DAMASK_EICMD/trunk/CPFEM.f90

883 lines
27 KiB
Fortran

! ---------------------------
MODULE CPFEM
! ---------------------------
! *** CPFEM engine ***
use prec, only: pRe,pIn
implicit none
! ****************************************************************
! *** General variables for the material behaviour calculation ***
! ****************************************************************
real(pRe), allocatable :: CPFEM_stress_all (:,:,:)
real(pRe), allocatable :: CPFEM_jacobi_all (:,:,:,:)
real(pRe), allocatable :: CPFEM_results (:,:,:,:)
real(pRe), allocatable :: CPFEM_thickness (:,:)
real(pRe), allocatable :: CPFEM_ini_ori (:,:,:,:)
real(pRe), allocatable :: CPFEM_sigma_old (:,:,:,:)
real(pRe), allocatable :: CPFEM_sigma_new (:,:,:,:)
real(pRe), allocatable :: CPFEM_Fp_old (:,:,:,:,:)
real(pRe), allocatable :: CPFEM_Fp_new (:,:,:,:,:)
real(pRe), allocatable :: CPFEM_tauc_slip_old(:,:,:,:)
real(pRe), allocatable :: CPFEM_tauc_slip_new(:,:,:,:)
real(pRe), allocatable :: CPFEM_g_old (:,:,:,:)
real(pRe), allocatable :: CPFEM_g_new (:,:,:,:)
real(pRe), allocatable :: CPFEM_jaco_old (:,:,:,:)
real(pRe), allocatable :: CPFEM_mat (:,:)
CONTAINS
!***********************************************************************
!*** This routine allocates the arrays defined in module mpie ***
!*** and initializes them ***
!***********************************************************************
subroutine ALLOCATION(mpie_numel,mpie_nip)
use prec, only: pRe,pIn
use IO, only: _error
use math
use mesh
use constitutive
implicit none
integer(pIn) i
! *** mpie.marc parameters ***
allocate(CPFEM_stress_all(6,mesh_Nelems,mesh_Nips))
allocate(CPFEM_jacobi_all(6,6,mesh_Nelems,mesh_Nips))
CPFEM_stress_all=0.0_pRe
CPFEM_jacobi_all=0.0_pRe
! *** User defined results ***
allocate(CPFEM_results(constitutive_Nresults,
& constitutive_maxNgrains,
& mesh_Nelems,mesh_Nips))
CPFEM_results=0.0_pRe
! *** Relative sheet thickness ***
allocate(CPFEM_thickness(mesh_Nelems,mesh_Nips))
CPFEM_thickness=0.0_pRe
! *** Initial orientations ***
allocate(CPFEM_ini_ori(3,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
CPFEM_ini_ori=0.0_pRe
! *** Second Piola-Kirchoff stress tensor at (t=t0) and (t=t1) ***
allocate(CPFEM_sigma_old(6,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
CPFEM_sigma_old=0.0_pRe
CPFEM_sigma_new=0.0_pRe
! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
allocate(CPFEM_Fp_old(3,3,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
CPFEM_Fp_old=0.0_pRe
CPFEM_Fp_new=0.0_pRe
do i=1,3
CPFEM_Fp_old(i,i,:,:,:)=1.0_pRe
CPFEM_Fp_new(i,i,:,:,:)=1.0_pRe
enddo
! QUESTION: would it be wise to outsource these to _constitutive_ ??
! *** Slip resistances at (t=t0) and (t=t1) ***
allocate(CPFEM_tauc_slip_old(nslip,constitutive_maxNgrains,mesh_Nelems,
& mesh_Nips))
allocate(CPFEM_tauc_slip_new(nslip,constitutive_maxNgrains,mesh_Nelems,
& mesh_Nips))
CPFEM_tauc_slip_old=0.0_pRe
CPFEM_tauc_slip_new=0.0_pRe
! *** Cumulative shear at (t=t0) and (t=t1) ***
! QUESTION which nslip to use here ?!?
