!---------------------------------------------------------------------------------------------------- !> @brief internal microstructure state for all plasticity constitutive models !---------------------------------------------------------------------------------------------------- submodule(phase) mechanics enum, bind(c); enumerator :: & ELASTICITY_UNDEFINED_ID, & ELASTICITY_HOOKE_ID, & STIFFNESS_DEGRADATION_UNDEFINED_ID, & STIFFNESS_DEGRADATION_DAMAGE_ID, & PLASTICITY_UNDEFINED_ID, & PLASTICITY_NONE_ID, & PLASTICITY_ISOTROPIC_ID, & PLASTICITY_PHENOPOWERLAW_ID, & PLASTICITY_KINEHARDENING_ID, & PLASTICITY_DISLOTWIN_ID, & PLASTICITY_DISLOTUNGSTEN_ID, & PLASTICITY_NONLOCAL_ID, & KINEMATICS_UNDEFINED_ID, & KINEMATICS_CLEAVAGE_OPENING_ID, & KINEMATICS_SLIPPLANE_OPENING_ID, & KINEMATICS_THERMAL_EXPANSION_ID end enum integer(kind(KINEMATICS_UNDEFINED_ID)), dimension(:,:), allocatable :: & phase_kinematics integer(kind(ELASTICITY_UNDEFINED_ID)), dimension(:), allocatable :: & phase_elasticity !< elasticity of each phase integer(kind(STIFFNESS_DEGRADATION_UNDEFINED_ID)), dimension(:,:), allocatable :: & phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase 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(PLASTICITY_undefined_ID)), dimension(:), allocatable :: & phase_plasticity !< plasticity of each phase interface module subroutine eigendeformation_init(phases) class(tNode), pointer :: phases end subroutine eigendeformation_init module subroutine plastic_init end subroutine plastic_init module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,instance,me) real(pReal), dimension(3,3), intent(out) :: & Li !< inleastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLi_dMi !< derivative of Li with respect to Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mi !< Mandel stress integer, intent(in) :: & instance, & me end subroutine plastic_isotropic_LiAndItsTangent module function plastic_dotState(subdt,co,ip,el,ph,me) result(broken) integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el, & !< element ph, & me real(pReal), intent(in) :: & subdt !< timestep logical :: broken end function plastic_dotState module function plastic_deltaState(co, ip, el, ph, me) result(broken) integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el, & !< element ph, & me logical :: & broken end function plastic_deltaState module subroutine phase_LiAndItsTangents(Li, dLi_dS, dLi_dFi, & S, Fi, ph,me) integer, intent(in) :: & ph,me 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, co, ip, el) integer, intent(in) :: & co, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), intent(in), dimension(3,3) :: & S, & !< 2nd Piola-Kirchhoff stress Fi !< intermediate deformation gradient real(pReal), intent(out), dimension(3,3) :: & Lp !< plastic velocity gradient real(pReal), intent(out), dimension(3,3,3,3) :: & dLp_dS, & dLp_dFi !< derivative of Lp with respect to Fi end subroutine plastic_LpAndItsTangents 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 module function plastic_dislotwin_homogenizedC(ph,me) result(homogenizedC) real(pReal), dimension(6,6) :: homogenizedC integer, intent(in) :: ph,me end function plastic_dislotwin_homogenizedC end interface type :: tOutput !< new requested output (per phase) character(len=pStringLen), allocatable, dimension(:) :: & label end type tOutput type(tOutput), allocatable, dimension(:) :: output_constituent 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) class(tNode), pointer :: & phases integer :: & el, & ip, & co, & ph, & me, & stiffDegradationCtr, & Nconstituents class(tNode), pointer :: & num_crystallite, & phase, & mech, & elastic, & stiffDegradation print'(/,a)', ' <<<+- phase:mechanics init -+>>>' !