!---------------------------------------------------------------------------------------------------- !> @brief internal microstructure state for all plasticity constitutive models !---------------------------------------------------------------------------------------------------- submodule(constitutive) constitutive_mech integer(kind(ELASTICITY_undefined_ID)), dimension(:), allocatable :: & phase_elasticity !< elasticity of each phase integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: & phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase interface module function plastic_none_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_none_init module function plastic_isotropic_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_isotropic_init module function plastic_phenopowerlaw_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_phenopowerlaw_init module function plastic_kinehardening_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_kinehardening_init module function plastic_dislotwin_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_dislotwin_init module function plastic_dislotungsten_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function plastic_dislotungsten_init module function plastic_nonlocal_init() result(myPlasticity) logical, dimension(:), allocatable :: & myPlasticity end function 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_dislotungsten_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_dislotungsten_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_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_maxNconstituents,discretization_nIPs,discretization_Nelems), 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_dislotungsten_dependentState(instance,of) integer, intent(in) :: & instance, & of end subroutine plastic_dislotungsten_dependentState module subroutine plastic_nonlocal_dependentState(F, Fp, instance, of, ip, el) real(pReal), dimension(3,3), intent(in) :: & F, & !< deformation gradient Fp !< plastic deformation gradient integer, intent(in) :: & instance, & of, & ip, & !< current integration point el !< current element number 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 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_dislotungsten_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_dislotungsten_results module subroutine plastic_nonlocal_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group end subroutine plastic_nonlocal_results end interface contains !-------------------------------------------------------------------------------------------------- !> @brief Initialize mechanical field related constitutive models !> @details Initialize elasticity, plasticity and stiffness degradation models. !-------------------------------------------------------------------------------------------------- module subroutine mech_init integer :: & p, & stiffDegradationCtr class(tNode), pointer :: & phases, & phase, & mech, & elastic, & stiffDegradation print'(/,a)', ' <<<+- constitutive_mech init -+>>>' !------------------------------------------------------------------------------------------------- ! 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) mech => phase%get('mechanics') elastic => mech%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 => mech%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) mech => phase%get('mechanics') stiffDegradation => mech%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 ! initialize plasticity allocate(plasticState(phases%length)) allocate(phase_plasticity(phases%length),source = PLASTICITY_undefined_ID) allocate(phase_plasticityInstance(phases%length),source = 0) allocate(phase_localPlasticity(phases%length), source=.true.) where(plastic_none_init()) phase_plasticity = PLASTICITY_NONE_ID where(plastic_isotropic_init()) phase_plasticity = PLASTICITY_ISOTROPIC_ID where(plastic_phenopowerlaw_init()) phase_plasticity = PLASTICITY_PHENOPOWERLAW_ID where(plastic_kinehardening_init()) phase_plasticity = PLASTICITY_KINEHARDENING_ID where(plastic_dislotwin_init()) phase_plasticity = PLASTICITY_DISLOTWIN_ID where(plastic_dislotungsten_init()) phase_plasticity = PLASTICITY_DISLOTUNGSTEN_ID where(plastic_nonlocal_init()) phase_plasticity = PLASTICITY_NONLOCAL_ID do p = 1, phases%length phase_elasticityInstance(p) = count(phase_elasticity(1:p) == phase_elasticity(p)) phase_plasticityInstance(p) = count(phase_plasticity(1:p) == phase_plasticity(p)) enddo end subroutine mech_init !-------------------------------------------------------------------------------------------------- !> @brief checks if a plastic module is active or not !-------------------------------------------------------------------------------------------------- module function plastic_active(plastic_label) result(active_plastic) character(len=*), intent(in) :: plastic_label !< type of plasticity model logical, dimension(:), allocatable :: active_plastic class(tNode), pointer :: & phases, & phase, & mech, & pl integer :: p phases => config_material%get('phase') allocate(active_plastic(phases%length), source = .false. ) do p = 1, phases%length phase => phases%get(p) mech => phase%get('mechanics') pl => mech%get('plasticity') if(pl%get_asString('type') == plastic_label) active_plastic(p) = .true. enddo end function plastic_active !-------------------------------------------------------------------------------------------------- !> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to !> the elastic and intermediate deformation gradients using Hooke's law !-------------------------------------------------------------------------------------------------- module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi, ipc, ip, el) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & Fe, & !< elastic deformation gradient Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & S !< 2nd Piola-Kirchhoff stress tensor 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(material_homogenizationMemberAt(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 calls microstructure function of the different plasticity constitutive models !-------------------------------------------------------------------------------------------------- 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 integer :: & ho, & !