pInt ! outer counter
! former state guessed, if none specified Outer: do ! outer iteration: State
if (all(state_new == 0.0_pReal)) state_new = state_old iOuter = iOuter+1
RstateS = state_new if (iOuter > nOuter) then
iState = 0_pInt msg = 'limit Outer iteration'
debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1
Rstress = Tstar_v
Rstress_old=Rstress
state: do ! outer iteration: state
iState = iState+1
if (iState > nState) then
msg = 'limit state iteration'
debug_stateLoopDistribution(nState) = debug_stateLoopDistribution(nState)+1
return return
endif endif
call constitutive_Microstructure(state_new,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) call constitutive_Microstructure(state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
C_66 = constitutive_HomogenizedC(state_new, grain, CPFEM_in, cp_en) C_66 = constitutive_HomogenizedC(state, grain, CPFEM_in, cp_en)
C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor
iStress = 0_pInt iInner = 0_pInt
stress: do ! inner iteration: stress leapfrog = 1.0_pReal ! correction as suggested by invdRdLp-step
iStress = iStress+1 maxleap = 1024.0_pReal ! preassign maximum acceleration level
if (iStress > nStress) then ! too many loops required
msg = 'limit stress iteration' Inner: do ! inner iteration: Lp
debug_stressLoopDistribution(nStress) = debug_stateLoopDistribution(nStress)+1 iInner = iInner+1
if (iInner > nInner) then ! too many loops required
msg = 'limit Inner iteration'
debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1
return return
endif endif
p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal B = math_i3 - dt*Lpguess
forall(i=1:3) Tstar_v(i)=Tstar_v(i)-p_hydro BT = transpose(B)
call constitutive_LpAndItsTangent(Lp,dLp,Tstar_v,state_new,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
B = math_I3-dt*Lp
! B = B / math_det3x3(B)**(1.0_pReal/3.0_pReal)
AB = matmul(A,B) AB = matmul(A,B)
T_elastic= 0.5_pReal*matmul(C_66,math_Mandel33to6(matmul(transpose(B),AB)-math_I3)) BTA = matmul(BT,A)
p_hydro=(T_elastic(1)+T_elastic(2)+T_elastic(3))/3.0_pReal Tstar_v = 0.5_pReal*matmul(C_66,math_mandel33to6(matmul(BT,AB)-math_I3))
forall(i=1:3) T_elastic(i)=T_elastic(i)-p_hydro Tstar = math_Mandel6to33(Tstar_v)
Rstress = Tstar_v - T_elastic p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal
! step size control: if residuum does not improve redo iteration with reduced step size forall(i=1:3) Tstar_v(i) = Tstar_v(i)-p_hydro ! subtract hydrostatic pressure
if(maxval(abs(Rstress)) > maxval(abs(Rstress_old)) .and. & call constitutive_LpAndItsTangent(Lp,dLp, &
maxval(abs(Rstress)) > abstol_ResStress .and. iStress > 1) then Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en)
Tstar_v=Tstar_v+0.5*dTstar_v Rinner = Lpguess - Lp ! update current residuum
dTstar_v=0.5*dTstar_v if (( maxval(abs(Rinner)) < abstol_Inner ) .or. &
cycle ( 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 endif
if (iStress > 1 .and. &
(maxval(abs(Tstar_v)) < abstol_Stress .or. maxval(abs(Rstress/maxval(abs(Tstar_v)))) < reltol_Stress)) exit stress
! update stress guess using inverse of dRes/dTstar (Newton--Raphson) Lpguess = Lpguess_old ! start from current guess
LTL = 0.0_pReal Rinner = Rinner_old ! use current residuum
do i=1,3 forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess
do j=1,3 Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l)
do k=1,3
do l=1,3
do m=1,3
LTL(i,j,k,l) = LTL(i,j,k,l) + dLp(j,i,m,k)*AB(m,l) + AB(m,i)*dLp(m,j,k,l)
enddo
enddo
enddo
enddo
enddo
Jacobi = math_identity2nd(6) + 0.5_pReal*dt*matmul(C_66,math_Mandel3333to66(LTL))
j = 0_pInt
call math_invert6x6(Jacobi,invJacobi,dummy,failed)
do while (failed .and. j <= nReg)
forall (i=1:6) Jacobi(i,i) = 1.05_pReal*maxval(Jacobi(i,:)) ! regularization
call math_invert6x6(Jacobi,invJacobi,dummy,failed)
j = j+1
enddo
if (failed) then
msg = 'regularization Jacobi'
return
endif
dTstar_v = matmul(invJacobi,Rstress) ! correction to Tstar
Rstress_old=Rstress
Tstar_v = Tstar_v-dTstar_v
enddo Inner
enddo stress debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
debug_stressLoopDistribution(iStress) = debug_stressLoopDistribution(iStress)+1 ROuter = state - state_old - &
Tstar_v = 0.5_pReal*matmul(C_66,math_Mandel33to6(matmul(transpose(B),AB)-math_I3)) dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),&
!if ((printer==1_pInt).AND.(CPFEM_in==1_pInt).AND.(cp_en==1_pInt)) then grain,CPFEM_in,cp_en) ! evolution of microstructure
!write(6,'(A10, 24ES12.3)') 'state_new', state_new state = state - ROuter
!write(6,'(A10, 6ES12.3)') 'Tstar_v', Tstar_v if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer
!endif
dstate = dt*constitutive_dotState(Tstar_v,state_new,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) ! evolution of microstructure
Rstate = state_new - (state_old+dstate)
RstateS = 0.0_pReal
forall (i=1:constitutive_Nstatevars(grain,CPFEM_in,cp_en), state_new(i)/=0.0_pReal) &
RstateS(i) = Rstate(i)/state_new(i)
state_new = state_old+dstate
if (maxval(abs(RstateS)) < reltol_State) exit state enddo Outer
enddo state
debug_stateLoopDistribution(iState) = debug_stateLoopDistribution(iState)+1
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
invFp_new = matmul(invFp_old,B) invFp_new = matmul(invFp_old,B)
call math_invert3x3(invFp_new,Fp_new,det,failed) call math_invert3x3(invFp_new,Fp_new,det,failed)
if (failed) then if (failed) then
msg = 'inversion Fp_new' msg = 'inversion Fp_new'
return return
endif endif
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! det = det(InvFp_new) !! 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) 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 return
END SUBROUTINE END SUBROUTINE
@ -526,7 +546,7 @@ stress: do ! inner iteration: stress
FUNCTION CPFEM_CauchyStress(PK_v,Fe) FUNCTION CPFEM_CauchyStress(PK_v,Fe)
!*********************************************************************** !***********************************************************************
!*** Cauchy stress calculation *** !*** Cauchy stress calculation ***
!*********************************************************************** !***********************************************************************
use prec, only: pReal,pInt use prec, only: pReal,pInt
use math, only: math_Mandel33to6,math_Mandel6to33,math_det3x3 use math, only: math_Mandel33to6,math_Mandel6to33,math_det3x3

