767 lines
27 KiB
Fortran
767 lines
27 KiB
Fortran
! ---------------------------
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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), allocatable :: CPFEM_jacobi_all (:,:,:,:)
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real(pReal), allocatable :: CPFEM_ffn_all (:,:,:,:)
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real(pReal), allocatable :: CPFEM_ffn1_all (:,:,:,:)
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real(pReal), allocatable :: CPFEM_results (:,:,:,:)
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real(pReal), allocatable :: CPFEM_ini_ori (:,:,:,:)
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real(pReal), allocatable :: CPFEM_sigma_old (:,:,:,:)
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real(pReal), allocatable :: CPFEM_sigma_new (:,:,:,:)
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real(pReal), allocatable :: CPFEM_Fp_old (:,:,:,:,:)
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real(pReal), allocatable :: CPFEM_Fp_new (:,:,:,:,:)
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real(pReal), allocatable :: constitutive_state_old (:,:,:,:)
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real(pReal), allocatable :: constitutive_state_new (:,:,:,:)
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real(pReal), 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 = 4_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_error
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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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CPFEM_timefactor_max = 0.0_pReal
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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
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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 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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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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forall(i=1:3)
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CPFEM_ffn_all(i,i,:,:,:) = 1.0_pReal
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CPFEM_ffn1_all(i,i,:,:,:) = 1.0_pReal
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endforall
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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_Nresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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CPFEM_results = 0.0_pReal
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!
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! *** Initial orientations ***
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! allocate(CPFEM_ini_ori(3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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! CPFEM_ini_ori = 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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forall(i=1:3)
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CPFEM_Fp_old(i,i,:,:,:) = 1.0_pReal
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CPFEM_Fp_new(i,i,:,:,:) = 1.0_pReal
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endforall
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!
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! QUESTION: would it be wise to outsource these to _constitutive_ ?? YES!
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! *** Slip resistances at (t=t0) and (t=t1) ***
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allocate(constitutive_state_old(constitutive_Nstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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allocate(constitutive_state_new(constitutive_Nstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
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state_tauc_slip_old = 0.0_pReal
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state_tauc_slip_new = 0.0_pReal
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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_thickness: ', shape(CPFEM_thickness)
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! write(6,*) 'CPFEM_ini_ori: ', shape(CPFEM_ini_ori)
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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,*) 'constitutive_state_old: ', shape(constitutive_state_old)
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write(6,*) 'constitutive_state_new: ', shape(constitutive_state_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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integer(pInt) CPFEM_cn, cp_en ,CPFEM_in
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real(pReal) CPFEM_dt, CPFEM_s(6), CPFEM_d(6, 6), CPFEM_ffn(3,3),CPFEM_ffn1(3,3)
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! QUESTION which nslip to use?
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real(pReal) Fp_old(3,3), tauc_slip_old(constitutive_maxNslip), tauc_slip_new(constitutive_maxNslip), g_old(constitutive_maxNslip)
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real(pReal) g_new(constitutive_maxNslip), Tstar_v(6), Fp_new(3,3), cs(6), phi1mis(2), PHImis(2), phi2mis(2), cd(6,6)
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real(pReal) ori_mat(3,3),hh6(6,6)
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integer(pInt) jpara,nori
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real(pReal) phi1, PHI, phi2, scatter, vf, alpha1, alpha2, beta1, &
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beta2, phi1_s, PHI_s, phi2_s, p10, P0, p20, p11, P1, p21, &
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dgmax,dgmaxc , orimis
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integer(pInt) i, iori, iconv, ising, icut
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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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! Fp_old = CPFEM_Fp_old(:,:,iori,CPFEM_in,cp_en)
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! tauc_slip_old = constitutive_state_old(:,iori,CPFEM_in,cp_en)
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! tauc_slip_new = tauc_slip_old
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! g_old = CPFEM_g_old(:,iori,CPFEM_in,cp_en)
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! Tstar_v = CPFEM_sigma_old(:,iori,CPFEM_in,cp_en)
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! data from constitutive?
