789 lines
37 KiB
Fortran
789 lines
37 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_Temperature
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_bar !average FFN per IP
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_ffn !individual FFN per grain
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_bar !average FFN1 per IP
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_ffn1 !individual FFN1 per grain
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar !average PK1 per IP
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_PK1 !individual PK1 per grain
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real(pReal), dimension (:,:,:,:,:,:), allocatable :: CPFEM_dPdF_bar !average dPdF per IP
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real(pReal), dimension (:,:,:,:,:,:), allocatable :: CPFEM_dPdF_bar_old !old average dPdF per IP
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real(pReal), dimension (:,:,:,:,:,:,:),allocatable :: CPFEM_dPdF !individual dPdF per grain
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real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_bar
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_bar
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_knownGood
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Lp_old
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real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Lp_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_Fe_new
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real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_Tstar_v
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logical, dimension (:,:,:), allocatable :: crystallite_converged !individual convergence flag per grain
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integer(pInt), dimension(:,:), allocatable :: CPFEM_execution_IP
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integer(pInt), dimension(2) :: CPFEM_execution_elem
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integer(pInt) :: CPFEM_Nresults = 5_pInt ! phase, volfrac, three Euler angles
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logical :: CPFEM_init_done = .false. ! remember whether init has been done already
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logical :: CPFEM_calc_done = .false. ! remember whether first IP has already calced the results
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real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal
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!
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CONTAINS
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!
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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(Temperature)
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!
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use prec
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use math, only: math_EulertoR, math_I3, math_identity2nd
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use FEsolving, only: parallelExecution
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use mesh
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use material
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use constitutive
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!
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implicit none
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!
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real(pReal) Temperature
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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_Temperature(mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = Temperature
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allocate(CPFEM_ffn_bar(3,3,mesh_maxNips,mesh_NcpElems))
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forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_bar(:,:,i,e) = math_I3
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allocate(CPFEM_ffn(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems))
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forall(g=1:homogenization_maxNgrains,e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn(:,:,g,i,e) = math_I3
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allocate(CPFEM_ffn1_bar(3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_bar = CPFEM_ffn_bar
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allocate(CPFEM_ffn1(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1 = CPFEM_ffn
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allocate(CPFEM_PK1_bar(3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_bar = 0.0_pReal
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allocate(CPFEM_PK1(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1 = 0.0_pReal
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allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal
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allocate(CPFEM_dPdF_bar_old(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar_old = 0.0_pReal
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allocate(CPFEM_dPdF(3,3,3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF = 0.0_pReal
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allocate(CPFEM_stress_bar(6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_bar = 0.0_pReal
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allocate(CPFEM_jaco_bar(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_bar = 0.0_pReal
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allocate(CPFEM_jaco_knownGood(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_knownGood = 0.0_pReal
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!
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! *** User defined results ***
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allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxSizePostResults,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems))
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CPFEM_results = 0.0_pReal
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!
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! *** Plastic velocity gradient ***
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allocate(CPFEM_Lp_old(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Lp_old = 0.0_pReal
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allocate(CPFEM_Lp_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Lp_new = 0.0_pReal
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! *** Plastic deformation gradient at (t=t0) and (t=t1) ***
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allocate(CPFEM_Fp_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal
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allocate(CPFEM_Fp_old(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems))
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forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:homogenization_maxNgrains) &
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CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(material_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation
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! *** Elastic deformation gradient at (t=t1) ***
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allocate(CPFEM_Fe_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fe_new = 0.0_pReal
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! *** Stress vector at (t=t1) ***
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allocate(CPFEM_Tstar_v(6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Tstar_v = 0.0_pReal
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!
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allocate(crystallite_converged(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)); crystallite_converged = .false.