13
trunk/IO.f90
View File

@ -559,6 +559,7 @@
SUBROUTINE IO_error(ID) SUBROUTINE IO_error(ID)
use prec, only: pInt use prec, only: pInt
use debug use debug
implicit none implicit none
@ -567,11 +568,17 @@
select case (ID) select case (ID)
case (100) case (100)
msg='Unable to open input file.' msg='Unable to open input file.'
case (110) case (110)
msg='No materials specified via State Variable 2.' msg='No materials specified via State Variable 2.'
case (120) case (120)
msg='No textures specified via State Variable 3.' msg='No textures specified via State Variable 3.'
case (200) case (200)
msg='Error reading from material+texture file' msg='Error reading from material+texture file'
case (300) case (300)
@ -579,10 +586,13 @@
&elements with three direct stress components' &elements with three direct stress components'
case (400) case (400)
msg='Unknown alloy number specified' msg='Unknown alloy number specified'
case (500) case (500)
msg='Unknown lattice type specified' msg='Unknown lattice type specified'
case (600) case (600)
msg='Convergence not reached' msg='Convergence not reached'
case (650)
msg='Polar decomposition failed'
case (700) case (700)
msg='Singular matrix in stress iteration' msg='Singular matrix in stress iteration'
case default case default
@ -592,9 +602,12 @@
write(6,*) 'MPIE Material Routine Ver. 0.0 by the coding team' write(6,*) 'MPIE Material Routine Ver. 0.0 by the coding team'
write(6,*) write(6,*)
write(6,*) msg write(6,*) msg
write(6,*) write(6,*)
call debug_info() call debug_info()
call flush(6) call flush(6)
call quit(9000+ID) call quit(9000+ID)
! ABAQUS returns in some cases ! ABAQUS returns in some cases

31
trunk/prec.f90
View File

@ -7,26 +7,19 @@
! *** Precision of real and integer variables *** ! *** Precision of real and integer variables ***
integer, parameter :: pReal = 8 integer, parameter :: pReal = 8
integer, parameter :: pInt = 4 integer, parameter :: pInt = 4
real(pReal), parameter :: relevantStrain = 1e-7
! *** Numerical parameters *** ! *** Numerical parameters ***
! *** How frequently the jacobian is recalculated *** ! *** How frequently the jacobian is recalculated ***
integer (pInt), parameter :: ijaco = 1_pInt integer(pInt), parameter :: ijaco = 1_pInt ! frequency of FEM Jacobi update
! *** Maximum number of internal cutbacks in time step *** integer(pInt), parameter :: nCutback = 10_pInt ! cutbacks in time-step integration
integer(pInt), parameter :: nCutback = 7_pInt integer(pInt), parameter :: nReg = 1_pInt ! regularization attempts for Jacobi inversion
! *** Maximum number of regularization attempts for Jacobi inversion *** real(pReal), parameter :: pert_e = 1.0e-5_pReal ! strain perturbation for FEM Jacobi
integer(pInt), parameter :: nReg = 1_pInt integer(pInt), parameter :: nOuter = 10_pInt ! outer loop limit
! *** Perturbation of strain array for numerical calculation of FEM Jacobi matrix *** integer(pInt), parameter :: nInner = 200_pInt ! inner loop limit
real(pReal), parameter :: pert_e=1.0e-5_pReal real(pReal), parameter :: reltol_Outer = 1.0e-4_pReal ! relative tolerance in outer loop (state)
! *** Maximum number of iterations in outer (state variables) loop *** real(pReal), parameter :: reltol_Inner = 1.0e-6_pReal ! relative tolerance in inner loop (Lp)
integer(pInt), parameter :: nState = 500_pInt real(pReal), parameter :: abstol_Inner = 1.0e-8_pReal ! absolute tolerance in inner loop (Lp)
! *** Convergence criteria for outer (state variables) loop ***
real(pReal), parameter :: reltol_State = 1.0e-6_pReal
! *** Maximum number of iterations in inner (stress) loop ***
integer(pInt), parameter :: nStress = 1000_pInt
! *** Convergence criteria for inner (stress) loop ***
real(pReal), parameter :: reltol_Stress = 1.0e-6_pReal
! *** Convergence criteria for inner (stress) loop ***
real(pReal), parameter :: abstol_Stress = 1.0e3_pReal
! *** Convergence criteria for inner (stress) loop ***
real(pReal), parameter :: abstol_ResStress = 1.0_pReal
END MODULE prec END MODULE prec