< homogenization tme, & !< thermal member position instance, of ho = material_homogenizationAt(el) tme = material_homogenizationMemberAt(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_DISLOTUNGSTEN_ID) plasticityType call plastic_dislotungsten_dependentState(instance,of) case (PLASTICITY_NONLOCAL_ID) plasticityType call plastic_nonlocal_dependentState (F,Fp,instance,of,ip,el) end select plasticityType end subroutine constitutive_plastic_dependentState !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the velocity gradient ! ToDo: Discuss whether it makes sense if crystallite handles the configuration conversion, i.e. ! Mp in, dLp_dMp out !-------------------------------------------------------------------------------------------------- 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 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 = material_homogenizationMemberAt(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_DISLOTUNGSTEN_ID) plasticityType call plastic_dislotungsten_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_plastic_LpAndItsTangents !-------------------------------------------------------------------------------------------------- !> @brief contains the constitutive equation for calculating the rate of change of microstructure !-------------------------------------------------------------------------------------------------- module function constitutive_collectDotState(S, FArray, Fi, FpArray, subdt, ipc, ip, el,phase,of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in) :: & subdt !< timestep real(pReal), intent(in), dimension(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: & FArray, & !< elastic deformation gradient FpArray !< plastic deformation gradient real(pReal), intent(in), dimension(3,3) :: & Fi !< intermediate deformation gradient real(pReal), intent(in), dimension(3,3) :: & S !< 2nd Piola Kirchhoff stress (vector notation) 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 = material_homogenizationMemberAt(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))) 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 !-------------------------------------------------------------------------------------------------- module function constitutive_deltaState(S, Fi, ipc, ip, el, phase, of) result(broken) integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el, & !< element phase, & of real(pReal), intent(in), dimension(3,3) :: & S, & !< 2nd Piola Kirchhoff stress Fi !< intermediate deformation gradient real(pReal), dimension(3,3) :: & Mp integer :: & 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 end function constitutive_deltaState !-------------------------------------------------------------------------------------------- !> @brief writes plasticity constitutive results to HDF5 output file !-------------------------------------------------------------------------------------------- module subroutine plastic_results integer :: p character(len=:), allocatable :: group plasticityLoop: do p=1,size(material_name_phase) group = '/current/phase/'//trim(material_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_DISLOTUNGSTEN_ID) call plastic_dislotungsten_results(phase_plasticityInstance(p),group) case(PLASTICITY_NONLOCAL_ID) call plastic_nonlocal_results(phase_plasticityInstance(p),group) end select enddo plasticityLoop end subroutine plastic_results !-------------------------------------------------------------------------------------------------- !> @brief calculation of stress (P) with time integration based on a residuum in Lp and !> intermediate acceleration of the Newton-Raphson correction !-------------------------------------------------------------------------------------------------- function integrateStress(ipc,ip,el,timeFraction) result(broken) integer, intent(in):: el, & ! element index ip, & ! integration point index ipc ! grain index real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep Fp_new, & ! plastic deformation gradient at end of timestep invFp_new, & ! inverse of Fp_new invFp_current, & ! inverse of Fp_current Lpguess, & ! current guess for plastic velocity gradient Lpguess_old, & ! known last good guess for plastic velocity gradient Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law residuumLp, & ! current residuum of plastic velocity gradient residuumLp_old, & ! last residuum of plastic velocity gradient deltaLp, & ! direction of next guess Fi_new, & ! gradient of intermediate deformation stages invFi_new, & invFi_current, & ! inverse of Fi_current Liguess, & ! current guess for intermediate velocity gradient Liguess_old, & ! known last good guess for intermediate velocity gradient Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law residuumLi, & ! current residuum of intermediate velocity gradient residuumLi_old, & ! last residuum of intermediate velocity gradient deltaLi, & ! direction of next guess Fe, & ! elastic deformation gradient S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration A, & B, & temp_33 real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme) dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme) real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress dS_dFi, & dFe_dLp, & ! partial derivative of elastic deformation gradient dFe_dLi, & dFi_dLi, & dLp_dFi, & dLi_dFi, & dLp_dS, & dLi_dS real(pReal) steplengthLp, & steplengthLi, & dt, & ! time increment atol_Lp, & atol_Li, & devNull integer NiterationStressLp, & ! number of stress integrations NiterationStressLi, & ! number of inner stress integrations ierr, & ! error indicator for LAPACK o, & p, & m, & jacoCounterLp, & jacoCounterLi ! counters to check for Jacobian update logical :: error,broken broken = .true. if (present(timeFraction)) then dt = crystallite_subdt(ipc,ip,el) * timeFraction F = crystallite_subF0(1:3,1:3,ipc,ip,el) & + (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction else dt = crystallite_subdt(ipc,ip,el) F = crystallite_subF(1:3,1:3,ipc,ip,el) endif call constitutive_plastic_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), & crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el) p = material_phaseAt(ipc,el) m = material_phaseMemberAt(ipc,ip,el) Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess Liguess = constitutive_mech_Li(p)%data(1:3,1:3,m) ! take