!-------------------------------------------------------------------------------------------------- !> @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, only: & pInt implicit none private integer(pInt), public, protected :: & constitutive_plasticity_maxSizePostResults, & constitutive_plasticity_maxSizeDotState, & constitutive_source_maxSizePostResults, & constitutive_source_maxSizeDotState public :: & constitutive_init, & constitutive_homogenizedC, & constitutive_microstructure, & constitutive_LpAndItsTangents, & constitutive_LiAndItsTangents, & constitutive_initialFi, & constitutive_SandItsTangents, & constitutive_collectDotState, & constitutive_collectDeltaState, & constitutive_postResults private :: & constitutive_hooke_SandItsTangents contains !-------------------------------------------------------------------------------------------------- !> @brief allocates arrays pointing to array of the various constitutive modules !-------------------------------------------------------------------------------------------------- subroutine constitutive_init() #if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800 use, intrinsic :: iso_fortran_env, only: & compiler_version, & compiler_options #endif use prec, only: & pReal use debug, only: & debug_constitutive, & debug_levelBasic use numerics, only: & worldrank use IO, only: & IO_error, & IO_open_file, & IO_checkAndRewind, & IO_open_jobFile_stat, & IO_write_jobFile, & IO_write_jobIntFile, & IO_timeStamp use config, only: & config_phase use mesh, only: & FE_geomtype use config, only: & material_Nphase, & material_localFileExt, & phase_name, & material_configFile, & config_deallocate use material, only: & material_phase, & phase_plasticity, & phase_plasticityInstance, & phase_Nsources, & phase_source, & phase_kinematics, & ELASTICITY_hooke_ID, & PLASTICITY_none_ID, & PLASTICITY_isotropic_ID, & PLASTICITY_phenopowerlaw_ID, & PLASTICITY_kinehardening_ID, & PLASTICITY_dislotwin_ID, & PLASTICITY_disloucla_ID, & PLASTICITY_nonlocal_ID ,& SOURCE_thermal_dissipation_ID, & SOURCE_thermal_externalheat_ID, & SOURCE_damage_isoBrittle_ID, & SOURCE_damage_isoDuctile_ID, & SOURCE_damage_anisoBrittle_ID, & SOURCE_damage_anisoDuctile_ID, & KINEMATICS_cleavage_opening_ID, & KINEMATICS_slipplane_opening_ID, & KINEMATICS_thermal_expansion_ID, & ELASTICITY_HOOKE_label, & PLASTICITY_NONE_label, & PLASTICITY_ISOTROPIC_label, & PLASTICITY_PHENOPOWERLAW_label, & PLASTICITY_KINEHARDENING_label, & PLASTICITY_DISLOTWIN_label, & PLASTICITY_DISLOUCLA_label, & PLASTICITY_NONLOCAL_label, & SOURCE_thermal_dissipation_label, & SOURCE_thermal_externalheat_label, & SOURCE_damage_isoBrittle_label, & SOURCE_damage_isoDuctile_label, & SOURCE_damage_anisoBrittle_label, & SOURCE_damage_anisoDuctile_label, & plasticState, & sourceState use plastic_none use plastic_isotropic use plastic_phenopowerlaw use plastic_kinehardening use plastic_dislotwin use plastic_disloucla use 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 integer(pInt), parameter :: FILEUNIT = 204_pInt integer(pInt) :: & o, & !< counter in output loop ph, & !< counter in phase loop s, & !< counter in source loop ins !< instance of plasticity/source integer(pInt), dimension(:,:), pointer :: thisSize character(len=64), dimension(:,:), pointer :: thisOutput character(len=32) :: outputName !< name of output, intermediate fix until HDF5 output is ready logical :: knownPlasticity, knownSource, nonlocalConstitutionPresent nonlocalConstitutionPresent = .false. !-------------------------------------------------------------------------------------------------- ! open material.config if (.not. IO_open_jobFile_stat(FILEUNIT,material_localFileExt)) & ! no local material configuration present... call IO_open_file(FILEUNIT,material_configFile) ! ... open material.config file !