485 lines
20 KiB
Fortran
485 lines
20 KiB
Fortran
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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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!*** allocate the arrays defined in module CPFEM ***
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!*** and initialize 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_EulertoR
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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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integer(pInt) e,i,g
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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)) ; CPFEM_ffn_all = 0.0_pReal
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allocate(CPFEM_ffn1_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_all = 0.0_pReal
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allocate(CPFEM_stress_all( 6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_all = 0.0_pReal
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allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems)) ; 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)) ; CPFEM_sigma_old = 0.0_pReal
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allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; 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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forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:constitutive_maxNgrains) &
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CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(constitutive_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation
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allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; 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)) ; 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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!***********************************************************************
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!*** perform initialization at first call, update variables and ***
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!*** call 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, CPFEM_en, CPFEM_in)
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!
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use prec, only: pReal,pInt
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use math, only: math_init
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use mesh, only: mesh_init,mesh_FEasCP
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use crystal, only: crystal_Init
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use constitutive, only: constitutive_init,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, CPFEM_en, CPFEM_in, cp_en
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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 math_init()
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call mesh_init()
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call crystal_Init()
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call constitutive_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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if (CPFEM_inc==CPFEM_inc_old) then ! not a new increment
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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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else ! new increment
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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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cp_en = mesh_FEasCP('elem',CPFEM_en)
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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_stressIP(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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!*** calculate the material behaviour at IP level ***
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!**********************************************************
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SUBROUTINE CPFEM_stressIP(&
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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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use prec, only: pReal,pInt,ijaco,nCutback
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use math, only: math_pDecomposition,math_RtoEuler
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use IO, only: IO_error
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use mesh, only: mesh_element
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use constitutive
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!
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implicit none
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integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt
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character(len=128) msg
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integer(pInt) CPFEM_cn,cp_en,CPFEM_in,grain,i
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logical updateJaco,error
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real(pReal) CPFEM_dt,dt,t,volfrac
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real(pReal), dimension(6) :: cs,Tstar_v
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real(pReal), dimension(6,6) :: cd
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real(pReal), dimension(3,3) :: Fe,U,R,deltaFg
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real(pReal), dimension(3,3,2) :: Fg,Fp
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real(pReal), dimension(constitutive_maxNstatevars,2) :: state
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updateJaco = (mod(CPFEM_cn,ijaco)==0) ! update consistent tangent every ijaco'th iteration
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CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress
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if (updateJaco) CPFEM_jaco_old(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent
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! -------------- grain loop -----------------
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do grain = 1,texture_Ngrains(mesh_element(4,cp_en))
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! -------------------------------------------
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i = 0_pInt ! cutback counter
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state(:,i_now) = constitutive_state_old(:,grain,CPFEM_in,cp_en)
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Fg(:,:,i_now) = CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
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Fp(:,:,i_now) = CPFEM_Fp_old(:,:,grain,CPFEM_in,cp_en)
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deltaFg = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en)
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dt = CPFEM_dt
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Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess
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Fg(:,:,i_then) = Fg(:,:,i_now)
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state(:,i_then) = 0.0_pReal ! state_old as initial guess
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t = 0.0_pReal
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! ------- crystallite integration -----------
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do
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! -------------------------------------------
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if (t+dt < CPFEM_dt) then ! intermediate solution
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t = t+dt ! next time inc
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Fg(:,:,i_then) = Fg(:,:,i_then)+deltaFg ! corresponding Fg
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else ! full step solution
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t = CPFEM_dt ! final time
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Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg
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endif
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call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Fp(:,:,i_then),Fe,state(:,i_then),&
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dt,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,&
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Fg(:,:,i_now),Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now))
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if (msg == 'ok') then ! solution converged
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if (t == CPFEM_dt) exit ! reached final "then"
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else ! solution not found
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i = i+1_pInt ! inc cutback counter
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! write(6,*) 'ncut:', i
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if (i > nCutback) then ! limit exceeded?