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vf = constitutive_volfrac(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, dgmaxc, 1_pInt)
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!
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!
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! call CPFEM_stress(CPFEM_dt,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
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! & g_old,g_new,tauc_slip_old,
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! & tauc_slip_new,
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! & Tstar_v,cs,cd,p11,P1,p21,dgmaxc,1,iconv,ising,
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! & icut,CPFEM_en,CPFEM_in,CPFEM_inc)
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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, dgmaxc, 0_pInt)
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! call CPFEM_stress(CPFEM_tinc,CPFEM_ffn,CPFEM_ffn1,Fp_old,Fp_new,
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! & g_old,g_new,tauc_slip_old,
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! & tauc_slip_new,
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! & Tstar_v,cs,hh6,p11,P1,p21,dgmaxc,0,iconv,
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! & ising,icut,CPFEM_en,CPFEM_in,CPFEM_inc)
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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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! *** 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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! state_tauc_slip_new(:,iori,CPFEM_in,cp_en) = tauc_slip_new
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! CPFEM_g_new(:,iori,CPFEM_in,cp_en) = g_new
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! CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v
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!
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! *** Calculation of the misorientation ***
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!phi1mis(1)=p10
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! PHImis(1)=P0
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! phi2mis(1)=p20
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! phi1mis(2)=p11
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! PHImis(2)=P1
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! phi2mis(2)=p21
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! call CPFEM_misori(phi1mis,PHImis,phi2mis,orimis)
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!
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! *** Update the results plotted in MENTAT ***
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! CPFEM_results(1,iori,cp_en,CPFEM_in) = p11
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! CPFEM_results(2,iori,cp_en,CPFEM_in) = P1
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! CPFEM_results(3,iori,cp_en,CPFEM_in) = p21
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! CPFEM_results(4,iori,cp_en,CPFEM_in) = sum(g_new)
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!
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! *** Evaluation of the maximum shear ***
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dgmax=max(dgmax,dgmaxc)
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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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! *** Restoration of the old jacobian if necessary ***
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if (jpara==0) then
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CPFEM_d=CPFEM_jaco_old(:,:,CPFEM_in,cp_en)
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else
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! *** Store the new jacobian ***
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CPFEM_jaco_old(:,:,CPFEM_in,cp_en)=CPFEM_d
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endif
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! *** Calculate timefactor ***
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CPFEM_timefactor=dgmax/dgs
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!
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return
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end subroutine
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!call CPFEM_stress(cs, cd, CPFEM_dt,cp_en,CPFEM_in, ising, icut, iconv, dgmaxc, 1)
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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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dgmaxc,& ! maximum shear
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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 CPFEM, only: CPFEM_ffn_all, CPFEM_ffn1_all
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implicit none
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!
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! *** Definition of variables ***
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integer(pInt) isjaco,iconv,ising,icut,CPFEM_en,CPFEM_in,CPFEM_inc
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real(pReal) CPFEM_tinc,CPFEM_ffn(3,3),CPFEM_ffn1(3,3),Fp_old(3,3)
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real(pReal) Fp_new(3,3),g_old(nslip),g_new(nslip)
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real(pReal) tauc_slip_old(nslip),tauc_slip_new(nslip)
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real(pReal) Tstar_v(6)
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real(pReal) cs(6),dcs_de(6,6),phi1,PHI,phi2,dgmaxc
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integer(pInt) jcut
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real(pReal) Tstar_v_h(6),tauc_slip_new_h(nslip)
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real(pReal) dt_i,delta_Fg(3,3),Fg_i(3,3)
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real(pReal) tauc_slip_new_i(nslip),time,mm(6,6)
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! *** Numerical parameters ***
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integer(pInt), parameter :: ncut=7_pInt
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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_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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! g_old = CPFEM_g_old(:,iori,CPFEM_in,cp_en)
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! g_new = 0_pReal
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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)
|
||
CPFEM_ffn1 = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)
|
||
!