-------------------------------------------------------------------------------------------------- ! parse plasticities from config file 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(FILEUNIT) if (any(phase_plasticity == PLASTICITY_DISLOTWIN_ID)) call plastic_dislotwin_init(FILEUNIT) if (any(phase_plasticity == PLASTICITY_DISLOUCLA_ID)) call plastic_disloucla_init if (any(phase_plasticity == PLASTICITY_NONLOCAL_ID)) then call plastic_nonlocal_init(FILEUNIT) call plastic_nonlocal_stateInit() endif !-------------------------------------------------------------------------------------------------- ! parse source mechanisms from config file call IO_checkAndRewind(FILEUNIT) if (any(phase_source == SOURCE_thermal_dissipation_ID)) call source_thermal_dissipation_init(FILEUNIT) if (any(phase_source == SOURCE_thermal_externalheat_ID)) call source_thermal_externalheat_init(FILEUNIT) if (any(phase_source == SOURCE_damage_isoBrittle_ID)) call source_damage_isoBrittle_init(FILEUNIT) if (any(phase_source == SOURCE_damage_isoDuctile_ID)) call source_damage_isoDuctile_init(FILEUNIT) if (any(phase_source == SOURCE_damage_anisoBrittle_ID)) call source_damage_anisoBrittle_init(FILEUNIT) if (any(phase_source == SOURCE_damage_anisoDuctile_ID)) call source_damage_anisoDuctile_init(FILEUNIT) !-------------------------------------------------------------------------------------------------- ! parse kinematic mechanisms from config file call IO_checkAndRewind(FILEUNIT) if (any(phase_kinematics == KINEMATICS_cleavage_opening_ID)) call kinematics_cleavage_opening_init(FILEUNIT) if (any(phase_kinematics == KINEMATICS_slipplane_opening_ID)) call kinematics_slipplane_opening_init(FILEUNIT) if (any(phase_kinematics == KINEMATICS_thermal_expansion_ID)) call kinematics_thermal_expansion_init(FILEUNIT) close(FILEUNIT) call config_deallocate('material.config/phase') write(6,'(/,a)') ' <<<+- constitutive init -+>>>' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" mainProcess: if (worldrank == 0) then !-------------------------------------------------------------------------------------------------- ! write description file for constitutive output call IO_write_jobFile(FILEUNIT,'outputConstitutive') PhaseLoop: do ph = 1_pInt,material_Nphase activePhase: if (any(material_phase == ph)) then ins = phase_plasticityInstance(ph) knownPlasticity = .true. ! assume valid plasticityType: select case(phase_plasticity(ph)) case (PLASTICITY_NONE_ID) plasticityType outputName = PLASTICITY_NONE_label thisOutput => null() thisSize => null() case (PLASTICITY_ISOTROPIC_ID) plasticityType outputName = PLASTICITY_ISOTROPIC_label thisOutput => plastic_isotropic_output thisSize => plastic_isotropic_sizePostResult case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType outputName = PLASTICITY_PHENOPOWERLAW_label thisOutput => plastic_phenopowerlaw_output thisSize => plastic_phenopowerlaw_sizePostResult case (PLASTICITY_KINEHARDENING_ID) plasticityType outputName = PLASTICITY_KINEHARDENING_label thisOutput => plastic_kinehardening_output thisSize => plastic_kinehardening_sizePostResult case (PLASTICITY_DISLOTWIN_ID) plasticityType outputName = PLASTICITY_DISLOTWIN_label thisOutput => plastic_dislotwin_output thisSize => plastic_dislotwin_sizePostResult case (PLASTICITY_DISLOUCLA_ID) plasticityType outputName = PLASTICITY_DISLOUCLA_label thisOutput => plastic_disloucla_output thisSize => plastic_disloucla_sizePostResult case (PLASTICITY_NONLOCAL_ID) plasticityType outputName = PLASTICITY_NONLOCAL_label thisOutput => plastic_nonlocal_output thisSize => plastic_nonlocal_sizePostResult case default plasticityType knownPlasticity = .false. end select plasticityType write(FILEUNIT,'(/,a,/)') '['//trim(phase_name(ph))//']' if (knownPlasticity) then write(FILEUNIT,'(a)') '(plasticity)'//char(9)//trim(outputName) if (phase_plasticity(ph) /= PLASTICITY_NONE_ID) then OutputPlasticityLoop: do o = 1_pInt,size(thisOutput(:,ins)) if(len(trim(thisOutput(o,ins))) > 0_pInt) & write(FILEUNIT,'(a,i4)') trim(thisOutput(o,ins))//char(9),thisSize(o,ins) enddo OutputPlasticityLoop endif endif SourceLoop: do s = 1_pInt, phase_Nsources(ph) knownSource = .true. ! assume valid sourceType: select case (phase_source(s,ph)) case (SOURCE_thermal_dissipation_ID) sourceType ins = source_thermal_dissipation_instance(ph) outputName = SOURCE_thermal_dissipation_label thisOutput => source_thermal_dissipation_output thisSize => source_thermal_dissipation_sizePostResult case (SOURCE_thermal_externalheat_ID) sourceType ins = source_thermal_externalheat_instance(ph) outputName = SOURCE_thermal_externalheat_label thisOutput => source_thermal_externalheat_output thisSize => source_thermal_externalheat_sizePostResult case (SOURCE_damage_isoBrittle_ID) sourceType ins = source_damage_isoBrittle_instance(ph) outputName = SOURCE_damage_isoBrittle_label thisOutput => source_damage_isoBrittle_output thisSize => source_damage_isoBrittle_sizePostResult case (SOURCE_damage_isoDuctile_ID) sourceType ins = source_damage_isoDuctile_instance(ph) outputName = SOURCE_damage_isoDuctile_label thisOutput => source_damage_isoDuctile_output thisSize => source_damage_isoDuctile_sizePostResult case (SOURCE_damage_anisoBrittle_ID) sourceType ins = source_damage_anisoBrittle_instance(ph) outputName = SOURCE_damage_anisoBrittle_label thisOutput => source_damage_anisoBrittle_output thisSize => source_damage_anisoBrittle_sizePostResult case (SOURCE_damage_anisoDuctile_ID) sourceType ins = source_damage_anisoDuctile_instance(ph) outputName = SOURCE_damage_anisoDuctile_label thisOutput => source_damage_anisoDuctile_output thisSize => source_damage_anisoDuctile_sizePostResult case default sourceType knownSource = .false. end select sourceType if (knownSource) then write(FILEUNIT,'(a)') '(source)'//char(9)//trim(outputName) OutputSourceLoop: do o = 1_pInt,size(thisOutput(:,ins)) if(len(trim(thisOutput(o,ins))) > 0_pInt) & write(FILEUNIT,'(a,i4)') trim(thisOutput(o,ins))//char(9),thisSize(o,ins) enddo OutputSourceLoop endif enddo SourceLoop endif activePhase enddo PhaseLoop close(FILEUNIT) endif mainProcess constitutive_plasticity_maxSizeDotState = 0_pInt constitutive_plasticity_maxSizePostResults = 0_pInt constitutive_source_maxSizeDotState = 0_pInt constitutive_source_maxSizePostResults = 0_pInt PhaseLoop2:do ph = 1_pInt,material_Nphase !-------------------------------------------------------------------------------------------------- ! partition and inititalize state plasticState(ph)%partionedState0 = plasticState(ph)%state0 plasticState(ph)%state = plasticState(ph)%partionedState0 forall(s = 1_pInt: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 state and output constitutive_plasticity_maxSizeDotState = max(constitutive_plasticity_maxSizeDotState, & plasticState(ph)%sizeDotState) constitutive_plasticity_maxSizePostResults = max(constitutive_plasticity_maxSizePostResults, & plasticState(ph)%sizePostResults) constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, & maxval(sourceState(ph)%p(:)%sizeDotState)) constitutive_source_maxSizePostResults = max(constitutive_source_maxSizePostResults, & maxval(sourceState(ph)%p(:)%sizePostResults)) enddo PhaseLoop2 end subroutine constitutive_init !-------------------------------------------------------------------------------------------------- !> @brief returns the homogenize elasticity matrix !> ToDo: homogenizedC66 would be more consistent !-------------------------------------------------------------------------------------------------- function constitutive_homogenizedC(ipc,ip,el) use prec, only: & pReal use material, only: & phase_plasticity, & material_phase, & PLASTICITY_DISLOTWIN_ID, & PLASTICITY_DISLOUCLA_ID use plastic_dislotwin, only: & plastic_dislotwin_homogenizedC use lattice, only: & lattice_C66 implicit none real(pReal), dimension(6,6) :: constitutive_homogenizedC integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element plasticityType: select case (phase_plasticity(material_phase(ipc,ip,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_phase (ipc,ip,el)) end select plasticityType end function constitutive_homogenizedC !-------------------------------------------------------------------------------------------------- !> @brief calls microstructure function of the different constitutive models !