!-------------------------------------------------------------------------------------------------- !> @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 geometry_plastic_nonlocal, only: & geometry_plastic_nonlocal_disable implicit none private integer(kind(ELASTICITY_undefined_ID)), dimension(:), allocatable, protected :: & phase_elasticity !< elasticity of each phase integer(kind(PLASTICITY_undefined_ID)), dimension(:), allocatable :: & !ToDo: old intel compiler complains about protected phase_plasticity !< plasticity of each phase integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: & ! ToDo: old intel compiler complains about protected phase_source, & !< active sources mechanisms of each phase phase_kinematics, & !< active kinematic mechanisms of each phase phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase integer, dimension(:), allocatable, public :: & ! ToDo: old intel compiler complains about protected 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: old intel compiler complains about protected 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 plastic_init end subroutine plastic_init module subroutine damage_init end subroutine damage_init module subroutine thermal_init end subroutine thermal_init 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 plastic_isotropic_dotState(Mp,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_isotropic_dotState module subroutine plastic_phenopowerlaw_dotState(Mp,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_phenopowerlaw_dotState module subroutine plastic_kinehardening_dotState(Mp,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_kinehardening_dotState module subroutine plastic_dislotwin_dotState(Mp,T,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T integer, intent(in) :: & instance, & of end subroutine plastic_dislotwin_dotState module subroutine plastic_disloTungsten_dotState(Mp,T,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T integer, intent(in) :: & instance, & of end subroutine plastic_disloTungsten_dotState module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, & instance,of,ip,el) real(pReal), dimension(3,3), intent(in) :: & Mp !< MandelStress real(pReal), dimension(3,3,homogenization_maxNgrains,discretization_nIP,discretization_nElem), intent(in) :: & F, & !< deformation gradient Fp !< plastic deformation gradient real(pReal), intent(in) :: & Temperature, & !< temperature timestep !< substepped crystallite time increment integer, intent(in) :: & instance, & of, & ip, & !< current integration point el !< current element number end subroutine plastic_nonlocal_dotState 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 pure module function kinematics_thermal_expansion_initialStrain(homog,phase,offset) result(initialStrain) integer, intent(in) :: & phase, & homog, & offset real(pReal), dimension(3,3) :: & initialStrain end function kinematics_thermal_expansion_initialStrain module subroutine plastic_nonlocal_updateCompatibility(orientation,instance,i,e) integer, intent(in) :: & instance, & i, & e type(rotation), dimension(1,discretization_nIP,discretization_nElem), 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 plastic_kinehardening_deltaState(Mp,instance,of) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_kinehardening_deltaState module subroutine plastic_nonlocal_deltaState(Mp,instance,of,ip,el) real(pReal), dimension(3,3), intent(in) :: & Mp integer, intent(in) :: & instance, & of, & ip, & el end subroutine plastic_nonlocal_deltaState 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 type :: tDebugOptions logical :: & basic, & extensive, & selective integer :: & element, & ip, & grain end type tDebugOptions type(tDebugOptions) :: debugConstitutive public :: & constitutive_init, & constitutive_homogenizedC, & constitutive_LpAndItsTangents, & constitutive_dependentState, & constitutive_LiAndItsTangents, & constitutive_initialFi, & constitutive_SandItsTangents, & constitutive_collectDotState, & constitutive_deltaState, & constitutive_damage_getRateAndItsTangents, & constitutive_thermal_getRateAndItsTangents, & constitutive_results, & constitutive_allocateState, & plastic_nonlocal_updateCompatibility, & plastic_active, & source_active, & kinematics_active contains !-------------------------------------------------------------------------------------------------- !> @brief Initialze constitutive models for individual physics !-------------------------------------------------------------------------------------------------- subroutine constitutive_init integer :: & p, & !< counter in phase loop s, & !