620 lines
24 KiB
Fortran
620 lines
24 KiB
Fortran
! last modified 28.03.07
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! ---------------------------
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MODULE CPFEM
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! ---------------------------
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! *** CPFEM engine ***
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!
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use prec, only: pReal,pInt
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implicit none
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!
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! ****************************************************************
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! *** General variables for the material behaviour calculation ***
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! ****************************************************************
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real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_all
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobi_all
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_all
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_all
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ini_ori
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_old
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_old
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integer(pInt) :: CPFEM_inc_old = 0_pInt
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integer(pInt) :: CPFEM_subinc_old = 1_pInt
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integer(pInt) :: CPFEM_Nresults = 3_pInt
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logical :: CPFEM_first_call = .true.
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CONTAINS
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!***********************************************************************
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!*** This routine checks for initialization, variables update and ***
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!*** calls the actual material model ***
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!***********************************************************************
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subroutine cpfem_general(ffn, ffn1, CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_dt, cp_en, CPFEM_in)
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!
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use prec, only: pReal,pInt
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! use CPFEM, only: CPFEM_ffn_all, CPFEM_ffn1_all, CPFEM_inc_old
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! use IO, only: IO_init
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use constitutive, only: constitutive_state_old, constitutive_state_new
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implicit none
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!
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real(pReal) ffn(3,3), ffn1(3,3), CPFEM_dt
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integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, cp_en, CPFEM_in
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!
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! initialization step
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if (CPFEM_first_call) then
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! three dimensional stress state ?
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! call IO_init()
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call mesh_init()
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call constitutive_init()
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call math_init()
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call CPFEM_init()
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CPFEM_first_call = .false.
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endif
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! not a new increment
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if (CPFEM_inc==CPFEM_inc_old) then
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! case of a new subincrement:update starting with subinc 2
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if (CPFEM_subinc > CPFEM_subinc_old) then
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CPFEM_sigma_old = CPFEM_sigma_new
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CPFEM_Fp_old = CPFEM_Fp_new
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constitutive_state_old = constitutive_state_new
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CPFEM_subinc_old = CPFEM_subinc
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endif
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! case of a new increment
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else
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CPFEM_sigma_old = CPFEM_sigma_new
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CPFEM_Fp_old = CPFEM_Fp_new
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constitutive_state_old = constitutive_state_new
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CPFEM_inc_old = CPFEM_inc
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CPFEM_subinc_old = 1_pInt
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endif
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!
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! get cp element number for fe element number
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CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn
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CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1
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call CPFEM_general_material(CPFEM_cn, CPFEM_dt, cp_en, CPFEM_in)
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return
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end subroutine
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!***********************************************************************
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!*** This routine allocates the arrays defined in module CPFEM ***
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!*** and initializes them ***
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!***********************************************************************
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subroutine CPFEM_init()
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!
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use prec, only: pReal,pInt
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! use math, only: math_I3
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use mesh
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use constitutive
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!
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implicit none
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!
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integer(pInt) i
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!
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! *** mpie.marc parameters ***
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allocate(CPFEM_ffn_all(3,3,mesh_maxNips,mesh_NcpElems))
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allocate(CPFEM_ffn1_all(3,3,mesh_maxNips,mesh_NcpElems))
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allocate(CPFEM_stress_all(6,mesh_maxNips,mesh_NcpElems))
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allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems))
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CPFEM_ffn_all = 0.0_pReal
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CPFEM_ffn1_all = 0.0_pReal
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CPFEM_stress_all = 0.0_pReal
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CPFEM_jacobi_all = 0.0_pReal
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!
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! *** User defined results !!! MISSING incorporate consti_Nresults ***
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allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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CPFEM_results = 0.0_pReal
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!
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! *** Second Piola-Kirchoff stress tensor at (t=t0) and (t=t1) ***
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allocate(CPFEM_sigma_old(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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CPFEM_sigma_old = 0.0_pReal
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CPFEM_sigma_new = 0.0_pReal
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!
