!---------------------------------------------------------------------------------------------------- !> @brief internal microstructure state for all plasticity constitutive models !---------------------------------------------------------------------------------------------------- submodule(phase) mechanical enum, bind(c); enumerator :: & PLASTIC_UNDEFINED_ID, & PLASTIC_NONE_ID, & PLASTIC_ISOTROPIC_ID, & PLASTIC_PHENOPOWERLAW_ID, & PLASTIC_KINEHARDENING_ID, & PLASTIC_DISLOTWIN_ID, & PLASTIC_DISLOTUNGSTEN_ID, & PLASTIC_NONLOCAL_ID, & EIGEN_UNDEFINED_ID, & EIGEN_CLEAVAGE_OPENING_ID, & EIGEN_THERMAL_EXPANSION_ID end enum type(tTensorContainer), dimension(:), allocatable :: & ! current value phase_mechanical_Fe, & phase_mechanical_Fi, & phase_mechanical_Fp, & phase_mechanical_F, & phase_mechanical_Li, & phase_mechanical_Lp, & phase_mechanical_S, & phase_mechanical_P, & ! converged value at end of last solver increment phase_mechanical_Fi0, & phase_mechanical_Fp0, & phase_mechanical_F0, & phase_mechanical_Li0, & phase_mechanical_Lp0, & phase_mechanical_S0 integer(kind(PLASTIC_undefined_ID)), dimension(:), allocatable :: & phase_plasticity !< plasticity of each phase interface module subroutine eigen_init(phases) type(tDict), pointer :: phases end subroutine eigen_init module subroutine elastic_init(phases) type(tDict), pointer :: phases end subroutine elastic_init module subroutine plastic_init end subroutine plastic_init module subroutine phase_hooke_SandItsTangents(S,dS_dFe,dS_dFi,Fe,Fi,ph,en) integer, intent(in) :: & ph, & en 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 end subroutine phase_hooke_SandItsTangents module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,ph,en) 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) :: & ph, & en end subroutine plastic_isotropic_LiAndItsTangent module function plastic_dotState(subdt,ph,en) result(dotState) integer, intent(in) :: & ph, & en real(pREAL), intent(in) :: & subdt !< timestep real(pREAL), dimension(plasticState(ph)%sizeDotState) :: & dotState end function plastic_dotState module function plastic_deltaState(ph, en) result(broken) integer, intent(in) :: & ph, & en logical :: & broken end function plastic_deltaState module subroutine phase_LiAndItsTangents(Li, dLi_dS, dLi_dFi, & S, Fi, ph,en) integer, intent(in) :: & ph,en 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 end subroutine phase_LiAndItsTangents module subroutine plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, & S, Fi, ph,en) integer, intent(in) :: & ph,en real(pREAL), intent(in), dimension(3,3) :: & S, & !< 2nd Piola-Kirchhoff stress Fi !< intermediate deformation gradient real(pREAL), intent(out), dimension(3,3) :: & Lp !< plastic velocity gradient real(pREAL), intent(out), dimension(3,3,3,3) :: & dLp_dS, & dLp_dFi !< derivative of Lp with respect to Fi end subroutine plastic_LpAndItsTangents module subroutine plastic_isotropic_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_isotropic_result module subroutine plastic_phenopowerlaw_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_phenopowerlaw_result module subroutine plastic_kinehardening_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_kinehardening_result module subroutine plastic_dislotwin_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_dislotwin_result module subroutine plastic_dislotungsten_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_dislotungsten_result module subroutine plastic_nonlocal_result(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group end subroutine plastic_nonlocal_result module function plastic_dislotwin_homogenizedC(ph,en) result(homogenizedC) real(pREAL), dimension(6,6) :: homogenizedC integer, intent(in) :: ph,en end function plastic_dislotwin_homogenizedC pure module function elastic_C66(ph,en) result(C66) real(pREAL), dimension(6,6) :: C66 integer, intent(in) :: ph, en end function elastic_C66 pure module function elastic_mu(ph,en,isotropic_bound) result(mu) real(pREAL) :: mu integer, intent(in) :: ph, en character(len=*), intent(in) :: isotropic_bound end function elastic_mu pure module function elastic_nu(ph,en,isotropic_bound) result(nu) real(pREAL) :: nu integer, intent(in) :: ph, en character(len=*), intent(in) :: isotropic_bound end function elastic_nu end interface type :: tOutput !< requested output (per phase) character(len=pSTRLEN), allocatable, dimension(:) :: & label end type tOutput type(tOutput), allocatable, dimension(:) :: output_mechanical procedure(integrateStateFPI), pointer :: integrateState contains !-------------------------------------------------------------------------------------------------- !> @brief Initialize mechanical field related constitutive models !> @details Initialize elasticity, plasticity and stiffness degradation models. !