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write(6,*) 'cutback limit --> '//msg
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write(6,*) 'Grain: ',grain
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',mesh_element(1,cp_en)
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call IO_error(600)
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return ! byebye
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else
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t = t-dt ! rewind time
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Fg(:,:,i_then) = Fg(:,:,i_then)-deltaFg ! rewind Fg
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dt = 0.5_pReal*dt ! cut time-step in half
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deltaFg = 0.5_pReal*deltaFg ! cut Fg-step in half
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endif
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endif
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enddo ! crystallite integration (cutback loop)
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! ---- update crystallite matrices at t = t1 ----
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CPFEM_Fp_new(:,:,grain,CPFEM_in,cp_en) = Fp(:,:,i_then)
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constitutive_state_new(:,grain,CPFEM_in,cp_en) = state(:,i_then)
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CPFEM_sigma_new(:,grain,CPFEM_in,cp_en) = Tstar_v
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! ---- update results plotted in MENTAT ----
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call math_pDecomposition(Fe,U,R,error) ! polar decomposition
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if (error) then
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write(6,*) 'polar decomposition'
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write(6,*) 'Grain: ',grain
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write(6,*) 'Integration point: ',CPFEM_in
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write(6,*) 'Element: ',mesh_element(1,cp_en)
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call IO_error(600)
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return
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endif
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CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R)) ! orientation
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CPFEM_results(4:3+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = &
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constitutive_post_results(Tstar_v,state(:,i_then),CPFEM_dt,grain,CPFEM_in,cp_en)
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! ---- contribute to IP result ----
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volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en)
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CPFEM_stress_all(:,CPFEM_in,cp_en) = CPFEM_stress_all(:,CPFEM_in,cp_en)+volfrac*cs ! average Cauchy stress
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if (updateJaco) CPFEM_jaco_old(:,:,CPFEM_in,cp_en) = CPFEM_jaco_old(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent
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enddo ! grain loop
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return
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END SUBROUTINE
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!********************************************************************
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! Calculates the stress for a single component
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! it is based on the paper by Kalidindi et al.:
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! J. Mech. Phys, Solids Vol. 40, No. 3, pp. 537-569, 1992
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! it is modified to use anisotropic elasticity matrix
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!********************************************************************
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subroutine CPFEM_stressCrystallite(&
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msg,& ! return message
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cs,& ! Cauchy stress vector
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dcs_de,& ! consistent tangent
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Tstar_v,& ! second Piola-Kirchoff stress tensor
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Fp_new,& ! new plastic deformation gradient
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Fe_new,& ! new "elastic" deformation gradient
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state_new,& ! new state variable array
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!
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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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grain,& ! grain number
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updateJaco,& ! boolean to calculate Jacobi matrix
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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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state_old) ! old state variable array
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use prec, only: pReal,pInt,pert_e
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use constitutive, only: constitutive_Nstatevars
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use math, only: math_Mandel6to33,mapMandel
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implicit none
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character(len=*) msg
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logical updateJaco
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integer(pInt) cp_en,CPFEM_in,grain,i
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real(pReal) dt
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real(pReal), dimension(3,3) :: Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,Fp_pert,Fe_new,Fe_pert,E_pert
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real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert
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real(pReal), dimension(6,6) :: dcs_de
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real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert
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call CPFEM_timeIntegration(msg,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step
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dt,cp_en,CPFEM_in,grain,Fg_new,Fp_old,state_old)
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if (msg /= 'ok') return
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cs = CPFEM_CauchyStress(Tstar_v,Fe_new) ! Cauchy stress
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if (updateJaco) then ! consistent tangent using numerical perturbation of Fg
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do i = 1,6 ! Fg component
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E_pert = 0.0_pReal
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E_pert(mapMandel(1,i),mapMandel(2,i)) = E_pert(mapMandel(1,i),mapMandel(2,i)) + pert_e/2.0_pReal
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E_pert(mapMandel(2,i),mapMandel(1,i)) = E_pert(mapMandel(2,i),mapMandel(1,i)) + pert_e/2.0_pReal
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Fg_pert = Fg_new+matmul(E_pert,Fg_old) ! perturbated Fg
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Tstar_v_pert = Tstar_v ! initial guess from end of time step
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state_pert = state_new ! initial guess from end of time step
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call CPFEM_timeIntegration(msg,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, &
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dt,cp_en,CPFEM_in,grain,Fg_pert,Fp_old,state_old)
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if (msg /= 'ok') then
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msg = 'consistent tangent --> '//msg
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return
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endif
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! Remark: (perturbated) Cauchy stress is Mandel hence dcs_de(:,4:6) is too large by sqrt(2)
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dcs_de(:,i) = (CPFEM_CauchyStress(Tstar_v_pert,Fe_pert)-cs)/pert_e
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enddo
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endif
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return
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END SUBROUTINE
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!***********************************************************************
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!*** fully-implicit two-level time integration ***
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!***********************************************************************
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SUBROUTINE CPFEM_timeIntegration(&
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msg,& ! return message
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Fp_new,& ! new plastic deformation gradient
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Fe_new,& ! new "elastic" deformation gradient
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Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0)
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state_new,& ! current microstructure at end of time inc (taken as guess if /= 0)
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!
