!-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @brief elasticity, plasticity, damage & thermal internal microstructure state !-------------------------------------------------------------------------------------------------- module constitutive use prec use math use rotations use IO use config use material use results use lattice use discretization use parallelization use HDF5_utilities use DAMASK_interface use FEsolving use results implicit none private real(pReal), dimension(:,:,:), allocatable, public :: & crystallite_dt !< requested time increment of each grain real(pReal), dimension(:,:,:), allocatable :: & crystallite_subdt, & !< substepped time increment of each grain crystallite_subFrac, & !< already calculated fraction of increment crystallite_subStep !< size of next integration step type(rotation), dimension(:,:,:), allocatable :: & crystallite_orientation !< current orientation real(pReal), dimension(:,:,:,:,:), allocatable :: & crystallite_F0, & !< def grad at start of FE inc crystallite_subF, & !< def grad to be reached at end of crystallite inc crystallite_subF0, & !< def grad at start of crystallite inc ! crystallite_Fe, & !< current "elastic" def grad (end of converged time step) ! crystallite_Fp, & !< current plastic def grad (end of converged time step) crystallite_Fp0, & !< plastic def grad at start of FE inc crystallite_partitionedFp0,& !< plastic def grad at start of homog inc crystallite_subFp0,& !< plastic def grad at start of crystallite inc ! crystallite_Fi, & !< current intermediate def grad (end of converged time step) crystallite_Fi0, & !< intermediate def grad at start of FE inc crystallite_partitionedFi0,& !< intermediate def grad at start of homog inc crystallite_subFi0,& !< intermediate def grad at start of crystallite inc ! crystallite_Lp0, & !< plastic velocitiy grad at start of FE inc crystallite_partitionedLp0, & !< plastic velocity grad at start of homog inc ! crystallite_Li, & !< current intermediate velocitiy grad (end of converged time step) crystallite_Li0, & !< intermediate velocitiy grad at start of FE inc crystallite_partitionedLi0, & !< intermediate velocity grad at start of homog inc ! crystallite_S0, & !< 2nd Piola-Kirchhoff stress vector at start of FE inc crystallite_partitionedS0 !< 2nd Piola-Kirchhoff stress vector at start of homog inc real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: & crystallite_P, & !< 1st Piola-Kirchhoff stress per grain crystallite_Lp, & !< current plastic velocitiy grad (end of converged time step) crystallite_S, & !< current 2nd Piola-Kirchhoff stress vector (end of converged time step) crystallite_partitionedF0 !< def grad at start of homog inc real(pReal), dimension(:,:,:,:,:), allocatable, public :: & crystallite_partitionedF !< def grad to be reached at end of homog inc logical, dimension(:,:,:), allocatable, public :: & crystallite_requested !< used by upper level (homogenization) to request crystallite calculation logical, dimension(:,:,:), allocatable :: & crystallite_converged !< convergence flag type :: tOutput !< new requested output (per phase) character(len=pStringLen), allocatable, dimension(:) :: & label end type tOutput type(tOutput), allocatable, dimension(:) :: output_constituent type :: tNumerics integer :: & iJacoLpresiduum, & !< frequency of Jacobian update of residuum in Lp nState, & !< state loop limit nStress !< stress loop limit real(pReal) :: & subStepMinCryst, & !< minimum (relative) size of sub-step allowed during cutback subStepSizeCryst, & !< size of first substep when cutback subStepSizeLp, & !< size of first substep when cutback in Lp calculation subStepSizeLi, & !< size of first substep when cutback in Li calculation stepIncreaseCryst, & !< increase of next substep size when previous substep converged rtol_crystalliteState, & !< relative tolerance in state loop rtol_crystalliteStress, & !< relative tolerance in stress loop atol_crystalliteStress !< absolute tolerance in stress loop end type tNumerics type(tNumerics) :: num ! numerics parameters. Better name? type :: tDebugOptions logical :: & basic, & extensive, & selective integer :: & element, & ip, & grain end type tDebugOptions type(tDebugOptions) :: debugCrystallite procedure(integrateStateFPI), pointer :: integrateState integer(kind(PLASTICITY_undefined_ID)), dimension(:), allocatable :: & phase_plasticity !< plasticity of each phase integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: & phase_source, & !< active sources mechanisms of each phase phase_kinematics !< active kinematic mechanisms of each phase integer, dimension(:), allocatable, public :: & !< ToDo: should be protected (bug in Intel compiler) phase_Nsources, & !< number of source mechanisms active in each phase phase_Nkinematics, & !< number of kinematic mechanisms active in each phase phase_NstiffnessDegradations, & !< number of stiffness degradation mechanisms active in each phase phase_plasticityInstance, & !< instance of particular plasticity of each phase phase_elasticityInstance !< instance of particular elasticity of each phase logical, dimension(:), allocatable, public :: & ! ToDo: should be protected (bug in Intel Compiler) phase_localPlasticity !< flags phases with local constitutive law type(tPlasticState), allocatable, dimension(:), public :: & plasticState type(tSourceState), allocatable, dimension(:), public :: & sourceState integer, public, protected :: & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizeDotState interface module subroutine mech_init end subroutine mech_init module subroutine damage_init end subroutine damage_init module subroutine thermal_init end subroutine thermal_init module function constitutive_collectDotState(S, FArray, Fi, FpArray, subdt, ipc, ip, el,phase,of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in) :: & subdt !< timestep real(pReal), intent(in), dimension(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: & FArray, & !< elastic deformation gradient FpArray !< plastic deformation gradient real(pReal), intent(in), dimension(3,3) :: & Fi !< intermediate deformation gradient real(pReal), intent(in), dimension(3,3) :: & S !< 2nd Piola Kirchhoff stress (vector notation) logical :: broken end function constitutive_collectDotState module function constitutive_deltaState(S, Fi, ipc, ip, el, phase, of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in), dimension(3,3) :: & S, & !< 2nd Piola Kirchhoff stress Fi !< intermediate deformation gradient logical :: & broken end function constitutive_deltaState module function plastic_active(plastic_label) result(active_plastic) character(len=*), intent(in) :: plastic_label logical, dimension(:), allocatable :: active_plastic end function plastic_active module function source_active(source_label,src_length) result(active_source) character(len=*), intent(in) :: source_label integer, intent(in) :: src_length logical, dimension(:,:), allocatable :: active_source end function source_active module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics) character(len=*), intent(in) :: kinematics_label integer, intent(in) :: kinematics_length logical, dimension(:,:), allocatable :: active_kinematics end function kinematics_active module subroutine source_damage_anisoBrittle_dotState(S, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & S end subroutine source_damage_anisoBrittle_dotState module subroutine source_damage_anisoDuctile_dotState(ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element end subroutine source_damage_anisoDuctile_dotState module subroutine source_damage_isoDuctile_dotState(ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element end subroutine source_damage_isoDuctile_dotState module subroutine source_thermal_externalheat_dotState(phase, of) integer, intent(in) :: & phase, & of end subroutine source_thermal_externalheat_dotState module subroutine constitutive_damage_getRateAndItsTangents(phiDot, dPhiDot_dPhi, phi, ip, el) integer, intent(in) :: & ip, & !< integration point number el !< element number real(pReal), intent(in) :: & phi !< damage parameter real(pReal), intent(inout) :: & phiDot, & dPhiDot_dPhi end subroutine constitutive_damage_getRateAndItsTangents module subroutine constitutive_thermal_getRateAndItsTangents(TDot, dTDot_dT, T, S, Lp, ip, el) integer, intent(in) :: & ip, & !< integration point number el !< element number real(pReal), intent(in) :: & T real(pReal), intent(in), dimension(:,:,:,:,:) :: & S, & !< current 2nd Piola Kitchoff stress vector Lp !< plastic velocity gradient real(pReal), intent(inout) :: & TDot, & dTDot_dT end subroutine constitutive_thermal_getRateAndItsTangents module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC) real(pReal), dimension(6,6) :: & homogenizedC integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element end function plastic_dislotwin_homogenizedC module subroutine plastic_nonlocal_updateCompatibility(orientation,instance,i,e) integer, intent(in) :: & instance, & i, & e type(rotation), dimension(1,discretization_nIPs,discretization_Nelems), intent(in) :: & orientation !< crystal orientation end subroutine plastic_nonlocal_updateCompatibility module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,instance,of) real(pReal), dimension(3,3), intent(out) :: & Li !< inleastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLi_dMi !