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! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
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allocate(CPFEM_Fp_old(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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CPFEM_Fp_old = 0.0_pReal
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CPFEM_Fp_new = 0.0_pReal
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!
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! *** Old jacobian (consistent tangent) ***
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allocate(CPFEM_jaco_old(6,6,mesh_maxNips,mesh_NcpElems))
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CPFEM_jaco_old = 0.0_pReal
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!
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! *** Output to MARC output file ***
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write(6,*)
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write(6,*) 'Arrays allocated:'
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write(6,*) 'CPFEM_ffn_all: ', shape(CPFEM_ffn_all)
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write(6,*) 'CPFEM_ffn1_all: ', shape(CPFEM_ffn1_all)
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write(6,*) 'CPFEM_stress_all: ', shape(CPFEM_stress_all)
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write(6,*) 'CPFEM_jacobi_all: ', shape(CPFEM_jacobi_all)
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write(6,*) 'CPFEM_results: ', shape(CPFEM_results)
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write(6,*) 'CPFEM_sigma_old: ', shape(CPFEM_sigma_old)
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write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new)
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write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old)
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write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new)
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write(6,*) 'CPFEM_jaco_old: ', shape(CPFEM_jaco_old)
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write(6,*)
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call flush(6)
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return
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end subroutine
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!
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!
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subroutine CPFEM_general_material(&
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CPFEM_cn,& ! Cycle number
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CPFEM_dt,& ! Time increment (dt)
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cp_en,& ! Element number
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CPFEM_in) ! Integration point number
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!***********************************************************************
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!*** This routine calculates the material behaviour ***
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!***********************************************************************
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use prec, only: pReal,pInt
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! use IO, only: IO_error
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use math
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use mesh
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use constitutive
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!
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implicit none
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!
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! *** Definition of variables ***
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! *** Subroutine parameters ***
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real(pReal) CPFEM_dt
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integer(pInt) CPFEM_cn, cp_en ,CPFEM_in
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! *** Local variables ***
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real(pReal) vf, cs(6), cd(6,6), CPFEM_d(6,6), CPFEM_s(6)
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integer(pInt) jpara,nori, iori, ising, icut, iconv, CPFEM_en
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! *** Numerical parameters ***
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! *** How often the jacobian is recalculated ***
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integer (pInt), parameter :: ijaco = 5_pInt
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! *** Reference shear rate for the calculation of CPFEM_timefactor ***
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real (pReal), parameter :: dgs = 0.01_pReal
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!
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! *** Flag for recalculation of jacobian ***
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jpara = 1_pInt
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! get number of grains from cp element number and integration point number
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nori = constitutive_Ngrains(CPFEM_in,cp_en) !<21><><EFBFBD>
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!
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CPFEM_en = mesh_element(1,cp_en) ! remap back to FE id
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!
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CPFEM_s=0
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CPFEM_d=0
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!
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! *** Loop over all the components ***
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do iori=1,nori
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!
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! *** Initialization of the matrices for t=t0 ***
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! data from constitutive?
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vf = constitutive_matVolFrac(iori,CPFEM_in,cp_en)*constitutive_texVolFrac(iori,CPFEM_in,cp_en) !<21><><EFBFBD>
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! *** Calculation of the solution at t=t1 ***
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! QUESTION use the mod() as flag parameter in the call ??
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if (mod(CPFEM_cn,ijaco)==0) then !<21><><EFBFBD>
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call CPFEM_stress(cs, cd, CPFEM_dt,cp_en,CPFEM_in, iori, ising, icut, iconv, 1_pInt)
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! *** Evaluation of ising ***
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! *** ising=2 => singular matrix in jacobi calculation ***
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! *** => use old jacobi ***
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if (ising==2) jpara=0
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! *** Calculation of the consistent tangent ***
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CPFEM_d=CPFEM_d+vf*cd
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else
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call CPFEM_stress(cs, cd, CPFEM_dt,cp_en,CPFEM_in, iori, ising, icut, iconv, 0_pInt)
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jpara=0
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endif
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! *** Cases of unsuccessful calculations ***
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! *** Evaluation of ising ***
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! *** ising!=0 => singular matrix ***
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if (ising==1) then
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write(6,*) 'Singular matrix!'