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allocate(CPFEM_execution_IP(2,mesh_NcpElems)); CPFEM_execution_IP = 1_pInt
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forall (e = 1:mesh_NcpElems) CPFEM_execution_IP(2,e) = FE_Nips(mesh_element(2,e))
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CPFEM_execution_elem = (/1,mesh_NcpElems/)
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! *** Output to MARC output file ***
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!$OMP CRITICAL (write2out)
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write(6,*)
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write(6,*) 'CPFEM Initialization'
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write(6,*)
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write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature)
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write(6,*) 'CPFEM_ffn_bar: ', shape(CPFEM_ffn_bar)
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write(6,*) 'CPFEM_ffn: ', shape(CPFEM_ffn)
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write(6,*) 'CPFEM_ffn1_bar: ', shape(CPFEM_ffn1_bar)
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write(6,*) 'CPFEM_ffn1: ', shape(CPFEM_ffn1)
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write(6,*) 'CPFEM_PK1_bar: ', shape(CPFEM_PK1_bar)
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write(6,*) 'CPFEM_PK1: ', shape(CPFEM_PK1)
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write(6,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar)
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write(6,*) 'CPFEM_dPdF_bar_old: ', shape(CPFEM_dPdF_bar_old)
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write(6,*) 'CPFEM_dPdF: ', shape(CPFEM_dPdF)
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write(6,*) 'CPFEM_stress_bar: ', shape(CPFEM_stress_bar)
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write(6,*) 'CPFEM_jaco_bar: ', shape(CPFEM_jaco_bar)
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write(6,*) 'CPFEM_jaco_knownGood: ', shape(CPFEM_jaco_knownGood)
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write(6,*) 'CPFEM_results: ', shape(CPFEM_results)
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write(6,*) 'CPFEM_Lp_old: ', shape(CPFEM_Lp_old)
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write(6,*) 'CPFEM_Lp_new: ', shape(CPFEM_Lp_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_Fe_new: ', shape(CPFEM_Fe_new)
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write(6,*) 'CPFEM_Tstar_v: ', shape(CPFEM_Tstar_v)
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write(6,*) 'crystallite_converged:', shape(crystallite_converged)
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write(6,*)
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write(6,*) 'parallelExecution: ', parallelExecution
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call flush(6)
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!$OMP END CRITICAL (write2out)
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return
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!
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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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! CPFEM_mode computation mode (regular, collection, recycle)
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! ffn deformation gradient for t=t0
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! ffn1 deformation gradient for t=t1
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! Temperature temperature
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! CPFEM_dt time increment
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! CPFEM_en element number
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! CPFEM_in intergration point number
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! CPFEM_stress stress vector in Mandel notation
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! CPFEM_updateJaco flag to initiate computation of Jacobian
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! CPFEM_jaco jacobian in Mandel notation
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! CPFEM_ngens size of stress strain law
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!***********************************************************************
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SUBROUTINE CPFEM_general(CPFEM_mode, ffn, ffn1, Temperature, CPFEM_dt,&
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CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_updateJaco, CPFEM_jaco, CPFEM_ngens)
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! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de
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!
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use prec, only: pReal,pInt
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use FEsolving
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use debug
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use math
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use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, mesh_maxNips, mesh_element
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use lattice, only: lattice_init
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use material
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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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integer(pInt) CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n
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real(pReal), dimension (3,3) :: ffn,ffn1,Kirchhoff_bar
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real(pReal), dimension (3,3,3,3) :: H_bar, H_bar_sym
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real(pReal), dimension(CPFEM_ngens) :: CPFEM_stress
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real(pReal), dimension(CPFEM_ngens,CPFEM_ngens) :: CPFEM_jaco, odd_jaco
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real(pReal) Temperature,CPFEM_dt,J_inverse
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integer(pInt) CPFEM_mode ! 1: regular computation with aged results&
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! 2: regular computation&
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! 3: collection of FEM data&
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! 4: recycling of former results (MARC speciality)&
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! 5: record tangent from former converged inc&
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! 6: restore tangent from former converged inc
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logical CPFEM_updateJaco
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!
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if (.not. CPFEM_init_done) then ! initialization step (three dimensional stress state check missing?)
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call math_init()
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call FE_init()
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call mesh_init()
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call lattice_init()
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call material_init()
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call constitutive_init()
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write (6,*) 'call CPFEM init'
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call CPFEM_init(Temperature)
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CPFEM_init_done = .true.
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endif
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!
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cp_en = mesh_FEasCP('elem',CPFEM_en)
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if (cp_en == 1 .and. CPFEM_in == 1) then
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write(6,'(a10,1x,f8.4,1x,a10,1x,i4,1x,a10,1x,i3,1x,a10,1x,i2,x,a10,1x,i2)') &
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'theTime',theTime,'theInc',theInc,'theCycle',theCycle,'theLovl',theLovl,&
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'mode',CPFEM_mode
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endif
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!
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select case (CPFEM_mode)
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case (1,2) ! regular computation (with aging of results if mode == 1)
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if (CPFEM_mode == 1) then ! age results at start of new increment
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CPFEM_Lp_old = CPFEM_Lp_new
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CPFEM_Fp_old = CPFEM_Fp_new
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forall (i = 1:homogenization_maxNgrains,&
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j = 1:mesh_maxNips, &
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k = 1:mesh_NcpElems) &
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constitutive_state_old(i,j,k)%p = constitutive_state_new(i,j,k)%p
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write (6,*) 'results aged.'