------------------------------------------------------------------------------------------------- ! initialize elasticity (hooke) !ToDO: Maybe move to elastic submodule along with function homogenizedC? allocate(phase_elasticity(phases%length), source = ELASTICITY_undefined_ID) allocate(phase_elasticityInstance(phases%length), source = 0) allocate(phase_NstiffnessDegradations(phases%length),source=0) allocate(output_constituent(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_Lp0(phases%length)) allocate(phase_mechanical_Lp(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 Nconstituents = count(material_phaseAt == ph) * discretization_nIPs allocate(phase_mechanical_Fi(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Fe(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Fi0(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Fp(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Fp0(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Li(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Li0(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Lp0(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_Lp(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_S(ph)%data(3,3,Nconstituents),source=0.0_pReal) allocate(phase_mechanical_P(ph)%data(3,3,Nconstituents),source=0.0_pReal) allocate(phase_mechanical_S0(ph)%data(3,3,Nconstituents),source=0.0_pReal) allocate(phase_mechanical_F(ph)%data(3,3,Nconstituents)) allocate(phase_mechanical_F0(ph)%data(3,3,Nconstituents)) phase => phases%get(ph) mech => phase%get('mechanics') #if defined(__GFORTRAN__) output_constituent(ph)%label = output_asStrings(mech) #else output_constituent(ph)%label = mech%get_asStrings('output',defaultVal=emptyStringArray) #endif elastic => mech%get('elasticity') if(elastic%get_asString('type') == 'hooke') then phase_elasticity(ph) = 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(ph) = stiffDegradation%length enddo allocate(phase_stiffnessDegradation(maxval(phase_NstiffnessDegradations),phases%length), & source=STIFFNESS_DEGRADATION_undefined_ID) if(maxVal(phase_NstiffnessDegradations)/=0) then do ph = 1, phases%length phase => phases%get(ph) 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,ph) = STIFFNESS_DEGRADATION_damage_ID enddo enddo endif !$OMP PARALLEL DO PRIVATE(ph,me) do el = 1, size(material_phaseMemberAt,3); do ip = 1, size(material_phaseMemberAt,2) do co = 1, homogenization_Nconstituents(material_homogenizationAt(el)) ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) phase_mechanical_Fp0(ph)%data(1:3,1:3,me) = material_orientation0(co,ip,el)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005) phase_mechanical_Fp0(ph)%data(1:3,1:3,me) = phase_mechanical_Fp0(ph)%data(1:3,1:3,me) & / math_det33(phase_mechanical_Fp0(ph)%data(1:3,1:3,me))**(1.0_pReal/3.0_pReal) phase_mechanical_Fi0(ph)%data(1:3,1:3,me) = math_I3 phase_mechanical_F0(ph)%data(1:3,1:3,me) = math_I3 phase_mechanical_Fe(ph)%data(1:3,1:3,me) = math_inv33(matmul(phase_mechanical_Fi0(ph)%data(1:3,1:3,me), & phase_mechanical_Fp0(ph)%data(1:3,1:3,me))) ! assuming that euler angles are given in internal strain free configuration phase_mechanical_Fp(ph)%data(1:3,1:3,me) = phase_mechanical_Fp0(ph)%data(1:3,1:3,me) phase_mechanical_Fi(ph)%data(1:3,1:3,me) = phase_mechanical_Fi0(ph)%data(1:3,1:3,me) phase_mechanical_F(ph)%data(1:3,1:3,me) = phase_mechanical_F0(ph)%data(1:3,1:3,me) enddo enddo; enddo !$OMP END PARALLEL DO ! initialize plasticity allocate(plasticState(phases%length)) allocate(phase_plasticity(phases%length),source = PLASTICITY_undefined_ID) allocate(phase_plasticInstance(phases%length),source = 0) allocate(phase_localPlasticity(phases%length), source=.true.) call plastic_init() do ph = 1, phases%length phase_elasticityInstance(ph) = count(phase_elasticity(1:ph) == phase_elasticity(ph)) phase_plasticInstance(ph) = count(phase_plasticity(1:ph) == phase_plasticity(ph)) enddo num_crystallite => config_numerics%get('crystallite',defaultVal=emptyDict) select case(num_crystallite%get_asString('integrator',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 eigendeformation_init(phases) end subroutine mechanical_init !-------------------------------------------------------------------------------------------------- !> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to !> the elastic and intermediate deformation gradients using Hooke's law !-------------------------------------------------------------------------------------------------- subroutine phase_hooke_SandItsTangents(S, dS_dFe, dS_dFi, & Fe, Fi, co, ip, el) integer, intent(in) :: & co, & !