< derivative of Li with respect to Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mi !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_isotropic_LiAndItsTangent module subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el) integer, intent(in) :: & ipc, & !< grain number ip, & !< integration point number el !< element number real(pReal), intent(in), dimension(3,3) :: & S real(pReal), intent(out), dimension(3,3) :: & Ld !< damage velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor) end subroutine kinematics_cleavage_opening_LiAndItsTangent module subroutine kinematics_slipplane_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el) integer, intent(in) :: & ipc, & !< grain number ip, & !< integration point number el !< element number real(pReal), intent(in), dimension(3,3) :: & S real(pReal), intent(out), dimension(3,3) :: & Ld !< damage velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor) end subroutine kinematics_slipplane_opening_LiAndItsTangent module subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar, ipc, ip, el) integer, intent(in) :: & ipc, & !< grain number ip, & !< integration point number el !< element number real(pReal), intent(out), dimension(3,3) :: & Li !< thermal velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLi_dTstar !< derivative of Li with respect to Tstar (4th-order tensor defined to be zero) end subroutine kinematics_thermal_expansion_LiAndItsTangent module subroutine source_damage_isoBrittle_deltaState(C, Fe, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & Fe real(pReal), intent(in), dimension(6,6) :: & C end subroutine source_damage_isoBrittle_deltaState module subroutine plastic_results end subroutine plastic_results module subroutine damage_results end subroutine damage_results end interface interface constitutive_LpAndItsTangents module subroutine constitutive_plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, & S, Fi, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & S, & !< 2nd Piola-Kirchhoff stress Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & Lp !< plastic velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLp_dS, & dLp_dFi !< derivative of Lp with respect to Fi end subroutine constitutive_plastic_LpAndItsTangents end interface constitutive_LpAndItsTangents interface constitutive_dependentState module subroutine constitutive_plastic_dependentState(F, Fp, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & F, & !< elastic deformation gradient Fp !< plastic deformation gradient end subroutine constitutive_plastic_dependentState end interface constitutive_dependentState interface constitutive_SandItsTangents module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & Fe, & !< elastic deformation gradient Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & S !< 2nd Piola-Kirchhoff stress tensor real(pReal), intent(out), dimension(3,3,3,3) :: & dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient end subroutine constitutive_hooke_SandItsTangents end interface constitutive_SandItsTangents type(tDebugOptions) :: debugConstitutive public :: & constitutive_init, & constitutive_homogenizedC, & constitutive_LpAndItsTangents, & constitutive_dependentState, & constitutive_LiAndItsTangents, & constitutive_SandItsTangents, & constitutive_collectDotState, & constitutive_collectDotState_source, & constitutive_deltaState, & constitutive_deltaState_source, & constitutive_damage_getRateAndItsTangents, & constitutive_thermal_getRateAndItsTangents, & constitutive_results, & constitutive_allocateState, & constitutive_forward, & constitutive_restore, & plastic_nonlocal_updateCompatibility, & plastic_active, & source_active, & kinematics_active public :: & crystallite_init, & crystallite_stress, & crystallite_stressTangent, & crystallite_orientations, & crystallite_push33ToRef, & crystallite_results, & crystallite_restartWrite, & crystallite_restartRead, & crystallite_forward, & crystallite_initializeRestorationPoints, & crystallite_windForward, & crystallite_restore contains !-------------------------------------------------------------------------------------------------- !> @brief Initialze constitutive models for individual physics !-------------------------------------------------------------------------------------------------- subroutine constitutive_init integer :: & p, & !< counter in phase loop s !< counter in source loop class (tNode), pointer :: & debug_constitutive, & phases debug_constitutive => config_debug%get('constitutive', defaultVal=emptyList) debugConstitutive%basic = debug_constitutive%contains('basic') debugConstitutive%extensive = debug_constitutive%contains('extensive') debugConstitutive%selective = debug_constitutive%contains('selective') debugConstitutive%element = config_debug%get_asInt('element',defaultVal = 1) debugConstitutive%ip = config_debug%get_asInt('integrationpoint',defaultVal = 1) debugConstitutive%grain = config_debug%get_asInt('grain',defaultVal = 1) !-------------------------------------------------------------------------------------------------- ! initialize constitutive laws call mech_init call damage_init call thermal_init print'(/,a)', ' <<<+- constitutive init -+>>>'; flush(IO_STDOUT) phases => config_material%get('phase') constitutive_source_maxSizeDotState = 0 PhaseLoop2:do p = 1,phases%length !-------------------------------------------------------------------------------------------------- ! partition and initialize state plasticState(p)%partitionedState0 = plasticState(p)%state0 plasticState(p)%state = plasticState(p)%partitionedState0 forall(s = 1:phase_Nsources(p)) sourceState(p)%p(s)%partitionedState0 = sourceState(p)%p(s)%state0 sourceState(p)%p(s)%state = sourceState(p)%p(s)%partitionedState0 end forall constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, & maxval(sourceState(p)%p%sizeDotState)) enddo PhaseLoop2 constitutive_plasticity_maxSizeDotState = maxval(plasticState%sizeDotState) end subroutine constitutive_init !-------------------------------------------------------------------------------------------------- !> @brief checks if a source mechanism is active or not !-------------------------------------------------------------------------------------------------- module function source_active(source_label,src_length) result(active_source) character(len=*), intent(in) :: source_label !< name of source mechanism integer, intent(in) :: src_length !< max. number of sources in system logical, dimension(:,:), allocatable :: active_source class(tNode), pointer :: & phases, & phase, & sources, & src integer :: p,s phases => config_material%get('phase') allocate(active_source(src_length,phases%length), source = .false. ) do p = 1, phases%length phase => phases%get(p) sources => phase%get('source',defaultVal=emptyList) do s = 1, sources%length src => sources%get(s) if(src%get_asString('type') == source_label) active_source(s,p) = .true. enddo enddo end function source_active !-------------------------------------------------------------------------------------------------- !> @brief checks if a kinematic mechanism is active or not !-------------------------------------------------------------------------------------------------- module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics) character(len=*), intent(in) :: kinematics_label !< name of kinematic mechanism integer, intent(in) :: kinematics_length !< max. number of kinematics in system logical, dimension(:,:), allocatable :: active_kinematics class(tNode), pointer :: & phases, & phase, & kinematics, & kinematics_type integer :: p,k phases => config_material%get('phase') allocate(active_kinematics(kinematics_length,phases%length), source = .false. ) do p = 1, phases%length phase => phases%get(p) kinematics => phase%get('kinematics',defaultVal=emptyList) do k = 1, kinematics%length kinematics_type => kinematics%get(k) if(kinematics_type%get_asString('type') == kinematics_label) active_kinematics(k,p) = .true. enddo enddo end function kinematics_active !-------------------------------------------------------------------------------------------------- !> @brief returns the homogenize elasticity matrix !> ToDo: homogenizedC66 would be more consistent !-------------------------------------------------------------------------------------------------- function constitutive_homogenizedC(ipc,ip,el) real(pReal), dimension(6,6) :: & constitutive_homogenizedC integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el))) case (PLASTICITY_DISLOTWIN_ID) plasticityType constitutive_homogenizedC = plastic_dislotwin_homogenizedC(ipc,ip,el) case default plasticityType constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(ipc,el)) end select plasticityType end function constitutive_homogenizedC !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient ! ToDo: MD: S is Mi? !-------------------------------------------------------------------------------------------------- subroutine constitutive_LiAndItsTangents(Li, dLi_dS, dLi_dFi, & S, Fi, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & S !< 2nd Piola-Kirchhoff stress real(pReal), intent(in), dimension(3,3) :: & Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & Li !< intermediate velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLi_dS, & !< derivative of Li with respect to S dLi_dFi real(pReal), dimension(3,3) :: & my_Li, & !