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CPFEM 

changed consistent tangent scheme to D.Tjahjanto Diss version
fixed nasty bug in decision when to calculate new values (CPFEM_general)

prec
precision values should now be on safe side.
This commit is contained in:
Philip Eisenlohr 2008-02-18 18:11:24 +00:00
parent 199c65cdba
commit 2b567ad20d
2 changed files with 75 additions and 65 deletions
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132
trunk/CPFEM.f90
View File

@ -21,7 +21,7 @@
real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new
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_jacobian
real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
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
@ -68,8 +68,8 @@
CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(constitutive_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation 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 allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal
! !
! *** Old jacobian (consistent tangent) *** ! *** FEM jacobian (consistent tangent) ***
allocate(CPFEM_jaco_old(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_old = 0.0_pReal allocate(CPFEM_jacobian(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobian = 0.0_pReal
! !
! !
! *** Output to MARC output file *** ! *** Output to MARC output file ***
@ -85,14 +85,14 @@
write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new) write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new)
write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old) write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old)
write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new) write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new)
write(6,*) 'CPFEM_jaco_old: ', shape(CPFEM_jaco_old) write(6,*) 'CPFEM_jacobian: ', shape(CPFEM_jacobian)
write(6,*) write(6,*)
call flush(6) call flush(6)
return return
END SUBROUTINE END SUBROUTINE
!
!
!*********************************************************************** !***********************************************************************
!*** perform initialization at first call, update variables and *** !*** perform initialization at first call, update variables and ***
!*** call the actual material model *** !*** call the actual material model ***
@ -102,29 +102,30 @@
! !
use prec, only: pReal,pInt use prec, only: pReal,pInt
use debug use debug
use math, only: math_init, invnrmMandel, math_identity2nd 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 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,material_Cslip_66 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,j, e 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) 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 ! odd cycle: record data for use in even cycle and return stiff result for this odd 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) cp_en = mesh_FEasCP('elem',CPFEM_en)
CPFEM_Temperature(CPFEM_in, cp_en) = Temperature CPFEM_Temperature(CPFEM_in, cp_en) = Temperature
CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn
CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1 CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1
CPFEM_stress(1:CPFEM_ngens) = CPFEM_odd_stress CPFEM_stress(1:CPFEM_ngens) = CPFEM_odd_stress
CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens) 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 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_cn /= CPFEM_cycle_old .and. CPFEM_stress_recovery) then
if (CPFEM_first_call) then ! initialization step if (CPFEM_first_call) then ! initialization step
! three dimensional stress state ? ! three dimensional stress state ?
call math_init() call math_init()
@ -134,6 +135,7 @@
call CPFEM_init() call CPFEM_init()
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 if (CPFEM_inc == CPFEM_inc_old) then ! not a new increment
@ -160,7 +162,7 @@
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) 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
@ -169,13 +171,9 @@
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
! 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) = 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_jacobian(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)
end if end if
return return
@ -214,7 +212,7 @@
updateJaco = (mod(CPFEM_cn,2_pInt*ijaco)==0) ! update consistent tangent every ijaco'th iteration 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 CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress
if (updateJaco) CPFEM_jaco_old(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent
! -------------- grain loop ----------------- ! -------------- grain loop -----------------
do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
@ -266,7 +264,7 @@
i = i+1_pInt ! inc cutback counter i = i+1_pInt ! inc cutback counter
if (i > nCutback) then ! limit exceeded? if (i > nCutback) then ! limit exceeded?
debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1 debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1
write(6,*) 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 write(6,*) 'cutback limit --> '//msg
call IO_error(600) call IO_error(600)
return ! byebye return ! byebye
@ -286,7 +284,7 @@
! ---- contribute to IP result ---- ! ---- contribute to IP result ----
volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en) 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 CPFEM_stress_all(:,CPFEM_in,cp_en) = CPFEM_stress_all(:,CPFEM_in,cp_en)+volfrac*cs ! average Cauchy stress
if (updateJaco) CPFEM_jaco_old(:,:,CPFEM_in,cp_en) = CPFEM_jaco_old(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = CPFEM_jacobian(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent
! ---- update results plotted in MENTAT ---- ! ---- update results plotted in MENTAT ----
call math_pDecomposition(Fe,U,R,error) ! polar decomposition call math_pDecomposition(Fe,U,R,error) ! polar decomposition
if (error) then if (error) then
@ -315,7 +313,7 @@
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-Kirchhoff stress tensor
Lp,& ! guess of plastic velocity gradient 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
@ -331,18 +329,20 @@
Fp_old,& ! old plastic deformation gradient Fp_old,& ! old plastic deformation gradient
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_Fg
use debug use debug
use constitutive, only: constitutive_Nstatevars use constitutive, only: constitutive_Nstatevars
use mesh, only: mesh_element use mesh, only: mesh_element
use math, only: math_Mandel6to33,mapMandel use math, only: math_Mandel6to33,math_Mandel33to6,math_Mandel3333to66,math_I3,math_det3x3,math_invert3x3
implicit none implicit none
character(len=*) msg character(len=*) msg
logical updateJaco logical updateJaco,error
integer(pInt) cp_en,CPFEM_in,grain,i integer(pInt) cp_en,CPFEM_in,grain,i,j,k,l,m,n
real(pReal) dt real(pReal) dt,invJ,det
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(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) :: 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
@ -350,25 +350,49 @@
call CPFEM_timeIntegration(msg,Lp,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,Fg_old,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 ! solution not reached --> report back
cs = CPFEM_CauchyStress(Tstar_v,Fe_new) ! Cauchy stress Tstar = math_Mandel6to33(Tstar_v) ! second PK in intermediate
if (updateJaco) then ! consistent tangent using numerical perturbation of Fg tau = matmul(Fe_new,matmul(Tstar,transpose(Fe_new))) ! Kirchhoff stress
do i = 1,6 ! Fg component invJ = 1.0_pReal/math_det3x3(Fe_new) ! inverse dilatation of Fe
E_pert = 0.0_pReal cs = math_Mandel33to6(invJ*tau) ! Cauchy stress
E_pert(mapMandel(1,i),mapMandel(2,i)) = E_pert(mapMandel(1,i),mapMandel(2,i)) + pert_e/2.0_pReal if (updateJaco) then ! consistent tangent using numerical perturbation of Fg (D.Tjahjanto Diss p.106)
E_pert(mapMandel(2,i),mapMandel(1,i)) = E_pert(mapMandel(2,i),mapMandel(1,i)) + pert_e/2.0_pReal 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
Fg_pert = Fg_new+matmul(E_pert,Fg_old) ! perturbated Fg call math_invert3x3(Fp_pert,invFp_pert,det,error)
Tstar_v_pert = Tstar_v ! initial guess from end of time step if (error) then
state_pert = state_new ! initial guess from end of time step msg = 'inversion of Fp_pert'
call CPFEM_timeIntegration(msg,Lp,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, & return
dt,cp_en,CPFEM_in,grain,Fg_pert,Fg_old,Fp_old,state_old) endif
if (msg /= 'ok') then P_pert = matmul(Fe_pert,&
msg = 'consistent tangent --> '//msg matmul(math_mandel6to33(Tstar_v_pert),transpose(invFp_pert))) ! perturbed first PK
return A(:,:,k,l) = (P_pert-P)/pert_Fg ! dP_ij/dFg_kl
endif enddo
! Remark: (perturbated) Cauchy stress is Mandel hence dcs_de(:,4:6) is too large by sqrt(2)
dcs_de(:,i) = (CPFEM_CauchyStress(Tstar_v_pert,Fe_pert)-cs)/pert_e
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 endif
return return
@ -523,8 +547,8 @@ Inner: do ! inner iteration: Lp
debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1 debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
ROuter = state - state_old - & ROuter = state - state_old - &
dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),& dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),&
grain,CPFEM_in,cp_en) ! evolution of microstructure grain,CPFEM_in,cp_en) ! residuum from evolution of microstructure
state = state - ROuter state = state - ROuter ! update of microstructure
if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer
enddo Outer enddo Outer
@ -539,24 +563,10 @@ Inner: do ! inner iteration: Lp
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by 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) ! calc resulting Fe 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 forall (i=1:3) Tstar_v(i) = Tstar_v(i)+p_hydro ! add hydrostatic component back
return return
END SUBROUTINE END SUBROUTINE
FUNCTION CPFEM_CauchyStress(PK_v,Fe)
!***********************************************************************
!*** Cauchy stress calculation ***
!***********************************************************************
use prec, only: pReal,pInt
use math, only: math_Mandel33to6,math_Mandel6to33,math_det3x3
implicit none
! *** Subroutine parameters ***
real(pReal) PK_v(6), Fe(3,3), CPFEM_CauchyStress(6)
CPFEM_CauchyStress = math_Mandel33to6(matmul(matmul(Fe,math_Mandel6to33(PK_v)),transpose(Fe))/math_det3x3(Fe))
return
END FUNCTION
END MODULE END MODULE