< 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 i, j, ph, me ho = material_homogenizationAt(el) C = math_66toSym3333(phase_homogenizedC(material_phaseAt(co,el),material_phaseMemberAt(co,ip,el))) DegradationLoop: do d = 1, phase_NstiffnessDegradations(material_phaseAt(co,el)) degradationType: select case(phase_stiffnessDegradation(d,material_phaseAt(co,el))) case (STIFFNESS_DEGRADATION_damage_ID) degradationType C = C * phase_damage_get_phi(co,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 phase_hooke_SandItsTangents module subroutine mechanical_results(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph if (phase_plasticity(ph) /= PLASTICITY_NONE_ID) & call results_closeGroup(results_addGroup(group//'plastic/')) select case(phase_plasticity(ph)) case(PLASTICITY_ISOTROPIC_ID) call plastic_isotropic_results(phase_plasticInstance(ph),group//'plastic/') case(PLASTICITY_PHENOPOWERLAW_ID) call plastic_phenopowerlaw_results(phase_plasticInstance(ph),group//'plastic/') case(PLASTICITY_KINEHARDENING_ID) call plastic_kinehardening_results(phase_plasticInstance(ph),group//'plastic/') case(PLASTICITY_DISLOTWIN_ID) call plastic_dislotwin_results(phase_plasticInstance(ph),group//'plastic/') case(PLASTICITY_DISLOTUNGSTEN_ID) call plastic_dislotungsten_results(phase_plasticInstance(ph),group//'plastic/') case(PLASTICITY_NONLOCAL_ID) call plastic_nonlocal_results(phase_plasticInstance(ph),group//'plastic/') end select call crystallite_results(group,ph) end subroutine mechanical_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(F,subFp0,subFi0,Delta_t,co,ip,el) result(broken) real(pReal), dimension(3,3), intent(in) :: F,subFp0,subFi0 real(pReal), intent(in) :: Delta_t integer, intent(in):: el, & ! element index ip, & ! integration point index co ! grain index 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, & devNull integer NiterationStressLp, & ! number of stress integrations NiterationStressLi, & ! number of inner stress integrations ierr, & ! error indicator for LAPACK o, & p, & ph, & me, & jacoCounterLp, & jacoCounterLi ! counters to check for Jacobian update logical :: error,broken broken = .true. ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) call plastic_dependentState(co,ip,el) Lpguess = phase_mechanical_Lp(ph)%data(1:3,1:3,me) ! take as first guess Liguess = phase_mechanical_Li(ph)%data(1:3,1:3,me) ! take as first guess call math_invert33(invFp_current,devNull,error,subFp0) if (error) return ! error call math_invert33(invFi_current,devNull,error,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, co, ip, el) call plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, & S, Fi_new, co, 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) = - Delta_t * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -Delta_t * 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 phase_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, & S, Fi_new, ph,me) !* 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) = -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 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 phase_mechanical_P(ph)%data(1:3,1:3,me) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new))) phase_mechanical_S(ph)%data(1:3,1:3,me) = S phase_mechanical_Lp(ph)%data(1:3,1:3,me) = Lpguess phase_mechanical_Li(ph)%data(1:3,1:3,me) = Liguess phase_mechanical_Fp(ph)%data(1:3,1:3,me) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize phase_mechanical_Fi(ph)%data(1:3,1:3,me) = Fi_new phase_mechanical_Fe(ph)%data(1:3,1:3,me) = 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,co,ip,el) 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) :: & el, & !< element index in element loop ip, & !< integration point index in ip loop co !< grain index in grain loop logical :: & broken integer :: & NiterationState, & !< number of iterations in state loop ph, & me, & sizeDotState real(pReal) :: & zeta real(pReal), dimension(phase_plasticity_maxSizeDotState) :: & r ! state residuum real(pReal), dimension(phase_plasticity_maxSizeDotState,2) :: & dotState ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) broken = plastic_dotState(Delta_t, co,ip,el,ph,me) if(broken) return sizeDotState = plasticState(ph)%sizeDotState plasticState(ph)%state(1:sizeDotState,me) = subState0 & + plasticState(ph)%dotState (1:sizeDotState,me) * Delta_t dotState(1:sizeDotState,2) = 0.0_pReal iteration: do NiterationState = 1, num%nState if(nIterationState > 