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endif
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if (outdatedFFN1 .or. any(abs(ffn1 - CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en)) > relevantStrain)) then
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if (.not. outdatedFFN1) write(6,'(i5,x,i2,x,a10,/,3(3(f10.3,x),/))') cp_en,CPFEM_in,'FFN1 now:',ffn1(:,1),ffn1(:,2),ffn1(:,3)
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outdatedFFN1 = .true.
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CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress
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CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens)
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else
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if (.not. parallelExecution) then
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CPFEM_execution_elem(1) = cp_en
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CPFEM_execution_elem(2) = cp_en
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CPFEM_execution_IP(1,cp_en) = CPFEM_in
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CPFEM_execution_IP(2,cp_en) = CPFEM_in
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call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt)
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elseif (.not. CPFEM_calc_done) then
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call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt) ! parallel execution inside
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CPFEM_calc_done = .true.
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endif
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! translate from P and dP/dF to CS and dCS/dE
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Kirchhoff_bar = math_mul33x33(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en)))
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J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en))
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CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel33to6(J_inverse*Kirchhoff_bar)
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!
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H_bar = 0.0_pReal
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forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
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H_bar(i,j,k,l) = H_bar(i,j,k,l) + &
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CPFEM_ffn1_bar(j,m,CPFEM_in,cp_en) * &
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CPFEM_ffn1_bar(l,n,CPFEM_in,cp_en) * &
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CPFEM_dPdF_bar(i,m,k,n,CPFEM_in,cp_en) - &
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math_I3(j,l)*CPFEM_ffn1_bar(i,m,CPFEM_in,cp_en)*CPFEM_PK1_bar(k,m,CPFEM_in,cp_en) + &
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0.5_pReal*(math_I3(i,k)*Kirchhoff_bar(j,l) + math_I3(j,l)*Kirchhoff_bar(i,k) + &
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math_I3(i,l)*Kirchhoff_bar(j,k) + math_I3(j,k)*Kirchhoff_bar(i,l))
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forall(i=1:3,j=1:3,k=1:3,l=1:3) &
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H_bar_sym(i,j,k,l)= 0.25_pReal*(H_bar(i,j,k,l) +H_bar(j,i,k,l) +H_bar(i,j,l,k) +H_bar(j,i,l,k))
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CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel3333to66(J_inverse*H_bar)
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endif
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case (3) ! collect and return odd result
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CPFEM_Temperature(CPFEM_in,cp_en) = Temperature
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CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) = ffn
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CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) = ffn1
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CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress
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CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens)
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CPFEM_calc_done = .false.
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case (4) ! do nothing since we can recycle the former results (MARC specialty)
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case (5) ! record consistent tangent at beginning of new increment (while recycling)
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CPFEM_jaco_knownGood = CPFEM_jaco_bar
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case (6) ! restore consistent tangent after cutback
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CPFEM_jaco_bar = CPFEM_jaco_knownGood
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end select
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!
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! return the local stress and the jacobian from storage
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CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en)
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CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en)
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!
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return
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!
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END SUBROUTINE
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!
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!
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!**********************************************************
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!*** calculate the material point behaviour ***
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!**********************************************************
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SUBROUTINE CPFEM_MaterialPoint(&
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updateJaco,& ! flag to initiate Jacobian updating
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CPFEM_dt) ! Time increment (dt)
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!
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use prec
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use debug
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use math, only: math_pDecomposition,math_RtoEuler,inDeg
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use IO, only: IO_error
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use mesh, only: mesh_element, mesh_NcpElems, FE_Nips
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use material, only: homogenization_Ngrains,material_phase,material_volfrac
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use constitutive
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implicit none
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!
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logical, intent(in) :: updateJaco
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real(pReal), intent(in) :: CPFEM_dt
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integer(pInt) g,i,e
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logical error
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real(pReal) volfrac
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real(pReal), dimension(3,3) :: U,R
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!$OMP PARALLEL DO
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do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
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do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
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forall (g = 1:homogenization_Ngrains(mesh_element(3,e))) ! number of grains of this homogenization
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CPFEM_ffn(:,:,g,i,e) = CPFEM_ffn_bar(:,:,i,e) ! Taylor homogenization (why not using former ffn1??)