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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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grain,& ! grain number
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Fg_new,& ! new total def gradient
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Fp_old,& ! former plastic def gradient
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state_old) ! former microstructure
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use prec
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use constitutive, only: constitutive_Nstatevars,&
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constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent
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use math
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implicit none
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character(len=*) msg
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integer(pInt) cp_en, CPFEM_in, grain
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integer(pInt) iState,iStress,dummy, i,j,k,l,m
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real(pReal) dt,det, p_hydro
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real(pReal), dimension(6) :: Tstar_v,dTstar_v,Rstress, T_elastic, Rstress_old
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real(pReal), dimension(6,6) :: C_66,Jacobi,invJacobi
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real(pReal), dimension(3,3) :: Fg_new,Fp_old,Fp_new,Fe_new,invFp_old,invFp_new,Lp,A,B,AB
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real(pReal), dimension(3,3,3,3) :: dLp, LTL
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real(pReal), dimension(constitutive_Nstatevars(grain, CPFEM_in, cp_en)) :: state_old,state_new,dstate,Rstate,RstateS
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logical failed
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msg = 'ok' ! error-free so far
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call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp
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if (failed) then
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msg = 'inversion Fp_old'
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return
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endif
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C_66 = constitutive_HomogenizedC(grain, CPFEM_in, cp_en)
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A = matmul(Fg_new,invFp_old) ! actually Fe
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A = matmul(transpose(A), A)
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! former state guessed, if none specified
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if (all(state_new == 0.0_pReal)) state_new = state_old
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RstateS = state_new
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iState = 0_pInt
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Rstress = Tstar_v
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Rstress_old=Rstress
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state: do ! outer iteration: state
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iState = iState+1
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if (iState > nState) then
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msg = 'limit state iteration'
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return
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endif
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iStress = 0_pInt
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stress: do ! inner iteration: stress
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iStress = iStress+1
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if (iStress > nStress) then ! too many loops required
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msg = 'limit stress iteration'
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return
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endif
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p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal
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forall(i=1:3) Tstar_v(i)=Tstar_v(i)-p_hydro
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call constitutive_LpAndItsTangent(Lp,dLp, Tstar_v,state_new,grain,CPFEM_in,cp_en)