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',CPFEM_en
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call IO_error(700)
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! CPFEM_timefactor=1.e5_pReal
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return
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endif
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! *** Evaluation of icut ***
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! *** icut!=0 => too many cutbacks ***
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if (icut==1) then
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write(6,*) 'Too many cutbacks'
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',CPFEM_en
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call IO_error(600)
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! CPFEM_timefactor=1.e5_pReal
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return
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endif
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! *** Evaluation of iconv ***
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! *** iconv!=0 => no convergence ***
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if (iconv==1) then
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write(6,*) 'Inner loop did not converge!'
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',CPFEM_en
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call IO_error(600)
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! CPFEM_timefactor=1.e5_pReal
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return
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else if (iconv==2) then
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write(6,*) 'Outer loop did not converge!'
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',CPFEM_en
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call IO_error(600)
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! CPFEM_timefactor=1.e5_pReal
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return
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endif
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! *** Evaluation of the average Cauchy stress ***
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CPFEM_s=CPFEM_s+vf*cs
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enddo
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! *** End of the loop over the components ***
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! *************************************
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! *** End of the CP-FEM Calculation ***
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! *************************************
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! *** Store the new stress ***
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CPFEM_stress_all(:,CPFEM_in,cp_en)=CPFEM_s
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! *** Store the new jacobian ***
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if (jpara/=0) CPFEM_jaco_old(:,:,CPFEM_in,cp_en)=CPFEM_d
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return
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end subroutine
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!
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!
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subroutine CPFEM_stress(&
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cs,& ! stress vector
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cd,& ! Jacoby matrix
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CPFEM_dt,& ! Time increment (dt)
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cp_en,& ! Element number
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CPFEM_in,& ! Integration point number
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iori,& ! number of orintation
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ising,& ! flag for singular matrix
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icut,& ! flag for too many cut backs
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iconv,& ! flag for non convergence
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isjaco) ! flag whether to calculate Jacoby matrix
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!********************************************************************
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! This routine calculates the stress for a single component
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! and manages the independent time incrmentation
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!********************************************************************
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use prec, only: pReal,pInt
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use constitutive, only: constitutive_Nstatevars, constitutive_state_old, constitutive_state_new, constitutive_Nresults,&
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constitutive_results
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implicit none
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!
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! *** Definition of variables ***
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! *** Subroutine parameters ***
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real(pReal) cs(6), cd(6,6), CPFEM_dt
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integer(pInt) cp_en ,CPFEM_in, iori, ising, icut, iconv, isjaco
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! *** Local variables ***
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real(pReal) Fp_old(3,3), Fp_new(3,3), state_old(constitutive_Nstatevars(iori, CPFEM_in, cp_en))
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real(pReal) state_new(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), Tstar_v(6), CPFEM_ffn(3,3), CPFEM_ffn1(3,3)
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real(pReal) Tstar_v_h(6), state_new_h(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), phi1, PHI, phi2, dt_i
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real(pReal) delta_Fg(3,3), Fg_i(3,3), state_new_i(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), time
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integer(pInt) jcut
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! *** Numerical parameters ***
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integer(pInt), parameter :: ncut=7_pInt
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!
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icut=0
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!
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! *** Initialization of the matrices for t=t0 ***
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Fp_old = CPFEM_Fp_old(:,:,iori,CPFEM_in,cp_en)
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Fp_new = 0.0_pReal
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state_old = constitutive_state_old(:,iori,CPFEM_in,cp_en)
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state_new = state_old
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Tstar_v = CPFEM_sigma_old(:,iori,CPFEM_in,cp_en)
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CPFEM_ffn = CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
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CPFEM_ffn1 = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)
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!