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CPFEM_ffn1(:,:,g,i,e) = CPFEM_ffn1_bar(:,:,i,e) ! Taylor homogenization
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end forall
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enddo
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enddo
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!$OMP END PARALLEL DO
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call SingleCrystallite(updateJaco,CPFEM_dt)
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!******************************************************************************************************
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! check convergence of homogenization if needed
|
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!******************************************************************************************************
|
|
|
|
! calculate average quantities per ip and post results
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
CPFEM_PK1_bar(:,:,i,e) = sum(CPFEM_PK1(:,:,:,i,e),3)/homogenization_Ngrains(mesh_element(3,e))
|
|
if (updateJaco) &
|
|
CPFEM_dPdF_bar(:,:,:,:,i,e) = &
|
|
sum(CPFEM_dPdF(:,:,:,:,:,i,e),5)/homogenization_Ngrains(mesh_element(3,e)) ! add up crystallite stiffnesses (may have "holes" corresponding to former avg tangent)
|
|
do g = 1,homogenization_Ngrains(mesh_element(3,e))
|
|
call math_pDecomposition(CPFEM_Fe_new(:,:,g,i,e),U,R,error) ! polar decomposition
|
|
if (error) call IO_error(650,e,i,g)
|
|
CPFEM_results(1,g,i,e) = material_phase(g,i,e)
|
|
CPFEM_results(2,g,i,e) = material_volFrac(g,i,e)
|
|
CPFEM_results(3:5,g,i,e) = math_RtoEuler(transpose(R))*inDeg ! orientation
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
return
|
|
|
|
END SUBROUTINE
|
|
|
|
|
|
!********************************************************************
|
|
! Calculates the stress and jacobi (if wanted) for all or a single component
|
|
!********************************************************************
|
|
subroutine SingleCrystallite(&
|
|
updateJaco,& ! update of Jacobian required
|
|
dt) ! time increment
|
|
|
|
use prec, only: pReal,pInt,pert_Fg,subStepMin, nCutback
|
|
use debug
|
|
use math
|
|
use IO, only: IO_error
|
|
use mesh, only: mesh_element, FE_Nips
|
|
use material, only: homogenization_Ngrains
|
|
use constitutive
|
|
|
|
implicit none
|
|
|
|
character (len=128) msg
|
|
logical updateJaco, JacoOK, allConverged
|
|
real(preal) dt
|
|
real(pReal), dimension(3,3) :: Fg_pert,Lp_pert, P_pert, Fp_pert, Fe_pert
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal), dimension(constitutive_maxSizeState) :: state
|
|
integer(pInt) g,i,e,k,l,iOuter,mySizeState
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
forall (g = 1:homogenization_Ngrains(mesh_element(3,e))) ! number of grains of this homogenization
|
|
crystallite_converged(g,i,e) = .false.
|
|
constitutive_state_new(g,i,e)%p = constitutive_state_old(g,i,e)%p
|
|
CPFEM_Lp_new(:,:,g,i,e) = CPFEM_Lp_old(:,:,g,i,e)
|
|
end forall
|
|
end do
|
|
end do
|
|
!$OMP END PARALLEL DO
|
|
|
|
iOuter = 0_pInt
|
|
allConverged = .false.
|
|
|
|
do while (.not. allConverged)
|
|
iOuter = iOuter + 1_pInt ! count state integation loops
|
|
if (iOuter > nOuter) call IO_error(600) ! too many loops required --> croak
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
do g = 1,homogenization_Ngrains(mesh_element(3,e)) ! number of grains of this homogenization
|
|
if (.not. crystallite_converged(g,i,e)) then
|
|
call integrateStress(msg,CPFEM_Tstar_v(:,g,i,e),CPFEM_PK1(:,:,g,i,e), &
|
|
CPFEM_Fp_new(:,:,g,i,e),CPFEM_Fe_new(:,:,g,i,e),CPFEM_Lp_new(:,:,g,i,e), &
|
|
CPFEM_ffn1(:,:,g,i,e),dt,g,i,e)
|
|
if (msg /= 'ok') call IO_error(610,e,i,g,msg)
|
|
endif
|
|
end do
|
|
end do
|
|
end do
|
|
!$OMP END PARALLEL DO
|
|
|
|
allConverged = .true. ! assume best case
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
do g = 1,homogenization_Ngrains(mesh_element(3,e)) ! number of grains of this homogenization
|
|
if (crystallite_converged(g,i,e)) cycle ! this one is already fine
|
|
if (integrateState(CPFEM_Tstar_v(:,g,i,e),dt,g,i,e)) then ! state integration now converged?
|
|
crystallite_converged(g,i,e) = .true.
|
|
!$OMP CRITICAL (out)
|
|
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
|
|
!$OMP END CRITICAL (out)
|
|
else
|
|
allConverged = .false. ! this one requires additional round...