< intermediate velocity gradient FiInv, & temp_33 real(pReal), dimension(3,3,3,3) :: & my_dLi_dS real(pReal) :: & detFi integer :: & k, i, j, & instance, of Li = 0.0_pReal dLi_dS = 0.0_pReal dLi_dFi = 0.0_pReal plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el))) case (PLASTICITY_isotropic_ID) plasticityType of = material_phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phaseAt(ipc,el)) call plastic_isotropic_LiAndItsTangent(my_Li, my_dLi_dS, S ,instance,of) case default plasticityType my_Li = 0.0_pReal my_dLi_dS = 0.0_pReal end select plasticityType Li = Li + my_Li dLi_dS = dLi_dS + my_dLi_dS KinematicsLoop: do k = 1, phase_Nkinematics(material_phaseAt(ipc,el)) kinematicsType: select case (phase_kinematics(k,material_phaseAt(ipc,el))) case (KINEMATICS_cleavage_opening_ID) kinematicsType call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el) case (KINEMATICS_slipplane_opening_ID) kinematicsType call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el) case (KINEMATICS_thermal_expansion_ID) kinematicsType call kinematics_thermal_expansion_LiAndItsTangent(my_Li, my_dLi_dS, ipc, ip, el) case default kinematicsType my_Li = 0.0_pReal my_dLi_dS = 0.0_pReal end select kinematicsType Li = Li + my_Li dLi_dS = dLi_dS + my_dLi_dS enddo KinematicsLoop FiInv = math_inv33(Fi) detFi = math_det33(Fi) Li = matmul(matmul(Fi,Li),FiInv)*detFi !< push forward to intermediate configuration temp_33 = matmul(FiInv,Li) do i = 1,3; do j = 1,3 dLi_dS(1:3,1:3,i,j) = matmul(matmul(Fi,dLi_dS(1:3,1:3,i,j)),FiInv)*detFi dLi_dFi(1:3,1:3,i,j) = dLi_dFi(1:3,1:3,i,j) + Li*FiInv(j,i) dLi_dFi(1:3,i,1:3,j) = dLi_dFi(1:3,i,1:3,j) + math_I3*temp_33(j,i) + Li*FiInv(j,i) enddo; enddo end subroutine constitutive_LiAndItsTangents !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the rate of change of microstructure !-------------------------------------------------------------------------------------------------- function constitutive_collectDotState_source(S, ipc, ip, el,phase,of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in), dimension(3,3) :: & S !< 2nd Piola Kirchhoff stress (vector notation) integer :: & i !< counter in source loop logical :: broken broken = .false. SourceLoop: do i = 1, phase_Nsources(phase) sourceType: select case (phase_source(i,phase)) case (SOURCE_damage_anisoBrittle_ID) sourceType call source_damage_anisoBrittle_dotState(S, ipc, ip, el) ! correct stress? case (SOURCE_damage_isoDuctile_ID) sourceType call source_damage_isoDuctile_dotState(ipc, ip, el) case (SOURCE_damage_anisoDuctile_ID) sourceType call source_damage_anisoDuctile_dotState(ipc, ip, el) case (SOURCE_thermal_externalheat_ID) sourceType call source_thermal_externalheat_dotState(phase,of) end select sourceType broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%dotState(:,of))) enddo SourceLoop end function constitutive_collectDotState_source !-------------------------------------------------------------------------------------------------- !> @brief for constitutive models having an instantaneous change of state !> will return false if delta state is not needed/supported by the constitutive model !-------------------------------------------------------------------------------------------------- function constitutive_deltaState_source(Fe, ipc, ip, el, phase, of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in), dimension(3,3) :: & Fe !< elastic deformation gradient integer :: & i, & myOffset, & mySize logical :: & broken broken = .false. sourceLoop: do i = 1, phase_Nsources(phase) sourceType: select case (phase_source(i,phase)) case (SOURCE_damage_isoBrittle_ID) sourceType call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(ipc,ip,el), Fe, & ipc, ip, el) broken = any(IEEE_is_NaN(sourceState(phase)%p(i)%deltaState(:,of))) if(.not. broken) then myOffset = sourceState(phase)%p(i)%offsetDeltaState mySize = sourceState(phase)%p(i)%sizeDeltaState sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) = & sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) + sourceState(phase)%p(i)%deltaState(1:mySize,of) endif end select sourceType enddo SourceLoop end function constitutive_deltaState_source !-------------------------------------------------------------------------------------------------- !> @brief Allocate the components of the state structure for a given phase !-------------------------------------------------------------------------------------------------- subroutine constitutive_allocateState(state, & Nconstituents,sizeState,sizeDotState,sizeDeltaState) class(tState), intent(out) :: & state integer, intent(in) :: & Nconstituents, & sizeState, & sizeDotState, & sizeDeltaState state%sizeState = sizeState state%sizeDotState = sizeDotState state%sizeDeltaState = sizeDeltaState state%offsetDeltaState = sizeState-sizeDeltaState ! deltaState occupies latter part of state by definition allocate(state%atol (sizeState), source=0.0_pReal) allocate(state%state0 (sizeState,Nconstituents), source=0.0_pReal) allocate(state%partitionedState0(sizeState,Nconstituents), source=0.0_pReal) allocate(state%subState0 (sizeState,Nconstituents), source=0.0_pReal) allocate(state%state (sizeState,Nconstituents), source=0.0_pReal) allocate(state%dotState (sizeDotState,Nconstituents), source=0.0_pReal) allocate(state%deltaState(sizeDeltaState,Nconstituents), source=0.0_pReal) end subroutine constitutive_allocateState !-------------------------------------------------------------------------------------------------- !> @brief Restore data after homog cutback. !-------------------------------------------------------------------------------------------------- subroutine constitutive_restore(i,e) integer, intent(in) :: & i, & !< integration point number e !< element number integer :: & c, & !< constituent number s do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(material_phaseAt(c,e))%p(s)%state( :,material_phasememberAt(c,i,e)) = & sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e)) enddo enddo end subroutine constitutive_restore !-------------------------------------------------------------------------------------------------- !> @brief Forward data after successful increment. ! ToDo: Any guessing for the current states possible? !-------------------------------------------------------------------------------------------------- subroutine constitutive_forward integer :: i, j do i = 1, size(sourceState) do j = 1,phase_Nsources(i) sourceState(i)%p(j)%state0 = sourceState(i)%p(j)%state enddo; enddo end subroutine constitutive_forward !-------------------------------------------------------------------------------------------------- !> @brief writes constitutive results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine constitutive_results call plastic_results call damage_results end subroutine constitutive_results !-------------------------------------------------------------------------------------------------- !> @brief allocates and initialize per grain variables !-------------------------------------------------------------------------------------------------- subroutine crystallite_init integer :: & p, & c, & !< counter in integration point component loop i, & !< counter in integration point loop e, & !< counter in element loop cMax, & !< maximum number of integration point components iMax, & !< maximum number of integration points eMax !< maximum number of elements class(tNode), pointer :: & num_crystallite, & debug_crystallite, & ! pointer to debug options for crystallite phases, & phase, & mech print'(/,a)', ' <<<+- crystallite init -+>>>' debug_crystallite => config_debug%get('crystallite', defaultVal=emptyList) debugCrystallite%basic = debug_crystallite%contains('basic') debugCrystallite%extensive = debug_crystallite%contains('extensive') debugCrystallite%selective = debug_crystallite%contains('selective') debugCrystallite%element = config_debug%get_asInt('element', defaultVal=1) debugCrystallite%ip = config_debug%get_asInt('integrationpoint', defaultVal=1) debugCrystallite%grain = config_debug%get_asInt('grain', defaultVal=1) cMax = homogenization_maxNconstituents iMax = discretization_nIPs eMax = discretization_Nelems allocate(crystallite_partitionedF(3,3,cMax,iMax,eMax),source=0.0_pReal) allocate(crystallite_S0, & crystallite_F0, crystallite_Fi0,crystallite_Fp0, & crystallite_Li0,crystallite_Lp0, & crystallite_partitionedS0, & crystallite_partitionedF0,crystallite_partitionedFp0,crystallite_partitionedFi0, & crystallite_partitionedLp0,crystallite_partitionedLi0, & crystallite_S,crystallite_P, & crystallite_Fe,crystallite_Fi,crystallite_Fp, & crystallite_Li,crystallite_Lp, & crystallite_subF,crystallite_subF0, & crystallite_subFp0,crystallite_subFi0, & source = crystallite_partitionedF) allocate(crystallite_dt(cMax,iMax,eMax),source=0.0_pReal) allocate(crystallite_subdt,crystallite_subFrac,crystallite_subStep, & source = crystallite_dt) allocate(crystallite_orientation(cMax,iMax,eMax)) allocate(crystallite_requested(cMax,iMax,eMax), source=.false.) allocate(crystallite_converged(cMax,iMax,eMax), source=.true.) num_crystallite => config_numerics%get('crystallite',defaultVal=emptyDict) num%subStepMinCryst = num_crystallite%get_asFloat ('subStepMin', defaultVal=1.0e-3_pReal) num%subStepSizeCryst = num_crystallite%get_asFloat ('subStepSize', defaultVal=0.25_pReal) num%stepIncreaseCryst = num_crystallite%get_asFloat ('stepIncrease', defaultVal=1.5_pReal) num%subStepSizeLp = num_crystallite%get_asFloat ('subStepSizeLp', defaultVal=0.5_pReal) num%subStepSizeLi = num_crystallite%get_asFloat ('subStepSizeLi', defaultVal=0.5_pReal) num%rtol_crystalliteState = num_crystallite%get_asFloat ('rtol_State', defaultVal=1.0e-6_pReal) num%rtol_crystalliteStress = num_crystallite%get_asFloat ('rtol_Stress', defaultVal=1.0e-6_pReal) num%atol_crystalliteStress = num_crystallite%get_asFloat ('atol_Stress', defaultVal=1.0e-8_pReal) num%iJacoLpresiduum = num_crystallite%get_asInt ('iJacoLpresiduum', defaultVal=1) num%nState = num_crystallite%get_asInt ('nState', defaultVal=20) num%nStress = num_crystallite%get_asInt ('nStress', defaultVal=40) if(num%subStepMinCryst <= 0.0_pReal) call IO_error(301,ext_msg='subStepMinCryst') if(num%subStepSizeCryst <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeCryst') if(num%stepIncreaseCryst <= 0.0_pReal) call IO_error(301,ext_msg='stepIncreaseCryst') if(num%subStepSizeLp <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeLp') if(num%subStepSizeLi <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeLi') if(num%rtol_crystalliteState <= 0.0_pReal) call IO_error(301,ext_msg='rtol_crystalliteState') if(num%rtol_crystalliteStress <= 0.0_pReal) call IO_error(301,ext_msg='rtol_crystalliteStress') if(num%atol_crystalliteStress <= 0.0_pReal) call IO_error(301,ext_msg='atol_crystalliteStress') if(num%iJacoLpresiduum < 1) call IO_error(301,ext_msg='iJacoLpresiduum') if(num%nState < 1) call IO_error(301,ext_msg='nState') if(num%nStress< 1) call IO_error(301,ext_msg='nStress') select case(num_crystallite%get_asString('integrator',defaultVal='FPI')) case('FPI') integrateState => integrateStateFPI case('Euler') integrateState => integrateStateEuler case('AdaptiveEuler') integrateState => integrateStateAdaptiveEuler case('RK4') integrateState => integrateStateRK4 case('RKCK45') integrateState => integrateStateRKCK45 case default call IO_error(301,ext_msg='integrator') end select phases => config_material%get('phase') allocate(output_constituent(phases%length)) do p = 1, phases%length phase => phases%get(p) mech => phase%get('mechanics',defaultVal = emptyDict) #if defined(__GFORTRAN__) output_constituent(p)%label = output_asStrings(mech) #else output_constituent(p)%label = mech%get_asStrings('output',defaultVal=emptyStringArray) #endif enddo #ifdef DEBUG if (debugCrystallite%basic) then print'(a42,1x,i10)', ' # of elements: ', eMax print'(a42,1x,i10)', ' # of integration points/element: ', iMax print'(a42,1x,i10)', 'max # of constituents/integration point: ', cMax flush(IO_STDOUT) endif #endif !$OMP PARALLEL DO PRIVATE(i,c) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1), FEsolving_execIP(2); do c = 1, homogenization_Nconstituents(material_homogenizationAt(e)) crystallite_Fp0(1:3,1:3,c,i,e) = material_orientation0(c,i,e)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005) crystallite_Fp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) & / math_det33(crystallite_Fp0(1:3,1:3,c,i,e))**(1.0_pReal/3.0_pReal) crystallite_Fi0(1:3,1:3,c,i,e) = math_I3 crystallite_F0(1:3,1:3,c,i,e) = math_I3 crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(matmul(crystallite_Fi0(1:3,1:3,c,i,e), & crystallite_Fp0(1:3,1:3,c,i,e))) ! assuming that euler angles are given in internal strain free configuration crystallite_Fp(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) crystallite_Fi(1:3,1:3,c,i,e) = crystallite_Fi0(1:3,1:3,c,i,e) crystallite_requested(c,i,e) = .true. enddo; enddo enddo !$OMP END PARALLEL DO crystallite_partitionedFp0 = crystallite_Fp0 crystallite_partitionedFi0 = crystallite_Fi0 crystallite_partitionedF0 = crystallite_F0 crystallite_partitionedF = crystallite_F0 call crystallite_orientations() !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2) do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) call constitutive_dependentState(crystallite_partitionedF0(1:3,1:3,c,i,e), & crystallite_partitionedFp0(1:3,1:3,c,i,e), & c,i,e) ! update dependent state variables to be consistent with basic states enddo enddo enddo !$OMP END PARALLEL DO end subroutine crystallite_init !-------------------------------------------------------------------------------------------------- !> @brief calculate stress (P) !-------------------------------------------------------------------------------------------------- function crystallite_stress() logical, dimension(discretization_nIPs,discretization_Nelems) :: crystallite_stress real(pReal) :: & formerSubStep integer :: & NiterationCrystallite, & ! number of iterations in crystallite loop c, & !< counter in integration point component loop i, & !< counter in integration point loop e, & !< counter in element loop s logical, dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: todo !ToDo: need to set some values to false for different Ngrains real(pReal), dimension(:,:,:,:,:), allocatable :: & subLp0,& !< plastic velocity grad at start of crystallite inc subLi0 !< intermediate velocity grad at start of crystallite inc todo = .false. subLp0 = crystallite_partitionedLp0 subLi0 = crystallite_partitionedLi0 !-------------------------------------------------------------------------------------------------- ! initialize to starting condition crystallite_subStep = 0.0_pReal !$OMP PARALLEL DO elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2); do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) homogenizationRequestsCalculation: if (crystallite_requested(c,i,e)) then plasticState (material_phaseAt(c,e))%subState0( :,material_phaseMemberAt(c,i,e)) = & plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phaseMemberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(material_phaseAt(c,e))%p(s)%subState0( :,material_phaseMemberAt(c,i,e)) = & sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phaseMemberAt(c,i,e)) enddo crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_partitionedFp0(1:3,1:3,c,i,e) crystallite_subFi0(1:3,1:3,c,i,e) = crystallite_partitionedFi0(1:3,1:3,c,i,e) crystallite_subF0(1:3,1:3,c,i,e) = crystallite_partitionedF0(1:3,1:3,c,i,e) crystallite_subFrac(c,i,e) = 0.0_pReal crystallite_subStep(c,i,e) = 1.0_pReal/num%subStepSizeCryst todo(c,i,e) = .true. crystallite_converged(c,i,e) = .false. ! pretend failed step of 1/subStepSizeCryst endif homogenizationRequestsCalculation enddo; enddo enddo elementLooping1 !$OMP END PARALLEL DO NiterationCrystallite = 0 cutbackLooping: do while (any(todo(:,FEsolving_execIP(1):FEsolving_execIP(2),FEsolving_execELem(1):FEsolving_execElem(2)))) NiterationCrystallite = NiterationCrystallite + 1 #ifdef DEBUG if (debugCrystallite%extensive) & print'(a,i6)', '<< CRYST stress >> crystallite iteration ',NiterationCrystallite #endif !$OMP PARALLEL DO PRIVATE(formerSubStep) elementLooping3: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2) do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) !-------------------------------------------------------------------------------------------------- ! wind forward if (crystallite_converged(c,i,e)) then formerSubStep = crystallite_subStep(c,i,e) crystallite_subFrac(c,i,e) = crystallite_subFrac(c,i,e) + crystallite_subStep(c,i,e) crystallite_subStep(c,i,e) = min(1.0_pReal - crystallite_subFrac(c,i,e), & num%stepIncreaseCryst * crystallite_subStep(c,i,e)) todo(c,i,e) = crystallite_subStep(c,i,e) > 0.0_pReal ! still time left to integrate on? if (todo(c,i,e)) then crystallite_subF0 (1:3,1:3,c,i,e) = crystallite_subF(1:3,1:3,c,i,e) subLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e) subLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e) crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e) crystallite_subFi0(1:3,1:3,c,i,e) = crystallite_Fi (1:3,1:3,c,i,e) plasticState( material_phaseAt(c,e))%subState0(:,material_phaseMemberAt(c,i,e)) & = plasticState(material_phaseAt(c,e))%state( :,material_phaseMemberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState( material_phaseAt(c,e))%p(s)%subState0(:,material_phaseMemberAt(c,i,e)) & = sourceState(material_phaseAt(c,e))%p(s)%state( :,material_phaseMemberAt(c,i,e)) enddo endif !-------------------------------------------------------------------------------------------------- ! cut back (reduced time and restore) else crystallite_subStep(c,i,e) = num%subStepSizeCryst * crystallite_subStep(c,i,e) crystallite_Fp (1:3,1:3,c,i,e) = crystallite_subFp0(1:3,1:3,c,i,e) crystallite_Fi (1:3,1:3,c,i,e) = crystallite_subFi0(1:3,1:3,c,i,e) crystallite_S (1:3,1:3,c,i,e) = crystallite_S0 (1:3,1:3,c,i,e) if (crystallite_subStep(c,i,e) < 1.0_pReal) then ! actual (not initial) cutback crystallite_Lp (1:3,1:3,c,i,e) = subLp0(1:3,1:3,c,i,e) crystallite_Li (1:3,1:3,c,i,e) = subLi0(1:3,1:3,c,i,e) endif plasticState (material_phaseAt(c,e))%state( :,material_phaseMemberAt(c,i,e)) & = plasticState(material_phaseAt(c,e))%subState0(:,material_phaseMemberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState( material_phaseAt(c,e))%p(s)%state( :,material_phaseMemberAt(c,i,e)) & = sourceState(material_phaseAt(c,e))%p(s)%subState0(:,material_phaseMemberAt(c,i,e)) enddo ! cant restore dotState here, since not yet calculated in first cutback after initialization todo(c,i,e) = crystallite_subStep(c,i,e) > num%subStepMinCryst ! still on track or already done (beyond repair) endif !