allocate(CPFEM_g_old(nslip,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
allocate(CPFEM_g_new(nslip,constitutive_maxNgrains,mesh_Nelems,mesh_Nips))
CPFEM_g_old=0.0_pRe
CPFEM_g_new=0.0_pRe
! *** Old jacobian (consistent tangent) ***
allocate(CPFEM_jaco_old(6,6,mesh_Nelems,mesh_Nips))
! *** Output to MARC output file ***
write(6,*)
write(6,*) 'Arrays allocated:'
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_thickness: ', shape(CPFEM_thickness)
write(6,*) 'CPFEM_ini_ori: ', shape(CPFEM_ini_ori)
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_tauc_slip_old: ', shape(CPFEM_tauc_slip_old)
write(6,*) 'CPFEM_tauc_slip_new: ', shape(CPFEM_tauc_slip_new)
write(6,*) 'CPFEM_g_old: ', shape(CPFEM_g_old)
write(6,*) 'CPFEM_g_new: ', shape(CPFEM_g_new)
write(6,*) 'CPFEM_jaco_old: ', shape(CPFEM_jaco_old)
write(6,*)
call flush(6)
return
end
subroutine CPFEM_general_material(
& CPFEM_s, ! Stress vector
& CPFEM_d, ! Jacobi matrix (consistent tangent)
& CPFEM_ndi, ! Dimension
& CPFEM_ffn, ! Deformation gradient at begin of increment
& CPFEM_ffn1, ! Deformation gradient at end of increment
& CPFEM_inc, ! Increment number
& CPFEM_subinc, ! Subincrement number
& CPFEM_cn, ! Cycle number
& CPFEM_tinc, ! Time increment (dt)
& CPFEM_timefactor, ! Factor for timestep correction
! & mesh_Nelems, ! Number of elements in mesh
! & CPFEM_nip, ! Maximum number of integration points per element
& CPFEM_en, ! Element number
& CPFEM_in, ! Integration point number
& CPFEM_mn, ! Material number
& CPFEM_dimStress ! Dimension of stress/strain vector
&)
!***********************************************************************
!*** This routine calculates the material behaviour ***
!***********************************************************************
use prec, only: pRe,pIn
use IO, only _error
use math
use mesh
use constitutive
implicit none
! *** Definition of variables ***
integer(pIn) CPFEM_ndi,CPFEM_inc,CPFEM_subinc,CPFEM_cn,
& CPFEM_en,CPFEM_in,CPFEM_mn,CPFEM_dimStress
real(pRe) CPFEM_timefactor,CPFEM_tinc,CPFEM_s(CPFEM_dimStress),
& CPFEM_d(CPFEM_dimStress,CPFEM_dimStress),
& CPFEM_ffn(3,3),CPFEM_ffn1(3,3)
! QUESTION which nslip to use?
real(pRe) Fp_old(3,3),tauc_slip_old(nslip),
& tauc_slip_new(nslip),g_old(nslip),
& g_new(nslip),Tstar_v(6),
& Fp_new(3,3),cs(6),phi1mis(2),PHImis(2),phi2mis(2),
& cd(6,6),ori_mat(3,3),hh6(6,6)
integer(pIn) jpara,nori
real(pRe) phi1,PHI,phi2,scatter,vf,alpha1,alpha2,beta1,
& beta2,phi1_s,PHI_s,phi2_s,p10,P0,p20,p11,P1,p21,
& dgmax,dgmaxc,orimis
integer(pIn) i,iori,iconv,ising,icut
! *** Numerical parameters ***
! *** How often the jacobian is recalculated ***
integer (pIn), parameter :: ijaco=1_pIn
! *** Reference shear rate for the calculation of CPFEM_timefactor ***
real (pRe), parameter :: dgs=0.01_pRe
! *** Initialization step ***
if (CPFEM_first_call==1_pIn) then
call INITIALIZATION(mesh_Nelems,CPFEM_nip)
CPFEM_first_call=0_pIn
endif
! *** Case of a new increment ***
