!-------------------------------------------------------------------------------------------------- !> @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_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_subFp0,& !< plastic def grad at start of crystallite 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_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 :: & 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 :: tTensorContainer real(pReal), dimension(:,:,:), allocatable :: data end type type(tTensorContainer), dimension(:), allocatable :: & constitutive_mech_Fi, & constitutive_mech_Fi0, & constitutive_mech_partionedFi0, & constitutive_mech_Li, & constitutive_mech_Li0, & constitutive_mech_partionedLi0, & constitutive_mech_Fp, & constitutive_mech_Fp0, & constitutive_mech_partionedFp0 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 ! == cleaned:begin ================================================================================= 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 subroutine mech_results(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph end subroutine mech_results module subroutine damage_results(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph end subroutine damage_results module subroutine mech_restart_read(fileHandle) integer(HID_T), intent(in) :: fileHandle end subroutine mech_restart_read module subroutine mech_initializeRestorationPoints(ph,me) integer, intent(in) :: ph, me end subroutine mech_initializeRestorationPoints module subroutine constitutive_mech_windForward(ph,me) integer, intent(in) :: ph, me end subroutine constitutive_mech_windForward module subroutine constitutive_mech_forward end subroutine constitutive_mech_forward ! == cleaned:end =================================================================================== module subroutine source_damage_anisoBrittle_dotState(S, co, ip, el) integer, intent(in) :: & co, & !< 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(co, ip, el) integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el !< element end subroutine source_damage_anisoDuctile_dotState module subroutine source_damage_isoDuctile_dotState(co, ip, el) integer, intent(in) :: & co, & !< 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(co,ip,el) result(homogenizedC) real(pReal), dimension(6,6) :: & homogenizedC integer, intent(in) :: & co, & !< 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, co, ip, el) integer, intent(in) :: & co, & !< 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, co, ip, el) integer, intent(in) :: & co, & !< 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, co, ip, el) integer, intent(in) :: & co, & !< 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, co, ip, el) integer, intent(in) :: & co, & !< 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 constitutive_plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, & S, Fi, co, ip, el) integer, intent(in) :: & co, & !< 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 module subroutine constitutive_plastic_dependentState(F, co, ip, el) integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & F !< elastic deformation gradient end subroutine constitutive_plastic_dependentState module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, co, ip, el) integer, intent(in) :: & co, & !< 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 module subroutine integrateStateFPI(g,i,e) integer, intent(in) :: e, i, g end subroutine integrateStateFPI end interface type(tDebugOptions) :: debugConstitutive public :: & constitutive_init, & constitutive_homogenizedC, & constitutive_LiAndItsTangents, & constitutive_damage_getRateAndItsTangents, & constitutive_thermal_getRateAndItsTangents, & constitutive_results, & constitutive_allocateState, & constitutive_forward, & constitutive_restore, & plastic_nonlocal_updateCompatibility, & source_active, & kinematics_active, & converged, & crystallite_init, & crystallite_stress, & crystallite_stressTangent, & crystallite_orientations, & crystallite_push33ToRef, & crystallite_restartWrite, & crystallite_restartRead, & constitutive_initializeRestorationPoints, & constitutive_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 !-------------------------------------------------------------------------------------------------- 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 !-------------------------------------------------------------------------------------------------- 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(co,ip,el) real(pReal), dimension(6,6) :: & constitutive_homogenizedC integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el !< element plasticityType: select case (phase_plasticity(material_phaseAt(co,el))) case (PLASTICITY_DISLOTWIN_ID) plasticityType constitutive_homogenizedC = plastic_dislotwin_homogenizedC(co,ip,el) case default plasticityType constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(co,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, co, ip, el) integer, intent(in) :: & co, & !