|
|
endif
|
|
end do
|
|
end do
|
|
end do
|
|
!$OMP END PARALLEL DO
|
|
|
|
end do ! all crystallites converged
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
forall (g = 1:homogenization_Ngrains(mesh_element(3,e))) & ! number of grains of this homogenization
|
|
CPFEM_results(CPFEM_Nresults+1:CPFEM_Nresults+constitutive_sizePostResults(g,i,e),g,i,e) = &
|
|
constitutive_postResults(CPFEM_Tstar_v(:,g,i,e),CPFEM_Temperature(i,e),dt,g,i,e)
|
|
end do
|
|
end do
|
|
!$OMP END PARALLEL DO
|
|
|
|
if(updateJaco) then ! Jacobian required
|
|
|
|
!$OMP CRITICAL (write2out)
|
|
if (debugger) write (6,*) 'Jacobian calc'
|
|
!$OMP END CRITICAL (write2out)
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed
|
|
do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed
|
|
do g = 1,homogenization_Ngrains(mesh_element(3,e)) ! number of grains of this homogenization
|
|
mySizeState = constitutive_sizeState(g,i,e) ! number of state variables for this grain
|
|
state(1:mySizeState) = constitutive_state_new(g,i,e)%p ! remember unperturbed, converged state
|
|
do k = 1,3 ! perturbation...
|
|
do l = 1,3 ! ...components
|
|
Fg_pert = CPFEM_ffn1(:,:,g,i,e) ! initialize perturbed Fg
|
|
Fg_pert(k,l) = Fg_pert(k,l) + pert_Fg ! perturb single component
|
|
Lp_pert = CPFEM_Lp_new(:,:,g,i,e) ! initialize Lp
|
|
Fp_pert = CPFEM_Fp_new(:,:,g,i,e) ! initialize Fp
|
|
constitutive_state_new(g,i,e)%p = state(1:mySizeState) ! initial guess from end of time step
|
|
crystallite_converged(g,i,e) = .false.
|
|
iOuter = 0_pInt
|
|
do while(.not. crystallite_converged(g,i,e) .and. iOuter < nOuter)
|
|
iOuter = iOuter + 1_pInt
|
|
call integrateStress(msg,Tstar_v,P_pert,Fp_pert,Fe_pert,Lp_pert, Fg_pert,dt,g,i,e)
|
|
if (msg /= 'ok') exit
|
|
crystallite_converged(g,i,e) = integrateState(Tstar_v,dt,g,i,e)
|
|
end do
|
|
if (crystallite_converged(g,i,e)) &
|
|
CPFEM_dPdF(:,:,k,l,g,i,e) = (P_pert-CPFEM_PK1(:,:,g,i,e))/pert_Fg ! constructing tangent dP_ij/dFg_kl only if valid forward difference
|
|
!$OMP CRITICAL (out)
|
|
debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1
|
|
!$OMP END CRITICAL (out)
|
|
end do
|
|
end do
|
|
constitutive_state_new(g,i,e)%p = state(1:mySizeState) ! restore solution
|
|
end do
|
|
end do
|
|
end do
|
|
!$OMP END PARALLEL DO
|
|
endif
|
|
|
|
return
|
|
|
|
end subroutine
|
|
|
|
|
|
!********************************************************************
|
|
! Update the state for a single component
|
|
!********************************************************************
|
|
function integrateState(&
|
|
Tstar_v,& ! stress
|
|
dt,& ! time increment
|
|
g,& ! grain number
|
|
i,& ! integration point number
|
|
e& ! element number
|
|
)
|
|
use prec, only: pReal,pInt,reltol_Outer
|
|
use constitutive, only: constitutive_dotState,constitutive_sizeDotState,&
|
|
constitutive_state_old,constitutive_state_new
|
|
|
|
logical integrateState
|
|
|
|
integer(pInt) g,i,e,mySize
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal) dt
|
|
real(pReal), dimension(constitutive_sizeDotState(g,i,e)) :: residuum
|
|
|
|
mySize = constitutive_sizeDotState(g,i,e)
|
|
residuum = constitutive_state_new(g,i,e)%p(1:mySize) - constitutive_state_old(g,i,e)%p(1:mySize) - &
|
|
dt*constitutive_dotState(Tstar_v,CPFEM_Temperature(i,e),g,i,e) ! residuum from evolution of microstructure
|
|
constitutive_state_new(g,i,e)%p(1:mySize) = constitutive_state_new(g,i,e)%p(1:mySize) - residuum ! update of microstructure
|
|
integrateState = maxval(abs(residuum/constitutive_state_new(g,i,e)%p(1:mySize)),&
|
|
constitutive_state_new(g,i,e)%p(1:mySize) /= 0.0_pReal) < reltol_Outer
|
|
return
|
|
|
|
end function
|
|
|
|
|
|
!********************************************************************
|
|
! Calculates the stress for a single component
|
|
!********************************************************************
|
|
!***********************************************************************
|
|
!*** calculation of stress (P), stiffness (dPdF), ***
|
|
!*** and announcement of any ***
|
|
!*** acceleration of the Newton-Raphson correction ***
|
|
!***********************************************************************
|
|
subroutine integrateStress(&
|
|
msg,& ! return message
|
|
Tstar_v,& ! Stress vector
|
|
P,& ! first PK stress
|
|
Fp_new,& ! new plastic deformation gradient
|
|
Fe_new,& ! new "elastic" deformation gradient
|
|
Lp,& ! plastic velocity gradient
|
|
!