1) dotState(1:sizeDotState,2) = dotState(1:sizeDotState,1) dotState(1:sizeDotState,1) = plasticState(ph)%dotState(:,me) broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) if(broken) exit iteration broken = plastic_dotState(Delta_t, co,ip,el,ph,me) if(broken) exit iteration zeta = damper(plasticState(ph)%dotState(:,me),dotState(1:sizeDotState,1),& dotState(1:sizeDotState,2)) plasticState(ph)%dotState(:,me) = plasticState(ph)%dotState(:,me) * zeta & + dotState(1:sizeDotState,1) * (1.0_pReal - zeta) r(1:sizeDotState) = plasticState(ph)%state (1:sizeDotState,me) & - subState0 & - plasticState(ph)%dotState (1:sizeDotState,me) * Delta_t plasticState(ph)%state(1:sizeDotState,me) = plasticState(ph)%state(1:sizeDotState,me) & - r(1:sizeDotState) if (converged(r(1:sizeDotState),plasticState(ph)%state(1:sizeDotState,me),plasticState(ph)%atol(1:sizeDotState))) then broken = plastic_deltaState(co,ip,el,ph,me) 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 function integrateStateFPI !-------------------------------------------------------------------------------------------------- !> @brief integrate state with 1st order explicit Euler method !-------------------------------------------------------------------------------------------------- function integrateStateEuler(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el) 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) :: & el, & !< element index in element loop ip, & !< integration point index in ip loop co !< grain index in grain loop logical :: & broken integer :: & ph, & me, & sizeDotState ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) broken = plastic_dotState(Delta_t, co,ip,el,ph,me) if(broken) return sizeDotState = plasticState(ph)%sizeDotState plasticState(ph)%state(1:sizeDotState,me) = subState0 & + plasticState(ph)%dotState(1:sizeDotState,me) * Delta_t broken = plastic_deltaState(co,ip,el,ph,me) if(broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) 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,co,ip,el) 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) :: & el, & !< element index in element loop ip, & !< integration point index in ip loop co !< grain index in grain loop logical :: & broken integer :: & ph, & me, & sizeDotState real(pReal), dimension(phase_plasticity_maxSizeDotState) :: residuum_plastic ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) broken = plastic_dotState(Delta_t, co,ip,el,ph,me) if(broken) return sizeDotState = plasticState(ph)%sizeDotState residuum_plastic(1:sizeDotState) = - plasticState(ph)%dotstate(1:sizeDotState,me) * 0.5_pReal * Delta_t plasticState(ph)%state(1:sizeDotState,me) = subState0 & + plasticState(ph)%dotstate(1:sizeDotState,me) * Delta_t broken = plastic_deltaState(co,ip,el,ph,me) if(broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) if(broken) return broken = plastic_dotState(Delta_t, co,ip,el,ph,me) if(broken) return broken = .not. converged(residuum_plastic(1:sizeDotState) + 0.5_pReal * plasticState(ph)%dotState(:,me) * Delta_t, & plasticState(ph)%state(1:sizeDotState,me), & 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,co,ip,el) 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) :: co,ip,el 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 = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal] broken = integrateStateRK(F_0,F,subFp0,subFi0,subState0,Delta_t,co,ip,el,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,co,ip,el) 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) :: co,ip,el 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,co,ip,el,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,co,ip,el,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) :: & el, & !< element index in element loop ip, & !< integration point index in ip loop co !