< 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(co,el))) case (PLASTICITY_isotropic_ID) plasticityType of = material_phasememberAt(co,ip,el) instance = phase_plasticityInstance(material_phaseAt(co,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(co,el)) kinematicsType: select case (phase_kinematics(k,material_phaseAt(co,el))) case (KINEMATICS_cleavage_opening_ID) kinematicsType call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, co, ip, el) case (KINEMATICS_slipplane_opening_ID) kinematicsType call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, co, ip, el) case (KINEMATICS_thermal_expansion_ID) kinematicsType call kinematics_thermal_expansion_LiAndItsTangent(my_Li, my_dLi_dS, co, 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_damage_collectDotState(S, co, ip, el,phase,of) result(broken) integer, intent(in) :: & co, & !< 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, co, ip, el) ! correct stress? case (SOURCE_damage_isoDuctile_ID) sourceType call source_damage_isoDuctile_dotState(co, ip, el) case (SOURCE_damage_anisoDuctile_ID) sourceType call source_damage_anisoDuctile_dotState(co, ip, el) end select sourceType broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%dotState(:,of))) enddo SourceLoop end function constitutive_damage_collectDotState !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the rate of change of microstructure !-------------------------------------------------------------------------------------------------- function constitutive_thermal_collectDotState(ph,me) result(broken) integer, intent(in) :: ph, me logical :: broken integer :: i broken = .false. SourceLoop: do i = 1, phase_Nsources(ph) if (phase_source(i,ph) == SOURCE_thermal_externalheat_ID) & call source_thermal_externalheat_dotState(ph,me) broken = broken .or. any(IEEE_is_NaN(sourceState(ph)%p(i)%dotState(:,me))) enddo SourceLoop end function constitutive_thermal_collectDotState !-------------------------------------------------------------------------------------------------- !> @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_damage_deltaState(Fe, co, ip, el, phase, of) result(broken) integer, intent(in) :: & co, & !< 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(co,ip,el), Fe, & co, 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_damage_deltaState !-------------------------------------------------------------------------------------------------- !> @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 crystallite_F0 = crystallite_partitionedF crystallite_Lp0 = crystallite_Lp crystallite_S0 = crystallite_S call constitutive_mech_forward() 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 integer :: ph character(len=:), allocatable :: group call results_closeGroup(results_addGroup('/current/phase/')) do ph = 1, size(material_name_phase) group = '/current/phase/'//trim(material_name_phase(ph))//'/' call results_closeGroup(results_addGroup(group)) call mech_results(group,ph) call damage_results(group,ph) enddo end subroutine constitutive_results !-------------------------------------------------------------------------------------------------- !> @brief allocates and initialize per grain variables !-------------------------------------------------------------------------------------------------- subroutine crystallite_init integer :: & Nconstituents, & p, & m, & 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%extensive = debug_crystallite%contains('extensive') 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_Lp0, & crystallite_partitionedS0, & crystallite_partitionedF0,& crystallite_partitionedLp0, & crystallite_S,crystallite_P, & crystallite_Fe,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_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') phases => config_material%get('phase') allocate(constitutive_mech_Fi(phases%length)) allocate(constitutive_mech_Fi0(phases%length)) allocate(constitutive_mech_partionedFi0(phases%length)) allocate(constitutive_mech_Fp(phases%length)) allocate(constitutive_mech_Fp0(phases%length)) allocate(constitutive_mech_partionedFp0(phases%length)) allocate(constitutive_mech_Li(phases%length)) allocate(constitutive_mech_Li0(phases%length)) allocate(constitutive_mech_partionedLi0(phases%length)) do p = 1, phases%length Nconstituents = count(material_phaseAt == p) * discretization_nIPs allocate(constitutive_mech_Fi(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_Fi0(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_partionedFi0(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_Fp(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_Fp0(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_partionedFp0(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_Li(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_Li0(p)%data(3,3,Nconstituents)) allocate(constitutive_mech_partionedLi0(p)%data(3,3,Nconstituents)) enddo 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) !