-------------------------------------------------------------------------------------------------- subroutine constitutive_microstructure(orientations, Fe, Fp, ipc, ip, el) use prec, only: & pReal use material, only: & phasememberAt, & phase_plasticity, & phase_plasticityInstance, & material_phase, & material_homogenizationAt, & temperature, & thermalMapping, & PLASTICITY_dislotwin_ID, & PLASTICITY_disloucla_ID, & PLASTICITY_nonlocal_ID use plastic_nonlocal, only: & plastic_nonlocal_microstructure use plastic_dislotwin, only: & plastic_dislotwin_microstructure use plastic_disloUCLA, only: & plastic_disloUCLA_dependentState implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & Fe, & !< elastic deformation gradient Fp !< plastic deformation gradient integer(pInt) :: & ho, & !< homogenization tme, & !< thermal member position instance, of real(pReal), intent(in), dimension(:,:,:,:) :: & orientations !< crystal orientations as quaternions ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) plasticityType: select case (phase_plasticity(material_phase(ipc,ip,el))) case (PLASTICITY_DISLOTWIN_ID) plasticityType call plastic_dislotwin_microstructure(temperature(ho)%p(tme),ipc,ip,el) case (PLASTICITY_DISLOUCLA_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_disloUCLA_dependentState(instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_microstructure (Fe,Fp,ip,el) end select plasticityType end subroutine constitutive_microstructure !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient !-------------------------------------------------------------------------------------------------- subroutine constitutive_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, S6, Fi, ipc, ip, el) use prec, only: & pReal use math, only: & math_mul33x33, & math_Mandel6to33, & math_Mandel33to6, & math_Plain99to3333 use material, only: & phasememberAt, & phase_plasticity, & phase_plasticityInstance, & material_phase, & material_homogenizationAt, & temperature, & thermalMapping, & PLASTICITY_NONE_ID, & PLASTICITY_ISOTROPIC_ID, & PLASTICITY_PHENOPOWERLAW_ID, & PLASTICITY_KINEHARDENING_ID, & PLASTICITY_DISLOTWIN_ID, & PLASTICITY_DISLOUCLA_ID, & PLASTICITY_NONLOCAL_ID use plastic_isotropic, only: & plastic_isotropic_LpAndItsTangent use plastic_phenopowerlaw, only: & plastic_phenopowerlaw_LpAndItsTangent use plastic_kinehardening, only: & plastic_kinehardening_LpAndItsTangent use plastic_dislotwin, only: & plastic_dislotwin_LpAndItsTangent use plastic_disloucla, only: & plastic_disloucla_LpAndItsTangent use plastic_nonlocal, only: & plastic_nonlocal_LpAndItsTangent implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(6) :: & S6 !< 2nd Piola-Kirchhoff stress (vector notation) real(pReal), intent(in), dimension(3,3) :: & 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(9,9) :: & dLp_dMp99 !< derivative of Lp with respect to Mstar (matrix notation) real(pReal), dimension(3,3) :: & Mp, & !< Mandel stress work conjugate with Lp S !< 2nd Piola-Kirchhoff stress integer(pInt) :: & ho, & !< homogenization tme !< thermal member position integer(pInt) :: & i, j, instance, of ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) S = math_Mandel6to33(S6) Mp = math_mul33x33(math_mul33x33(transpose(Fi),Fi),S) plasticityType: select case (phase_plasticity(material_phase(ipc,ip,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_dMp99, math_Mandel33to6(Mp),ipc,ip,el) dLp_dMp = math_Plain99to3333(dLp_dMp99) ! ToDo: We revert here the last statement in plastic_xx_LpAndItsTanget case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_phenopowerlaw_LpAndItsTangent (Lp,dLp_dMp,Mp,instance,of) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_LpAndItsTangent (Lp,dLp_dMp99, math_Mandel33to6(Mp),ipc,ip,el) dLp_dMp = math_Plain99to3333(dLp_dMp99) ! ToDo: We revert here the last statement in plastic_xx_LpAndItsTanget case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_LpAndItsTangent (Lp,dLp_dMp99, math_Mandel33to6(Mp), & temperature(ho)%p(tme),ip,el) dLp_dMp = math_Plain99to3333(dLp_dMp99) ! ToDo: We revert here the last statement