-------------------------------------------------------------------------------------------------- ! prepare for integration if (todo(c,i,e)) then crystallite_subF(1:3,1:3,c,i,e) = crystallite_subF0(1:3,1:3,c,i,e) & + crystallite_subStep(c,i,e) *( crystallite_partitionedF (1:3,1:3,c,i,e) & -crystallite_partitionedF0(1:3,1:3,c,i,e)) crystallite_Fe(1:3,1:3,c,i,e) = matmul(crystallite_subF(1:3,1:3,c,i,e), & math_inv33(matmul(crystallite_Fi(1:3,1:3,c,i,e), & crystallite_Fp(1:3,1:3,c,i,e)))) crystallite_subdt(c,i,e) = crystallite_subStep(c,i,e) * crystallite_dt(c,i,e) crystallite_converged(c,i,e) = .false. call integrateState(c,i,e) call integrateSourceState(c,i,e) endif enddo enddo enddo elementLooping3 !$OMP END PARALLEL DO !-------------------------------------------------------------------------------------------------- ! integrate --- requires fully defined state array (basic + dependent state) where(.not. crystallite_converged .and. crystallite_subStep > num%subStepMinCryst) & ! do not try non-converged but fully cutbacked any further todo = .true. ! TODO: again unroll this into proper elementloop to avoid N^2 for single point evaluation enddo cutbackLooping ! return whether converged or not crystallite_stress = .false. elementLooping5: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2) crystallite_stress(i,e) = all(crystallite_converged(:,i,e)) enddo enddo elementLooping5 end function crystallite_stress !-------------------------------------------------------------------------------------------------- !> @brief Backup data for homog cutback. !-------------------------------------------------------------------------------------------------- subroutine crystallite_initializeRestorationPoints(i,e) integer, intent(in) :: & i, & !< integration point number e !< element number integer :: & c, & !< constituent number s do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) crystallite_partitionedFp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) crystallite_partitionedLp0(1:3,1:3,c,i,e) = crystallite_Lp0(1:3,1:3,c,i,e) crystallite_partitionedFi0(1:3,1:3,c,i,e) = crystallite_Fi0(1:3,1:3,c,i,e) crystallite_partitionedLi0(1:3,1:3,c,i,e) = crystallite_Li0(1:3,1:3,c,i,e) crystallite_partitionedF0(1:3,1:3,c,i,e) = crystallite_F0(1:3,1:3,c,i,e) crystallite_partitionedS0(1:3,1:3,c,i,e) = crystallite_S0(1:3,1:3,c,i,e) plasticState(material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e)) = & plasticState(material_phaseAt(c,e))%state0( :,material_phasememberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e)) = & sourceState(material_phaseAt(c,e))%p(s)%state0( :,material_phasememberAt(c,i,e)) enddo enddo end subroutine crystallite_initializeRestorationPoints !-------------------------------------------------------------------------------------------------- !> @brief Wind homog inc forward. !-------------------------------------------------------------------------------------------------- subroutine crystallite_windForward(i,e) integer, intent(in) :: & i, & !< integration point number e !< element number integer :: & c, & !< constituent number s do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) crystallite_partitionedF0 (1:3,1:3,c,i,e) = crystallite_partitionedF(1:3,1:3,c,i,e) crystallite_partitionedFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e) crystallite_partitionedLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e) crystallite_partitionedFi0(1:3,1:3,c,i,e) = crystallite_Fi (1:3,1:3,c,i,e) crystallite_partitionedLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e) crystallite_partitionedS0 (1:3,1:3,c,i,e) = crystallite_S (1:3,1:3,c,i,e) plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e)) = & plasticState (material_phaseAt(c,e))%state (:,material_phasememberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e)) = & sourceState(material_phaseAt(c,e))%p(s)%state (:,material_phasememberAt(c,i,e)) enddo enddo end subroutine crystallite_windForward !-------------------------------------------------------------------------------------------------- !> @brief Restore data after homog cutback. !-------------------------------------------------------------------------------------------------- subroutine crystallite_restore(i,e,includeL) integer, intent(in) :: & i, & !< integration point number e !< element number logical, intent(in) :: & includeL !< protect agains fake cutback integer :: & c !< constituent number do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) if (includeL) then crystallite_Lp(1:3,1:3,c,i,e) = crystallite_partitionedLp0(1:3,1:3,c,i,e) crystallite_Li(1:3,1:3,c,i,e) = crystallite_partitionedLi0(1:3,1:3,c,i,e) endif ! maybe protecting everything from overwriting makes more sense crystallite_Fp(1:3,1:3,c,i,e) = crystallite_partitionedFp0(1:3,1:3,c,i,e) crystallite_Fi(1:3,1:3,c,i,e) = crystallite_partitionedFi0(1:3,1:3,c,i,e) crystallite_S (1:3,1:3,c,i,e) = crystallite_partitionedS0 (1:3,1:3,c,i,e) plasticState (material_phaseAt(c,e))%state( :,material_phasememberAt(c,i,e)) = & plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e)) enddo end subroutine crystallite_restore !-------------------------------------------------------------------------------------------------- !> @brief Calculate tangent (dPdF). !-------------------------------------------------------------------------------------------------- function crystallite_stressTangent(c,i,e) result(dPdF) real(pReal), dimension(3,3,3,3) :: dPdF integer, intent(in) :: & c, & !< counter in constituent loop i, & !< counter in integration point loop e !< counter in element loop integer :: & o, & p real(pReal), dimension(3,3) :: devNull, & invSubFp0,invSubFi0,invFp,invFi, & temp_33_1, temp_33_2, temp_33_3, temp_33_4 real(pReal), dimension(3,3,3,3) :: dSdFe, & dSdF, & dSdFi, & dLidS, & ! tangent in lattice configuration dLidFi, & dLpdS, & dLpdFi, & dFidS, & dFpinvdF, & rhs_3333, & lhs_3333, & temp_3333 real(pReal), dimension(9,9):: temp_99 logical :: error call constitutive_SandItsTangents(devNull,dSdFe,dSdFi, & crystallite_Fe(1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e),c,i,e) call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, & crystallite_S (1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e), & c,i,e) invFp = math_inv33(crystallite_Fp(1:3,1:3,c,i,e)) invFi = math_inv33(crystallite_Fi(1:3,1:3,c,i,e)) invSubFp0 = math_inv33(crystallite_subFp0(1:3,1:3,c,i,e)) invSubFi0 = math_inv33(crystallite_subFi0(1:3,1:3,c,i,e)) if (sum(abs(dLidS)) < tol_math_check) then dFidS = 0.0_pReal else lhs_3333 = 0.0_pReal; rhs_3333 = 0.0_pReal do o=1,3; do p=1,3 lhs_3333(1:3,1:3,o,p) = lhs_3333(1:3,1:3,o,p) & + crystallite_subdt(c,i,e)*matmul(invSubFi0,dLidFi(1:3,1:3,o,p)) lhs_3333(1:3,o,1:3,p) = lhs_3333(1:3,o,1:3,p) & + invFi*invFi(p,o) rhs_3333(1:3,1:3,o,p) = rhs_3333(1:3,1:3,o,p) & - crystallite_subdt(c,i,e)*matmul(invSubFi0,dLidS(1:3,1:3,o,p)) enddo; enddo call math_invert(temp_99,error,math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600,el=e,ip=i,g=c, & ext_msg='inversion error in analytic tangent calculation') dFidS = 0.0_pReal else dFidS = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif dLidS = math_mul3333xx3333(dLidFi,dFidS) + dLidS endif call constitutive_LpAndItsTangents(devNull,dLpdS,dLpdFi, & crystallite_S (1:3,1:3,c,i,e), & crystallite_Fi(1:3,1:3,c,i,e),c,i,e) ! call constitutive law to calculate Lp tangent in lattice configuration dLpdS = math_mul3333xx3333(dLpdFi,dFidS) + dLpdS !-------------------------------------------------------------------------------------------------- ! calculate dSdF temp_33_1 = transpose(matmul(invFp,invFi)) temp_33_2 = matmul(crystallite_subF(1:3,1:3,c,i,e),invSubFp0) temp_33_3 = matmul(matmul(crystallite_subF(1:3,1:3,c,i,e),invFp), invSubFi0) do o=1,3; do p=1,3 rhs_3333(p,o,1:3,1:3) = matmul(dSdFe(p,o,1:3,1:3),temp_33_1) temp_3333(1:3,1:3,p,o) = matmul(matmul(temp_33_2,dLpdS(1:3,1:3,p,o)), invFi) & + matmul(temp_33_3,dLidS(1:3,1:3,p,o)) enddo; enddo lhs_3333 = crystallite_subdt(c,i,e)*math_mul3333xx3333(dSdFe,temp_3333) & + math_mul3333xx3333(dSdFi,dFidS) call math_invert(temp_99,error,math_eye(9)+math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600,el=e,ip=i,g=c, & ext_msg='inversion error in analytic tangent calculation') dSdF = rhs_3333 else dSdF = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif !-------------------------------------------------------------------------------------------------- ! calculate dFpinvdF temp_3333 = math_mul3333xx3333(dLpdS,dSdF) do o=1,3; do p=1,3 dFpinvdF(1:3,1:3,p,o) = -crystallite_subdt(c,i,e) & * matmul(invSubFp0, matmul(temp_3333(1:3,1:3,p,o),invFi)) enddo; enddo !-------------------------------------------------------------------------------------------------- ! assemble dPdF temp_33_1 = matmul(crystallite_S(1:3,1:3,c,i,e),transpose(invFp)) temp_33_2 = matmul(invFp,temp_33_1) temp_33_3 = matmul(crystallite_subF(1:3,1:3,c,i,e),invFp) temp_33_4 = matmul(temp_33_3,crystallite_S(1:3,1:3,c,i,e)) dPdF = 0.0_pReal do p=1,3 dPdF(p,1:3,p,1:3) = transpose(temp_33_2) enddo do o=1,3; do p=1,3 dPdF(1:3,1:3,p,o) = dPdF(1:3,1:3,p,o) & + matmul(matmul(crystallite_subF(1:3,1:3,c,i,e), & dFpinvdF(1:3,1:3,p,o)),temp_33_1) & + matmul(matmul(temp_33_3,dSdF(1:3,1:3,p,o)), & transpose(invFp)) & + matmul(temp_33_4,transpose(dFpinvdF(1:3,1:3,p,o))) enddo; enddo end function crystallite_stressTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates orientations !