as first guess call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el)) if (error) return ! error call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el)) if (error) return ! error A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp jacoCounterLi = 0 steplengthLi = 1.0_pReal residuumLi_old = 0.0_pReal Liguess_old = Liguess NiterationStressLi = 0 LiLoop: do NiterationStressLi = NiterationStressLi + 1 if (NiterationStressLi>num%nStress) return ! error invFi_new = matmul(invFi_current,math_I3 - dt*Liguess) Fi_new = math_inv33(invFi_new) jacoCounterLp = 0 steplengthLp = 1.0_pReal residuumLp_old = 0.0_pReal Lpguess_old = Lpguess NiterationStressLp = 0 LpLoop: do NiterationStressLp = NiterationStressLp + 1 if (NiterationStressLp>num%nStress) return ! error B = math_I3 - dt*Lpguess Fe = matmul(matmul(A,B), invFi_new) call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi_new, ipc, ip, el) call constitutive_plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, & S, Fi_new, ipc, ip, el) !* update current residuum and check for convergence of loop atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_crystalliteStress) ! minimum lower cutoff residuumLp = Lpguess - Lp_constitutive if (any(IEEE_is_NaN(residuumLp))) then return ! error elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance exit LpLoop elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLp_old = residuumLp ! ...remember old values and... Lpguess_old = Lpguess steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction Lpguess = Lpguess_old & + deltaLp * stepLengthLp cycle LpLoop endif calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then jacoCounterLp = jacoCounterLp + 1 do o=1,3; do p=1,3 dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) enddo; enddo dRLp_dLp = math_eye(9) & - math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp)) temp_9 = math_33to9(residuumLp) call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp if (ierr /= 0) return ! error deltaLp = - math_9to33(temp_9) endif calculateJacobiLi Lpguess = Lpguess & + deltaLp * steplengthLp enddo LpLoop call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, & S, Fi_new, ipc, ip, el) !* update current residuum and check for convergence of loop atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_crystalliteStress) ! minimum lower cutoff residuumLi = Liguess - Li_constitutive if (any(IEEE_is_NaN(residuumLi))) then return ! error elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance exit LiLoop elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)... residuumLi_old = residuumLi ! ...remember old values and... Liguess_old = Liguess steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction) else ! not converged and residuum not improved... steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction Liguess = Liguess_old & + deltaLi * steplengthLi cycle LiLoop endif calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then jacoCounterLi = jacoCounterLi + 1 temp_33 = matmul(matmul(A,B),invFi_current) do o=1,3; do p=1,3 dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j) dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current enddo; enddo do o=1,3; do p=1,3 dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new) enddo; enddo dRLi_dLi = math_eye(9) & - math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) & + math_mul3333xx3333(dS_dFi, dFi_dLi))) & - math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi)) temp_9 = math_33to9(residuumLi) call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li if (ierr /= 0) return ! error deltaLi = - math_9to33(temp_9) endif calculateJacobiLp Liguess = Liguess & + deltaLi * steplengthLi enddo LiLoop invFp_new = matmul(invFp_current,B) call math_invert33(Fp_new,devNull,error,invFp_new) if (error) return ! error p = material_phaseAt(ipc,el) m = material_phaseMemberAt(ipc,ip,el) crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new))) crystallite_S (1:3,1:3,ipc,ip,el) = S crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess constitutive_mech_Li(p)%data(1:3,1:3,m) = Liguess crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize constitutive_mech_Fi(p)%data(1:3,1:3,m) = Fi_new crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new) broken = .false. end function integrateStress !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with adaptive 1st order explicit Euler method !> using Fixed Point Iteration to adapt the stepsize !-------------------------------------------------------------------------------------------------- module subroutine integrateStateFPI(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & NiterationState, & !< number of iterations in state loop p, & c, & s, & size_pl integer, dimension(maxval(phase_Nsources)) :: & size_so real(pReal) :: & zeta real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: & r ! state residuum real(pReal), dimension(constitutive_plasticity_maxSizeDotState,2) :: & plastic_dotState real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState logical :: & broken p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return size_pl = plasticState(p)%sizeDotState plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) & + plasticState(p)%dotState (1:size_pl,c) & * crystallite_subdt(g,i,e) plastic_dotState(1:size_pl,2) = 0.0_pReal iteration: do NiterationState = 1, num%nState if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1) plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c) broken = integrateStress(g,i,e) if(broken) exit iteration broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) exit iteration zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),& plastic_dotState(1:size_pl,2)) plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta & + plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta) r(1:size_pl) = plasticState(p)%state (1:size_pl,c) & - plasticState(p)%subState0(1:size_pl,c) & - plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e) plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) & - r(1:size_pl) crystallite_converged(g,i,e) = converged(r(1:size_pl), & plasticState(p)%state(1:size_pl,c), & plasticState(p)%atol(1:size_pl)) if(crystallite_converged(g,i,e)) then broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c) exit iteration endif enddo iteration contains !