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! *** First attempt to calculate Tstar and tauc with initial timestep ***
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! save copies of Tstar_v and state_new
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Tstar_v_h = Tstar_v
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state_new_h = state_new
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call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, iori, ising, icut, iconv, isjaco, phi1, PHI, phi2,&
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CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,state_old, state_new, Tstar_v)
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if ((iconv==0).AND.(ising==0)) then
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! *** Update the differents matrices for t=t1 ***
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CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new
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constitutive_state_new(:,iori,CPFEM_in,cp_en) = state_new
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CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v
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! *** Update the results plotted in MENTAT ***
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CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1
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CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI
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CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2
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CPFEM_results(4:3+constitutive_Nresults(iori,CPFEM_in,cp_en),iori,CPFEM_in,cp_en)=&
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constitutive_results(1:constitutive_Nresults(iori,CPFEM_in,cp_en),iori,CPFEM_in,cp_en)!<21><><EFBFBD><EFBFBD>
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return
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endif
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!
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! *** Calculation of stress and resistences with a cut timestep ***
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! *** when first try did not converge ***
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jcut=1_pInt
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dt_i=0.5_pReal*CPFEM_dt
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delta_Fg=0.5_pReal*(CPFEM_ffn1-CPFEM_ffn)
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Fg_i=CPFEM_ffn+delta_Fg
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Tstar_v=Tstar_v_h
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state_new_i=state_new_h
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! *** Start time ***
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time=dt_i
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do while (time<=CPFEM_dt)
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call CPFEM_stress_int(cs, cd, time, cp_en,CPFEM_in, iori, ising, icut, iconv, isjaco, phi1, PHI, phi2,&
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CPFEM_ffn, Fg_i,Fp_old,Fp_new,state_old, state_new_i, Tstar_v)
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if ((iconv==0).AND.(ising==0)) then
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time=time+dt_i
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Fg_i=Fg_i+delta_Fg
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Tstar_v_h=Tstar_v
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state_new_h=state_new_i
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else
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jcut=jcut+1_pInt
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if (jcut>ncut) then
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icut=1_pInt
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return
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endif
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dt_i=0.5_pReal*dt_i
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time=time-dt_i
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delta_Fg=0.5_pReal*delta_Fg
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Fg_i=Fg_i-delta_Fg
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Tstar_v=Tstar_v_h
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state_new_i=state_new_h
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endif
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enddo
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!
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! *** Final calculation of stress and resistences with full timestep ***
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state_new=state_new_i
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call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, iori, ising, icut, iconv, isjaco, phi1, PHI, phi2,&
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CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,state_old, state_new, Tstar_v)
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! *** Update the differents matrices for t=t1 ***
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CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new
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constitutive_state_new(:,iori,CPFEM_in,cp_en) = state_new
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CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v
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! *** Update the results plotted in MENTAT ***
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CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1
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CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI
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CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2
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return
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end subroutine
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!
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!
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subroutine CPFEM_stress_int(&
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cs,& ! Cauchy stress vector
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dcs_de,& ! Consistent tangent
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dt,& ! Time increment
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cp_en,& ! Element number
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CPFEM_in,& ! Integration point number
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iori,& ! number of orintation
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ising,& ! flag for singular matrix
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icut,& ! flag for too many cut backs
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iconv,& ! flag for non convergence
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isjaco,& ! flag whether to calculate Jacoby matrix
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phi1,& ! Euler angle
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PHI,& ! Euler angle
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phi2,& ! Euler angle
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Fg_old,& ! Old global deformation gradient
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Fg_new,& ! New global deformation gradient
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Fp_old,& ! Old plastic deformation gradient
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Fp_new,& ! New plastic deformation gradient
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state_old,& ! Old state variable array
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state_new,& ! New state variable array
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Tstar_v) ! Second Piola-Kirschoff stress tensor
|
||
!********************************************************************
|
||
! This routine 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
|
||
!********************************************************************
|
||
use prec, only: pReal,pInt
|
||
use constitutive, only: constitutive_Nstatevars
|
||
use math, only: math_Mandel6to33
|
||
implicit none
|
||
!