-------------------------------------------------------------------------------------------------- subroutine crystallite_orientations integer & c, & !< counter in integration point component loop i, & !< counter in integration point loop e !< counter in element loop !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2) do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) call crystallite_orientation(c,i,e)%fromMatrix(transpose(math_rotationalPart(crystallite_Fe(1:3,1:3,c,i,e)))) enddo; enddo; enddo !$OMP END PARALLEL DO nonlocalPresent: if (any(plasticState%nonlocal)) then !$OMP PARALLEL DO do e = FEsolving_execElem(1),FEsolving_execElem(2) if (plasticState(material_phaseAt(1,e))%nonlocal) then do i = FEsolving_execIP(1),FEsolving_execIP(2) call plastic_nonlocal_updateCompatibility(crystallite_orientation, & phase_plasticityInstance(material_phaseAt(1,e)),i,e) enddo endif enddo !$OMP END PARALLEL DO endif nonlocalPresent end subroutine crystallite_orientations !-------------------------------------------------------------------------------------------------- !> @brief Map 2nd order tensor to reference config !-------------------------------------------------------------------------------------------------- function crystallite_push33ToRef(ipc,ip,el, tensor33) real(pReal), dimension(3,3) :: crystallite_push33ToRef real(pReal), dimension(3,3), intent(in) :: tensor33 real(pReal), dimension(3,3) :: T integer, intent(in):: & el, & ip, & ipc T = matmul(material_orientation0(ipc,ip,el)%asMatrix(), & ! ToDo: initial orientation correct? transpose(math_inv33(crystallite_subF(1:3,1:3,ipc,ip,el)))) crystallite_push33ToRef = matmul(transpose(T),matmul(tensor33,T)) end function crystallite_push33ToRef !-------------------------------------------------------------------------------------------------- !> @brief writes crystallite results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine crystallite_results integer :: p,o real(pReal), allocatable, dimension(:,:,:) :: selected_tensors real(pReal), allocatable, dimension(:,:) :: selected_rotations character(len=:), allocatable :: group,structureLabel do p=1,size(material_name_phase) group = trim('current/phase')//'/'//trim(material_name_phase(p))//'/mechanics' call results_closeGroup(results_addGroup(group)) do o = 1, size(output_constituent(p)%label) select case (output_constituent(p)%label(o)) case('F') selected_tensors = select_tensors(crystallite_partitionedF,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'deformation gradient','1') case('F_e') selected_tensors = select_tensors(crystallite_Fe,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'elastic deformation gradient','1') case('F_p') selected_tensors = select_tensors(crystallite_Fp,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'plastic deformation gradient','1') case('F_i') selected_tensors = select_tensors(crystallite_Fi,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'inelastic deformation gradient','1') case('L_p') selected_tensors = select_tensors(crystallite_Lp,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'plastic velocity gradient','1/s') case('L_i') selected_tensors = select_tensors(crystallite_Li,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'inelastic velocity gradient','1/s') case('P') selected_tensors = select_tensors(crystallite_P,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'First Piola-Kirchhoff stress','Pa') case('S') selected_tensors = select_tensors(crystallite_S,p) call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),& 'Second Piola-Kirchhoff stress','Pa') case('O') select case(lattice_structure(p)) case(lattice_ISO_ID) structureLabel = 'aP' case(lattice_FCC_ID) structureLabel = 'cF' case(lattice_BCC_ID) structureLabel = 'cI' case(lattice_BCT_ID) structureLabel = 'tI' case(lattice_HEX_ID) structureLabel = 'hP' case(lattice_ORT_ID) structureLabel = 'oP' end select selected_rotations = select_rotations(crystallite_orientation,p) call results_writeDataset(group,selected_rotations,output_constituent(p)%label(o),& 'crystal orientation as quaternion','q_0 ') call results_addAttribute('Lattice',structureLabel,group//'/'//output_constituent(p)%label(o)) end select enddo enddo contains !------------------------------------------------------------------------------------------------ !> @brief select tensors for output !------------------------------------------------------------------------------------------------ function select_tensors(dataset,instance) integer, intent(in) :: instance real(pReal), dimension(:,:,:,:,:), intent(in) :: dataset real(pReal), allocatable, dimension(:,:,:) :: select_tensors integer :: e,i,c,j allocate(select_tensors(3,3,count(material_phaseAt==instance)*discretization_nIPs)) j=0 do e = 1, size(material_phaseAt,2) do i = 1, discretization_nIPs do c = 1, size(material_phaseAt,1) !ToDo: this needs to be changed for varying Ngrains if (material_phaseAt(c,e) == instance) then j = j + 1 select_tensors(1:3,1:3,j) = dataset(1:3,1:3,c,i,e) endif enddo enddo enddo end function select_tensors !-------------------------------------------------------------------------------------------------- !> @brief select rotations for output !-------------------------------------------------------------------------------------------------- function select_rotations(dataset,instance) integer, intent(in) :: instance type(rotation), dimension(:,:,:), intent(in) :: dataset real(pReal), allocatable, dimension(:,:) :: select_rotations integer :: e,i,c,j allocate(select_rotations(4,count(material_phaseAt==instance)*homogenization_maxNconstituents*discretization_nIPs)) j=0 do e = 1, size(material_phaseAt,2) do i = 1, discretization_nIPs do c = 1, size(material_phaseAt,1) !ToDo: this needs to be changed for varying Ngrains if (material_phaseAt(c,e) == instance) then j = j + 1 select_rotations(1:4,j) = dataset(c,i,e)%asQuaternion() endif enddo enddo enddo end function select_rotations end subroutine crystallite_results !-------------------------------------------------------------------------------------------------- !> @brief calculation of stress (P) with time integration based on a residuum in Lp and !> intermediate acceleration of the Newton-Raphson correction !-------------------------------------------------------------------------------------------------- function integrateStress(ipc,ip,el,timeFraction) result(broken) integer, intent(in):: el, & ! element index ip, & ! integration point index ipc ! grain index real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep Fp_new, & ! plastic deformation gradient at end of timestep invFp_new, & ! inverse of Fp_new invFp_current, & ! inverse of Fp_current Lpguess, & ! current guess for plastic velocity gradient Lpguess_old, & ! known last good guess for plastic velocity gradient Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law residuumLp, & ! current residuum of plastic velocity gradient residuumLp_old, & ! last residuum of plastic velocity gradient deltaLp, & ! direction of next guess Fi_new, & ! gradient of intermediate deformation stages invFi_new, & invFi_current, & ! inverse of Fi_current Liguess, & ! current guess for intermediate velocity gradient Liguess_old, & ! known last good guess for intermediate velocity gradient Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law residuumLi, & ! current residuum of intermediate velocity gradient residuumLi_old, & ! last residuum of intermediate velocity gradient deltaLi, & ! direction of next guess Fe, & ! elastic deformation gradient S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration A, & B, & temp_33 real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme) dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme) real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress dS_dFi, & dFe_dLp, & ! partial derivative of elastic deformation gradient dFe_dLi, & dFi_dLi, & dLp_dFi, & dLi_dFi, & dLp_dS, & dLi_dS real(pReal) steplengthLp, & steplengthLi, & dt, & ! time increment atol_Lp, & atol_Li, & devNull integer NiterationStressLp, & ! number of stress integrations NiterationStressLi, & ! number of inner stress integrations ierr, & ! error indicator for LAPACK o, & p, & jacoCounterLp, & jacoCounterLi ! counters to check for Jacobian update logical :: error,broken broken = .true. if (present(timeFraction)) then dt = crystallite_subdt(ipc,ip,el) * timeFraction F = crystallite_subF0(1:3,1:3,ipc,ip,el) & + (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction else dt = crystallite_subdt(ipc,ip,el) F = crystallite_subF(1:3,1:3,ipc,ip,el) endif call constitutive_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), & crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el) Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess Liguess = crystallite_Li(1:3,1:3,ipc,ip,el) ! take as first guess call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el)) if (error) return ! error call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el)) if (error) return ! error A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp jacoCounterLi = 0 steplengthLi = 1.0_pReal residuumLi_old = 0.0_pReal Liguess_old = Liguess NiterationStressLi = 0 LiLoop: do NiterationStressLi = NiterationStressLi + 1 if (NiterationStressLi>num%nStress) return ! error invFi_new = matmul(invFi_current,math_I3 - dt*Liguess) Fi_new = math_inv33(invFi_new) jacoCounterLp = 0 steplengthLp = 1.0_pReal residuumLp_old = 0.0_pReal Lpguess_old = Lpguess NiterationStressLp = 0 LpLoop: do NiterationStressLp = NiterationStressLp + 1 if (NiterationStressLp>num%nStress) return ! error B = math_I3 - dt*Lpguess Fe = matmul(matmul(A,B), invFi_new) call constitutive_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi_new, ipc, ip, el) call constitutive_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, & S, Fi_new, ipc, ip, el) !