4
trunk/prec.f90
View File

@ -7,7 +7,7 @@
! *** 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 real(pReal), parameter :: relevantStrain = 1.0e-7_pReal
! *** Numerical parameters *** ! *** Numerical parameters ***
@ -17,7 +17,7 @@
integer(pInt), parameter :: nReg = 1_pInt ! regularization attempts for Jacobi inversion integer(pInt), parameter :: nReg = 1_pInt ! regularization attempts for Jacobi inversion
real(pReal), parameter :: pert_Fg = 1.0e-5_pReal ! strain perturbation for FEM Jacobi real(pReal), parameter :: pert_Fg = 1.0e-5_pReal ! strain perturbation for FEM Jacobi
integer(pInt), parameter :: nOuter = 10_pInt ! outer loop limit integer(pInt), parameter :: nOuter = 10_pInt ! outer loop limit
integer(pInt), parameter :: nInner = 200_pInt ! inner loop limit integer(pInt), parameter :: nInner = 1000_pInt ! inner loop limit
real(pReal), parameter :: reltol_Outer = 1.0e-4_pReal ! relative tolerance in outer loop (state) real(pReal), parameter :: reltol_Outer = 1.0e-4_pReal ! relative tolerance in outer loop (state)
real(pReal), parameter :: reltol_Inner = 1.0e-6_pReal ! relative tolerance in inner loop (Lp) real(pReal), parameter :: reltol_Inner = 1.0e-6_pReal ! relative tolerance in inner loop (Lp)
real(pReal), parameter :: abstol_Inner = 1.0e-8_pReal ! absolute tolerance in inner loop (Lp) real(pReal), parameter :: abstol_Inner = 1.0e-8_pReal ! absolute tolerance in inner loop (Lp)