in plastic_xx_LpAndItsTanget case (PLASTICITY_DISLOTWIN_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_dislotwin_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOUCLA_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_disloucla_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of) end select plasticityType #ifdef __INTEL_COMPILER forall(i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) #else do concurrent(i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) #endif dLp_dFi(i,j,1:3,1:3) = math_mul33x33(math_mul33x33(Fi,S),transpose(dLp_dMp(i,j,1:3,1:3))) + & math_mul33x33(math_mul33x33(Fi,dLp_dMp(i,j,1:3,1:3)),S) dLp_dS(i,j,1:3,1:3) = math_mul33x33(math_mul33x33(transpose(Fi),Fi),dLp_dMp(i,j,1:3,1:3)) ! ToDo: @PS: why not: dLp_dMp:(FiT Fi) #ifdef __INTEL_COMPILER end forall #else enddo #endif end subroutine constitutive_LpAndItsTangents !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient !-------------------------------------------------------------------------------------------------- subroutine constitutive_LiAndItsTangents(Li, dLi_dS, dLi_dFi, S6, Fi, ipc, ip, el) use prec, only: & pReal use math, only: & math_I3, & math_inv33, & math_det33, & math_mul33x33 use material, only: & phase_plasticity, & material_phase, & phase_kinematics, & phase_Nkinematics, & PLASTICITY_isotropic_ID, & KINEMATICS_cleavage_opening_ID, & KINEMATICS_slipplane_opening_ID, & KINEMATICS_thermal_expansion_ID use plastic_isotropic, only: & plastic_isotropic_LiAndItsTangent use kinematics_cleavage_opening, only: & kinematics_cleavage_opening_LiAndItsTangent use kinematics_slipplane_opening, only: & kinematics_slipplane_opening_LiAndItsTangent use kinematics_thermal_expansion, only: & kinematics_thermal_expansion_LiAndItsTangent implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(6) :: & S6 !< 2nd Piola-Kirchhoff stress (vector notation) 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 real(pReal), dimension(3,3,3,3) :: & my_dLi_dS real(pReal), dimension(3,3) :: & FiInv, & temp_33 real(pReal) :: & detFi integer(pInt) :: & k !< counter in kinematics loop integer(pInt) :: & i, j Li = 0.0_pReal dLi_dS = 0.0_pReal dLi_dFi = 0.0_pReal plasticityType: select case (phase_plasticity(material_phase(ipc,ip,el))) case (PLASTICITY_isotropic_ID) plasticityType call plastic_isotropic_LiAndItsTangent(my_Li, my_dLi_dS, S6, ipc, ip, el) 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_pInt, phase_Nkinematics(material_phase(ipc,ip,el)) kinematicsType: select case (phase_kinematics(k,material_phase(ipc,ip,el))) case (KINEMATICS_cleavage_opening_ID) kinematicsType call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S6, ipc, ip, el) case (KINEMATICS_slipplane_opening_ID) kinematicsType call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S6, 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 = math_mul33x33(math_mul33x33(Fi,Li),FiInv)*detFi !< push forward to intermediate configuration temp_33 = math_mul33x33(FiInv,Li) do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt dLi_dS(1:3,1:3,i,j) = math_mul33x33(math_mul33x33(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) end do; end do end subroutine constitutive_LiAndItsTangents !-------------------------------------------------------------------------------------------------- !> @brief collects initial intermediate deformation gradient !-------------------------------------------------------------------------------------------------- pure function constitutive_initialFi(ipc, ip, el) use prec, only: & pReal use math, only: & math_I3, & math_inv33, & math_mul33x33 use material, only: & phase_kinematics, & phase_Nkinematics, & material_phase, & KINEMATICS_thermal_expansion_ID use kinematics_thermal_expansion, only: & kinematics_thermal_expansion_initialStrain implicit none integer(pInt), 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(pInt) :: & k !< counter in kinematics loop constitutive_initialFi = math_I3 KinematicsLoop: do k = 1_pInt, phase_Nkinematics(material_phase(ipc,ip,el)) !