< grain index in grain loop logical :: broken integer :: & stage, & ! stage index in integration stage loop n, & ph, & me, & sizeDotState real(pReal), dimension(phase_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) broken = plastic_dotState(Delta_t,co,ip,el,ph,me) if(broken) return sizeDotState = plasticState(ph)%sizeDotState do stage = 1, size(A,1) plastic_RKdotState(1:sizeDotState,stage) = plasticState(ph)%dotState(:,me) plasticState(ph)%dotState(:,me) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1) do n = 2, stage plasticState(ph)%dotState(:,me) = plasticState(ph)%dotState(:,me) & + A(n,stage) * plastic_RKdotState(1:sizeDotState,n) enddo plasticState(ph)%state(1:sizeDotState,me) = subState0 & + plasticState(ph)%dotState (1:sizeDotState,me) * Delta_t broken = integrateStress(F_0 + (F - F_0) * Delta_t * C(stage),subFp0,subFi0,Delta_t * C(stage),co,ip,el) if(broken) exit broken = plastic_dotState(Delta_t*C(stage),co,ip,el,ph,me) if(broken) exit enddo if(broken) return plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (ph)%dotState(:,me) plasticState(ph)%dotState(:,me) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B) plasticState(ph)%state(1:sizeDotState,me) = subState0 & + plasticState(ph)%dotState (1:sizeDotState,me) * Delta_t if(present(DB)) & broken = .not. converged(matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) * Delta_t, & plasticState(ph)%state(1:sizeDotState,me), & plasticState(ph)%atol(1:sizeDotState)) if(broken) return broken = plastic_deltaState(co,ip,el,ph,me) if(broken) return broken = integrateStress(F,subFp0,subFi0,Delta_t,co,ip,el) end function integrateStateRK !-------------------------------------------------------------------------------------------------- !> @brief writes crystallite results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine crystallite_results(group,ph) character(len=*), intent(in) :: group integer, intent(in) :: ph integer :: ou real(pReal), allocatable, dimension(:,:) :: selected_rotations character(len=:), allocatable :: structureLabel call results_closeGroup(results_addGroup(group//'/mechanics/')) do ou = 1, size(output_constituent(ph)%label) select case (output_constituent(ph)%label(ou)) case('F') call results_writeDataset(group//'/mechanics/',phase_mechanical_F(ph)%data,'F',& 'deformation gradient','1') case('F_e') call results_writeDataset(group//'/mechanics/',phase_mechanical_Fe(ph)%data,'F_e',& 'elastic deformation gradient','1') case('F_p') call results_writeDataset(group//'/mechanics/',phase_mechanical_Fp(ph)%data,'F_p', & 'plastic deformation gradient','1') case('F_i') call results_writeDataset(group//'/mechanics/',phase_mechanical_Fi(ph)%data,'F_i', & 'inelastic deformation gradient','1') case('L_p') call results_writeDataset(group//'/mechanics/',phase_mechanical_Lp(ph)%data,'L_p', & 'plastic velocity gradient','1/s') case('L_i') call results_writeDataset(group//'/mechanics/',phase_mechanical_Li(ph)%data,'L_i', & 'inelastic velocity gradient','1/s') case('P') call results_writeDataset(group//'/mechanics/',phase_mechanical_P(ph)%data,'P', & 'First Piola-Kirchhoff stress','Pa') case('S') call results_writeDataset(group//'/mechanics/',phase_mechanical_S(ph)%data,'S', & 'Second Piola-Kirchhoff stress','Pa') case('O') select case(lattice_structure(ph)) case(lattice_ISO_ID) structureLabel = 'aP' case(lattice_FCC_ID) structureLabel = 'cF' case(lattice_BCC_ID) structureLabel = 'cI' case(lattice_BCT_ID) structureLabel = 'tI' case(lattice_HEX_ID) structureLabel = 'hP' case(lattice_ORT_ID) structureLabel = 'oP' end select selected_rotations = select_rotations(crystallite_orientation,ph) call results_writeDataset(group//'/mechanics/',selected_rotations,output_constituent(ph)%label(ou),& 'crystal orientation as quaternion','q_0 (q_1 q_2 q_3)') call results_addAttribute('Lattice',structureLabel,group//'/mechanics/'//output_constituent(ph)%label(ou)) end select enddo contains !-------------------------------------------------------------------------------------------------- !> @brief select rotations for output !-------------------------------------------------------------------------------------------------- function select_rotations(dataset,ph) integer, intent(in) :: ph type(rotation), dimension(:,:,:), intent(in) :: dataset real(pReal), allocatable, dimension(:,:) :: select_rotations integer :: el,ip,co,j allocate(select_rotations(4,count(material_phaseAt==ph)*homogenization_maxNconstituents*discretization_nIPs)) j=0 do el = 1, size(material_phaseAt,2) do ip = 1, discretization_nIPs do co = 1, size(material_phaseAt,1) !ToDo: this needs to be changed for varying Ngrains if (material_phaseAt(co,el) == ph) then j = j + 1 select_rotations(1:4,j) = dataset(co,ip,el)%asQuaternion() endif enddo enddo enddo end function select_rotations end subroutine crystallite_results !