-------------------------------------------------------------------------------------------------- module subroutine mechanical_init(phases, num_mech) type(tDict), pointer :: & phases, & num_mech integer :: & ce, & co, & ma, & ph, & en, & Nmembers type(tDict), pointer :: & phase, & mech, & num_mech_plastic, & num_mech_eigen character(len=:), allocatable :: extmsg print'(/,1x,a)', '<<<+- phase:mechanical init -+>>>' !------------------------------------------------------------------------------------------------- allocate(output_mechanical(phases%length)) allocate(phase_mechanical_Fe(phases%length)) allocate(phase_mechanical_Fi(phases%length)) allocate(phase_mechanical_Fi0(phases%length)) allocate(phase_mechanical_Fp(phases%length)) allocate(phase_mechanical_Fp0(phases%length)) allocate(phase_mechanical_F(phases%length)) allocate(phase_mechanical_F0(phases%length)) allocate(phase_mechanical_Li(phases%length)) allocate(phase_mechanical_Li0(phases%length)) allocate(phase_mechanical_Lp(phases%length)) allocate(phase_mechanical_Lp0(phases%length)) allocate(phase_mechanical_S(phases%length)) allocate(phase_mechanical_P(phases%length)) allocate(phase_mechanical_S0(phases%length)) do ph = 1, phases%length Nmembers = count(material_ID_phase == ph) allocate(phase_mechanical_Fe(ph)%data(3,3,Nmembers)) allocate(phase_mechanical_Fi(ph)%data(3,3,Nmembers)) allocate(phase_mechanical_Fp(ph)%data(3,3,Nmembers)) allocate(phase_mechanical_F(ph)%data(3,3,Nmembers)) allocate(phase_mechanical_Li(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_Li0(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_Lp(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_Lp0(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_S(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_P(ph)%data(3,3,Nmembers),source=0.0_pREAL) allocate(phase_mechanical_S0(ph)%data(3,3,Nmembers),source=0.0_pREAL) phase => phases%get_dict(ph) mech => phase%get_dict('mechanical') #if defined(__GFORTRAN__) output_mechanical(ph)%label = output_as1dStr(mech) #else output_mechanical(ph)%label = mech%get_as1dStr('output',defaultVal=emptyStrArray) #endif end do do ce = 1, size(material_ID_phase,2) ma = discretization_materialAt((ce-1)/discretization_nIPs+1) do co = 1,homogenization_Nconstituents(material_ID_homogenization(ce)) ph = material_ID_phase(co,ce) en = material_entry_phase(co,ce) phase_mechanical_F(ph)%data(1:3,1:3,en) = math_I3 phase_mechanical_Fp(ph)%data(1:3,1:3,en) = material_O_0(ma)%data(co)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005) phase_mechanical_Fe(ph)%data(1:3,1:3,en) = matmul(material_V_e_0(ma)%data(1:3,1:3,co), & transpose(phase_mechanical_Fp(ph)%data(1:3,1:3,en))) phase_mechanical_Fi(ph)%data(1:3,1:3,en) = material_O_0(ma)%data(co)%rotate(math_inv33(material_V_e_0(ma)%data(1:3,1:3,co))) end do end do do ph = 1, phases%length phase_mechanical_F0(ph)%data = phase_mechanical_F(ph)%data phase_mechanical_Fp0(ph)%data = phase_mechanical_Fp(ph)%data phase_mechanical_Fi0(ph)%data = phase_mechanical_Fi(ph)%data end do call elastic_init(phases) allocate(plasticState(phases%length)) allocate(phase_plasticity(phases%length),source = PLASTIC_UNDEFINED_ID) call plastic_init() do ph = 1,phases%length plasticState(ph)%state0 = plasticState(ph)%state end do num_mech_plastic => num_mech%get_dict('plastic', defaultVal=emptyDict) num_mech_eigen => num_mech%get_dict('eigen', defaultVal=emptyDict) num%subStepMinCryst = num_mech%get_asReal ('sub_step_min', defaultVal=1.0e-3_pREAL) num%subStepSizeCryst = num_mech%get_asReal ('sub_step_size', defaultVal=0.25_pREAL) num%stepIncreaseCryst = num_mech%get_asReal ('step_increase', defaultVal=1.5_pREAL) num%rtol_crystalliteState = num_mech%get_asReal ('eps_rel_state', defaultVal=1.0e-6_pREAL) num%nState = num_mech%get_asInt ('N_iter_state_max', defaultVal=20) num%nStress = num_mech%get_asInt ('N_iter_stress_max', defaultVal=40) num%subStepSizeLp = num_mech_plastic%get_asReal ('sub_step_size_Lp', defaultVal=0.5_pREAL) num%rtol_Lp = num_mech_plastic%get_asReal ('eps_rel_Lp', defaultVal=1.0e-6_pREAL) num%atol_Lp = num_mech_plastic%get_asReal ('eps_abs_Lp', defaultVal=1.0e-8_pREAL) num%iJacoLpresiduum = num_mech_plastic%get_asInt ('f_update_jacobi_Lp', defaultVal=1) num%subStepSizeLi = num_mech_eigen%get_asReal ('sub_step_size_Li', defaultVal=0.5_pREAL) num%rtol_Li = num_mech_eigen%get_asReal ('eps_rel_Li', defaultVal=num%rtol_Lp) num%atol_Li = num_mech_eigen%get_asReal ('eps_abs_Li', defaultVal=num%atol_Lp) num%iJacoLiresiduum = num_mech_eigen%get_asInt ('f_update_jacobi_Li', defaultVal=num%iJacoLpresiduum) extmsg = '' if (num%subStepMinCryst <= 0.0_pREAL) extmsg = trim(extmsg)//' sub_step_min' if (num%subStepSizeCryst <= 0.0_pREAL) extmsg = trim(extmsg)//' sub_step_size' if (num%stepIncreaseCryst <= 0.0_pREAL) extmsg = trim(extmsg)//' step_increase' if (num%subStepSizeLp <= 0.0_pREAL) extmsg = trim(extmsg)//' sub_step_size_Lp' if (num%subStepSizeLi <= 0.0_pREAL) extmsg = trim(extmsg)//' sub_step_size_Li' if (num%rtol_Lp <= 0.0_pREAL) extmsg = trim(extmsg)//' epl_rel_Lp' if (num%atol_Lp <= 0.0_pREAL) extmsg = trim(extmsg)//' eps_abs_Lp' if (num%rtol_Li <= 0.0_pREAL) extmsg = trim(extmsg)//' eps_rel_Li' if (num%atol_Li <= 0.0_pREAL) extmsg = trim(extmsg)//' eps_abs_Li' if (num%iJacoLpresiduum < 1) extmsg = trim(extmsg)//' f_jacobi_residuum_update_Lp' if (num%iJacoLiresiduum < 1) extmsg = trim(extmsg)//' f_jacobi_residuum_update_Li' if (num%nState < 1) extmsg = trim(extmsg)//' N_iter_state_max' if (num%nStress < 1) extmsg = trim(extmsg)//' N_iter_stress_max' if (extmsg /= '') call IO_error(301,ext_msg=trim(extmsg)) select case(num_mech_plastic%get_asStr('integrator_state',defaultVal='FPI')) case('FPI') integrateState => integrateStateFPI case('Euler') integrateState => integrateStateEuler case('AdaptiveEuler') integrateState => integrateStateAdaptiveEuler case('RK4') integrateState => integrateStateRK4 case('RKCK45') integrateState => integrateStateRKCK45 case default call IO_error(301,ext_msg='integrator') end select call eigen_init(phases) end subroutine mechanical_init module subroutine mechanical_result(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph call results(group,ph) select case(phase_plasticity(ph)) case(PLASTIC_ISOTROPIC_ID) call plastic_isotropic_result(ph,group//'mechanical/') case(PLASTIC_PHENOPOWERLAW_ID) call plastic_phenopowerlaw_result(ph,group//'mechanical/') case(PLASTIC_KINEHARDENING_ID) call plastic_kinehardening_result(ph,group//'mechanical/') case(PLASTIC_DISLOTWIN_ID) call plastic_dislotwin_result(ph,group//'mechanical/') case(PLASTIC_DISLOTUNGSTEN_ID) call plastic_dislotungsten_result(ph,group//'mechanical/') case(PLASTIC_NONLOCAL_ID) call plastic_nonlocal_result(ph,group//'mechanical/') end select end subroutine mechanical_result !-------------------------------------------------------------------------------------------------- !> @brief calculation of stress (P) with time integration based on a residuum in Lp and !> intermediate acceleration of the Newton-Raphson correction !-------------------------------------------------------------------------------------------------- function integrateStress(F,subFp0,subFi0,Delta_t,ph,en) result(broken) real(pREAL), dimension(3,3), intent(in) :: F,subFp0,subFi0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: ph, en real(pREAL), dimension(3,3):: 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, & atol_Lp, & atol_Li integer NiterationStressLp, & ! number of stress integrations NiterationStressLi, & ! number of inner stress integrations ierr, & ! error indicator for LAPACK o, & p, & jacoCounterLp, & jacoCounterLi ! counters to check for Jacobian update logical :: error,broken broken = .true. call plastic_dependentState(ph,en) Lpguess = phase_mechanical_Lp(ph)%data(1:3,1:3,en) ! take as first guess Liguess = phase_mechanical_Li(ph)%data(1:3,1:3,en) ! take as first guess call math_invert33(invFp_current,error=error,A=subFp0) if (error) return ! error call math_invert33(invFi_current,error=error,A=subFi0) 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 - Delta_t*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 - Delta_t*Lpguess Fe = matmul(matmul(A,B), invFi_new) call phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi_new, ph, en) call plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, & S, Fi_new, ph,en) !* update current residuum and check for convergence of loop atol_Lp = max(num%rtol_Lp * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_Lp) ! 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 end if calculateJacobiLp: 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) = - Delta_t * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -Delta_t * A(i,k) invFi(l,j) end do; end do 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) end if calculateJacobiLp Lpguess = Lpguess & + deltaLp * steplengthLp end do LpLoop call phase_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, & S, Fi_new, ph,en) !* update current residuum and check for convergence of loop atol_Li = max(num%rtol_Li * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error num%atol_Li) ! 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 end if calculateJacobiLi: if (mod(jacoCounterLi, num%iJacoLiresiduum) == 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) = -Delta_t*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -Delta_t * A(i,k) invFi(l,j) dFi_dLi(1:3,o,1:3,p) = -Delta_t*math_I3(o,p)*invFi_current end do; end do 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) end do; end do 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) end if calculateJacobiLi Liguess = Liguess & + deltaLi * steplengthLi end do LiLoop invFp_new = matmul(invFp_current,B) call math_invert33(Fp_new,error=error,A=invFp_new) if (error) return ! error phase_mechanical_P(ph)%data(1:3,1:3,en) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new))) phase_mechanical_S(ph)%data(1:3,1:3,en) = S phase_mechanical_Lp(ph)%data(1:3,1:3,en) = Lpguess phase_mechanical_Li(ph)%data(1:3,1:3,en) = Liguess phase_mechanical_Fp(ph)%data(1:3,1:3,en) = Fp_new / math_det33(Fp_new)**(1.0_pREAL/3.0_pREAL) ! regularize phase_mechanical_Fi(ph)%data(1:3,1:3,en) = Fi_new phase_mechanical_Fe(ph)%data(1:3,1:3,en) = 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 !