if (CPFEM_inc.NE.CPFEM_inc_old) then
CPFEM_sigma_old=CPFEM_sigma_new
CPFEM_Fp_old=CPFEM_Fp_new
CPFEM_tauc_slip_old=CPFEM_tauc_slip_new
CPFEM_g_old=CPFEM_g_new
CPFEM_inc_old=CPFEM_inc
CPFEM_subinc_old=1_pIn
CPFEM_timefactor_max=0.0_pRe
endif
! *** case of a new subincrement:update starting with subinc 2 ***
if (CPFEM_subinc.GT.CPFEM_subinc_old) then
CPFEM_sigma_old=CPFEM_sigma_new
CPFEM_Fp_old=CPFEM_Fp_new
CPFEM_tauc_slip_old=CPFEM_tauc_slip_new
CPFEM_g_old=CPFEM_g_new
CPFEM_subinc_old=CPFEM_subinc
endif
! *** Flag for recalculation of jacobian ***
jpara=1_pIn
! ************************************
! *** Orientation initialization ***
! ************************************
! *** Number of components per state ***
nori=CPFEM_mat(CPFEM_mn,1)
if (CPFEM_inc==0_pIn) then
! *** Three dimensional stress state ***
if (CPFEM_ndi.NE.3_pIn) then
call CPFEM_error(300)
endif
if ((CPFEM_en==1_pIn).AND.(CPFEM_in==1_pIn)) then
write(6,*) 'MPIE Material Routine Ver. 0.1 by L. Hantcherli'
write(6,*)
write(6,*) 'Orientation initialization'
call flush(6)
endif
i=1
do while (i.LE.nori)
! *** Direct ODF sampling ***
if (CPFEM_mat(CPFEM_mn,2)==2) then
call CPFEM_odf_ori(CPFEM_cko(CPFEM_mn,:,:,:,:),
& CPFEM_odfmax(CPFEM_mn),phi1,PHI,phi2)
else
! *** Gauss/Spherical component ***
if (CPFEM_mat(CPFEM_mn,7*i-4)==1) then
phi1=CPFEM_mat(CPFEM_mn,7*i-3)
PHI=CPFEM_mat(CPFEM_mn,7*i-2)
phi2=CPFEM_mat(CPFEM_mn,7*i-1)
scatter=CPFEM_mat(CPFEM_mn,7*i+1)
! *** Random orientation to this component to represent ***
! *** random fraction of texture using halton series ***
if (phi1==400.0) then
call CPFEM_halton_ori(phi1,PHI,phi2,scatter)
! *** ELSE modify orientation to represent gauss distribution ***
else if (scatter.GT.0.1) then
call CPFEM_gauss(phi1,PHI,phi2,scatter)
endif
! *** Fiber component ***
else if (CPFEM_mat(CPFEM_mn,7*i-4)==2) then
alpha1=CPFEM_mat(CPFEM_mn,7*i-3)
alpha2=CPFEM_mat(CPFEM_mn,7*i-2)
beta1=CPFEM_mat(CPFEM_mn,7*i-1)
beta2=CPFEM_mat(CPFEM_mn,7*i)
scatter=CPFEM_mat(CPFEM_mn,7*i+1)
! *** Random orientation to this component to represent ***
! *** random fraction of texture using random numbers ***
if (alpha1==400.0) then
call CPFEM_random_ori(phi1,PHI,phi2,scatter)
! *** ELSE calculate orientation to represent fiber component ***
else if (scatter.GT.0.1) then
call CPFEM_fiber(alpha1,alpha2,beta1,beta2,
& scatter,phi1,PHI,phi2)
endif
else
call CPFEM_error(510)
endif
endif
CPFEM_ini_ori(1,i,CPFEM_en,CPFEM_in)=phi1
CPFEM_ini_ori(2,i,CPFEM_en,CPFEM_in)=PHI
CPFEM_ini_ori(3,i,CPFEM_en,CPFEM_in)=phi2
! *** Orientation matrix ***
call CPFEM_euldreh(phi1,PHI,phi2,ori_mat)
CPFEM_Fp_old(:,:,i,CPFEM_en,CPFEM_in)=ori_mat
i=i+1
! *** If symmetric component, creation of additional three orientations ***
if (CPFEM_mat(CPFEM_mn,2)==1) then
! *** First one ***
phi1_s=180.0_pRe-phi1
if (phi1_s.LT.0.0_pRe) phi1_s=phi1_s+360.0_pRe
PHI_s=180.0_pRe-PHI
if (PHI_s.LT.0.0_pRe) PHI_s=PHI_s+360.0_pRe
phi2_s=phi2+180.0_pRe
