!############################################################## MODULE CPFEM !############################################################## ! *** CPFEM engine *** ! use prec, only: pReal,pInt implicit none ! ! **************************************************************** ! *** General variables for the material behaviour calculation *** ! **************************************************************** real(pReal), dimension (:,:), allocatable :: CPFEM_Temperature real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_bar !average FFN per IP real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_ffn !individual FFN per grain real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_bar !average FFN1 per IP real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_ffn1 !individual FFN1 per grain real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar !average PK1 per IP real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_PK1 !individual PK1 per grain real(pReal), dimension (:,:,:,:,:,:), allocatable :: CPFEM_dPdF_bar !average dPdF per IP real(pReal), dimension (:,:,:,:,:,:), allocatable :: CPFEM_dPdF_bar_old !old average dPdF per IP real(pReal), dimension (:,:,:,:,:,:,:),allocatable :: CPFEM_dPdF !individual dPdF per grain real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_knownGood real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Lp_old real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Lp_new real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fe_new real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_Tstar_v logical, dimension (:,:,:), allocatable :: crystallite_converged !individual convergence flag per grain integer(pInt), dimension(:,:), allocatable :: CPFEM_execution_IP integer(pInt), dimension(2) :: CPFEM_execution_elem integer(pInt) :: CPFEM_Nresults = 5_pInt ! phase, volfrac, three Euler angles logical :: CPFEM_init_done = .false. ! remember whether init has been done already logical :: CPFEM_calc_done = .false. ! remember whether first IP has already calced the results real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal ! CONTAINS ! !********************************************************* !*** allocate the arrays defined in module CPFEM *** !*** and initialize them *** !********************************************************* SUBROUTINE CPFEM_init(Temperature) ! use prec use math, only: math_EulertoR, math_I3, math_identity2nd use FEsolving, only: parallelExecution use mesh use material use constitutive ! implicit none ! real(pReal) Temperature integer(pInt) e,i,g ! ! *** mpie.marc parameters *** allocate(CPFEM_Temperature(mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = Temperature allocate(CPFEM_ffn_bar(3,3,mesh_maxNips,mesh_NcpElems)) forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_bar(:,:,i,e) = math_I3 allocate(CPFEM_ffn(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) forall(g=1:homogenization_maxNgrains,e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn(:,:,g,i,e) = math_I3 allocate(CPFEM_ffn1_bar(3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_bar = CPFEM_ffn_bar allocate(CPFEM_ffn1(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1 = CPFEM_ffn allocate(CPFEM_PK1_bar(3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_bar = 0.0_pReal allocate(CPFEM_PK1(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1 = 0.0_pReal allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal allocate(CPFEM_dPdF_bar_old(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar_old = 0.0_pReal allocate(CPFEM_dPdF(3,3,3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF = 0.0_pReal allocate(CPFEM_stress_bar(6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_bar = 0.0_pReal allocate(CPFEM_jaco_bar(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_bar = 0.0_pReal allocate(CPFEM_jaco_knownGood(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_knownGood = 0.0_pReal ! ! *** User defined results *** allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxSizePostResults,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) CPFEM_results = 0.0_pReal ! ! *** Plastic velocity gradient *** allocate(CPFEM_Lp_old(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Lp_old = 0.0_pReal allocate(CPFEM_Lp_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Lp_new = 0.0_pReal ! *** Plastic deformation gradient at (t=t0) and (t=t1) *** allocate(CPFEM_Fp_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal allocate(CPFEM_Fp_old(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:homogenization_maxNgrains) & CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(material_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation ! *** Elastic deformation gradient at (t=t1) *** allocate(CPFEM_Fe_new(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fe_new = 0.0_pReal ! *** Stress vector at (t=t1) *** allocate(CPFEM_Tstar_v(6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Tstar_v = 0.0_pReal ! allocate(crystallite_converged(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems)); crystallite_converged = .false. allocate(CPFEM_execution_IP(2,mesh_NcpElems)); CPFEM_execution_IP = 1_pInt forall (e = 1:mesh_NcpElems) CPFEM_execution_IP(2,e) = FE_Nips(mesh_element(2,e)) CPFEM_execution_elem = (/1,mesh_NcpElems/) ! *** Output to MARC output file *** !