< Warning: small initial strain assumption kinematicsType: select case (phase_kinematics(k,material_phase(ipc,ip,el))) case (KINEMATICS_thermal_expansion_ID) kinematicsType constitutive_initialFi = & constitutive_initialFi + kinematics_thermal_expansion_initialStrain(ipc, ip, el) 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) use prec, only: & pReal implicit none integer(pInt), 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) use prec, only: & pReal use math, only : & math_mul33x33, & math_mul3333xx33, & math_Mandel66to3333, & math_I3 use material, only: & material_phase, & material_homogenizationAt, & phase_NstiffnessDegradations, & phase_stiffnessDegradation, & damage, & damageMapping, & STIFFNESS_DEGRADATION_damage_ID implicit none integer(pInt), 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(pInt) :: & ho, & !< homogenization d !< counter in degradation loop integer(pInt) :: & i, j ho = material_homogenizationAt(el) C = math_Mandel66to3333(constitutive_homogenizedC(ipc,ip,el)) DegradationLoop: do d = 1_pInt, phase_NstiffnessDegradations(material_phase(ipc,ip,el)) degradationType: select case(phase_stiffnessDegradation(d,material_phase(ipc,ip,el))) case (STIFFNESS_DEGRADATION_damage_ID) degradationType C = C * damage(ho)%p(damageMapping(ho)%p(ip,el))**2_pInt end select degradationType enddo DegradationLoop E = 0.5_pReal*(math_mul33x33(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration S = math_mul3333xx33(C,math_mul33x33(math_mul33x33(transpose(Fi),E),Fi)) !< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration dS_dFe = 0.0_pReal forall (i=1_pInt:3_pInt, j=1_pInt:3_pInt) dS_dFe(i,j,1:3,1:3) = & math_mul33x33(Fe,math_mul33x33(math_mul33x33(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*math_mul33x33(math_mul33x33(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn end forall end subroutine constitutive_hooke_SandItsTangents !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the rate of change of microstructure !-------------------------------------------------------------------------------------------------- subroutine constitutive_collectDotState(S6, FeArray, Fi, FpArray, subdt, subfracArray,ipc, ip, el) use prec, only: & pReal, & pLongInt use debug, only: & debug_level, & debug_constitutive, & debug_levelBasic use math, only: & math_mul33x33, & math_Mandel6to33, & math_Mandel33to6, & math_mul33x33 use mesh, only: & mesh_NcpElems, & mesh_maxNips use material, only: & phasememberAt, & phase_plasticityInstance, & phase_plasticity, & phase_source, & phase_Nsources, & material_phase, & material_homogenizationAt, & temperature, & thermalMapping, & homogenization_maxNgrains, & PLASTICITY_none_ID, & PLASTICITY_isotropic_ID, & PLASTICITY_phenopowerlaw_ID, & PLASTICITY_kinehardening_ID, & PLASTICITY_dislotwin_ID, & PLASTICITY_disloucla_ID, & PLASTICITY_nonlocal_ID, & SOURCE_damage_isoDuctile_ID, & SOURCE_damage_anisoBrittle_ID, & SOURCE_damage_anisoDuctile_ID, & SOURCE_thermal_externalheat_ID use plastic_isotropic, only: & plastic_isotropic_dotState use plastic_phenopowerlaw, only: & plastic_phenopowerlaw_dotState use plastic_kinehardening, only: & plastic_kinehardening_dotState use plastic_dislotwin, only: & plastic_dislotwin_dotState use plastic_disloucla, only: & plastic_disloucla_dotState use plastic_nonlocal, only: & plastic_nonlocal_dotState use source_damage_isoDuctile, only: & source_damage_isoDuctile_dotState use source_damage_anisoBrittle, only: & source_damage_anisoBrittle_dotState use source_damage_anisoDuctile, only: & source_damage_anisoDuctile_dotState use source_thermal_externalheat, only: & source_thermal_externalheat_dotState implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in) :: & subdt !< timestep real(pReal), intent(in), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: & subfracArray !< subfraction of timestep real(pReal), intent(in), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: & FeArray, & !< elastic deformation gradient FpArray !< plastic deformation gradient real(pReal), intent(in), dimension(3,3) :: & Fi !