!-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @brief elasticity, plasticity, internal microstructure state !-------------------------------------------------------------------------------------------------- module constitutive use prec use math use rotations use debug use numerics use IO use config use material use results use lattice use discretization use geometry_plastic_nonlocal use source_thermal_dissipation use source_thermal_externalheat use source_damage_isoBrittle use source_damage_isoDuctile use source_damage_anisoBrittle use source_damage_anisoDuctile use kinematics_cleavage_opening use kinematics_slipplane_opening use kinematics_thermal_expansion implicit none private integer, public, protected :: & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizeDotState interface module subroutine plastic_none_init end subroutine plastic_none_init module subroutine plastic_isotropic_init end subroutine plastic_isotropic_init module subroutine plastic_phenopowerlaw_init end subroutine plastic_phenopowerlaw_init module subroutine plastic_kinehardening_init end subroutine plastic_kinehardening_init module subroutine plastic_dislotwin_init end subroutine plastic_dislotwin_init module subroutine plastic_disloUCLA_init end subroutine plastic_disloUCLA_init module subroutine plastic_nonlocal_init end subroutine plastic_nonlocal_init module subroutine plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_isotropic_LpAndItsTangent pure module subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_phenopowerlaw_LpAndItsTangent pure module subroutine plastic_kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & instance, & of end subroutine plastic_kinehardening_LpAndItsTangent module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T integer, intent(in) :: & instance, & of end subroutine plastic_dislotwin_LpAndItsTangent pure module subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T integer, intent(in) :: & instance, & of end subroutine plastic_disloUCLA_LpAndItsTangent module subroutine plastic_nonlocal_LpAndItsTangent(Lp,dLp_dMp, & Mp,Temperature,instance,of,ip,el) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & Temperature integer, intent(in) :: & instance, & of, & ip, & !< current integration point el !< current element number end subroutine plastic_nonlocal_LpAndItsTangent 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 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_disloUCLA_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_disloUCLA_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 plastic_dislotwin_dependentState(T,instance,of) integer, intent(in) :: & instance, & of real(pReal), intent(in) :: & T end subroutine plastic_dislotwin_dependentState module subroutine plastic_disloUCLA_dependentState(instance,of) integer, intent(in) :: & instance, & of end subroutine plastic_disloUCLA_dependentState module subroutine plastic_nonlocal_dependentState(F, Fp, instance, of, ip, el) real(pReal), dimension(3,3), intent(in) :: & F, & Fp integer, intent(in) :: & instance, & of, & ip, & el end subroutine plastic_nonlocal_dependentState 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 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_nIP,discretization_nElem), intent(in) :: & orientation !< crystal orientation end subroutine plastic_nonlocal_updateCompatibility module subroutine plastic_isotropic_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_isotropic_results module subroutine plastic_phenopowerlaw_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_phenopowerlaw_results module subroutine plastic_kinehardening_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_kinehardening_results module subroutine plastic_dislotwin_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_dislotwin_results module subroutine plastic_disloUCLA_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_disloUCLA_results module subroutine plastic_nonlocal_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_nonlocal_results end interface public :: & plastic_nonlocal_updateCompatibility, & constitutive_init, & constitutive_homogenizedC, & constitutive_dependentState, & constitutive_LpAndItsTangents, & constitutive_LiAndItsTangents, & constitutive_initialFi, & constitutive_SandItsTangents, & constitutive_collectDotState, & constitutive_deltaState, & constitutive_results contains !-------------------------------------------------------------------------------------------------- !> @brief allocates arrays pointing to array of the various constitutive modules !-------------------------------------------------------------------------------------------------- subroutine constitutive_init integer :: & ph, & !< counter in phase loop s !< counter in source loop !-------------------------------------------------------------------------------------------------- ! initialized plasticity if (any(phase_plasticity == PLASTICITY_NONE_ID)) call plastic_none_init if (any(phase_plasticity == PLASTICITY_ISOTROPIC_ID)) call plastic_isotropic_init if (any(phase_plasticity == PLASTICITY_PHENOPOWERLAW_ID)) call plastic_phenopowerlaw_init if (any(phase_plasticity == PLASTICITY_KINEHARDENING_ID)) call plastic_kinehardening_init if (any(phase_plasticity == PLASTICITY_DISLOTWIN_ID)) call plastic_dislotwin_init if (any(phase_plasticity == PLASTICITY_DISLOUCLA_ID)) call plastic_disloucla_init if (any(phase_plasticity == PLASTICITY_NONLOCAL_ID)) then call plastic_nonlocal_init else call geometry_plastic_nonlocal_disable endif !-------------------------------------------------------------------------------------------------- ! initialize source mechanisms if (any(phase_source == SOURCE_thermal_dissipation_ID)) call source_thermal_dissipation_init if (any(phase_source == SOURCE_thermal_externalheat_ID)) call source_thermal_externalheat_init if (any(phase_source == SOURCE_damage_isoBrittle_ID)) call source_damage_isoBrittle_init if (any(phase_source == SOURCE_damage_isoDuctile_ID)) call source_damage_isoDuctile_init if (any(phase_source == SOURCE_damage_anisoBrittle_ID)) call source_damage_anisoBrittle_init if (any(phase_source == SOURCE_damage_anisoDuctile_ID)) call source_damage_anisoDuctile_init !