if (phi2_s.GT.360.0_pRe) phi2_s=phi2_s-360.0_pRe
CPFEM_ini_ori(1,i,CPFEM_en,CPFEM_in)=phi1_s
CPFEM_ini_ori(2,i,CPFEM_en,CPFEM_in)=PHI_s
CPFEM_ini_ori(3,i,CPFEM_en,CPFEM_in)=phi2_s
! *** Orientation matrix for initial orientation ***
call CPFEM_euldreh(phi1_s,PHI_s,phi2_s,ori_mat)
CPFEM_Fp_old(:,:,i,CPFEM_en,CPFEM_in)=ori_mat
i=i+1
! *** Second one ***
phi1_s=360.0_pRe-phi1
PHI_s=180.0_pRe-PHI
if (PHI_s.LT.0.0_pRe) PHI_s=PHI_s+360.0_pRe
phi2_s=phi2+180.0_pRe
if (phi2_s.GT.360.0_pRe) phi2_s=phi2_s-360.0_pRe
CPFEM_ini_ori(1,i,CPFEM_en,CPFEM_in)=phi1_s
CPFEM_ini_ori(2,i,CPFEM_en,CPFEM_in)=PHI_s
CPFEM_ini_ori(3,i,CPFEM_en,CPFEM_in)=phi2_s
! *** Orientation matrix for initial orientation ***
call CPFEM_euldreh(phi1_s,PHI_s,phi2_s,ori_mat)
CPFEM_Fp_old(:,:,i,CPFEM_en,CPFEM_in)=ori_mat
i=i+1
! *** Third one ***
phi1_s=phi1+180.0_pRe
if (phi1_s.GT.360.0_pRe) phi1_s=phi1_s-360.0_pRe
PHI_s=PHI
phi2_s=phi2
CPFEM_ini_ori(1,i,CPFEM_en,CPFEM_in)=phi1_s
CPFEM_ini_ori(2,i,CPFEM_en,CPFEM_in)=PHI_s
CPFEM_ini_ori(3,i,CPFEM_en,CPFEM_in)=phi2_s
! *** Orientation matrix for initial orientation ***
call CPFEM_euldreh(phi1_s,PHI_s,phi2_s,ori_mat)
CPFEM_Fp_old(:,:,i,CPFEM_en,CPFEM_in)=ori_mat
i=i+1
else if ((CPFEM_mat(CPFEM_mn,2).NE.0).AND.
& (CPFEM_mat(CPFEM_mn,2).NE.2)) then
call CPFEM_error(520)
endif
enddo
CPFEM_tauc_slip_old(:,:,CPFEM_en,CPFEM_in)=s0_slip
endif
! ************************************
! *** CP-FEM Calculation ***
! ************************************
! *** Reinitialization of stress and consistent tangent ***
CPFEM_s=0
CPFEM_d=0
! *** Loop over all the components ***
do iori=1,nori
! *** Initialization of the matrices for t=t0 ***
Fp_old=CPFEM_Fp_old(:,:,iori,CPFEM_en,CPFEM_in)
tauc_slip_old=CPFEM_tauc_slip_old(:,iori,CPFEM_en,CPFEM_in)
tauc_slip_new=tauc_slip_old
g_old=CPFEM_g_old(:,iori,CPFEM_en,CPFEM_in)
Tstar_v=CPFEM_sigma_old(:,iori,CPFEM_en,CPFEM_in)
p10=CPFEM_ini_ori(1,iori,CPFEM_en,CPFEM_in)
P0=CPFEM_ini_ori(2,iori,CPFEM_en,CPFEM_in)
p20=CPFEM_ini_ori(3,iori,CPFEM_en,CPFEM_in)
vf=CPFEM_mat(CPFEM_mn,7*iori+2)
! *** Calculation of the solution at t=t1 ***
if (modulo(CPFEM_cn,ijaco).EQ.0) then
call CPFEM_stress(CPFEM_tinc,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
& g_old,g_new,tauc_slip_old,
& tauc_slip_new,
& Tstar_v,cs,cd,p11,P1,p21,dgmaxc,1,iconv,ising,
& icut,CPFEM_en,CPFEM_in,CPFEM_inc)
! *** Evaluation of ising ***
! *** ising=2 => singular matrix in jacobi calculation ***
! *** => use old jacobi ***
if (ising==2) then
jpara=0
endif
! *** Calculation of the consistent tangent ***
CPFEM_d=CPFEM_d+vf*cd
else
call CPFEM_stress(CPFEM_tinc,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
& g_old,g_new,tauc_slip_old,
& tauc_slip_new,
& Tstar_v,cs,hh6,p11,P1,p21,dgmaxc,0,iconv,
& ising,icut,CPFEM_en,CPFEM_in,CPFEM_inc)
jpara=0
endif
! *** Cases of unsuccessful calculations ***
! *** Evaluation od ising ***
! *** ising!=0 => singular matrix ***
if (ising==1) then
write(6,*) 'Singular matrix!'