* update current residuum and check for convergence of loop atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_crystalliteStress) ! minimum lower cutoff residuumLp = Lpguess - Lp_constitutive if (any(IEEE_is_NaN(residuumLp))) then return ! error elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance exit LpLoop elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLp_old = residuumLp ! ...remember old values and... Lpguess_old = Lpguess steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction Lpguess = Lpguess_old & + deltaLp * stepLengthLp cycle LpLoop endif calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then jacoCounterLp = jacoCounterLp + 1 do o=1,3; do p=1,3 dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) enddo; enddo dRLp_dLp = math_eye(9) & - math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp)) temp_9 = math_33to9(residuumLp) call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp if (ierr /= 0) return ! error deltaLp = - math_9to33(temp_9) endif calculateJacobiLi Lpguess = Lpguess & + deltaLp * steplengthLp enddo LpLoop call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, & S, Fi_new, ipc, ip, el) !* update current residuum and check for convergence of loop atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_crystalliteStress) ! minimum lower cutoff residuumLi = Liguess - Li_constitutive if (any(IEEE_is_NaN(residuumLi))) then return ! error elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance exit LiLoop elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLi_old = residuumLi ! ...remember old values and... Liguess_old = Liguess steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction Liguess = Liguess_old & + deltaLi * steplengthLi cycle LiLoop endif calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then jacoCounterLi = jacoCounterLi + 1 temp_33 = matmul(matmul(A,B),invFi_current) do o=1,3; do p=1,3 dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current enddo; enddo do o=1,3; do p=1,3 dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new) enddo; enddo dRLi_dLi = math_eye(9) & - math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) & + math_mul3333xx3333(dS_dFi, dFi_dLi))) & - math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi)) temp_9 = math_33to9(residuumLi) call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li if (ierr /= 0) return ! error deltaLi = - math_9to33(temp_9) endif calculateJacobiLp Liguess = Liguess & + deltaLi * steplengthLi enddo LiLoop invFp_new = matmul(invFp_current,B) call math_invert33(Fp_new,devNull,error,invFp_new) if (error) return ! error crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new))) crystallite_S (1:3,1:3,ipc,ip,el) = S crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess crystallite_Li (1:3,1:3,ipc,ip,el) = Liguess crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize crystallite_Fi (1:3,1:3,ipc,ip,el) = Fi_new crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new) broken = .false. end function integrateStress !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with adaptive 1st order explicit Euler method !> using Fixed Point Iteration to adapt the stepsize !-------------------------------------------------------------------------------------------------- subroutine integrateStateFPI(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & NiterationState, & !< number of iterations in state loop p, & c, & s, & size_pl integer, dimension(maxval(phase_Nsources)) :: & size_so real(pReal) :: & zeta real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: & r ! state residuum real(pReal), dimension(constitutive_plasticity_maxSizeDotState,2) :: & plastic_dotState real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState logical :: & broken p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return size_pl = plasticState(p)%sizeDotState plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) & + plasticState(p)%dotState (1:size_pl,c) & * crystallite_subdt(g,i,e) plastic_dotState(1:size_pl,2) = 0.0_pReal iteration: do NiterationState = 1, num%nState if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1) plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c) broken = integrateStress(g,i,e) if(broken) exit iteration broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) exit iteration zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),& plastic_dotState(1:size_pl,2)) plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta & + plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta) r(1:size_pl) = plasticState(p)%state (1:size_pl,c) & - plasticState(p)%subState0(1:size_pl,c) & - plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e) plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) & - r(1:size_pl) crystallite_converged(g,i,e) = converged(r(1:size_pl), & plasticState(p)%state(1:size_pl,c), & plasticState(p)%atol(1:size_pl)) if(crystallite_converged(g,i,e)) then broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c) exit iteration endif enddo iteration contains !-------------------------------------------------------------------------------------------------- !> @brief calculate the damping for correction of state and dot state !-------------------------------------------------------------------------------------------------- real(pReal) pure function damper(current,previous,previous2) real(pReal), dimension(:), intent(in) ::& current, previous, previous2 real(pReal) :: dot_prod12, dot_prod22 dot_prod12 = dot_product(current - previous, previous - previous2) dot_prod22 = dot_product(previous - previous2, previous - previous2) if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22) else damper = 1.0_pReal endif end function damper end subroutine integrateStateFPI !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with adaptive 1st order explicit Euler method !> using Fixed Point Iteration to adapt the stepsize !-------------------------------------------------------------------------------------------------- subroutine integrateSourceState(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & NiterationState, & !< number of iterations in state loop p, & c, & s, & size_pl integer, dimension(maxval(phase_Nsources)) :: & size_so real(pReal) :: & zeta real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: & r ! state residuum real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState logical :: & broken p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState_source(crystallite_S(1:3,1:3,g,i,e), g,i,e,p,c) if(broken) return do s = 1, phase_Nsources(p) size_so(s) = sourceState(p)%p(s)%sizeDotState sourceState(p)%p(s)%state(1:size_so(s),c) = sourceState(p)%p(s)%subState0(1:size_so(s),c) & + sourceState(p)%p(s)%dotState (1:size_so(s),c) & * crystallite_subdt(g,i,e) source_dotState(1:size_so(s),2,s) = 0.0_pReal enddo iteration: do NiterationState = 1, num%nState do s = 1, phase_Nsources(p) if(nIterationState > 1) source_dotState(1:size_so(s),2,s) = source_dotState(1:size_so(s),1,s) source_dotState(1:size_so(s),1,s) = sourceState(p)%p(s)%dotState(:,c) enddo broken = constitutive_collectDotState_source(crystallite_S(1:3,1:3,g,i,e), g,i,e,p,c) if(broken) exit iteration do s = 1, phase_Nsources(p) zeta = damper(sourceState(p)%p(s)%dotState(:,c), & source_dotState(1:size_so(s),1,s),& source_dotState(1:size_so(s),2,s)) sourceState(p)%p(s)%dotState(:,c) = sourceState(p)%p(s)%dotState(:,c) * zeta & + source_dotState(1:size_so(s),1,s)* (1.0_pReal - zeta) r(1:size_so(s)) = sourceState(p)%p(s)%state (1:size_so(s),c) & - sourceState(p)%p(s)%subState0(1:size_so(s),c) & - sourceState(p)%p(s)%dotState (1:size_so(s),c) * crystallite_subdt(g,i,e) sourceState(p)%p(s)%state(1:size_so(s),c) = sourceState(p)%p(s)%state(1:size_so(s),c) & - r(1:size_so(s)) crystallite_converged(g,i,e) = & crystallite_converged(g,i,e) .and. converged(r(1:size_so(s)), & sourceState(p)%p(s)%state(1:size_so(s),c), & sourceState(p)%p(s)%atol(1:size_so(s))) enddo if(crystallite_converged(g,i,e)) then broken = constitutive_deltaState_source(crystallite_Fe(1:3,1:3,g,i,e),g,i,e,p,c) exit iteration endif enddo iteration contains !-------------------------------------------------------------------------------------------------- !> @brief calculate the damping for correction of state and dot state !-------------------------------------------------------------------------------------------------- real(pReal) pure function damper(current,previous,previous2) real(pReal), dimension(:), intent(in) ::& current, previous, previous2 real(pReal) :: dot_prod12, dot_prod22 dot_prod12 = dot_product(current - previous, previous - previous2) dot_prod22 = dot_product(previous - previous2, previous - previous2) if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22) else damper = 1.0_pReal endif end function damper end subroutine integrateSourceState !