|
||
! *** Definition of variables ***
|
||
! *** Subroutine parameters ***
|
||
integer(pInt) cp_en, CPFEM_in, iori, ising, icut, iconv, isjaco
|
||
real(pReal) cs(6), dcs_de(6,6), dt, phi1, PHI, phi2, Fg_old(3,3), Fg_new(3,3)
|
||
real(pReal) Fp_old(3,3), Fp_new(3,3), state_old(constitutive_Nstatevars(iori, CPFEM_in, cp_en))
|
||
real(pReal) state_new(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), Tstar_v(6)
|
||
! *** Local variables ***
|
||
integer(pInt) ic
|
||
real(pReal) Fe(3,3), R(3,3), U(3,3), dev(6), dF(3,3), Fg2(3,3), sgm2(6)
|
||
real(pReal) state2(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), Fp2(3,3), cs1(6)
|
||
! *** Numerical parameters ***
|
||
real(pReal), parameter :: pert_ct=1.0e-5_pReal
|
||
! *** Error treatment ***
|
||
iconv = 0
|
||
ising = 0
|
||
|
||
! *********************************************
|
||
! *** Calculation of the new Cauchy stress ***
|
||
! *********************************************
|
||
|
||
! *** Call Newton-Raphson method ***
|
||
call NEWTON_RAPHSON(dt,cp_en,CPFEM_in,iori,Fg_old,Fg_new,Fp_old,Fp_new,Fe,state_old,state_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)
|
||
!
|
||
! *** Choice of the calculation of the consistent tangent ***
|
||
if (isjaco==0) return
|
||
!
|
||
! *********************************************
|
||
! *** 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<=3) dev(ic) = pert_ct
|
||
if(ic>3) dev(ic) = pert_ct/2
|
||
dF=matmul(math_Mandel6to33(dev),Fg_old)
|
||
Fg2=Fg_new+dF
|
||
sgm2=Tstar_v
|
||
state2=state_new
|
||
|
||
! *** Calculation of the perturbated Cauchy stress ***
|
||
call NEWTON_RAPHSON(dt,cp_en,CPFEM_in,iori,Fg_old,Fg2,Fp_old,Fp2,Fe,state_old,state2,sgm2,cs1,iconv,ising)
|
||
!
|
||
! *** Consistent tangent ***
|
||
dcs_de(:,ic)=(cs1-cs)/pert_ct
|
||
enddo
|
||
!
|
||
return
|
||
end subroutine
|
||
!
|
||
!