< counter in source loop stiffDegradationCtr class (tNode), pointer :: & debug_constitutive, & phases, & phase, & elastic, & stiffDegradation 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 elasticity (hooke) !ToDO: Maybe move to elastic submodule along with function homogenizedC? phases => config_material%get('phase') allocate(phase_elasticity(phases%length), source = ELASTICITY_undefined_ID) allocate(phase_elasticityInstance(phases%length), source = 0) allocate(phase_NstiffnessDegradations(phases%length),source=0) do p = 1, phases%length phase => phases%get(p) elastic => phase%get('elasticity') if(elastic%get_asString('type') == 'hooke') then phase_elasticity(p) = ELASTICITY_HOOKE_ID else call IO_error(200,ext_msg=elastic%get_asString('type')) endif stiffDegradation => phase%get('stiffness_degradation',defaultVal=emptyList) ! check for stiffness degradation mechanisms phase_NstiffnessDegradations(p) = stiffDegradation%length enddo allocate(phase_stiffnessDegradation(maxval(phase_NstiffnessDegradations),phases%length), & source=STIFFNESS_DEGRADATION_undefined_ID) if(maxVal(phase_NstiffnessDegradations)/=0) then do p = 1, phases%length phase => phases%get(p) stiffDegradation => phase%get('stiffness_degradation',defaultVal=emptyList) do stiffDegradationCtr = 1, stiffDegradation%length if(stiffDegradation%get_asString(stiffDegradationCtr) == 'damage') & phase_stiffnessDegradation(stiffDegradationCtr,p) = STIFFNESS_DEGRADATION_damage_ID enddo enddo endif do p = 1, phases%length phase_elasticityInstance(p) = count(phase_elasticity(1:p) == phase_elasticity(p)) enddo !-------------------------------------------------------------------------------------------------- ! initialize constitutive laws call plastic_init call damage_init call thermal_init write(6,'(/,a)') ' <<<+- constitutive init -+>>>'; flush(6) constitutive_source_maxSizeDotState = 0 PhaseLoop2:do p = 1,phases%length !-------------------------------------------------------------------------------------------------- ! partition and initialize state plasticState(p)%partionedState0 = plasticState(p)%state0 plasticState(p)%state = plasticState(p)%partionedState0 forall(s = 1:phase_Nsources(p)) sourceState(p)%p(s)%partionedState0 = sourceState(p)%p(s)%state0 sourceState(p)%p(s)%state = sourceState(p)%p(s)%partionedState0 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 collects initial intermediate deformation gradient !-------------------------------------------------------------------------------------------------- pure function constitutive_initialFi(ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), dimension(3,3) :: & constitutive_initialFi !< composite initial intermediate deformation gradient integer :: & k !< counter in kinematics loop integer :: & phase, & homog, offset constitutive_initialFi = math_I3 phase = material_phaseAt(ipc,el) KinematicsLoop: do k = 1, phase_Nkinematics(phase) !< Warning: small initial strain assumption kinematicsType: select case (phase_kinematics(k,phase)) case (KINEMATICS_thermal_expansion_ID) kinematicsType homog = material_homogenizationAt(el) offset = thermalMapping(homog)%p(ip,el) constitutive_initialFi = & constitutive_initialFi + kinematics_thermal_expansion_initialStrain(homog,phase,offset) end select kinematicsType enddo KinematicsLoop end function constitutive_initialFi !-------------------------------------------------------------------------------------------------- !> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to !> the elastic/intermediate deformation gradients depending on the selected elastic law !! (so far no case switch because only Hooke is implemented) !-------------------------------------------------------------------------------------------------- subroutine constitutive_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 call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el) end subroutine constitutive_SandItsTangents !-------------------------------------------------------------------------------------------------- !> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to !> the elastic and intermediate deformation gradients using Hooke's law !-------------------------------------------------------------------------------------------------- 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 in lattice configuration 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 real(pReal), dimension(3,3) :: E real(pReal), dimension(3,3,3,3) :: C integer :: & ho, & !< homogenization d !< counter in degradation loop integer :: & i, j ho = material_homogenizationAt(el) C = math_66toSym3333(constitutive_homogenizedC(ipc,ip,el)) DegradationLoop: do d = 1, phase_NstiffnessDegradations(material_phaseAt(ipc,el)) degradationType: select case(phase_stiffnessDegradation(d,material_phaseAt(ipc,el))) case (STIFFNESS_DEGRADATION_damage_ID) degradationType C = C * damage(ho)%p(damageMapping(ho)%p(ip,el))**2 end select degradationType enddo DegradationLoop E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration S = math_mul3333xx33(C,matmul(matmul(transpose(Fi),E),Fi)) !< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration do i =1, 3;do j=1,3 dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko dS_dFi(i,j,1:3,1:3) = 2.0_pReal*matmul(matmul(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn enddo; enddo end subroutine constitutive_hooke_SandItsTangents !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the rate of change of microstructure !-------------------------------------------------------------------------------------------------- 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_maxNgrains,discretization_nIP,discretization_nElem) :: & 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) real(pReal), dimension(3,3) :: & Mp integer :: & ho, & !< homogenization tme, & !< thermal member position i, & !< counter in source loop instance logical :: broken ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) instance = phase_plasticityInstance(phase) Mp = matmul(matmul(transpose(Fi),Fi),S) plasticityType: select case (phase_plasticity(phase)) case (PLASTICITY_ISOTROPIC_ID) plasticityType call plastic_isotropic_dotState(Mp,instance,of) case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType call plastic_phenopowerlaw_dotState(Mp,instance,of) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_dotState(Mp,instance,of) case (PLASTICITY_DISLOTWIN_ID) plasticityType call plastic_dislotwin_dotState(Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOTUNGSTEN_ID) plasticityType call plastic_disloTungsten_dotState(Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_dotState(Mp,FArray,FpArray,temperature(ho)%p(tme),subdt, & instance,of,ip,el) end select plasticityType broken = any(IEEE_is_NaN(plasticState(phase)%dotState(:,of))) 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 !-------------------------------------------------------------------------------------------------- !> @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(S, Fe, 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 Fe, & !< elastic deformation gradient Fi !< intermediate deformation gradient real(pReal), dimension(3,3) :: & Mp integer :: & i, & instance, & myOffset, & mySize logical :: & broken Mp = matmul(matmul(transpose(Fi),Fi),S) instance = phase_plasticityInstance(phase) plasticityType: select case (phase_plasticity(phase)) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_deltaState(Mp,instance,of) broken = any(IEEE_is_NaN(plasticState(phase)%deltaState(:,of))) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_deltaState(Mp,instance,of,ip,el) broken = any(IEEE_is_NaN(plasticState(phase)%deltaState(:,of))) case default broken = .false. end select plasticityType if(.not. broken) then select case(phase_plasticity(phase)) case (PLASTICITY_NONLOCAL_ID,PLASTICITY_KINEHARDENING_ID) myOffset = plasticState(phase)%offsetDeltaState mySize = plasticState(phase)%sizeDeltaState plasticState(phase)%state(myOffset + 1:myOffset + mySize,of) = & plasticState(phase)%state(myOffset + 1:myOffset + mySize,of) + plasticState(phase)%deltaState(1:mySize,of) end select endif 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 = broken .or. 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 !-------------------------------------------------------------------------------------------------- !> @brief Allocate the components of the state structure for a given phase !-------------------------------------------------------------------------------------------------- subroutine constitutive_allocateState(state, & NipcMyPhase,sizeState,sizeDotState,sizeDeltaState) class(tState), intent(out) :: & state integer, intent(in) :: & NipcMyPhase, & 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,NipcMyPhase), source=0.0_pReal) allocate(state%partionedState0(sizeState,NipcMyPhase), source=0.0_pReal) allocate(state%subState0 (sizeState,NipcMyPhase), source=0.0_pReal) allocate(state%state (sizeState,NipcMyPhase), source=0.0_pReal) allocate(state%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal) allocate(state%deltaState(sizeDeltaState,NipcMyPhase), source=0.0_pReal) end subroutine constitutive_allocateState !-------------------------------------------------------------------------------------------------- !> @brief writes constitutive results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine constitutive_results call plastic_results call damage_results end subroutine constitutive_results end module constitutive