-------------------------------------------------------------------------------------------------- function integrateStateFPI(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: & ph, & en logical :: & broken integer :: & NiterationState, & !< number of iterations in state loop sizeDotState real(pREAL) :: & zeta real(pREAL), dimension(plasticState(ph)%sizeDotState) :: & r, & ! state residuum dotState real(pREAL), dimension(plasticState(ph)%sizeDotState,2) :: & dotState_last broken = .true. dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) return sizeDotState = plasticState(ph)%sizeDotState plasticState(ph)%state(1:sizeDotState,en) = subState0 + dotState * Delta_t iteration: do NiterationState = 1, num%nState dotState_last(1:sizeDotState,2) = merge(dotState_last(1:sizeDotState,1),0.0_pREAL, nIterationState > 1) dotState_last(1:sizeDotState,1) = dotState broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en) if (broken) exit iteration dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) exit iteration zeta = damper(dotState,dotState_last(1:sizeDotState,1),dotState_last(1:sizeDotState,2)) dotState = dotState * zeta & + dotState_last(1:sizeDotState,1) * (1.0_pREAL - zeta) r = plasticState(ph)%state(1:sizeDotState,en) & - subState0 & - dotState * Delta_t plasticState(ph)%state(1:sizeDotState,en) = plasticState(ph)%state(1:sizeDotState,en) - r if (converged(r,plasticState(ph)%state(1:sizeDotState,en),plasticState(ph)%atol(1:sizeDotState))) then broken = plastic_deltaState(ph,en) exit iteration end if end do iteration contains !-------------------------------------------------------------------------------------------------- !> @brief calculate the damping for correction of state and dot state !-------------------------------------------------------------------------------------------------- real(pREAL) pure function damper(omega_0,omega_1,omega_2) real(pREAL), dimension(:), intent(in) :: & omega_0, omega_1, omega_2 real(pREAL) :: dot_prod12, dot_prod22 dot_prod12 = dot_product(omega_0-omega_1, omega_1-omega_2) dot_prod22 = dot_product(omega_1-omega_2, omega_1-omega_2) if (min(dot_product(omega_0,omega_1),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 end if end function damper end function integrateStateFPI !-------------------------------------------------------------------------------------------------- !> @brief integrate state with 1st order explicit Euler method !-------------------------------------------------------------------------------------------------- function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: & ph, & en !< grain index in grain loop logical :: & broken real(pREAL), dimension(plasticState(ph)%sizeDotState) :: & dotState integer :: & sizeDotState broken = .true. dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) return sizeDotState = plasticState(ph)%sizeDotState #ifndef __INTEL_LLVM_COMPILER plasticState(ph)%state(1:sizeDotState,en) = subState0 + dotState*Delta_t #else plasticState(ph)%state(1:sizeDotState,en) = IEEE_FMA(dotState,Delta_t,subState0) #endif broken = plastic_deltaState(ph,en) if (broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en) end function integrateStateEuler !-------------------------------------------------------------------------------------------------- !> @brief integrate stress, state with 1st order Euler method with adaptive step size !-------------------------------------------------------------------------------------------------- function integrateStateAdaptiveEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: & ph, & en logical :: & broken integer :: & sizeDotState real(pREAL), dimension(plasticState(ph)%sizeDotState) :: & r, & dotState broken = .true. dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) return sizeDotState = plasticState(ph)%sizeDotState r = - dotState * 0.5_pREAL * Delta_t #ifndef __INTEL_LLVM_COMPILER plasticState(ph)%state(1:sizeDotState,en) = subState0 + dotState*Delta_t #else plasticState(ph)%state(1:sizeDotState,en) = IEEE_FMA(dotState,Delta_t,subState0) #endif broken = plastic_deltaState(ph,en) if (broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en) if (broken) return dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) return broken = .not. converged(r + 0.5_pREAL * dotState * Delta_t, & plasticState(ph)%state(1:sizeDotState,en), & plasticState(ph)%atol(1:sizeDotState)) end function integrateStateAdaptiveEuler !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the classic Runge Kutta method !--------------------------------------------------------------------------------------------------- function integrateStateRK4(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: ph, en logical :: broken 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 = [6.0_pREAL, 3.0_pREAL, 3.0_pREAL, 6.0_pREAL]**(-1) broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C) end function integrateStateRK4 !