|
||
subroutine NEWTON_RAPHSON(&
|
||
dt,&
|
||
cp_en,& ! Element number
|
||
CPFEM_in,& ! Integration point number
|
||
iori,& ! number of orintation
|
||
Fg_old,&
|
||
Fg_new,&
|
||
Fp_old,&
|
||
Fp_new,&
|
||
Fe,&
|
||
state_old,&
|
||
state_new,&
|
||
Tstar_v,&
|
||
cs,&
|
||
iconv,&
|
||
ising)
|
||
!***********************************************************************
|
||
!*** NEWTON-RAPHSON Calculation ***
|
||
!***********************************************************************
|
||
use prec, only: pReal,pInt
|
||
use constitutive, only: constitutive_Nstatevars, constitutive_HomogenizedC, constitutive_dotState
|
||
use math
|
||
implicit none
|
||
! *** Definition of variables ***
|
||
! *** Subroutine parameters ***
|
||
integer(pInt) cp_en, CPFEM_in, iori, iconv, ising
|
||
real(pReal) dt,Fg_old(3,3),Fg_new(3,3),Fp_old(3,3),Fp_new(3,3), Fe(3,3)
|
||
real(pReal) state_old(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), state_new(constitutive_Nstatevars(iori, CPFEM_in, cp_en))
|
||
real(pReal) Tstar_v(6), cs(6)
|
||
! *** Local variables ***
|
||
real(pReal) tol_in, tol_out, invFp_old(3,3), det, A(3,3), C_66(6,6), Lp(3,3), dLp(3,3,3,3)
|
||
real(pReal) I3tLp(3,3), help(3,3), help1(3,3,3,3), Tstar0_v(6), R1(6), R1s(6), norm1, tdLp(3,3)
|
||
real(pReal) dstate(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), R2(constitutive_Nstatevars(iori, CPFEM_in, cp_en))
|
||
real(pReal) R2s(constitutive_Nstatevars(iori, CPFEM_in, cp_en)), norm2, invFp_new(3,3), Estar(3,3)
|
||
real(pReal) Estar_v(6), Jacobi(6,6), invJacobi(6,6), dTstar_v(6), help2(6,6)
|
||
integer(pInt) iouter, iinner , dummy, err, i, j, k, l, m
|
||
! *** Numerical parameters ***
|
||
integer(pInt), parameter :: nouter = 50_pInt
|
||
real(pReal), parameter :: tol_outer = 1.0e-4_pReal
|
||
integer(pInt), parameter :: ninner = 2000_pInt
|
||
real(pReal), parameter :: tol_inner = 1.0e-3_pReal
|
||
real(pReal), parameter :: crite = 1.0e-1_pReal
|
||
|
||
! crite=eta*constitutive_s0_slip/constitutive_n_slip !<21><><EFBFBD>
|
||
!
|
||
! *** Tolerances ***
|
||
! tol_in = tol_inner*s0_slip !<21><><EFBFBD>
|
||
! tol_out = tol_outer*s0_slip !<21><><EFBFBD>
|
||
!
|
||
! *** Error treatment ***
|
||
iconv = 0
|
||
ising = 0
|
||
!
|
||
! initialize new state
|
||
state_new=state_old
|
||
! *** Calculation of Fp_old(-1) ***
|
||
call invert3x3(Fp_old, invFp_old, det, err) !<21><><EFBFBD>
|
||
if (err==1_pInt) then
|
||
ising=1
|
||
return
|
||
endif
|
||
!
|
||
! *** Calculation of A and T*0 (see Kalidindi) ***
|
||
A = matmul(Fg_new,invFp_old) ! actually Fe
|
||
A = matmul(transpose(A), A)
|
||
C_66=constitutive_HomogenizedC(iori, CPFEM_in, cp_en) !<21><><EFBFBD>
|
||
Tstar_v=matmul(C_66, math_Mandel33to6(A-math_I3)) ! fully elastic guess
|
||
! QUESTION follow former plastic slope to guess better?
|
||
!
|
||
! *** Second level of iterative procedure: Resistences ***
|
||
do iouter=1,nouter
|
||
! *** First level of iterative procedure: Stresses ***
|
||
do iinner=1,ninner
|
||
!
|
||
! *** Calculation of gdot_slip ***
|
||
call constitutive_LpAndItsTangent(Tstar_v, iori, CPFEM_in, cp_en, Lp, dLp)
|
||
I3tLp = math_I3-dt*Lp
|
||
help=matmul(transpose(I3tLp),matmul(A, I3tLp))-math_I3
|
||
Tstar0_v = 0.5_pReal * matmul(C_66, math_Mandel33to6(help))
|
||
R1=Tstar_v-Tstar0_v
|
||
if (maxval(abs(R1/maxval(abs(Tstar_v)))) < tol_inner) goto 100
|
||
!