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',CPFEM_en
call CPFEM_error(700)
CPFEM_timefactor=1.e5_pRe
return
endif
! *** Evaluation of icut ***
! *** icut!=0 => too many cutbacks ***
if (icut==1) then
write(6,*) 'Too many cutbacks'
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',CPFEM_en
call CPFEM_error(600)
CPFEM_timefactor=1.e5_pRe
return
endif
! *** Evaluation of iconv ***
! *** iconv!=0 => no convergence ***
if (iconv==1) then
write(6,*) 'Inner loop did not converged!'
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element:',CPFEM_en
call CPFEM_error(600)
CPFEM_timefactor=1.e5_pRe
return
else
if (iconv==2) then
write(6,*) 'Outer loop did not converged!'
write(6,*) 'Integration point: ',CPFEM_in
write(6,*) 'Element: ',CPFEM_en
call CPFEM_error(600)
CPFEM_timefactor=1.e5_pRe
return
endif
endif
! *** Update the differents matrices for t=t1 ***
CPFEM_Fp_new(:,:,iori,CPFEM_en,CPFEM_in)=Fp_new
CPFEM_tauc_slip_new(:,iori,CPFEM_en,CPFEM_in)=tauc_slip_new
CPFEM_g_new(:,iori,CPFEM_en,CPFEM_in)=g_new
CPFEM_sigma_new(:,iori,CPFEM_en,CPFEM_in)=Tstar_v
! *** Calculation of the misorientation ***
phi1mis(1)=p10
PHImis(1)=P0
phi2mis(1)=p20
phi1mis(2)=p11
PHImis(2)=P1
phi2mis(2)=p21
call CPFEM_misori(phi1mis,PHImis,phi2mis,orimis)
! *** Update the results plotted in MENTAT ***
CPFEM_results(1,iori,CPFEM_en,CPFEM_in)=p11
CPFEM_results(2,iori,CPFEM_en,CPFEM_in)=P1
CPFEM_results(3,iori,CPFEM_en,CPFEM_in)=p21
CPFEM_results(4,iori,CPFEM_en,CPFEM_in)=orimis
CPFEM_results(5,iori,CPFEM_en,CPFEM_in)=sum(g_new)
CPFEM_results(7,iori,CPFEM_en,CPFEM_in)=sum(tauc_slip_new)/nslip
CPFEM_results(21,iori,CPFEM_en,CPFEM_in)=vf
! *** Evaluation of the maximum shear ***
dgmax=max(dgmax,dgmaxc)
! *** Evaluation of the average Cauchy stress ***
CPFEM_s=CPFEM_s+vf*cs
enddo
! *** End of the loop over the components ***
! *************************************
! *** End of the CP-FEM Calculation ***
! *************************************
! *** Approximate relative element thickness ***
call CPFEM_thick(CPFEM_ffn1,CPFEM_en,CPFEM_in)
! *** Restoration of the old jacobian if necessary ***
if (jpara==0) then
CPFEM_d=CPFEM_jaco_old(:,:,CPFEM_en,CPFEM_in)
else
! *** Store the new jacobian ***
CPFEM_jaco_old(:,:,CPFEM_en,CPFEM_in)=CPFEM_d
endif
! *** Calculate timefactor ***
CPFEM_timefactor=dgmax/dgs
return
end
subroutine CPFEM_stress(
&CPFEM_tinc,
&CPFEM_ffn,
&CPFEM_ffn1,
&Fp_old,
&Fp_new,
&g_old,
&g_new,
&tauc_slip_old,
&tauc_slip_new,
&Tstar_v,
&cs,
&dcs_de,
&phi1,
&PHI,
&phi2,
&dgmaxc,
&isjaco,
&iconv,
&ising,
&icut,
&CPFEM_en,
&CPFEM_in,
&CPFEM_inc
&)
c********************************************************************
c This routine calculates the stress for a single component
c and manages the independent time incrmentation
c********************************************************************
use mpie
use prec, only: pRe,pIn
implicit none
! *** Definition of variables ***
integer(pIn) isjaco,iconv,ising,icut,CPFEM_en,CPFEM_in,CPFEM_inc
real(pRe) CPFEM_tinc,CPFEM_ffn(3,3),CPFEM_ffn1(3,3),Fp_old(3,3),
& Fp_new(3,3),g_old(nslip),g_new(nslip),
& tauc_slip_old(nslip),tauc_slip_new(nslip),