--------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with the Cash-Carp method !--------------------------------------------------------------------------------------------------- function integrateStateRKCK45(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t integer, intent(in) :: ph, en logical :: broken 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] broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C,DB) end function integrateStateRKCK45 !-------------------------------------------------------------------------------------------------- !> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an !! embedded explicit Runge-Kutta method !-------------------------------------------------------------------------------------------------- function integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,ph,en,A,B,C,DB) result(broken) real(pREAL), intent(in),dimension(3,3) :: F_0,F,subFp0,subFi0 real(pREAL), intent(in),dimension(:) :: subState0 real(pREAL), intent(in) :: Delta_t real(pREAL), dimension(:,:), intent(in) :: A real(pREAL), dimension(:), intent(in) :: B, C real(pREAL), dimension(:), intent(in), optional :: DB integer, intent(in) :: & ph, & en logical :: broken integer :: & stage, & ! stage index in integration stage loop n, & sizeDotState real(pREAL), dimension(plasticState(ph)%sizeDotState) :: & dotState real(pREAL), dimension(plasticState(ph)%sizeDotState,size(B)) :: & plastic_RKdotState broken = .true. dotState = plastic_dotState(Delta_t,ph,en) if (any(IEEE_is_NaN(dotState))) return sizeDotState = plasticState(ph)%sizeDotState do stage = 1, size(A,1) plastic_RKdotState(1:sizeDotState,stage) = dotState dotState = A(1,stage) * plastic_RKdotState(1:sizeDotState,1) do n = 2, stage #ifndef __INTEL_LLVM_COMPILER dotState = dotState + A(n,stage)*plastic_RKdotState(1:sizeDotState,n) #else dotState = IEEE_FMA(A(n,stage),plastic_RKdotState(1:sizeDotState,n),dotState) #endif end do #ifndef __INTEL_LLVM_COMPILER plasticState(ph)%state(1:sizeDotState,en) = subState0 + dotState*Delta_t #else plasticState(ph)%state(1:sizeDotState,en) = IEEE_FMA(dotState,Delta_t,subState0) #endif broken = integrateStress(F_0+(F-F_0)*Delta_t*C(stage),subFp0,subFi0,Delta_t*C(stage), ph,en) if (broken) exit dotState = plastic_dotState(Delta_t*C(stage), ph,en) if (any(IEEE_is_NaN(dotState))) exit end do if (broken) return plastic_RKdotState(1:sizeDotState,size(B)) = dotState dotState = matmul(plastic_RKdotState,B) #ifndef __INTEL_LLVM_COMPILER plasticState(ph)%state(1:sizeDotState,en) = subState0 + dotState*Delta_t #else plasticState(ph)%state(1:sizeDotState,en) = IEEE_FMA(dotState,Delta_t,subState0) #endif if (present(DB)) & broken = .not. converged(matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) * Delta_t, & plasticState(ph)%state(1:sizeDotState,en), & plasticState(ph)%atol(1:sizeDotState)) if (broken) return broken = plastic_deltaState(ph,en) if (broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,ph,en) end function integrateStateRK !-------------------------------------------------------------------------------------------------- !> @brief Write mechanical results to HDF5 output file. !-------------------------------------------------------------------------------------------------- subroutine results(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph integer :: ou call result_closeGroup(result_addGroup(group//'/mechanical')) do ou = 1, size(output_mechanical(ph)%label) select case (output_mechanical(ph)%label(ou)) case('F') call result_writeDataset(phase_mechanical_F(ph)%data,group//'/mechanical/','F',& 'deformation gradient','1') case('F_e') call result_writeDataset(phase_mechanical_Fe(ph)%data,group//'/mechanical/','F_e',& 'elastic deformation gradient','1') case('F_p') call result_writeDataset(phase_mechanical_Fp(ph)%data,group//'/mechanical/','F_p', & 'plastic deformation gradient','1') case('F_i') call result_writeDataset(phase_mechanical_Fi(ph)%data,group//'/mechanical/','F_i', & 'inelastic deformation gradient','1') case('L_p') call result_writeDataset(phase_mechanical_Lp(ph)%data,group//'/mechanical/','L_p', & 'plastic velocity gradient','1/s') case('L_i') call result_writeDataset(phase_mechanical_Li(ph)%data,group//'/mechanical/','L_i', & 'inelastic velocity gradient','1/s') case('P') call result_writeDataset(phase_mechanical_P(ph)%data,group//'/mechanical/','P', & 'first Piola-Kirchhoff stress','Pa') case('S') call result_writeDataset(phase_mechanical_S(ph)%data,group//'/mechanical/','S', & 'second Piola-Kirchhoff stress','Pa') case('O') call result_writeDataset(to_quaternion(phase_O(ph)%data),group//'/mechanical','O', & 'crystal orientation as quaternion q_0 (q_1 q_2 q_3)','1') call result_addAttribute('lattice',phase_lattice(ph),group//'/mechanical/O') if (any(phase_lattice(ph) == ['hP', 'tI'])) & call result_addAttribute('c/a',phase_cOverA(ph),group//'/mechanical/O') end select end do contains !-------------------------------------------------------------------------------------------------- !