-------------------------------------------------------------------------------------------------- ! initialize kinematic mechanisms if (any(phase_kinematics == KINEMATICS_cleavage_opening_ID)) call kinematics_cleavage_opening_init if (any(phase_kinematics == KINEMATICS_slipplane_opening_ID)) call kinematics_slipplane_opening_init if (any(phase_kinematics == KINEMATICS_thermal_expansion_ID)) call kinematics_thermal_expansion_init write(6,'(/,a)') ' <<<+- constitutive init -+>>>'; flush(6) constitutive_source_maxSizeDotState = 0 PhaseLoop2:do ph = 1,material_Nphase !-------------------------------------------------------------------------------------------------- ! partition and inititalize state plasticState(ph)%partionedState0 = plasticState(ph)%state0 plasticState(ph)%state = plasticState(ph)%partionedState0 forall(s = 1:phase_Nsources(ph)) sourceState(ph)%p(s)%partionedState0 = sourceState(ph)%p(s)%state0 sourceState(ph)%p(s)%state = sourceState(ph)%p(s)%partionedState0 end forall !-------------------------------------------------------------------------------------------------- ! determine max size of source state constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, & maxval(sourceState(ph)%p%sizeDotState)) enddo PhaseLoop2 constitutive_plasticity_maxSizeDotState = maxval(plasticState%sizeDotState) end subroutine constitutive_init !-------------------------------------------------------------------------------------------------- !> @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 calls microstructure function of the different constitutive models !-------------------------------------------------------------------------------------------------- subroutine constitutive_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 integer :: & ho, & !< homogenization tme, & !< thermal member position instance, of ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) of = material_phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phaseAt(ipc,el)) plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el))) case (PLASTICITY_DISLOTWIN_ID) plasticityType call plastic_dislotwin_dependentState(temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOUCLA_ID) plasticityType call plastic_disloUCLA_dependentState(instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_dependentState (F,Fp,instance,of,ip,el) end select plasticityType end subroutine constitutive_dependentState !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient ! ToDo: Discuss wheter it makes sense if crystallite handles the configuration conversion, i.e. ! Mp in, dLp_dMp out !-------------------------------------------------------------------------------------------------- subroutine constitutive_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 real(pReal), dimension(3,3,3,3) :: & dLp_dMp !< derivative of Lp with respect to Mandel stress real(pReal), dimension(3,3) :: & Mp !< Mandel stress work conjugate with Lp integer :: & ho, & !< homogenization tme !< thermal member position integer :: & i, j, instance, of ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) Mp = matmul(matmul(transpose(Fi),Fi),S) of = material_phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phaseAt(ipc,el)) plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el))) case (PLASTICITY_NONE_ID) plasticityType Lp = 0.0_pReal dLp_dMp = 0.0_pReal case (PLASTICITY_ISOTROPIC_ID) plasticityType call plastic_isotropic_LpAndItsTangent (Lp,dLp_dMp,Mp,instance,of) case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType call plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_LpAndItsTangent (Lp,dLp_dMp,Mp, temperature(ho)%p(tme),instance,of,ip,el) case (PLASTICITY_DISLOTWIN_ID) plasticityType call plastic_dislotwin_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOUCLA_ID) plasticityType call plastic_disloucla_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of) end select plasticityType do i=1,3; do j=1,3 dLp_dFi(i,j,1:3,1:3) = matmul(matmul(Fi,S),transpose(dLp_dMp(i,j,1:3,1:3))) + & matmul(matmul(Fi,dLp_dMp(i,j,1:3,1:3)),S) dLp_dS(i,j,1:3,1:3) = matmul(matmul(transpose(Fi),Fi),dLp_dMp(i,j,1:3,1:3)) ! ToDo: @PS: why not: dLp_dMp:(FiT Fi) enddo; enddo end subroutine constitutive_LpAndItsTangents !-------------------------------------------------------------------------------------------------- !> @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 intermeidate deformation gradients using Hookes 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_DISLOUCLA_ID) plasticityType call plastic_disloucla_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 writes constitutive results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine constitutive_results integer :: p character(len=pStringLen) :: group do p=1,size(config_name_phase) group = trim('current/constituent')//'/'//trim(config_name_phase(p)) call results_closeGroup(results_addGroup(group)) group = trim(group)//'/plastic' call results_closeGroup(results_addGroup(group)) select case(phase_plasticity(p)) case(PLASTICITY_ISOTROPIC_ID) call plastic_isotropic_results(phase_plasticityInstance(p),group) case(PLASTICITY_PHENOPOWERLAW_ID) call plastic_phenopowerlaw_results(phase_plasticityInstance(p),group) case(PLASTICITY_KINEHARDENING_ID) call plastic_kinehardening_results(phase_plasticityInstance(p),group) case(PLASTICITY_DISLOTWIN_ID) call plastic_dislotwin_results(phase_plasticityInstance(p),group) case(PLASTICITY_DISLOUCLA_ID) call plastic_disloUCLA_results(phase_plasticityInstance(p),group) case(PLASTICITY_NONLOCAL_ID) call plastic_nonlocal_results(phase_plasticityInstance(p),group) end select enddo end subroutine constitutive_results end module constitutive