|
|
Fg_new,& ! new global deformation gradient
|
|
dt,& ! time increment
|
|
g,& ! grain number
|
|
i,& ! integration point number
|
|
e) ! element number
|
|
|
|
use prec, only: pReal,pInt,pert_Fg,subStepMin, nCutback
|
|
use debug
|
|
use constitutive, only: constitutive_state_new
|
|
use math
|
|
! use CPFEM
|
|
!
|
|
implicit none
|
|
!
|
|
character(len=*) msg
|
|
logical error,success
|
|
integer(pInt) e,i,g, nCutbacks, maxCutbacks
|
|
real(pReal) Temperature
|
|
real(pReal) dt,dt_aim,subFrac,subStep,det
|
|
real(pReal), dimension(3,3) :: Lp,Lp_interpolated,inv
|
|
real(pReal), dimension(3,3) :: Fg_current,Fg_new,Fg_aim,deltaFg
|
|
real(pReal), dimension(3,3) :: Fp_current,Fp_new
|
|
real(pReal), dimension(3,3) :: Fe_current,Fe_new
|
|
real(pReal), dimension(3,3) :: P
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
|
|
deltaFg = Fg_new - CPFEM_ffn(:,:,g,i,e)
|
|
subFrac = 0.0_pReal
|
|
subStep = 1.0_pReal
|
|
nCutbacks = 0_pInt
|
|
maxCutbacks = 0_pInt
|
|
Fg_current = CPFEM_ffn(:,:,g,i,e) ! initialize to start of inc
|
|
Fp_current = CPFEM_Fp_old(:,:,g,i,e)
|
|
call math_invert3x3(Fp_current,inv,det,error)
|
|
Fe_current = math_mul33x33(Fg_current,inv)
|
|
|
|
success = .false. ! pretend cutback
|
|
dt_aim = 0.0_pReal ! prevent initial Lp interpolation
|
|
Temperature = CPFEM_Temperature(i,e)
|
|
|
|
! begin the cutback loop
|
|
do while (subStep > subStepMin) ! continue until finished or too much cut backing
|
|
if (success) then ! wind forward
|
|
Fg_current = Fg_aim
|
|
Fe_current = Fe_new
|
|
Fp_current = Fp_new
|
|
elseif (dt_aim > 0.0_pReal) then
|
|
call math_invert3x3(Fg_aim,inv,det,error) ! inv of Fg_aim
|
|
Lp_interpolated = 0.5_pReal*Lp + &
|
|
0.5_pReal*(math_I3 - math_mul33x33(Fp_current,&
|
|
math_mul33x33(inv,Fe_current)))/dt_aim ! interpolate Lp and L
|
|
if (debugger) then
|
|
!$OMP CRITICAL (write2out)
|
|
write (6,*) 'Lp interpolation'
|
|
write (6,'(a,/,3(3(f12.7,x)/))') 'from',Lp(1:3,:)
|
|
write (6,'(a,/,3(3(f12.7,x)/))') 'to',Lp_interpolated(1:3,:)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
Lp = Lp_interpolated
|
|
endif
|
|
!
|
|
Fg_aim = Fg_current + subStep*deltaFg ! aim for Fg
|
|
dt_aim = subStep*dt ! aim for dt
|
|
if (debugger) then
|
|
!$OMP CRITICAL (write2out)
|
|
write (6,*) 'using these values'
|
|
write (6,'(a,/,3(4(f9.3,x)/))') 'state new / MPa',constitutive_state_new(g,i,e)%p/1e6_pReal
|
|
write (6,'(a,/,3(3(f12.7,x)/))') 'Fe current',Fe_current(1:3,:)
|
|
write (6,'(a,/,3(3(f12.7,x)/))') 'Fp current',Fp_current(1:3,:)
|
|
write (6,'(a,/,3(3(f12.7,x)/))') 'Lp (old=new guess)',Lp(1:3,:)
|
|
write (6,'(a20,f,x,a2,x,f)') 'integrating from ',subFrac,'to',(subFrac+subStep)
|
|
!$OMP END CRITICAL (write2out)
|
|
endif
|
|
|
|
call TimeIntegration(msg,Lp,Fp_new,Fe_new,Tstar_v,P, Fg_aim,Fp_current,Temperature,dt_aim,g,i,e)
|
|
|
|
if (msg == 'ok') then
|
|
subFrac = subFrac + subStep
|
|
subStep = min(1.0_pReal-subFrac, subStep*2.0_pReal) ! accelerate
|
|
nCutbacks = 0_pInt ! reset cutback counter
|
|
success = .true. ! keep current Lp
|
|
else
|
|
nCutbacks = nCutbacks + 1 ! record additional cutback
|
|
maxCutbacks = max(nCutbacks,maxCutbacks) ! remember maximum number of cutbacks
|
|
subStep = subStep / 2.0_pReal ! cut time step in half
|
|
success = .false. ! force Lp interpolation
|
|
endif
|
|
enddo ! potential substepping
|
|
!