> @brief Convert orientation array to quaternion array !-------------------------------------------------------------------------------------------------- function to_quaternion(dataset) type(tRotation), dimension(:), intent(in) :: dataset real(pREAL), dimension(4,size(dataset,1)) :: to_quaternion integer :: i do i = 1, size(dataset,1) to_quaternion(:,i) = dataset(i)%asQuaternion() end do end function to_quaternion end subroutine results !-------------------------------------------------------------------------------------------------- !> @brief Forward data after successful increment. ! ToDo: Any guessing for the current states possible? !-------------------------------------------------------------------------------------------------- module subroutine mechanical_forward() integer :: ph do ph = 1, size(plasticState) phase_mechanical_Fi0(ph) = phase_mechanical_Fi(ph) phase_mechanical_Fp0(ph) = phase_mechanical_Fp(ph) phase_mechanical_F0(ph) = phase_mechanical_F(ph) phase_mechanical_Li0(ph) = phase_mechanical_Li(ph) phase_mechanical_Lp0(ph) = phase_mechanical_Lp(ph) phase_mechanical_S0(ph) = phase_mechanical_S(ph) plasticState(ph)%state0 = plasticState(ph)%state end do end subroutine mechanical_forward !-------------------------------------------------------------------------------------------------- !> @brief calculate stress (P) !-------------------------------------------------------------------------------------------------- module function phase_mechanical_constitutive(Delta_t,co,ce) result(converged_) real(pREAL), intent(in) :: Delta_t integer, intent(in) :: & co, & ce logical :: converged_ real(pREAL) :: & formerSubStep integer :: & ph, en, sizeDotState logical :: todo real(pREAL) :: subFrac,subStep real(pREAL), dimension(3,3) :: & subFp0, & subFi0, & subLp0, & subLi0, & subF0, & subF real(pREAL), dimension(plasticState(material_ID_phase(co,ce))%sizeState) :: subState0 ph = material_ID_phase(co,ce) en = material_entry_phase(co,ce) subState0 = plasticState(ph)%state0(:,en) subLi0 = phase_mechanical_Li0(ph)%data(1:3,1:3,en) subLp0 = phase_mechanical_Lp0(ph)%data(1:3,1:3,en) subFp0 = phase_mechanical_Fp0(ph)%data(1:3,1:3,en) subFi0 = phase_mechanical_Fi0(ph)%data(1:3,1:3,en) subF0 = phase_mechanical_F0(ph)%data(1:3,1:3,en) subFrac = 0.0_pREAL todo = .true. subStep = 1.0_pREAL/num%subStepSizeCryst converged_ = .false. ! pretend failed step of 1/subStepSizeCryst todo = .true. cutbackLooping: do while (todo) if (converged_) then formerSubStep = subStep subFrac = subFrac + subStep subStep = min(1.0_pREAL - subFrac, num%stepIncreaseCryst * subStep) todo = subStep > 0.0_pREAL ! still time left to integrate on? if (todo) then subF0 = subF subLp0 = phase_mechanical_Lp(ph)%data(1:3,1:3,en) subLi0 = phase_mechanical_Li(ph)%data(1:3,1:3,en) subFp0 = phase_mechanical_Fp(ph)%data(1:3,1:3,en) subFi0 = phase_mechanical_Fi(ph)%data(1:3,1:3,en) subState0 = plasticState(ph)%state(:,en) end if !-------------------------------------------------------------------------------------------------- ! cut back (reduced time and restore) else subStep = num%subStepSizeCryst * subStep phase_mechanical_Fp(ph)%data(1:3,1:3,en) = subFp0 phase_mechanical_Fi(ph)%data(1:3,1:3,en) = subFi0 phase_mechanical_S(ph)%data(1:3,1:3,en) = phase_mechanical_S0(ph)%data(1:3,1:3,en) if (subStep < 1.0_pREAL) then ! actual (not initial) cutback phase_mechanical_Lp(ph)%data(1:3,1:3,en) = subLp0 phase_mechanical_Li(ph)%data(1:3,1:3,en) = subLi0 end if plasticState(ph)%state(:,en) = subState0 todo = subStep > num%subStepMinCryst ! still on track or already done (beyond repair) end if !-------------------------------------------------------------------------------------------------- ! prepare for integration if (todo) then sizeDotState = plasticState(ph)%sizeDotState subF = subF0 & + subStep * (phase_mechanical_F(ph)%data(1:3,1:3,en) - phase_mechanical_F0(ph)%data(1:3,1:3,en)) converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * Delta_t,ph,en) end if end do cutbackLooping end function phase_mechanical_constitutive !-------------------------------------------------------------------------------------------------- !> @brief Restore data after homog cutback. !-------------------------------------------------------------------------------------------------- module subroutine mechanical_restore(ce,includeL) integer, intent(in) :: ce logical, intent(in) :: & includeL !< protect agains fake cutback integer :: & co, ph, en do co = 1,homogenization_Nconstituents(material_ID_homogenization(ce)) ph = material_ID_phase(co,ce) en = material_entry_phase(co,ce) if (includeL) then phase_mechanical_Lp(ph)%data(1:3,1:3,en) = phase_mechanical_Lp0(ph)%data(1:3,1:3,en) phase_mechanical_Li(ph)%data(1:3,1:3,en) = phase_mechanical_Li0(ph)%data(1:3,1:3,en) end if ! maybe protecting everything from overwriting makes more sense phase_mechanical_Fp(ph)%data(1:3,1:3,en) = phase_mechanical_Fp0(ph)%data(1:3,1:3,en) phase_mechanical_Fi(ph)%data(1:3,1:3,en) = phase_mechanical_Fi0(ph)%data(1:3,1:3,en) phase_mechanical_S(ph)%data(1:3,1:3,en) = phase_mechanical_S0(ph)%data(1:3,1:3,en) plasticState(ph)%state(:,en) = plasticState(ph)%State0(:,en) end do end subroutine mechanical_restore !