-------------------------------------------------------------------------------------------------- !> @brief Wind homog inc forward. !-------------------------------------------------------------------------------------------------- module subroutine mechanical_windForward(ph,me) integer, intent(in) :: ph, me phase_mechanical_Fp0(ph)%data(1:3,1:3,me) = phase_mechanical_Fp(ph)%data(1:3,1:3,me) phase_mechanical_Fi0(ph)%data(1:3,1:3,me) = phase_mechanical_Fi(ph)%data(1:3,1:3,me) phase_mechanical_F0(ph)%data(1:3,1:3,me) = phase_mechanical_F(ph)%data(1:3,1:3,me) phase_mechanical_Li0(ph)%data(1:3,1:3,me) = phase_mechanical_Li(ph)%data(1:3,1:3,me) phase_mechanical_Lp0(ph)%data(1:3,1:3,me) = phase_mechanical_Lp(ph)%data(1:3,1:3,me) phase_mechanical_S0(ph)%data(1:3,1:3,me) = phase_mechanical_S(ph)%data(1:3,1:3,me) plasticState(ph)%State0(:,me) = plasticState(ph)%state(:,me) end subroutine mechanical_windForward !-------------------------------------------------------------------------------------------------- !> @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 enddo end subroutine mechanical_forward !-------------------------------------------------------------------------------------------------- !> @brief returns the homogenize elasticity matrix !> ToDo: homogenizedC66 would be more consistent !-------------------------------------------------------------------------------------------------- module function phase_homogenizedC(ph,me) result(C) real(pReal), dimension(6,6) :: C integer, intent(in) :: ph, me plasticType: select case (phase_plasticity(ph)) case (PLASTICITY_DISLOTWIN_ID) plasticType C = plastic_dislotwin_homogenizedC(ph,me) case default plasticType C = lattice_C66(1:6,1:6,ph) end select plasticType end function phase_homogenizedC !-------------------------------------------------------------------------------------------------- !> @brief calculate stress (P) !-------------------------------------------------------------------------------------------------- module function crystallite_stress(dt,co,ip,el) result(converged_) real(pReal), intent(in) :: dt integer, intent(in) :: & co, & ip, & el logical :: converged_ real(pReal) :: & formerSubStep integer :: & so, ph, me, sizeDotState logical :: todo real(pReal) :: subFrac,subStep real(pReal), dimension(3,3) :: & subFp0, & subFi0, & subLp0, & subLi0, & subF0, & subF real(pReal), dimension(:), allocatable :: subState0 ph = material_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) sizeDotState = plasticState(ph)%sizeDotState subLi0 = phase_mechanical_Li0(ph)%data(1:3,1:3,me) subLp0 = phase_mechanical_Lp0(ph)%data(1:3,1:3,me) subState0 = plasticState(ph)%State0(:,me) do so = 1, phase_Nsources(ph) damageState(ph)%p(so)%subState0(:,me) = damageState(ph)%p(so)%state0(:,me) enddo subFp0 = phase_mechanical_Fp0(ph)%data(1:3,1:3,me) subFi0 = phase_mechanical_Fi0(ph)%data(1:3,1:3,me) subF0 = phase_mechanical_F0(ph)%data(1:3,1:3,me) subFrac = 0.0_pReal subStep = 1.0_pReal/num%subStepSizeCryst todo = .true. 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,me) subLi0 = phase_mechanical_Li(ph)%data(1:3,1:3,me) subFp0 = phase_mechanical_Fp(ph)%data(1:3,1:3,me) subFi0 = phase_mechanical_Fi(ph)%data(1:3,1:3,me) subState0 = plasticState(ph)%state(:,me) do so = 1, phase_Nsources(ph) damageState(ph)%p(so)%subState0(:,me) = damageState(ph)%p(so)%state(:,me) enddo endif !-------------------------------------------------------------------------------------------------- ! cut back (reduced time and restore) else subStep = num%subStepSizeCryst * subStep phase_mechanical_Fp(ph)%data(1:3,1:3,me) = subFp0 phase_mechanical_Fi(ph)%data(1:3,1:3,me) = subFi0 phase_mechanical_S(ph)%data(1:3,1:3,me) = phase_mechanical_S0(ph)%data(1:3,1:3,me) ! why no subS0 ? is S0 of any use? if (subStep < 1.0_pReal) then ! actual (not initial) cutback phase_mechanical_Lp(ph)%data(1:3,1:3,me) = subLp0 phase_mechanical_Li(ph)%data(1:3,1:3,me) = subLi0 endif plasticState(ph)%state(:,me) = subState0 do so = 1, phase_Nsources(ph) damageState(ph)%p(so)%state(:,me) = damageState(ph)%p(so)%subState0(:,me) enddo todo = subStep > num%subStepMinCryst ! still on track or already done (beyond repair) endif !