|
|
!$OMP CRITICAL (cutback)
|
|
debug_cutbackDistribution(min(nCutback,maxCutbacks)+1) = debug_cutbackDistribution(min(nCutback,maxCutbacks)+1)+1
|
|
!$OMP END CRITICAL (cutback)
|
|
|
|
return
|
|
|
|
end subroutine
|
|
|
|
!
|
|
!***********************************************************************
|
|
!*** fully-implicit two-level time integration ***
|
|
!*** based on a residuum in Lp and intermediate ***
|
|
!*** acceleration of the Newton-Raphson correction ***
|
|
!***********************************************************************
|
|
SUBROUTINE TimeIntegration(&
|
|
msg,& ! return message
|
|
Lpguess,& ! guess of plastic velocity gradient
|
|
Fp_new,& ! new plastic deformation gradient
|
|
Fe_new,& ! new "elastic" deformation gradient
|
|
Tstar_v,& ! Stress vector
|
|
P,& ! 1st PK stress (taken as initial guess if /= 0)
|
|
Fg_new,& ! new total def gradient
|
|
Fp_old,& ! former plastic def gradient
|
|
Temperature,& ! temperature
|
|
dt,& ! time increment
|
|
grain,& ! grain number
|
|
ip,& ! integration point number
|
|
cp_en & ! element number
|
|
)
|
|
|
|
use prec
|
|
use debug
|
|
use mesh, only: mesh_element
|
|
use constitutive, only: constitutive_microstructure,constitutive_homogenizedC,constitutive_LpAndItsTangent,&
|
|
constitutive_state_new
|
|
use math
|
|
use IO
|
|
implicit none
|
|
!
|
|
character(len=*) msg
|
|
logical failed
|
|
integer(pInt) cp_en, ip, grain
|
|
integer(pInt) iInner,dummy, i,j,k,l,m,n
|
|
real(pReal) dt, Temperature, det, p_hydro, leapfrog,maxleap
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2
|
|
real(pReal), dimension(6,6) :: C_66
|
|
real(pReal), dimension(3,3) :: Fg_new,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new
|
|
real(pReal), dimension(3,3) :: P
|
|
real(pReal), dimension(3,3) :: Lp,Lpguess,Lpguess_old,Rinner,Rinner_old,A,B,BT,AB,BTA
|
|
real(pReal), dimension(3,3,3,3) :: C
|
|
|
|
msg = 'ok' ! error-free so far
|
|
eye2 = math_identity2nd(9)
|
|
|
|
call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp_old
|
|
if (failed) then
|
|
msg = 'inversion Fp_old'
|
|
return
|
|
endif
|
|
|
|
A = math_mul33x33(transpose(invFp_old), math_mul33x33(transpose(Fg_new),math_mul33x33(Fg_new,invFp_old)))
|
|
|
|
!$OMP CRITICAL (write2out)
|
|
if (debugger) write (6,'(a,/,3(3(f12.7,x)/))') 'Fg to be calculated',Fg_new
|
|
!$OMP END CRITICAL (write2out)
|
|
|
|
call constitutive_microstructure(Temperature,grain,ip,cp_en)
|
|
C_66 = constitutive_homogenizedC(grain,ip,cp_en)
|
|
C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor
|
|
|
|
iInner = 0_pInt
|
|
leapfrog = 1.0_pReal ! correction as suggested by invdRdLp-step
|
|
maxleap = 1024.0_pReal ! preassign maximum acceleration level
|
|
|
|
Lpguess_old = Lpguess ! consider present Lpguess good
|
|
|
|
Inner: do ! inner iteration: Lp
|
|
iInner = iInner+1
|
|
if (iInner > nInner) then ! too many loops required
|
|
Lpguess = Lpguess_old ! do not trust the last update but resort to former one
|
|
msg = 'limit Inner iteration'
|
|
return
|
|
endif
|
|
|
|
B = math_i3 - dt*Lpguess
|
|
BT = transpose(B)
|
|
AB = math_mul33x33(A,B)
|
|
BTA = math_mul33x33(BT,A)
|
|
Tstar_v = 0.5_pReal*math_mul66x6(C_66,math_mandel33to6(math_mul33x33(BT,AB)-math_I3))
|
|
p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal
|
|
forall(i=1:3) Tstar_v(i) = Tstar_v(i)-p_hydro ! subtract hydrostatic pressure
|
|
call constitutive_LpAndItsTangent(Lp,dLp, Tstar_v,Temperature,grain,ip,cp_en)
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Rinner = Lpguess - Lp ! update current residuum
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if (.not.(any(Rinner/=Rinner)) .and. & ! exclude any NaN in residuum
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( ( maxval(abs(Rinner)) < abstol_Inner) .or. & ! below abs tol .or.