-------------------------------------------------------------------------------------------------- !> @brief integrate state with 1st order explicit Euler method !-------------------------------------------------------------------------------------------------- subroutine integrateStateEuler(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & p, & c, & sizeDotState logical :: & broken p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) crystallite_converged(g,i,e) = .not. broken end subroutine integrateStateEuler !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 1st order Euler method with adaptive step size !-------------------------------------------------------------------------------------------------- subroutine integrateStateAdaptiveEuler(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & p, & c, & sizeDotState logical :: & broken real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e) plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e) broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) if(broken) return broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) & + 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%atol(1:sizeDotState)) end subroutine integrateStateAdaptiveEuler !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the classic Runge Kutta method !--------------------------------------------------------------------------------------------------- subroutine integrateStateRK4(g,i,e) integer, intent(in) :: g,i,e real(pReal), dimension(3,3), parameter :: & A = reshape([& 0.5_pReal, 0.0_pReal, 0.0_pReal, & 0.0_pReal, 0.5_pReal, 0.0_pReal, & 0.0_pReal, 0.0_pReal, 1.0_pReal],& shape(A)) real(pReal), dimension(3), parameter :: & C = [0.5_pReal, 0.5_pReal, 1.0_pReal] real(pReal), dimension(4), parameter :: & B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal] call integrateStateRK(g,i,e,A,B,C) end subroutine integrateStateRK4 !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the Cash-Carp method !--------------------------------------------------------------------------------------------------- subroutine integrateStateRKCK45(g,i,e) integer, intent(in) :: g,i,e real(pReal), dimension(5,5), parameter :: & A = reshape([& 1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, & 3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, & 3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, & -11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, & 1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],& shape(A)) real(pReal), dimension(5), parameter :: & C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal] real(pReal), dimension(6), parameter :: & B = & [37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, & 125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], & DB = B - & [2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,& 13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal] call integrateStateRK(g,i,e,A,B,C,DB) end subroutine integrateStateRKCK45 !-------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an !! embedded explicit Runge-Kutta method !-------------------------------------------------------------------------------------------------- subroutine integrateStateRK(g,i,e,A,B,CC,DB) real(pReal), dimension(:,:), intent(in) :: A real(pReal), dimension(:), intent(in) :: B, CC real(pReal), dimension(:), intent(in), optional :: DB integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & stage, & ! stage index in integration stage loop n, & p, & c, & sizeDotState logical :: & broken real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return do stage = 1,size(A,1) sizeDotState = plasticState(p)%sizeDotState plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c) plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1) do n = 2, stage sizeDotState = plasticState(p)%sizeDotState plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) & + A(n,stage) * plastic_RKdotState(1:sizeDotState,n) enddo sizeDotState = plasticState(p)%sizeDotState plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) broken = integrateStress(g,i,e,CC(stage)) if(broken) exit broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & crystallite_Fi(1:3,1:3,g,i,e), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c) if(broken) exit enddo if(broken) return sizeDotState = plasticState(p)%sizeDotState plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c) plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B) plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) if(present(DB)) & broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) & * crystallite_subdt(g,i,e), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%atol(1:sizeDotState)) if(broken) return broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) crystallite_converged(g,i,e) = .not. broken end subroutine integrateStateRK !-------------------------------------------------------------------------------------------------- !> @brief determines whether a point is converged !-------------------------------------------------------------------------------------------------- logical pure function converged(residuum,state,atol) real(pReal), intent(in), dimension(:) ::& residuum, state, atol real(pReal) :: & rTol rTol = num%rTol_crystalliteState converged = all(abs(residuum) <= max(atol, rtol*abs(state))) end function converged !-------------------------------------------------------------------------------------------------- !> @brief Write current restart information (Field and constitutive data) to file. ! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively !-------------------------------------------------------------------------------------------------- subroutine crystallite_restartWrite integer :: i integer(HID_T) :: fileHandle, groupHandle character(len=pStringLen) :: fileName, datasetName print*, ' writing field and constitutive data required for restart to file';flush(IO_STDOUT) write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5' fileHandle = HDF5_openFile(fileName,'a') call HDF5_write(fileHandle,crystallite_partitionedF,'F') call HDF5_write(fileHandle,crystallite_Fp, 'F_p') call HDF5_write(fileHandle,crystallite_Fi, 'F_i') call HDF5_write(fileHandle,crystallite_Lp, 'L_p') call HDF5_write(fileHandle,crystallite_Li, 'L_i') call HDF5_write(fileHandle,crystallite_S, 'S') groupHandle = HDF5_addGroup(fileHandle,'phase') do i = 1,size(material_name_phase) write(datasetName,'(i0,a)') i,'_omega' call HDF5_write(groupHandle,plasticState(i)%state,datasetName) enddo call HDF5_closeGroup(groupHandle) groupHandle = HDF5_addGroup(fileHandle,'homogenization') do i = 1, size(material_name_homogenization) write(datasetName,'(i0,a)') i,'_omega' call HDF5_write(groupHandle,homogState(i)%state,datasetName) enddo call HDF5_closeGroup(groupHandle) call HDF5_closeFile(fileHandle) end subroutine crystallite_restartWrite !-------------------------------------------------------------------------------------------------- !> @brief Read data for restart ! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively !-------------------------------------------------------------------------------------------------- subroutine crystallite_restartRead integer :: i integer(HID_T) :: fileHandle, groupHandle character(len=pStringLen) :: fileName, datasetName print'(/,a,i0,a)', ' reading restart information of increment from file' write(fileName,'(a,i0,a)') trim(getSolverJobName())//'_',worldrank,'.hdf5' fileHandle = HDF5_openFile(fileName) call HDF5_read(fileHandle,crystallite_F0, 'F') call HDF5_read(fileHandle,crystallite_Fp0,'F_p') call HDF5_read(fileHandle,crystallite_Fi0,'F_i') call HDF5_read(fileHandle,crystallite_Lp0,'L_p') call HDF5_read(fileHandle,crystallite_Li0,'L_i') call HDF5_read(fileHandle,crystallite_S0, 'S') groupHandle = HDF5_openGroup(fileHandle,'phase') do i = 1,size(material_name_phase) write(datasetName,'(i0,a)') i,'_omega' call HDF5_read(groupHandle,plasticState(i)%state0,datasetName) enddo call HDF5_closeGroup(groupHandle) groupHandle = HDF5_openGroup(fileHandle,'homogenization') do i = 1,size(material_name_homogenization) write(datasetName,'(i0,a)') i,'_omega' call HDF5_read(groupHandle,homogState(i)%state0,datasetName) enddo call HDF5_closeGroup(groupHandle) call HDF5_closeFile(fileHandle) end subroutine crystallite_restartRead !-------------------------------------------------------------------------------------------------- !> @brief Forward data after successful increment. ! ToDo: Any guessing for the current states possible? !-------------------------------------------------------------------------------------------------- subroutine crystallite_forward integer :: i, j crystallite_F0 = crystallite_partitionedF crystallite_Fp0 = crystallite_Fp crystallite_Lp0 = crystallite_Lp crystallite_Fi0 = crystallite_Fi crystallite_Li0 = crystallite_Li crystallite_S0 = crystallite_S do i = 1, size(plasticState) plasticState(i)%state0 = plasticState(i)%state enddo do i = 1,size(material_name_homogenization) homogState (i)%state0 = homogState (i)%state damageState (i)%state0 = damageState (i)%state enddo end subroutine crystallite_forward end module constitutive