-------------------------------------------------------------------------------------------------- ! prepare for integration if (todo) then subF = subF0 & + subStep * (phase_mechanical_F(ph)%data(1:3,1:3,me) - phase_mechanical_F0(ph)%data(1:3,1:3,me)) phase_mechanical_Fe(ph)%data(1:3,1:3,me) = matmul(subF,math_inv33(matmul(phase_mechanical_Fi(ph)%data(1:3,1:3,me), & phase_mechanical_Fp(ph)%data(1:3,1:3,me)))) converged_ = .not. integrateState(subF0,subF,subFp0,subFi0,subState0(1:sizeDotState),subStep * dt,co,ip,el) converged_ = converged_ .and. .not. integrateDamageState(subStep * dt,co,ip,el) endif enddo cutbackLooping end function crystallite_stress !-------------------------------------------------------------------------------------------------- !> @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, me do co = 1,homogenization_Nconstituents(material_homogenizationAt2(ce)) ph = material_phaseAt2(co,ce) me = material_phaseMemberAt2(co,ce) if (includeL) then phase_mechanical_Lp(ph)%data(1:3,1:3,me) = phase_mechanical_Lp0(ph)%data(1:3,1:3,me) phase_mechanical_Li(ph)%data(1:3,1:3,me) = phase_mechanical_Li0(ph)%data(1:3,1:3,me) endif ! maybe protecting everything from overwriting makes more sense phase_mechanical_Fp(ph)%data(1:3,1:3,me) = phase_mechanical_Fp0(ph)%data(1:3,1:3,me) phase_mechanical_Fi(ph)%data(1:3,1:3,me) = phase_mechanical_Fi0(ph)%data(1:3,1:3,me) phase_mechanical_S(ph)%data(1:3,1:3,me) = phase_mechanical_S0(ph)%data(1:3,1:3,me) plasticState(ph)%state(:,me) = plasticState(ph)%State0(:,me) enddo end subroutine mechanical_restore !-------------------------------------------------------------------------------------------------- !> @brief Calculate tangent (dPdF). !-------------------------------------------------------------------------------------------------- module function phase_mechanical_dPdF(dt,co,ip,el) result(dPdF) real(pReal), intent(in) :: dt integer, intent(in) :: & co, & !< counter in constituent loop ip, & !< counter in integration point loop el !< counter in element loop real(pReal), dimension(3,3,3,3) :: dPdF integer :: & o, & p, ph, me 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_phaseAt(co,el) me = material_phaseMemberAt(co,ip,el) call phase_hooke_SandItsTangents(devNull,dSdFe,dSdFi, & phase_mechanical_Fe(ph)%data(1:3,1:3,me), & phase_mechanical_Fi(ph)%data(1:3,1:3,me),co,ip,el) call phase_LiAndItsTangents(devNull,dLidS,dLidFi, & phase_mechanical_S(ph)%data(1:3,1:3,me), & phase_mechanical_Fi(ph)%data(1:3,1:3,me), & ph,me) invFp = math_inv33(phase_mechanical_Fp(ph)%data(1:3,1:3,me)) invFi = math_inv33(phase_mechanical_Fi(ph)%data(1:3,1:3,me)) invSubFp0 = math_inv33(phase_mechanical_Fp0(ph)%data(1:3,1:3,me)) invSubFi0 = math_inv33(phase_mechanical_Fi0(ph)%data(1:3,1:3,me)) 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 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)) * dt 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)) * dt enddo; enddo call math_invert(temp_99,error,math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600,el=el,ip=ip,g=co, & ext_msg='inversion error in analytic tangent calculation') dFidS = 0.0_pReal else dFidS = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif dLidS = math_mul3333xx3333(dLidFi,dFidS) + dLidS endif call plastic_LpAndItsTangents(devNull,dLpdS,dLpdFi, & phase_mechanical_S(ph)%data(1:3,1:3,me), & phase_mechanical_Fi(ph)%data(1:3,1:3,me),co,ip,el) 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,me),invSubFp0) temp_33_3 = matmul(matmul(phase_mechanical_F(ph)%data(1:3,1:3,me),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)) enddo; enddo lhs_3333 = math_mul3333xx3333(dSdFe,temp_3333) * dt & + math_mul3333xx3333(dSdFi,dFidS) call math_invert(temp_99,error,math_eye(9)+math_3333to99(lhs_3333)) if (error) then call IO_warning(warning_ID=600,el=el,ip=ip,g=co, & ext_msg='inversion error in analytic tangent calculation') dSdF = rhs_3333 else dSdF = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333) endif !-------------------------------------------------------------------------------------------------- ! 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)) * dt enddo; enddo !