$OMP CRITICAL (write2out) write(6,*) write(6,*) 'CPFEM Initialization' write(6,*) write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature) write(6,*) 'CPFEM_ffn_bar: ', shape(CPFEM_ffn_bar) write(6,*) 'CPFEM_ffn: ', shape(CPFEM_ffn) write(6,*) 'CPFEM_ffn1_bar: ', shape(CPFEM_ffn1_bar) write(6,*) 'CPFEM_ffn1: ', shape(CPFEM_ffn1) write(6,*) 'CPFEM_PK1_bar: ', shape(CPFEM_PK1_bar) write(6,*) 'CPFEM_PK1: ', shape(CPFEM_PK1) write(6,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar) write(6,*) 'CPFEM_dPdF_bar_old: ', shape(CPFEM_dPdF_bar_old) write(6,*) 'CPFEM_dPdF: ', shape(CPFEM_dPdF) write(6,*) 'CPFEM_stress_bar: ', shape(CPFEM_stress_bar) write(6,*) 'CPFEM_jaco_bar: ', shape(CPFEM_jaco_bar) write(6,*) 'CPFEM_jaco_knownGood: ', shape(CPFEM_jaco_knownGood) write(6,*) 'CPFEM_results: ', shape(CPFEM_results) write(6,*) 'CPFEM_Lp_old: ', shape(CPFEM_Lp_old) write(6,*) 'CPFEM_Lp_new: ', shape(CPFEM_Lp_new) write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old) write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new) write(6,*) 'CPFEM_Fe_new: ', shape(CPFEM_Fe_new) write(6,*) 'CPFEM_Tstar_v: ', shape(CPFEM_Tstar_v) write(6,*) 'crystallite_converged:', shape(crystallite_converged) write(6,*) write(6,*) 'parallelExecution: ', parallelExecution call flush(6) !$OMP END CRITICAL (write2out) return ! END SUBROUTINE ! ! !*********************************************************************** !*** perform initialization at first call, update variables and *** !*** call the actual material model *** ! ! CPFEM_mode computation mode (regular, collection, recycle) ! ffn deformation gradient for t=t0 ! ffn1 deformation gradient for t=t1 ! Temperature temperature ! CPFEM_dt time increment ! CPFEM_en element number ! CPFEM_in intergration point number ! CPFEM_stress stress vector in Mandel notation ! CPFEM_updateJaco flag to initiate computation of Jacobian ! CPFEM_jaco jacobian in Mandel notation ! CPFEM_ngens size of stress strain law !*********************************************************************** SUBROUTINE CPFEM_general(CPFEM_mode, ffn, ffn1, Temperature, CPFEM_dt,& CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_updateJaco, CPFEM_jaco, CPFEM_ngens) ! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de ! use prec, only: pReal,pInt use FEsolving use debug use math use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, mesh_maxNips, mesh_element use lattice, only: lattice_init use material use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new implicit none ! integer(pInt) CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n real(pReal), dimension (3,3) :: ffn,ffn1,Kirchhoff_bar real(pReal), dimension (3,3,3,3) :: H_bar, H_bar_sym real(pReal), dimension(CPFEM_ngens) :: CPFEM_stress real(pReal), dimension(CPFEM_ngens,CPFEM_ngens) :: CPFEM_jaco, odd_jaco real(pReal) Temperature,CPFEM_dt,J_inverse integer(pInt) CPFEM_mode ! 1: regular computation with aged results& ! 2: regular computation& ! 3: collection of FEM data& ! 4: recycling of former results (MARC speciality)& ! 5: record tangent from former converged inc& ! 6: restore tangent from former converged inc logical CPFEM_updateJaco ! if (.not. CPFEM_init_done) then ! initialization step (three dimensional stress state check missing?) call math_init() call FE_init() call mesh_init() call lattice_init() call material_init() call constitutive_init() write (6,*) 'call CPFEM init' call CPFEM_init(Temperature) CPFEM_init_done = .true. endif ! cp_en = mesh_FEasCP('elem',CPFEM_en) if (cp_en == 1 .and. CPFEM_in == 1) then write(6,'(a10,1x,f8.4,1x,a10,1x,i4,1x,a10,1x,i3,1x,a10,1x,i2,x,a10,1x,i2)') & 'theTime',theTime,'theInc',theInc,'theCycle',theCycle,'theLovl',theLovl,& 'mode',CPFEM_mode endif ! select case (CPFEM_mode) case (1,2) ! regular computation (with aging of results if mode == 1) if (CPFEM_mode == 1) then ! age results at start of new increment CPFEM_Lp_old = CPFEM_Lp_new CPFEM_Fp_old = CPFEM_Fp_new forall (i = 1:homogenization_maxNgrains,& j = 1:mesh_maxNips, & k = 1:mesh_NcpElems) & constitutive_state_old(i,j,k)%p = constitutive_state_new(i,j,k)%p write (6,*) 'results aged.' endif if (outdatedFFN1 .or. any(abs(ffn1 - CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en)) > relevantStrain)) then 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) outdatedFFN1 = .true. CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens) else if (.not. parallelExecution) then CPFEM_execution_elem(1) = cp_en CPFEM_execution_elem(2) = cp_en CPFEM_execution_IP(1,cp_en) = CPFEM_in CPFEM_execution_IP(2,cp_en) = CPFEM_in call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt) elseif (.not. CPFEM_calc_done) then call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt) ! parallel execution inside CPFEM_calc_done = .true. endif ! translate from P and dP/dF to CS and dCS/dE Kirchhoff_bar = math_mul33x33(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en))) J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en)) CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel33to6(J_inverse*Kirchhoff_bar) ! H_bar = 0.0_pReal forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) & H_bar(i,j,k,l) = H_bar(i,j,k,l) + & CPFEM_ffn1_bar(j,m,CPFEM_in,cp_en) * & CPFEM_ffn1_bar(l,n,CPFEM_in,cp_en) * & CPFEM_dPdF_bar(i,m,k,n,CPFEM_in,cp_en) - & math_I3(j,l)*CPFEM_ffn1_bar(i,m,CPFEM_in,cp_en)*CPFEM_PK1_bar(k,m,CPFEM_in,cp_en) + & 0.5_pReal*(math_I3(i,k)*Kirchhoff_bar(j,l) + math_I3(j,l)*Kirchhoff_bar(i,k) + & math_I3(i,l)*Kirchhoff_bar(j,k) + math_I3(j,k)*Kirchhoff_bar(i,l)) forall(i=1:3,j=1:3,k=1:3,l=1:3) & 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)) CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel3333to66(J_inverse*H_bar) endif case (3) ! collect and return odd result CPFEM_Temperature(CPFEM_in,cp_en) = Temperature CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) = ffn CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) = ffn1 CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens) CPFEM_calc_done = .false. case (4) ! do nothing since we can recycle the former results (MARC specialty) case (5) ! record consistent tangent at beginning of new increment (while recycling) CPFEM_jaco_knownGood = CPFEM_jaco_bar case (6) ! restore consistent tangent after cutback CPFEM_jaco_bar = CPFEM_jaco_knownGood end select ! ! return the local stress and the jacobian from storage CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) ! return ! END SUBROUTINE ! ! !********************************************************** !*** calculate the material point behaviour *** !********************************************************** SUBROUTINE CPFEM_MaterialPoint(& updateJaco,& ! flag to initiate Jacobian updating CPFEM_dt) ! Time increment (dt) ! use prec use debug use math, only: math_pDecomposition,math_RtoEuler,inDeg use IO, only: IO_error use mesh, only: mesh_element, mesh_NcpElems, FE_Nips use material, only: homogenization_Ngrains,material_phase,material_volfrac use constitutive implicit none ! logical, intent(in) :: updateJaco real(pReal), intent(in) :: CPFEM_dt integer(pInt) g,i,e logical error real(pReal) volfrac real(pReal), dimension(3,3) :: U,R !$OMP PARALLEL DO do e = CPFEM_execution_elem(1),CPFEM_execution_elem(2) ! iterate over elements to be processed do i = CPFEM_execution_IP(1,e),CPFEM_execution_IP(2,e) ! iterate over IPs of this element to be processed forall (g = 1:homogenization_Ngrains(mesh_element(3,e))) ! number of grains of this homogenization CPFEM_ffn(:,:,g,i,e) = CPFEM_ffn_bar(:,:,i,e) ! Taylor homogenization (why not using former ffn1??) CPFEM_ffn1(:,:,g,i,e) = CPFEM_ffn1_bar(:,:,i,e) ! Taylor homogenization end forall enddo enddo !$OMP END PARALLEL DO call SingleCrystallite(updateJaco,CPFEM_dt) !****************************************************************************************************** ! check convergence of homogenization if needed !****************************************************************************************************** ! 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) Rinner = Lpguess - Lp ! update current residuum if (.not.(any(Rinner/=Rinner)) .and. & ! exclude any NaN in residuum ( ( maxval(abs(Rinner)) < abstol_Inner) .or. & ! below abs tol .or. ( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and. maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner & ! below rel tol ) & ) & ) & exit Inner ! convergence ! ! check for acceleration/deceleration in Newton--Raphson correction ! if (any(Rinner/=Rinner) .and. & ! NaN occured at regular speed leapfrog == 1.0) then Lpguess = Lpguess_old ! restore known good guess msg = 'NaN present' ! croak for cutback return elseif (leapfrog > 1.0_pReal .and. & ! at fast pace ? (sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum sum(Rinner*Rinner_old) < 0.0_pReal) .or. & ! residuum changed sign (overshoot) any(Rinner/=Rinner) ) then ! NaN maxleap = 0.5_pReal * leapfrog ! limit next acceleration leapfrog = 1.0_pReal ! grinding halt else ! better residuum dTdLp = 0.0_pReal ! calc dT/dLp forall (i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) & dTdLp(3*(i-1)+j,3*(k-1)+l) = dTdLp(3*(i-1)+j,3*(k-1)+l) + & C(i,j,l,n)*AB(k,n)+C(i,j,m,l)*BTA(m,k) dTdLp = -0.5_pReal*dt*dTdLp dRdLp = eye2 - math_mul99x99(dLp,dTdLp) ! calc dR/dLp invdRdLp = 0.0_pReal call math_invert(9,dRdLp,invdRdLp,dummy,failed) ! invert dR/dLp --> dLp/dR if (failed) then msg = 'inversion dR/dLp' if (debugger) then !$OMP CRITICAL (write2out) write (6,*) msg write (6,'(a,/,9(9(e9.3,x)/))') 'dRdLp', dRdLp(1:9,:) write (6,'(a,/,3(4(f9.3,x)/))') 'state_new / MPa',constitutive_state_new(grain,ip,cp_en)%p/1e6_pReal write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:) write (6,'(a,/,3(3(e12.7,x)/))') 'Lp',Lp(1:3,:) write (6,'(a,/,6(f9.3,x))') 'Tstar / MPa',Tstar_v/1e6_pReal !$OMP END CRITICAL (write2out) 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 !##############################################################