< intermediate deformation gradient real(pReal), intent(in), dimension(6) :: & S6 !< 2nd Piola Kirchhoff stress (vector notation) real(pReal), dimension(3,3) :: & Mp integer(pInt) :: & ho, & !< homogenization tme, & !< thermal member position s, & !< counter in source loop instance, of ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) Mp = math_mul33x33(math_mul33x33(transpose(Fi),Fi),math_Mandel6to33(S6)) plasticityType: select case (phase_plasticity(material_phase(ipc,ip,el))) case (PLASTICITY_ISOTROPIC_ID) plasticityType call plastic_isotropic_dotState (math_Mandel33to6(Mp),ipc,ip,el) case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_phenopowerlaw_dotState(Mp,instance,of) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_dotState(math_Mandel33to6(Mp),ipc,ip,el) case (PLASTICITY_DISLOTWIN_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_dislotwin_dotState (Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOUCLA_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) call plastic_disloucla_dotState (Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_dotState (math_Mandel33to6(Mp),FeArray,FpArray,temperature(ho)%p(tme), & subdt,subfracArray,ip,el) end select plasticityType SourceLoop: do s = 1_pInt, phase_Nsources(material_phase(ipc,ip,el)) sourceType: select case (phase_source(s,material_phase(ipc,ip,el))) case (SOURCE_damage_anisoBrittle_ID) sourceType call source_damage_anisoBrittle_dotState (S6, 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( ipc, ip, el) end select sourceType enddo SourceLoop end subroutine 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 !-------------------------------------------------------------------------------------------------- subroutine constitutive_collectDeltaState(S6, Fe, Fi, ipc, ip, el) use prec, only: & pReal, & pLongInt use debug, only: & debug_level, & debug_constitutive, & debug_levelBasic use math, only: & math_Mandel6to33, & math_Mandel33to6, & math_mul33x33 use material, only: & phase_plasticity, & phase_source, & phase_Nsources, & material_phase, & PLASTICITY_KINEHARDENING_ID, & PLASTICITY_NONLOCAL_ID, & SOURCE_damage_isoBrittle_ID use plastic_kinehardening, only: & plastic_kinehardening_deltaState use plastic_nonlocal, only: & plastic_nonlocal_deltaState use source_damage_isoBrittle, only: & source_damage_isoBrittle_deltaState implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(6) :: & S6 !< 2nd Piola Kirchhoff stress (vector notation) real(pReal), intent(in), dimension(3,3) :: & Fe, & !< elastic deformation gradient Fi !< intermediate deformation gradient real(pReal), dimension(3,3) :: & Mstar integer(pInt) :: & s !< counter in source loop Mstar = math_mul33x33(math_mul33x33(transpose(Fi),Fi),math_Mandel6to33(S6)) plasticityType: select case (phase_plasticity(material_phase(ipc,ip,el))) case (PLASTICITY_KINEHARDENING_ID) plasticityType call plastic_kinehardening_deltaState(math_Mandel33to6(Mstar),ipc,ip,el) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_deltaState(math_Mandel33to6(Mstar),ip,el) end select plasticityType sourceLoop: do s = 1_pInt, phase_Nsources(material_phase(ipc,ip,el)) sourceType: select case (phase_source(s,material_phase(ipc,ip,el))) case (SOURCE_damage_isoBrittle_ID) sourceType call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(ipc,ip,el), Fe, & ipc, ip, el) end select sourceType enddo SourceLoop end subroutine constitutive_collectDeltaState !-------------------------------------------------------------------------------------------------- !> @brief returns array of constitutive results !