-------------------------------------------------------------------------------------------------- !> @brief calculate the damping for correction of state and dot state !-------------------------------------------------------------------------------------------------- real(pReal) pure function damper(current,previous,previous2) real(pReal), dimension(:), intent(in) ::& current, previous, previous2 real(pReal) :: dot_prod12, dot_prod22 dot_prod12 = dot_product(current - previous, previous - previous2) dot_prod22 = dot_product(previous - previous2, previous - previous2) if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22) else damper = 1.0_pReal endif end function damper end subroutine integrateStateFPI !-------------------------------------------------------------------------------------------------- !> @brief integrate state with 1st order explicit Euler method !-------------------------------------------------------------------------------------------------- module subroutine integrateStateEuler(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & p, & c, & sizeDotState logical :: & broken p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) crystallite_converged(g,i,e) = .not. broken end subroutine integrateStateEuler !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 1st order Euler method with adaptive step size !-------------------------------------------------------------------------------------------------- module subroutine integrateStateAdaptiveEuler(g,i,e) integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & p, & c, & sizeDotState logical :: & broken real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e) plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e) broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) if(broken) return broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return sizeDotState = plasticState(p)%sizeDotState crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) & + 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%atol(1:sizeDotState)) end subroutine integrateStateAdaptiveEuler !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the classic Runge Kutta method !--------------------------------------------------------------------------------------------------- module subroutine integrateStateRK4(g,i,e) integer, intent(in) :: g,i,e real(pReal), dimension(3,3), parameter :: & A = reshape([& 0.5_pReal, 0.0_pReal, 0.0_pReal, & 0.0_pReal, 0.5_pReal, 0.0_pReal, & 0.0_pReal, 0.0_pReal, 1.0_pReal],& shape(A)) real(pReal), dimension(3), parameter :: & C = [0.5_pReal, 0.5_pReal, 1.0_pReal] real(pReal), dimension(4), parameter :: & B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal] call integrateStateRK(g,i,e,A,B,C) end subroutine integrateStateRK4 !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the Cash-Carp method !--------------------------------------------------------------------------------------------------- module subroutine integrateStateRKCK45(g,i,e) integer, intent(in) :: g,i,e real(pReal), dimension(5,5), parameter :: & A = reshape([& 1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, & 3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, & 3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, & -11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, & 1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],& shape(A)) real(pReal), dimension(5), parameter :: & C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal] real(pReal), dimension(6), parameter :: & B = & [37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, & 125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], & DB = B - & [2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,& 13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal] call integrateStateRK(g,i,e,A,B,C,DB) end subroutine integrateStateRKCK45 !-------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an !! embedded explicit Runge-Kutta method !-------------------------------------------------------------------------------------------------- subroutine integrateStateRK(g,i,e,A,B,CC,DB) real(pReal), dimension(:,:), intent(in) :: A real(pReal), dimension(:), intent(in) :: B, CC real(pReal), dimension(:), intent(in), optional :: DB integer, intent(in) :: & e, & !< element index in element loop i, & !< integration point index in ip loop g !< grain index in grain loop integer :: & stage, & ! stage index in integration stage loop n, & p, & c, & sizeDotState logical :: & broken real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState p = material_phaseAt(g,e) c = material_phaseMemberAt(g,i,e) broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e), g,i,e,p,c) if(broken) return do stage = 1,size(A,1) sizeDotState = plasticState(p)%sizeDotState plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c) plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1) do n = 2, stage sizeDotState = plasticState(p)%sizeDotState plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) & + A(n,stage) * plastic_RKdotState(1:sizeDotState,n) enddo sizeDotState = plasticState(p)%sizeDotState plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) broken = integrateStress(g,i,e,CC(stage)) if(broken) exit broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), & crystallite_partitionedF0, & constitutive_mech_Fi(p)%data(1:3,1:3,c), & crystallite_partitionedFp0, & crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c) if(broken) exit enddo if(broken) return sizeDotState = plasticState(p)%sizeDotState plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c) plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B) plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) & + plasticState(p)%dotState (1:sizeDotState,c) & * crystallite_subdt(g,i,e) if(present(DB)) & broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) & * crystallite_subdt(g,i,e), & plasticState(p)%state(1:sizeDotState,c), & plasticState(p)%atol(1:sizeDotState)) if(broken) return broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), & constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c) if(broken) return broken = integrateStress(g,i,e) crystallite_converged(g,i,e) = .not. broken end subroutine integrateStateRK end submodule constitutive_mech