-------------------------------------------------------------------------------------------------- !> @brief Calculate tangent (dPdF). !-------------------------------------------------------------------------------------------------- module function phase_mechanical_dPdF(Delta_t,co,ce) result(dPdF) real(pREAL), intent(in) :: Delta_t integer, intent(in) :: & co, & !< counter in constituent loop ce real(pREAL), dimension(3,3,3,3) :: dPdF integer :: & o, & p, ph, en real(pREAL), dimension(3,3) :: devNull, & invSubFp0,invSubFi0,invFp,invFi, & temp_33_1, temp_33_2, temp_33_3 real(pREAL), dimension(3,3,3,3) :: dSdFe, & dSdF, & dSdFi, & dLidS, & ! tangent in lattice configuration dLidFi, & dLpdS, & dLpdFi, & dFidS, & dFpinvdF, & rhs_3333, & lhs_3333, & temp_3333 real(pREAL), dimension(9,9):: temp_99 logical :: error ph = material_ID_phase(co,ce) en = material_entry_phase(co,ce) call phase_hooke_SandItsTangents(devNull,dSdFe,dSdFi, & phase_mechanical_Fe(ph)%data(1:3,1:3,en), & phase_mechanical_Fi(ph)%data(1:3,1:3,en),ph,en) call phase_LiAndItsTangents(devNull,dLidS,dLidFi, & phase_mechanical_S(ph)%data(1:3,1:3,en), & phase_mechanical_Fi(ph)%data(1:3,1:3,en), & ph,en) invFp = math_inv33(phase_mechanical_Fp(ph)%data(1:3,1:3,en)) invFi = math_inv33(phase_mechanical_Fi(ph)%data(1:3,1:3,en)) invSubFp0 = math_inv33(phase_mechanical_Fp0(ph)%data(1:3,1:3,en)) invSubFi0 = math_inv33(phase_mechanical_Fi0(ph)%data(1:3,1:3,en)) if (sum(abs(dLidS)) < tol_math_check) then dFidS = 0.0_pREAL else lhs_3333 = 0.0_pREAL; rhs_3333 = 0.0_pREAL do o=1,3; do p=1,3 #ifndef __INTEL_LLVM_COMPILER lhs_3333(1:3,1:3,o,p) = lhs_3333(1:3,1:3,o,p) & + matmul(invSubFi0,dLidFi(1:3,1:3,o,p)) * Delta_t lhs_3333(1:3,o,1:3,p) = lhs_3333(1:3,o,1:3,p) & + invFi*invFi(p,o) rhs_3333(1:3,1:3,o,p) = rhs_3333(1:3,1:3,o,p) & - matmul(invSubFi0,dLidS(1:3,1:3,o,p)) * Delta_t #else lhs_3333(1:3,1:3,o,p) = IEEE_FMA(matmul(invSubFi0,dLidFi(1:3,1:3,o,p)),Delta_t,lhs_3333(1:3,1:3,o,p)) lhs_3333(1:3,o,1:3,p) = IEEE_FMA(invFi,invFi(p,o),lhs_3333(1:3,o,1:3,p)) rhs_3333(1:3,1:3,o,p) = IEEE_FMA(matmul(invSubFi0,dLidS(1:3,1:3,o,p)),-Delta_t,rhs_3333(1:3,1:3,o,p)) #endif end do; end do call math_invert(temp_99,error,math_3333to99(lhs_3333)) if (error) then call IO_warning(600,'inversion error in analytic tangent calculation', & label1='phase',ID1=ph,label2='entry',ID2=en) dFidS = 0.0_pREAL else dFidS = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) end if dLidS = math_mul3333xx3333(dLidFi,dFidS) + dLidS end if call plastic_LpAndItsTangents(devNull,dLpdS,dLpdFi, & phase_mechanical_S(ph)%data(1:3,1:3,en), & phase_mechanical_Fi(ph)%data(1:3,1:3,en),ph,en) dLpdS = math_mul3333xx3333(dLpdFi,dFidS) + dLpdS !-------------------------------------------------------------------------------------------------- ! calculate dSdF temp_33_1 = transpose(matmul(invFp,invFi)) temp_33_2 = matmul(phase_mechanical_F(ph)%data(1:3,1:3,en),invSubFp0) temp_33_3 = matmul(matmul(phase_mechanical_F(ph)%data(1:3,1:3,en),invFp), invSubFi0) do o=1,3; do p=1,3 rhs_3333(p,o,1:3,1:3) = matmul(dSdFe(p,o,1:3,1:3),temp_33_1) temp_3333(1:3,1:3,p,o) = matmul(matmul(temp_33_2,dLpdS(1:3,1:3,p,o)), invFi) & + matmul(temp_33_3,dLidS(1:3,1:3,p,o)) end do; end do #ifndef __INTEL_LLVM_COMPILER lhs_3333 = math_mul3333xx3333(dSdFe,temp_3333) * Delta_t & + math_mul3333xx3333(dSdFi,dFidS) #else lhs_3333 = IEEE_FMA(math_mul3333xx3333(dSdFe,temp_3333),Delta_t,math_mul3333xx3333(dSdFi,dFidS)) #endif call math_invert(temp_99,error,math_eye(9)+math_3333to99(lhs_3333)) if (error) then call IO_warning(600,'inversion error in analytic tangent calculation', & label1='phase',ID1=ph,label2='entry',ID2=en) dSdF = rhs_3333 else dSdF = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) end if !-------------------------------------------------------------------------------------------------- ! calculate dFpinvdF temp_3333 = math_mul3333xx3333(dLpdS,dSdF) do o=1,3; do p=1,3 dFpinvdF(1:3,1:3,p,o) = - matmul(invSubFp0, matmul(temp_3333(1:3,1:3,p,o),invFi)) * Delta_t end do; end do !-------------------------------------------------------------------------------------------------- ! assemble dPdF temp_33_1 = matmul(phase_mechanical_S(ph)%data(1:3,1:3,en),transpose(invFp)) temp_33_2 = matmul(phase_mechanical_F(ph)%data(1:3,1:3,en),invFp) temp_33_3 = matmul(temp_33_2,phase_mechanical_S(ph)%data(1:3,1:3,en)) dPdF = 0.0_pREAL do p=1,3 dPdF(p,1:3,p,1:3) = transpose(matmul(invFp,temp_33_1)) end do do o=1,3; do p=1,3 dPdF(1:3,1:3,p,o) = dPdF(1:3,1:3,p,o) & + matmul(matmul(phase_mechanical_F(ph)%data(1:3,1:3,en),dFpinvdF(1:3,1:3,p,o)),temp_33_1) & + matmul(matmul(temp_33_2,dSdF(1:3,1:3,p,o)),transpose(invFp)) & + matmul(temp_33_3,transpose(dFpinvdF(1:3,1:3,p,o))) end do; end do end function phase_mechanical_dPdF !