$OMP PARALLEL DO PRIVATE(p,m) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1), FEsolving_execIP(2); do c = 1, homogenization_Nconstituents(material_homogenizationAt(e)) p = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) constitutive_mech_Fp0(p)%data(1:3,1:3,m) = material_orientation0(c,i,e)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005) constitutive_mech_Fp0(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m) & / math_det33(constitutive_mech_Fp0(p)%data(1:3,1:3,m))**(1.0_pReal/3.0_pReal) constitutive_mech_Fi0(p)%data(1:3,1:3,m) = math_I3 crystallite_F0(1:3,1:3,c,i,e) = math_I3 crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(matmul(constitutive_mech_Fi0(p)%data(1:3,1:3,m), & constitutive_mech_Fp0(p)%data(1:3,1:3,m))) ! assuming that euler angles are given in internal strain free configuration constitutive_mech_Fp(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m) constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m) constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m) constitutive_mech_partionedFp0(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m) crystallite_requested(c,i,e) = .true. enddo; enddo enddo !$OMP END PARALLEL DO crystallite_partitionedF0 = crystallite_F0 crystallite_partitionedF = crystallite_F0 call crystallite_orientations() !$OMP PARALLEL DO PRIVATE(p,m) do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2) do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) p = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) call constitutive_plastic_dependentState(crystallite_partitionedF0(1:3,1:3,c,i,e), & c,i,e) ! update dependent state variables to be consistent with basic states enddo enddo enddo !$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, p, m logical, dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: todo !ToDo: need to set some values to false for different Ngrains real(pReal), dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: subFrac !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. allocate(subLi0(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems)) subLp0 = crystallite_partitionedLp0 !-------------------------------------------------------------------------------------------------- ! initialize to starting condition crystallite_subStep = 0.0_pReal !$OMP PARALLEL DO PRIVATE(p,m) elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2) do i = FEsolving_execIP(1),FEsolving_execIP(2); do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) p = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) subLi0(1:3,1:3,c,i,e) = constitutive_mech_partionedLi0(p)%data(1:3,1:3,m) homogenizationRequestsCalculation: if (crystallite_requested(c,i,e)) then plasticState (material_phaseAt(c,e))%subState0( :,material_phaseMemberAt(c,i,e)) = & plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phaseMemberAt(c,i,e)) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(material_phaseAt(c,e))%p(s)%subState0( :,material_phaseMemberAt(c,i,e)) = & sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phaseMemberAt(c,i,e)) enddo crystallite_subFp0(1:3,1:3,c,i,e) = constitutive_mech_partionedFp0(p)%data(1:3,1:3,m) crystallite_subFi0(1:3,1:3,c,i,e) = constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) crystallite_subF0(1:3,1:3,c,i,e) = crystallite_partitionedF0(1:3,1:3,c,i,e) subFrac(c,i,e) = 0.0_pReal crystallite_subStep(c,i,e) = 1.0_pReal/num%subStepSizeCryst todo(c,i,e) = .true. crystallite_converged(c,i,e) = .false. ! pretend failed step of 1/subStepSizeCryst endif homogenizationRequestsCalculation enddo; enddo enddo elementLooping1 !$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,p,m) 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)) p = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) !-------------------------------------------------------------------------------------------------- ! wind forward if (crystallite_converged(c,i,e)) then formerSubStep = crystallite_subStep(c,i,e) subFrac(c,i,e) = subFrac(c,i,e) + crystallite_subStep(c,i,e) crystallite_subStep(c,i,e) = min(1.0_pReal - 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) = constitutive_mech_Li(p)%data(1:3,1:3,m) crystallite_subFp0(1:3,1:3,c,i,e) = constitutive_mech_Fp(p)%data(1:3,1:3,m) crystallite_subFi0(1:3,1:3,c,i,e) = constitutive_mech_Fi(p)%data(1:3,1:3,m) 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) constitutive_mech_Fp(p)%data(1:3,1:3,m) = crystallite_subFp0(1:3,1:3,c,i,e) constitutive_mech_Fi(p)%data(1:3,1:3,m) = 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) constitutive_mech_Li(p)%data(1:3,1:3,m) = 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(constitutive_mech_Fi(p)%data(1:3,1:3,m), & constitutive_mech_Fp(p)%data(1:3,1:3,m)))) 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 constitutive_initializeRestorationPoints(i,e) integer, intent(in) :: & i, & !