& Tstar_v(6),
& cs(6),dcs_de(6,6),phi1,PHI,phi2,dgmaxc
integer(pIn) jcut
real(pRe) Tstar_v_h(6),tauc_slip_new_h(nslip),
& dt_i,delta_Fg(3,3),Fg_i(3,3),
& tauc_slip_new_i(nslip),time,mm(6,6)
! *** Numerical parameters ***
integer(pIn), parameter :: ncut=7_pIn
icut=0
! *** First attempt to calculate Tstar and tauc with initial timestep ***
Tstar_v_h=Tstar_v
tauc_slip_new_h=tauc_slip_new
call CPFEM_stress_int(CPFEM_tinc,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
& g_old,g_new,tauc_slip_old,
& tauc_slip_new,
& Tstar_v,cs,dcs_de,phi1,PHI,phi2,dgmaxc,
& isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc)
if ((iconv==0).AND.(ising==0)) then
return
endif
! *** Calculation of stress and resistences with a cut timestep ***
! *** when first try did not converge ***
jcut=1_pIn
dt_i=0.5*CPFEM_tinc
delta_Fg=0.5*(CPFEM_ffn1-CPFEM_ffn)
Fg_i=CPFEM_ffn+delta_Fg
Tstar_v=Tstar_v_h
tauc_slip_new_i=tauc_slip_new_h
! *** Start time ***
time=dt_i
do while (time.LE.CPFEM_tinc)
call CPFEM_stress_int(time,CPFEM_ffn,Fg_i,Fp_old,Fp_new,g_old,
& g_new,tauc_slip_old,
& tauc_slip_new_i,
& Tstar_v,cs,mm,phi1,PHI,
& phi2,dgmaxc,0_pIn,iconv,ising,CPFEM_en,
& CPFEM_in,CPFEM_inc)
if ((iconv==0).AND.(ising==0)) then
time=time+dt_i
Fg_i=Fg_i+delta_Fg
Tstar_v_h=Tstar_v
tauc_slip_new_h=tauc_slip_new_i
else
jcut=jcut+1
if (jcut.GT.ncut) then
icut=1
return
endif
dt_i=0.5*dt_i
time=time-dt_i
delta_Fg=0.5*delta_Fg
Fg_i=Fg_i-delta_Fg
Tstar_v=Tstar_v_h
tauc_slip_new_i=tauc_slip_new_h
endif
enddo
! *** Final calculation of stress and resistences withb full timestep ***
tauc_slip_new=tauc_slip_new_i
call CPFEM_stress_int(CPFEM_tinc,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
& g_old,g_new,tauc_slip_old,
& tauc_slip_new,
& Tstar_v,cs,dcs_de,phi1,PHI,phi2,dgmaxc,
& isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc)
return
end
subroutine CPFEM_stress_int(
&dt, ! Time increment
&Fg_old, ! Old global deformation gradient
&Fg_new, ! New global deformation gradient
&Fp_old, ! Old plastic deformation gradient
&Fp_new, ! New plastic deformation gradient
&g_old, ! Old cumulative plastic strain of a slip system
&g_new, ! New cumulative plastic strain of a slip system
&tauc_slip_old, ! Old resistence of a slip system
&tauc_slip_new, ! New resistence of a slip system
&Tstar_v, ! Second Piola-Kirschoff stress tensor
&cs, ! Cauchy stress vector
&dcs_de, ! Consistent tangent
&phi1, ! Euler angle phi1
&PHI, ! Euler angle PHI
&phi2, ! Euler angle phi2
&dgmaxc,
&isjaco,
&iconv,
&ising,
&CPFEM_en,
&CPFEM_in,
&CPFEM_inc
&)
c********************************************************************
c This routine calculates the stress for a single component
c it is based on the paper by Kalidindi et al.:
c J. Mech. Phys, Solids Vol. 40, No. 3, pp. 537-569, 1992
c it is modified to use anisotropic elasticity matrix
c********************************************************************
use mpie
use prec
implicit none
! *** Definition of variables ***
integer(pIn) isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc
real(pRe) dt,Fg_old(3,3),Fg_new(3,3),Fp_old(3,3),Fp_new(3,3),
& g_old(nslip),g_new(nslip),