|
||
! *** First attempt to calculate Tstar and tauc with initial timestep ***
|
||
Tstar_v_h=Tstar_v
|
||
state_new_h=state_new
|
||
call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, ising, icut, iconv, dgmaxc, isjaco, phi1, PHI, phi2,&
|
||
CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,g_old,g_new,state_old, state_new, Tstar_v)
|
||
if ((iconv==0).AND.(ising==0)) then
|
||
! *** Update the differents matrices for t=t1 ***
|
||
CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new
|
||
constituitive_state_new(:,iori,CPFEM_in,cp_en) = state_new
|
||
CPFEM_g_new(:,iori,CPFEM_in,cp_en) = g_new
|
||
CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v
|
||
! *** Update the results plotted in MENTAT ***
|
||
CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1
|
||
CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI
|
||
CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2
|
||
CPFEM_results(4,iori,CPFEM_in,cp_en) = sum(g_new)
|
||
return
|
||
endif
|
||
!
|
||
! *** Calculation of stress and resistences with a cut timestep ***
|
||
! *** when first try did not converge ***
|
||
jcut=1_pInt
|
||
dt_i=0.5_pReal*CPFEM_dt
|
||
delta_Fg=0.5_pReal*(CPFEM_ffn1-CPFEM_ffn)
|
||
Fg_i=CPFEM_ffn+delta_Fg
|
||
Tstar_v=Tstar_v_h
|
||
state_new_i=state_new_h
|
||
! *** Start time ***
|
||
time=dt_i
|
||
do while (time<=CPFEM_dt)
|
||
call CPFEM_stress_int(cs, cd, time, cp_en,CPFEM_in, ising, icut, iconv, dgmaxc, isjaco, phi1, PHI, phi2,&
|
||
CPFEM_ffn, Fg_i,Fp_old,Fp_new,g_old,g_new,state_old, state_new_i, Tstar_v)
|
||
! 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_pInt,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
|
||
state_new_h=state_new_i
|
||
else
|
||
jcut=jcut+1_pInt
|
||
if (jcut.GT.ncut) then
|
||
icut=1_pInt
|
||
return
|
||
endif
|
||
dt_i=0.5_pReal*dt_i
|
||
time=time-dt_i
|
||
delta_Fg=0.5_pReal*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 with full timestep ***
|
||
state_new=state_new_i
|
||
call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, ising, icut, iconv, dgmaxc, isjaco, phi1, PHI, phi2,&
|
||
CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,g_old,g_new,state_old, state_new, Tstar_v)
|
||
! 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)
|
||
! *** Update the differents matrices for t=t1 ***
|
||
CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new
|
||
constituitive_state_new(:,iori,CPFEM_in,cp_en) = state_new
|
||
CPFEM_g_new(:,iori,CPFEM_in,cp_en) = g_new
|
||
CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v
|
||
! *** Update the results plotted in MENTAT ***
|
||
CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1
|
||
CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI
|
||
CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2
|
||
CPFEM_results(4,iori,CPFEM_in,cp_en) = sum(g_new)
|
||
return
|
||
end subroutine
|
||
|
||
|
||
! call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, ising, icut, iconv, dgmaxc, isjaco,&
|
||
! CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,g_old,g_new,state_old, state_new, Tstar_v)
|
||
|
||
subroutine CPFEM_stress_int(&
|
||
cs,& ! Cauchy stress vector
|
||
dcs_de,& ! Consistent tangent
|
||
dt,& ! Time increment
|
||
cp_en,& ! cp element number
|
||
CPFEM_in,& ! integration point number
|
||
ising,& ! flag for singular matrix
|
||
icut,& ! flag for too many cut backs
|
||
iconv,& ! flag for non convergence
|
||
dgmaxc,& ! maximum shear
|
||
isjaco,& ! flag whether to calculate Jacoby matrix
|
||
phi1,& ! Euler angle
|
||
PHI,& ! Euler angle
|
||
phi2,& ! Euler angle
|
||
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
|
||
state_old,& ! Old resistence of a slip system
|
||
state_new,& ! New resistence of a slip system
|
||
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
|
||
implicit none
|
||
|
||
! *** Definition of variables ***
|
||
integer(pInt) isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc
|
||
real(pReal) 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(pInt) ic
|
||
real(pReal) 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(pReal), parameter :: pert_ct=1.0e-5_pReal
|
||
! maximum shear rate
|
||
dgmaxc = 0
|
||
! *** Error treatment ***
|
||
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,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)
|
||
!