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( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and.
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maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner & ! below rel tol
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) &
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) &
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) &
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exit Inner ! convergence
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!
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! check for acceleration/deceleration in Newton--Raphson correction
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!
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if (any(Rinner/=Rinner) .and. & ! NaN occured at regular speed
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leapfrog == 1.0) then
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Lpguess = Lpguess_old ! restore known good guess
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msg = 'NaN present' ! croak for cutback
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return
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elseif (leapfrog > 1.0_pReal .and. & ! at fast pace ?
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(sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum
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sum(Rinner*Rinner_old) < 0.0_pReal) .or. & ! residuum changed sign (overshoot)
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any(Rinner/=Rinner) ) then ! NaN
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maxleap = 0.5_pReal * leapfrog ! limit next acceleration
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leapfrog = 1.0_pReal ! grinding halt
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else ! better residuum
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dTdLp = 0.0_pReal ! calc dT/dLp
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forall (i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) &
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dTdLp(3*(i-1)+j,3*(k-1)+l) = dTdLp(3*(i-1)+j,3*(k-1)+l) + &
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C(i,j,l,n)*AB(k,n)+C(i,j,m,l)*BTA(m,k)
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dTdLp = -0.5_pReal*dt*dTdLp
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dRdLp = eye2 - math_mul99x99(dLp,dTdLp) ! calc dR/dLp
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invdRdLp = 0.0_pReal
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call math_invert(9,dRdLp,invdRdLp,dummy,failed) ! invert dR/dLp --> dLp/dR
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if (failed) then
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msg = 'inversion dR/dLp'
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if (debugger) then
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|
!$OMP CRITICAL (write2out)
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write (6,*) msg
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write (6,'(a,/,9(9(e9.3,x)/))') 'dRdLp', dRdLp(1:9,:)
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write (6,'(a,/,3(4(f9.3,x)/))') 'state_new / MPa',constitutive_state_new(grain,ip,cp_en)%p/1e6_pReal
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write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:)
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write (6,'(a,/,3(3(e12.7,x)/))') 'Lp',Lp(1:3,:)
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write (6,'(a,/,6(f9.3,x))') 'Tstar / MPa',Tstar_v/1e6_pReal
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!$OMP END CRITICAL (write2out)
|
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endif
|
|
return
|
|
endif
|
|
!
|
|
Rinner_old = Rinner ! remember current residuum
|
|
Lpguess_old = Lpguess ! remember current Lp guess
|
|
if (iInner > 1 .and. leapfrog < maxleap) leapfrog = 2.0_pReal * leapfrog ! accelerate if ok
|
|
endif
|
|
!
|
|
Lpguess = Lpguess_old ! start from current guess
|
|
Rinner = Rinner_old ! use current residuum
|
|
forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess
|
|
Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l)
|
|
enddo Inner
|
|
!
|
|
!$OMP CRITICAL (in)
|
|
debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1
|
|
!$OMP END CRITICAL (in)
|
|
invFp_new = math_mul33x33(invFp_old,B)
|
|
call math_invert3x3(invFp_new,Fp_new,det,failed)
|
|
if (failed) then
|
|
msg = 'inversion Fp_new^-1'
|
|
return
|
|
endif
|
|
|
|
Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !!
|
|
forall (i=1:3) Tstar_v(i) = Tstar_v(i) + p_hydro ! add hydrostatic component back
|
|
Fe_new = math_mul33x33(Fg_new,invFp_new) ! calc resulting Fe
|
|
P = math_mul33x33(Fe_new,math_mul33x33(math_Mandel6to33(Tstar_v),transpose(invFp_new))) ! first PK stress
|
|
|
|
return
|
|
!
|
|
END SUBROUTINE
|
|
!
|
|
END MODULE
|
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!##############################################################
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