-------------------------------------------------------------------------------------------------- function constitutive_postResults(S6, Fi, FeArray, ipc, ip, el) use prec, only: & pReal use math, only: & math_Mandel6to33, & math_mul33x33 use mesh, only: & mesh_NcpElems, & mesh_maxNips use material, only: & phasememberAt, & phase_plasticityInstance, & plasticState, & sourceState, & phase_plasticity, & phase_source, & phase_Nsources, & material_phase, & material_homogenizationAt, & temperature, & thermalMapping, & homogenization_maxNgrains, & PLASTICITY_NONE_ID, & PLASTICITY_ISOTROPIC_ID, & PLASTICITY_PHENOPOWERLAW_ID, & PLASTICITY_KINEHARDENING_ID, & PLASTICITY_DISLOTWIN_ID, & PLASTICITY_DISLOUCLA_ID, & PLASTICITY_NONLOCAL_ID, & SOURCE_damage_isoBrittle_ID, & SOURCE_damage_isoDuctile_ID, & SOURCE_damage_anisoBrittle_ID, & SOURCE_damage_anisoDuctile_ID use plastic_isotropic, only: & plastic_isotropic_postResults use plastic_phenopowerlaw, only: & plastic_phenopowerlaw_postResults use plastic_kinehardening, only: & plastic_kinehardening_postResults use plastic_dislotwin, only: & plastic_dislotwin_postResults use plastic_disloucla, only: & plastic_disloucla_postResults use plastic_nonlocal, only: & plastic_nonlocal_postResults use source_damage_isoBrittle, only: & source_damage_isoBrittle_postResults use source_damage_isoDuctile, only: & source_damage_isoDuctile_postResults use source_damage_anisoBrittle, only: & source_damage_anisoBrittle_postResults use source_damage_anisoDuctile, only: & source_damage_anisoDuctile_postResults implicit none integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults + & sum(sourceState(material_phase(ipc,ip,el))%p(:)%sizePostResults)) :: & constitutive_postResults real(pReal), intent(in), dimension(3,3) :: & Fi !< intermediate deformation gradient real(pReal), intent(in), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: & FeArray !< elastic deformation gradient real(pReal), intent(in), dimension(6) :: & S6 !< 2nd Piola Kirchhoff stress (vector notation) real(pReal), dimension(3,3) :: & Mp !< Mandel stress integer(pInt) :: & startPos, endPos integer(pInt) :: & ho, & !< homogenization tme, & !< thermal member position s, of, instance !< counter in source loop constitutive_postResults = 0.0_pReal Mp = math_mul33x33(math_mul33x33(transpose(Fi),Fi),math_Mandel6to33(S6)) ho = material_homogenizationAt(el) tme = thermalMapping(ho)%p(ip,el) startPos = 1_pInt endPos = plasticState(material_phase(ipc,ip,el))%sizePostResults plasticityType: select case (phase_plasticity(material_phase(ipc,ip,el))) case (PLASTICITY_ISOTROPIC_ID) plasticityType constitutive_postResults(startPos:endPos) = & plastic_isotropic_postResults(S6,ipc,ip,el) case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) constitutive_postResults(startPos:endPos) = & plastic_phenopowerlaw_postResults(Mp,instance,of) case (PLASTICITY_KINEHARDENING_ID) plasticityType constitutive_postResults(startPos:endPos) = & plastic_kinehardening_postResults(S6,ipc,ip,el) case (PLASTICITY_DISLOTWIN_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) constitutive_postResults(startPos:endPos) = & plastic_dislotwin_postResults(Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_DISLOUCLA_ID) plasticityType of = phasememberAt(ipc,ip,el) instance = phase_plasticityInstance(material_phase(ipc,ip,el)) constitutive_postResults(startPos:endPos) = & plastic_disloucla_postResults(Mp,temperature(ho)%p(tme),instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType constitutive_postResults(startPos:endPos) = & plastic_nonlocal_postResults (S6,FeArray,ip,el) end select plasticityType SourceLoop: do s = 1_pInt, phase_Nsources(material_phase(ipc,ip,el)) startPos = endPos + 1_pInt endPos = endPos + sourceState(material_phase(ipc,ip,el))%p(s)%sizePostResults sourceType: select case (phase_source(s,material_phase(ipc,ip,el))) case (SOURCE_damage_isoBrittle_ID) sourceType constitutive_postResults(startPos:endPos) = source_damage_isoBrittle_postResults(ipc, ip, el) case (SOURCE_damage_isoDuctile_ID) sourceType constitutive_postResults(startPos:endPos) = source_damage_isoDuctile_postResults(ipc, ip, el) case (SOURCE_damage_anisoBrittle_ID) sourceType constitutive_postResults(startPos:endPos) = source_damage_anisoBrittle_postResults(ipc, ip, el) case (SOURCE_damage_anisoDuctile_ID) sourceType constitutive_postResults(startPos:endPos) = source_damage_anisoDuctile_postResults(ipc, ip, el) end select sourceType enddo SourceLoop end function constitutive_postResults end module constitutive