& tauc_slip_old(nslip),tauc_slip_new(nslip),
& Tstar_v(6),
& cs(6),dcs_de(6,6),phi1,PHI,phi2,dgmaxc
integer(pIn) ic
real(pRe) gdot_slip(nslip),Fe(3,3),R(3,3),
& U(3,3),de(3,3),tauc2(nslip),Fp2(3,3),
& sgm2(6),cs1(6),dF(3,3),Fg2(3,3),dev(6)
! *** Numerical parameters ***
real(pRe), parameter :: pert_ct=1.0e-5_pRe
! *** Error treatment ***
dgmaxc=0
iconv=0
ising=0
! *********************************************
! *** Calculation of the new Cauchy stress ***
! *********************************************
! *** Call Newton-Raphson method ***
call NEWTON_RAPHSON(dt,Fg_old,Fg_new,Fp_old,Fp_new,Fe,gdot_slip,
& tauc_slip_old,tauc_slip_new,
& Tstar_v,cs,iconv,ising)
! *** Calculation of the new orientation ***
call math_pDecomposition(Fe,U,R,ising)
if (ising==1) then
return
endif
call math_RtoEuler(transpose(R),phi1,PHI,phi2)
! *** Evaluation of the maximum slip shear ***
dgmaxc=maxval(abs(gdot_slip*dt))
g_new=g_old+abs(gdot_slip)*dt
! *** Choice of the calculation of the consistent tangent ***
if (isjaco==0) then
return
endif
! *********************************************
! *** Calculation of the consistent tangent ***
! *********************************************
! *** Calculation of the consistent tangent with perturbation ***
! *** Perturbation on the component of Fg ***
do ic=1,6
! *** Method of small perturbation
dev=0
if(ic.le.3) dev(ic)=pert_ct
if(ic.gt.3) dev(ic)=pert_ct/2
call CPFEM_conv6to33(dev,de)
dF=matmul(de,Fg_old)
Fg2=Fg_new+dF
sgm2=Tstar_v
tauc2=tauc_slip_new
! *** Calculation of the perturbated Cauchy stress ***
call NEWTON_RAPHSON(dt,Fg_old,Fg2,Fp_old,Fp2,Fe,gdot_slip,
& tauc_slip_old,tauc2,
& sgm2,cs1,iconv,ising)
! *** Consistent tangent ***
dcs_de(:,ic)=(cs1-cs)/pert_ct
enddo
return
end
subroutine NEWTON_RAPHSON(
&dt,
&Fg_old,
&Fg_new,
&Fp_old,
&Fp_new,
&Fe,
&gdot_slip,
&tauc_slip_old,
&tauc_slip_new,
&Tstar_v,
&cs,
&iconv,
&ising
&)
!***********************************************************************
!*** NEWTON-RAPHSON Calculation ***
!***********************************************************************
use mpie
use prec
implicit none
! *** Definition of variables ***
integer(pIn) isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc
real(pRe) dt,Fg_old(3,3),Fg_new(3,3),Fp_old(3,3),Fp_new(3,3),
& g_old(nslip),g_new(nslip),
& tauc_slip_old(nslip),tauc_slip_new(nslip),
& Tstar_v(6),cs(6),dcs_de(6,6),phi1,PHI,phi2,dgmaxc
integer(pIn) i,j,k,iouter,iinner,ijac,ic
real(pRe) invFp_old(3,3),det,A(3,3),Estar0_v(6),Tstar0_v(6),
& mm(3,3),mm1(3,3),vv(6),Dslip(6,nslip),
& tau_slip(nslip),gdot_slip(nslip),
& R1(6),norm1,Tstar_v_per(6),R1_per(6),
& Jacobi(6,6),invJacobi(6,6),dTstar_v(6),R2(nslip),
& dtauc_slip(nslip),norm2,dLp(3,3),
& Estar(3,3),Estar_v(6),invFp_new(3,3),
& invFp2(3,3),Lp(3,3),Fe(3,3),
& R(3,3),U(3,3),dgdot_dtaucslip(nslip)
real(pRe) de(3,3),dev(6),tauc2(nslip),fp2(3,3),
& sgm2(6),cs1(6),df(3,3),
& fg2(3,3),tauc_old(nslip),crite,tol_in,tol_out
! *** Numerical parameters ***
integer(pIn), parameter :: nouter=50
real(pRe), parameter :: tol_outer=1.0e-4_pRe
integer(pIn), parameter :: ninner=2000
real(pRe), parameter :: tol_inner=1.0e-3_pRe