< integration point number e !< element number integer :: & c, & !< constituent number s,ph, me do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) ph = material_phaseAt(c,e) me = material_phaseMemberAt(c,i,e) crystallite_partitionedLp0(1:3,1:3,c,i,e) = crystallite_Lp0(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) call mech_initializeRestorationPoints(ph,me) 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 constitutive_initializeRestorationPoints !-------------------------------------------------------------------------------------------------- !> @brief Wind homog inc forward. !-------------------------------------------------------------------------------------------------- subroutine constitutive_windForward(i,e) integer, intent(in) :: & i, & !< integration point number e !< element number integer :: & c, & !< constituent number s, ph, me do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) ph = material_phaseAt(c,e) me = material_phaseMemberAt(c,i,e) crystallite_partitionedF0 (1:3,1:3,c,i,e) = crystallite_partitionedF(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_partitionedS0 (1:3,1:3,c,i,e) = crystallite_S (1:3,1:3,c,i,e) call constitutive_mech_windForward(ph,me) do s = 1, phase_Nsources(material_phaseAt(c,e)) sourceState(ph)%p(s)%partitionedState0(:,me) = sourceState(ph)%p(s)%state(:,me) enddo enddo end subroutine constitutive_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, p, m !< constituent number do c = 1,homogenization_Nconstituents(material_homogenizationAt(e)) p = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) if (includeL) then crystallite_Lp(1:3,1:3,c,i,e) = crystallite_partitionedLp0(1:3,1:3,c,i,e) constitutive_mech_Li(p)%data(1:3,1:3,m) = constitutive_mech_partionedLi0(p)%data(1:3,1:3,m) endif ! maybe protecting everything from overwriting makes more sense constitutive_mech_Fp(p)%data(1:3,1:3,m) = constitutive_mech_partionedFp0(p)%data(1:3,1:3,m) constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) 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, pp, m 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 pp = material_phaseAt(c,e) m = material_phaseMemberAt(c,i,e) call constitutive_hooke_SandItsTangents(devNull,dSdFe,dSdFi, & crystallite_Fe(1:3,1:3,c,i,e), & constitutive_mech_Fi(pp)%data(1:3,1:3,m),c,i,e) call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, & crystallite_S (1:3,1:3,c,i,e), & constitutive_mech_Fi(pp)%data(1:3,1:3,m), & c,i,e) invFp = math_inv33(constitutive_mech_Fp(pp)%data(1:3,1:3,m)) invFi = math_inv33(constitutive_mech_Fi(pp)%data(1:3,1:3,m)) 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_plastic_LpAndItsTangents(devNull,dLpdS,dLpdFi, & crystallite_S (1:3,1:3,c,i,e), & constitutive_mech_Fi(pp)%data(1:3,1:3,m),c,i,e) 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(co,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, & co T = matmul(material_orientation0(co,ip,el)%asMatrix(), & ! ToDo: initial orientation correct? transpose(math_inv33(crystallite_subF(1:3,1:3,co,ip,el)))) crystallite_push33ToRef = matmul(transpose(T),matmul(tensor33,T)) end function crystallite_push33ToRef !-------------------------------------------------------------------------------------------------- !> @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_thermal_collectDotState(p,c) broken = broken .or. constitutive_damage_collectDotState(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_thermal_collectDotState(p,c) broken = broken .or. constitutive_damage_collectDotState(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_damage_deltaState(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 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_Lp, 'L_p') 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) write(datasetName,'(i0,a)') i,'_F_i' call HDF5_write(groupHandle,constitutive_mech_Fi(i)%data,datasetName) write(datasetName,'(i0,a)') i,'_L_i' call HDF5_write(groupHandle,constitutive_mech_Li(i)%data,datasetName) write(datasetName,'(i0,a)') i,'_F_p' call HDF5_write(groupHandle,constitutive_mech_Fp(i)%data,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_Lp0,'L_p') 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) write(datasetName,'(i0,a)') i,'_F_i' call HDF5_read(groupHandle,constitutive_mech_Fi0(i)%data,datasetName) write(datasetName,'(i0,a)') i,'_L_i' call HDF5_read(groupHandle,constitutive_mech_Li0(i)%data,datasetName) write(datasetName,'(i0,a)') i,'_F_p' call HDF5_read(groupHandle,constitutive_mech_Fp0(i)%data,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 end module constitutive