|
||
! *** 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) 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
|
||
call math_conv6to33(dev,de)
|
||
dF=matmul(de,Fg_old)
|
||
Fg2=Fg_new+dF
|
||
sgm2=Tstar_v
|
||
state2=state_new
|
||
|
||
! *** Calculation of the perturbated Cauchy stress ***
|
||
call NEWTON_RAPHSON(dt,Fg_old,Fg2,Fp_old,Fp2,Fe,gdot,state_old,tauc2,sgm2,cs1,iconv,ising)
|
||
!
|
||
! *** Consistent tangent ***
|
||
dcs_de(:,ic)=(cs1-cs)/pert_ct
|
||
enddo
|
||
!
|
||
return
|
||
end subroutine
|
||
!
|
||
!
|
||
subroutine NEWTON_RAPHSON(
|
||
&dt,
|
||
&Fg_old,
|
||
&Fg_new,
|
||
&Fp_old,
|
||
&Fp_new,
|
||
&Fe,
|
||
&gdot_slip,
|
||
&state_old,
|
||
&state_new,
|
||
&Tstar_v,
|
||
&cs,
|
||
&iconv,
|
||
&ising
|
||
&)
|
||
!***********************************************************************
|
||
!*** NEWTON-RAPHSON Calculation ***
|
||
!***********************************************************************
|
||
use prec
|
||
implicit none
|
||
|
||
! *** Definition of variables ***
|
||
integer(pInt) isjaco,iconv,ising,CPFEM_en,CPFEM_in,CPFEM_inc
|
||
real(pReal) 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(pInt) i,j,k,iouter,iinner,ijac,ic
|
||
real(pReal) 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(pReal) 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(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 :: eta = 13.7_pReal
|
||
integer(pInt), parameter :: numerical = 0_pInt
|
||
real(pReal), parameter :: pert_nr = 1.0e-8_pReal
|
||
crite=eta*s0_slip/n_slip
|
||
!
|
||
! *** Tolerances ***
|
||
tol_in = tol_inner*s0_slip
|
||
tol_out = tol_outer*s0_slip
|
||
!
|
||
dgmaxc = 0
|
||
! *** Error treatment ***
|
||
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_pReal) then
|
||
ising=1
|
||
return
|
||
endif
|
||
!
|
||
! *** Calculation of A and T*0 (see Kalidindi) ***
|
||
! constitutive <20><><EFBFBD>
|
||
A=matmul(transpose(matmul(Fg_new,invFp_old)), matmul(Fg_new,invFp_old))
|
||
call math_conv33to6((A-I3)/2,Estar0_v)
|
||
Tstar0_v=matmul(Cslip_66,Estar0_v)
|
||
!
|
||
! *** Calculation of Dslip (see Kalidindi) ***
|
||
! constitutive <20><><EFBFBD>
|
||
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 ***
|
||
! constitutive <20><><EFBFBD>
|
||
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) goto 100
|
||
!
|
||
! *** 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_pReal+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_pReal) 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_pReal) 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) goto 200
|
||
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)
|
||
Fp_new=Fp_new/math_det3x3(Fp_new)**(1.0_pReal/3.0_pReal)
|
||
!
|
||
! *** Calculation of F*(t+dt) (see Kalidindi) ***
|
||
invFp_new=Fp_new
|
||
call invert(invFp_new,3,0,0,det,3)
|
||
if (det==0.0_pReal) then
|
||
ising=1
|
||
return
|
||
endif
|
||
Fe=matmul(Fg_new,invFp_new)
|
||
!
|
||
! *** Calculation of Estar ***
|
||
Estar=0.5_pReal*(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 |