real(pRe), parameter :: eta=13.7_pRe
integer(pIn), parameter :: numerical=0
real(pRe), parameter :: pert_nr=1.0e-8_pRe
crite=eta*s0_slip/n_slip
! *** Tolerences ***
tol_in=tol_inner*s0_slip
tol_out=tol_outer*s0_slip
! *** Error treatment ***
dgmaxc=0
iconv=0
ising=0
! *** Calculation of Fp_old(-1) ***
invFp_old=Fp_old
call invert(invFp_old,3,0,0,det,3)
if (det==0.0_pRe) then
ising=1
return
endif
! *** Calculation of A and T*0 (see Kalidindi) ***
A=matmul(transpose(matmul(Fg_new,invFp_old)),
& matmul(Fg_new,invFp_old))
call CPFEM_conv33to6((A-I3)/2,Estar0_v)
Tstar0_v=matmul(Cslip_66,Estar0_v)
! *** Calculation of Dslip (see Kalidindi) ***
do i=1,nslip
mm=matmul(A,Sslip(i,:,:))
mm1=(mm+transpose(mm))/2
vv = math_33to6(mm1)
Dslip(:,i)=matmul(Cslip_66,vv)
enddo
! *** Second level of iterative procedure: Resistences ***
do iouter=1,nouter
! *** First level of iterative procedure: Stresses ***
do iinner=1,ninner
! *** Calculation of gdot_slip ***
do i=1,nslip
tau_slip(i)=dot_product(Tstar_v,Sslip_v(i,:))
enddo
call slip_rate(tau_slip,tauc_slip_new,gdot_slip,
& dgdot_dtaucslip)
! *** Evaluation of Tstar and Gn (see Kalidindi) ***
vv=0
do i=1,nslip
vv=vv-gdot_slip(i)*Dslip(:,i)
enddo
R1=Tstar_v-Tstar0_v-vv*dt
norm1=maxval(abs(R1))
if (norm1.LT.tol_in) then
goto 100
endif
! *** Jacobi Calculation ***
if (numerical==1) then
! *** Perturbation method ***
else
! *** Analytical Calculation ***
Jacobi=0
do i=1,nslip
do j=1,6
do k=1,6
Jacobi(j,k)=Jacobi(j,k)
& +Dslip(j,i)*Sslip_v(i,k)*dgdot_dtaucslip(i)
enddo
enddo
enddo
Jacobi=Jacobi*dt
do i=1,6
Jacobi(i,i)=1.0_pRe+Jacobi(i,i)
enddo
endif
! *** End of the Jacobi calculation ***
! *** Inversion of the Jacobi matrix ***
invJacobi=Jacobi
call invert(invJacobi,6,0,0,det,6)
if (det==0.0_pRe) then
do i=1,6
Jacobi(i,i)=1.05d0*maxval(Jacobi(i,:))
enddo
invJacobi=Jacobi
call invert(invJacobi,6,0,0,det,6)
if (det==0.0_pRe) then
ising=1
return
endif
endif
dTstar_v=matmul(invJacobi,R1)
! *** Correction (see Kalidindi) ***
do i=1,6
if (abs(dTstar_v(i)).GT.crite) then
dTstar_v(i)=sign(crite,dTstar_v(i))
endif
enddo
Tstar_v=Tstar_v-dTstar_v
enddo
iconv=1
return
! *** End of the first level of iterative procedure ***
100 continue
call hardening(tauc_slip_new,gdot_slip,dtauc_slip)
! *** Arrays of residuals ***
R2=tauc_slip_new-tauc_slip_old-dtauc_slip*dt
norm2=maxval(abs(R2))
if (norm2.LT.tol_out) then
goto 200
endif
tauc_slip_new=tauc_slip_old+dtauc_slip*dt
enddo
iconv=2
return
! *** End of the second level of iterative procedure ***
200 continue
call plastic_vel_grad(dt,tau_slip,tauc_slip_new,Lp)
! *** Calculation of Fp(t+dt) (see Kalidindi) ***
dLp=I3+Lp*dt
Fp_new=matmul(dLp,Fp_old)
call CPFEM_determ(Fp_new,det)
Fp_new=Fp_new/det**(1.0_pRe/3.0_pRe)
! *** Calculation of F*(t+dt) (see Kalidindi) ***
invFp_new=Fp_new
call invert(invFp_new,3,0,0,det,3)
if (det==0.0_pRe) then
ising=1
return
endif
Fe=matmul(Fg_new,invFp_new)
! *** Calculation of Estar ***
Estar=0.5_pRe*(matmul(transpose(Fe),Fe)-I3)
call CPFEM_conv33to6(Estar,Estar_v)
! *** Calculation of the Cauchy stress ***
call cauchy_stress(Estar_v,Fe,cs)
return
end
end module