-------------------------------------------------------------------------------------------------- !< @brief Write restart information to file. !-------------------------------------------------------------------------------------------------- module subroutine mechanical_restartWrite(groupHandle,ph) integer(HID_T), intent(in) :: groupHandle integer, intent(in) :: ph call HDF5_write(plasticState(ph)%state,groupHandle,'omega_plastic') call HDF5_write(phase_mechanical_S(ph)%data,groupHandle,'S') call HDF5_write(phase_mechanical_F(ph)%data,groupHandle,'F') call HDF5_write(phase_mechanical_Fp(ph)%data,groupHandle,'F_p') call HDF5_write(phase_mechanical_Fi(ph)%data,groupHandle,'F_i') call HDF5_write(phase_mechanical_Lp(ph)%data,groupHandle,'L_p') call HDF5_write(phase_mechanical_Li(ph)%data,groupHandle,'L_i') end subroutine mechanical_restartWrite !-------------------------------------------------------------------------------------------------- !< @brief Read restart information from file. !-------------------------------------------------------------------------------------------------- module subroutine mechanical_restartRead(groupHandle,ph) integer(HID_T), intent(in) :: groupHandle integer, intent(in) :: ph call HDF5_read(plasticState(ph)%state0,groupHandle,'omega_plastic') call HDF5_read(phase_mechanical_S0(ph)%data,groupHandle,'S') call HDF5_read(phase_mechanical_F0(ph)%data,groupHandle,'F') call HDF5_read(phase_mechanical_Fp0(ph)%data,groupHandle,'F_p') call HDF5_read(phase_mechanical_Fi0(ph)%data,groupHandle,'F_i') call HDF5_read(phase_mechanical_Lp0(ph)%data,groupHandle,'L_p') call HDF5_read(phase_mechanical_Li0(ph)%data,groupHandle,'L_i') end subroutine mechanical_restartRead !-------------------------------------------------------------------------------------------------- !< @brief Get first Piola-Kirchhoff stress (for use by non-mech physics). !-------------------------------------------------------------------------------------------------- module function mechanical_S(ph,en) result(S) integer, intent(in) :: ph,en real(pREAL), dimension(3,3) :: S S = phase_mechanical_S(ph)%data(1:3,1:3,en) end function mechanical_S !-------------------------------------------------------------------------------------------------- !< @brief Get plastic velocity gradient (for use by non-mech physics). !-------------------------------------------------------------------------------------------------- module function mechanical_L_p(ph,en) result(L_p) integer, intent(in) :: ph,en real(pREAL), dimension(3,3) :: L_p L_p = phase_mechanical_Lp(ph)%data(1:3,1:3,en) end function mechanical_L_p !-------------------------------------------------------------------------------------------------- !< @brief Get elastic deformation gradient (for use by non-mech physics). !-------------------------------------------------------------------------------------------------- module function mechanical_F_e(ph,en) result(F_e) integer, intent(in) :: ph,en real(pREAL), dimension(3,3) :: F_e F_e = phase_mechanical_Fe(ph)%data(1:3,1:3,en) end function mechanical_F_e !-------------------------------------------------------------------------------------------------- !< @brief Get eigen deformation gradient (for use by non-mech physics). !-------------------------------------------------------------------------------------------------- module function mechanical_F_i(ph,en) result(F_i) integer, intent(in) :: ph,en real(pREAL), dimension(3,3) :: F_i F_i = phase_mechanical_Fi(ph)%data(1:3,1:3,en) end function mechanical_F_i !-------------------------------------------------------------------------------------------------- !< @brief Get second Piola-Kirchhoff stress (for use by homogenization). !-------------------------------------------------------------------------------------------------- module function phase_P(co,ce) result(P) integer, intent(in) :: co, ce real(pREAL), dimension(3,3) :: P P = phase_mechanical_P(material_ID_phase(co,ce))%data(1:3,1:3,material_entry_phase(co,ce)) end function phase_P !-------------------------------------------------------------------------------------------------- !< @brief Get deformation gradient (for use by homogenization). !-------------------------------------------------------------------------------------------------- module function phase_F(co,ce) result(F) integer, intent(in) :: co, ce real(pREAL), dimension(3,3) :: F F = phase_mechanical_F(material_ID_phase(co,ce))%data(1:3,1:3,material_entry_phase(co,ce)) end function phase_F !-------------------------------------------------------------------------------------------------- !< @brief Set deformation gradient (for use by homogenization). !-------------------------------------------------------------------------------------------------- module subroutine phase_set_F(F,co,ce) real(pREAL), dimension(3,3), intent(in) :: F integer, intent(in) :: co, ce phase_mechanical_F(material_ID_phase(co,ce))%data(1:3,1:3,material_entry_phase(co,ce)) = F end subroutine phase_set_F end submodule mechanical