|
||
! *** Jacobi Calculation: dRes/dTstar ***
|
||
help=matmul(A, I3tLp)
|
||
help1=0
|
||
forall(i=1:3, j=1:3, k=1:3, l=1:3,m=1:3)&
|
||
help1(i,j,k,l)=help1(i,j,k,l)+help(i,m)*dLp(m,j,k,l)+help(j,m)*dLp(m,i,l,k)
|
||
help2=math_Mandel3333to66(help1)
|
||
Jacobi= 0.5_pReal*matmul(C_66, help2) + math_identity2nd(6)
|
||
call math_invert6x6(Jacobi, invJacobi, dummy, err) !<21><><EFBFBD>
|
||
if (err==1_pInt) then
|
||
forall (i=1:6) Jacobi(i,i)=1.05d0*maxval(Jacobi(i,:)) ! regularization
|
||
call math_invert6x6(Jacobi, invJacobi, dummy, err)
|
||
if (err==1_pInt) then ! sorry, can't help here!!
|
||
ising=1
|
||
return
|
||
endif
|
||
endif
|
||
dTstar_v=matmul(invJacobi,R1) ! correction to Tstar
|
||
|
||
! *** Correction (see Kalidindi) ***
|
||
forall(i=1:6, abs(dTstar_v(i)) > crite*maxval(abs(Tstar_v))) &
|
||
dTstar_v(i) = sign(crite*maxval(abs(Tstar_v)),dTstar_v(i))
|
||
|
||
Tstar_v=Tstar_v-dTstar_v
|
||
!
|
||
enddo
|
||
iconv=1
|
||
return
|
||
! *** End of the first level of iterative procedure ***
|
||
|
||
100 dstate=dt*constitutive_dotState(Tstar_v, iori, CPFEM_in, cp_en)
|
||
! *** Arrays of residuals ***
|
||
R2=state_new-state_old-dstate
|
||
R2s=0.0_pReal
|
||
forall(i=1:constitutive_Nstatevars(iori, CPFEM_in, cp_en), state_new(i)/=0.0_pReal) R2s(i)=R2(i)/state_new(i)
|
||
if (maxval(abs(R2s)) < tol_outer) goto 200
|
||
state_new=state_old+dstate
|
||
enddo
|
||
iconv=2
|
||
return
|
||
! *** End of the second level of iterative procedure ***
|
||
|
||
! *** Calculation of Fp(t+dt) (see Kalidindi) ***
|
||
200 invFp_new=matmul(Fp_old, I3tLp)
|
||
call math_invert3x3(invFp_new, Fp_new, det, err) !<21><><EFBFBD>
|
||
if (err==1_pInt) then
|
||
ising=1
|
||
return
|
||
endif
|
||
Fp_new=Fp_new/math_det3x3(Fp_new)**(1.0_pReal/3.0_pReal)
|
||
!
|
||
! *** Calculation of F*(t+dt) (see Kalidindi) ***
|
||
Fe=matmul(Fg_new,invFp_new)
|
||
!
|
||
! *** Calculation of the Cauchy stress ***
|
||
! QUESTION seems to need Tstar, not Estar..??
|
||
cs = CPFEM_cauchy_stress(Tstar_v,Fe)
|
||
!
|
||
return
|
||
end subroutine
|
||
!
|
||
function CPFEM_cauchy_stress(PK_v, Fe)
|
||
!***********************************************************************
|
||
!*** Cauchy stress calculation ***
|
||
!***********************************************************************
|
||
use prec, only: pReal,pInt
|
||
use math, only math_Mandel33to6,math_Mandel6to33
|
||
implicit none
|
||
! *** Subroutine parameters ***
|
||
real(pReal) PK_v(6), Fe(3,3), CPFEM_cauchy_stress(6)
|
||
|
||
CPFEM_cauchy_stress = math_Mandel33to6(matmul(matmul(Fe,math_Mandel6to33(PK_v)),transpose(Fe))/math_det3x3(Fe))
|
||
end function
|
||
end module |