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B = math_I3-dt*Lp
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! B = B / math_det3x3(B)**(1.0_pReal/3.0_pReal)
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AB = matmul(A,B)
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T_elastic= 0.5_pReal*matmul(C_66,math_Mandel33to6(matmul(transpose(B),AB)-math_I3))
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p_hydro=(T_elastic(1)+T_elastic(2)+T_elastic(3))/3.0_pReal
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forall(i=1:3) T_elastic(i)=T_elastic(i)-p_hydro
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Rstress = Tstar_v - T_elastic
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! step size control: if residuum does not improve redo iteration with reduced step size
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if(maxval(abs(Rstress)) > maxval(abs(Rstress_old)) .and. &
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maxval(abs(Rstress)) > 1.0e-6 .and. iStress > 1) then
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! write(6,*) 'Hallo', iStress
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Tstar_v=Tstar_v+0.5*dTstar_v
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dTstar_v=0.5*dTstar_v
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cycle
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endif
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if (iStress > 1 .and. (maxval(abs(Tstar_v)) < 1.0e-3_pReal .or. maxval(abs(Rstress/maxval(abs(Tstar_v)))) < tol_Stress)) exit stress
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|
|
|
! update stress guess using inverse of dRes/dTstar (Newton--Raphson)
|
|
LTL = 0.0_pReal
|
|
do i=1,3
|
|
do j=1,3
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|
do k=1,3
|
|
do l=1,3
|
|
do m=1,3
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LTL(i,j,k,l) = LTL(i,j,k,l) + dLp(j,i,m,k)*AB(m,l) + AB(m,i)*dLp(m,j,k,l)
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enddo
|
|
enddo
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|
enddo
|
|
enddo
|
|
enddo
|
|
Jacobi = math_identity2nd(6) + 0.5_pReal*dt*matmul(C_66,math_Mandel3333to66(LTL))
|
|
j = 0_pInt
|
|
call math_invert6x6(Jacobi,invJacobi,dummy,failed)
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|
do while (failed .and. j <= nReg)
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|
forall (i=1:6) Jacobi(i,i) = 1.05_pReal*maxval(Jacobi(i,:)) ! regularization
|
|
call math_invert6x6(Jacobi,invJacobi,dummy,failed)
|
|
j = j+1
|
|
enddo
|
|
if (failed) then
|
|
msg = 'regularization Jacobi'
|
|
return
|
|
endif
|
|
dTstar_v = matmul(invJacobi,Rstress) ! correction to Tstar
|
|
Rstress_old=Rstress
|
|
Tstar_v = Tstar_v-dTstar_v
|
|
! write(999,*) Tstar_v, dTstar_v, Rstress
|
|
|
|
enddo stress
|
|
! write(6,*) 'istress', istress
|
|
Tstar_v = 0.5_pReal*matmul(C_66,math_Mandel33to6(matmul(transpose(B),AB)-math_I3))
|
|
dstate = dt*constitutive_dotState(Tstar_v,state_new,grain,CPFEM_in,cp_en) ! evolution of microstructure
|
|
Rstate = state_new - (state_old+dstate)
|
|
RstateS = 0.0_pReal
|
|
forall (i=1:constitutive_Nstatevars(grain,CPFEM_in,cp_en), state_new(i)/=0.0_pReal) &
|
|
RstateS(i) = Rstate(i)/state_new(i)
|
|
state_new = state_old+dstate
|
|
if (maxval(abs(RstateS)) < tol_State) exit state
|
|
|
|
enddo state
|
|
! write(6,*) 'istate', istate
|
|
! write(999,*) 'Tstar_v raus', Tstar_v
|
|
! write(999,*)
|
|
|
|
invFp_new = matmul(invFp_old,B)
|
|
call math_invert3x3(invFp_new,Fp_new,det,failed)
|
|
if (failed) then
|
|
msg = 'inversion Fp_new'
|
|
return
|
|
endif
|
|
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! det = det(InvFp_new) !!
|
|
Fe_new = matmul(Fg_new,invFp_new)
|
|
return
|
|
END SUBROUTINE
|
|
|
|
|
|
FUNCTION CPFEM_CauchyStress(PK_v,Fe)
|
|
!***********************************************************************
|
|
!*** Cauchy stress calculation ***
|
|
!***********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use math, only: math_Mandel33to6,math_Mandel6to33,math_det3x3
|
|
implicit none
|
|
! *** Subroutine parameters ***
|
|
real(pReal) PK_v(6), Fe(3,3), CPFEM_CauchyStress(6)
|
|
|
|
CPFEM_CauchyStress = math_Mandel33to6(matmul(matmul(Fe,math_Mandel6to33(PK_v)),transpose(Fe))/math_det3x3(Fe))
|
|
return
|
|
END FUNCTION
|
|
|
|
|
|
END MODULE
|