-------------------------------------------------------------------------------------------------- ! assemble dPdF temp_33_1 = matmul(phase_mechanical_S(ph)%data(1:3,1:3,me),transpose(invFp)) temp_33_2 = matmul(phase_mechanical_F(ph)%data(1:3,1:3,me),invFp) temp_33_3 = matmul(temp_33_2,phase_mechanical_S(ph)%data(1:3,1:3,me)) dPdF = 0.0_pReal do p=1,3 dPdF(p,1:3,p,1:3) = transpose(matmul(invFp,temp_33_1)) enddo 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,me),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))) enddo; enddo end function phase_mechanical_dPdF module subroutine mechanical_restartWrite(groupHandle,ph) integer(HID_T), intent(in) :: groupHandle integer, intent(in) :: ph call HDF5_write(groupHandle,plasticState(ph)%state,'omega') call HDF5_write(groupHandle,phase_mechanical_Fi(ph)%data,'F_i') call HDF5_write(groupHandle,phase_mechanical_Li(ph)%data,'L_i') call HDF5_write(groupHandle,phase_mechanical_Lp(ph)%data,'L_p') call HDF5_write(groupHandle,phase_mechanical_Fp(ph)%data,'F_p') call HDF5_write(groupHandle,phase_mechanical_S(ph)%data,'S') call HDF5_write(groupHandle,phase_mechanical_F(ph)%data,'F') end subroutine mechanical_restartWrite module subroutine mechanical_restartRead(groupHandle,ph) integer(HID_T), intent(in) :: groupHandle integer, intent(in) :: ph call HDF5_read(groupHandle,plasticState(ph)%state0,'omega') call HDF5_read(groupHandle,phase_mechanical_Fi0(ph)%data,'F_i') call HDF5_read(groupHandle,phase_mechanical_Li0(ph)%data,'L_i') call HDF5_read(groupHandle,phase_mechanical_Lp0(ph)%data,'L_p') call HDF5_read(groupHandle,phase_mechanical_Fp0(ph)%data,'F_p') call HDF5_read(groupHandle,phase_mechanical_S0(ph)%data,'S') call HDF5_read(groupHandle,phase_mechanical_F0(ph)%data,'F') end subroutine mechanical_restartRead !---------------------------------------------------------------------------------------------- !< @brief Get first Piola-Kichhoff stress (for use by non-mech physics) !---------------------------------------------------------------------------------------------- module function mechanical_S(ph,me) result(S) integer, intent(in) :: ph,me real(pReal), dimension(3,3) :: S S = phase_mechanical_S(ph)%data(1:3,1:3,me) end function mechanical_S !---------------------------------------------------------------------------------------------- !< @brief Get plastic velocity gradient (for use by non-mech physics) !---------------------------------------------------------------------------------------------- module function mechanical_L_p(ph,me) result(L_p) integer, intent(in) :: ph,me real(pReal), dimension(3,3) :: L_p L_p = phase_mechanical_Lp(ph)%data(1:3,1:3,me) end function mechanical_L_p !---------------------------------------------------------------------------------------------- !< @brief Get deformation gradient (for use by homogenization) !---------------------------------------------------------------------------------------------- module function phase_mechanical_getF(co,ip,el) result(F) integer, intent(in) :: co, ip, el real(pReal), dimension(3,3) :: F F = phase_mechanical_F(material_phaseAt(co,el))%data(1:3,1:3,material_phaseMemberAt(co,ip,el)) end function phase_mechanical_getF !---------------------------------------------------------------------------------------------- !< @brief Get elastic deformation gradient (for use by non-mech physics) !---------------------------------------------------------------------------------------------- module function mechanical_F_e(ph,me) result(F_e) integer, intent(in) :: ph,me real(pReal), dimension(3,3) :: F_e F_e = phase_mechanical_Fe(ph)%data(1:3,1:3,me) end function mechanical_F_e !---------------------------------------------------------------------------------------------- !< @brief Get second Piola-Kichhoff stress (for use by homogenization) !---------------------------------------------------------------------------------------------- module function phase_mechanical_getP(co,ip,el) result(P) integer, intent(in) :: co, ip, el real(pReal), dimension(3,3) :: P P = phase_mechanical_P(material_phaseAt(co,el))%data(1:3,1:3,material_phaseMemberAt(co,ip,el)) end function phase_mechanical_getP ! setter for homogenization module subroutine phase_mechanical_setF(F,co,ip,el) real(pReal), dimension(3,3), intent(in) :: F integer, intent(in) :: co, ip, el phase_mechanical_F(material_phaseAt(co,el))%data(1:3,1:3,material_phaseMemberAt(co,ip,el)) = F end subroutine phase_mechanical_setF end submodule mechanics