1272 lines
64 KiB
Fortran
1272 lines
64 KiB
Fortran
!----------------------------------------------------------------------------------------------------
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!> @brief internal microstructure state for all plasticity constitutive models
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!----------------------------------------------------------------------------------------------------
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submodule(constitutive) constitutive_mech
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integer(kind(ELASTICITY_undefined_ID)), dimension(:), allocatable :: &
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phase_elasticity !< elasticity of each phase
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integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: &
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phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase
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interface
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module function plastic_none_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_none_init
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module function plastic_isotropic_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_isotropic_init
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module function plastic_phenopowerlaw_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_phenopowerlaw_init
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module function plastic_kinehardening_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_kinehardening_init
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module function plastic_dislotwin_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_dislotwin_init
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module function plastic_dislotungsten_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_dislotungsten_init
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module function plastic_nonlocal_init() result(myPlasticity)
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logical, dimension(:), allocatable :: &
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myPlasticity
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end function plastic_nonlocal_init
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module subroutine plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_isotropic_LpAndItsTangent
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pure module subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_phenopowerlaw_LpAndItsTangent
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pure module subroutine plastic_kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_kinehardening_LpAndItsTangent
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module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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T
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_dislotwin_LpAndItsTangent
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pure module subroutine plastic_dislotungsten_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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T
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_dislotungsten_LpAndItsTangent
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module subroutine plastic_nonlocal_LpAndItsTangent(Lp,dLp_dMp, &
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Mp,Temperature,instance,of,ip,el)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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Temperature
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integer, intent(in) :: &
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instance, &
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of, &
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ip, & !< current integration point
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el !< current element number
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end subroutine plastic_nonlocal_LpAndItsTangent
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module subroutine plastic_isotropic_dotState(Mp,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_isotropic_dotState
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module subroutine plastic_phenopowerlaw_dotState(Mp,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_phenopowerlaw_dotState
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module subroutine plastic_kinehardening_dotState(Mp,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_kinehardening_dotState
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module subroutine plastic_dislotwin_dotState(Mp,T,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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T
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_dislotwin_dotState
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module subroutine plastic_disloTungsten_dotState(Mp,T,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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T
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_disloTungsten_dotState
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module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
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instance,of,ip,el)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< MandelStress
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real(pReal), dimension(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems), intent(in) :: &
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F, & !< deformation gradient
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Fp !< plastic deformation gradient
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real(pReal), intent(in) :: &
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Temperature, & !< temperature
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timestep !< substepped crystallite time increment
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integer, intent(in) :: &
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instance, &
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of, &
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ip, & !< current integration point
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el !< current element number
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end subroutine plastic_nonlocal_dotState
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module subroutine plastic_dislotwin_dependentState(T,instance,of)
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integer, intent(in) :: &
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instance, &
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of
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real(pReal), intent(in) :: &
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T
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end subroutine plastic_dislotwin_dependentState
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module subroutine plastic_dislotungsten_dependentState(instance,of)
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_dislotungsten_dependentState
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module subroutine plastic_nonlocal_dependentState(F, Fp, instance, of, ip, el)
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real(pReal), dimension(3,3), intent(in) :: &
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F, & !< deformation gradient
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Fp !< plastic deformation gradient
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integer, intent(in) :: &
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instance, &
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of, &
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ip, & !< current integration point
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el !< current element number
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end subroutine plastic_nonlocal_dependentState
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module subroutine plastic_kinehardening_deltaState(Mp,instance,of)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_kinehardening_deltaState
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module subroutine plastic_nonlocal_deltaState(Mp,instance,of,ip,el)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp
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integer, intent(in) :: &
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instance, &
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of, &
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ip, &
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el
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end subroutine plastic_nonlocal_deltaState
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module subroutine plastic_isotropic_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_isotropic_results
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module subroutine plastic_phenopowerlaw_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_phenopowerlaw_results
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module subroutine plastic_kinehardening_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_kinehardening_results
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module subroutine plastic_dislotwin_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_dislotwin_results
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module subroutine plastic_dislotungsten_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_dislotungsten_results
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module subroutine plastic_nonlocal_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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end subroutine plastic_nonlocal_results
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end interface
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Initialize mechanical field related constitutive models
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!> @details Initialize elasticity, plasticity and stiffness degradation models.
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!--------------------------------------------------------------------------------------------------
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module subroutine mech_init
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integer :: &
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p, &
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stiffDegradationCtr
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class(tNode), pointer :: &
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phases, &
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phase, &
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mech, &
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elastic, &
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stiffDegradation
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print'(/,a)', ' <<<+- constitutive_mech init -+>>>'
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!-------------------------------------------------------------------------------------------------
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! initialize elasticity (hooke) !ToDO: Maybe move to elastic submodule along with function homogenizedC?
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phases => config_material%get('phase')
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allocate(phase_elasticity(phases%length), source = ELASTICITY_undefined_ID)
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allocate(phase_elasticityInstance(phases%length), source = 0)
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allocate(phase_NstiffnessDegradations(phases%length),source=0)
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do p = 1, phases%length
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phase => phases%get(p)
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mech => phase%get('mechanics')
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elastic => mech%get('elasticity')
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if(elastic%get_asString('type') == 'hooke') then
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phase_elasticity(p) = ELASTICITY_HOOKE_ID
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else
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call IO_error(200,ext_msg=elastic%get_asString('type'))
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endif
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stiffDegradation => mech%get('stiffness_degradation',defaultVal=emptyList) ! check for stiffness degradation mechanisms
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phase_NstiffnessDegradations(p) = stiffDegradation%length
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enddo
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allocate(phase_stiffnessDegradation(maxval(phase_NstiffnessDegradations),phases%length), &
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source=STIFFNESS_DEGRADATION_undefined_ID)
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if(maxVal(phase_NstiffnessDegradations)/=0) then
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do p = 1, phases%length
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phase => phases%get(p)
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mech => phase%get('mechanics')
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stiffDegradation => mech%get('stiffness_degradation',defaultVal=emptyList)
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do stiffDegradationCtr = 1, stiffDegradation%length
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if(stiffDegradation%get_asString(stiffDegradationCtr) == 'damage') &
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phase_stiffnessDegradation(stiffDegradationCtr,p) = STIFFNESS_DEGRADATION_damage_ID
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enddo
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enddo
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endif
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! initialize plasticity
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allocate(plasticState(phases%length))
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allocate(phase_plasticity(phases%length),source = PLASTICITY_undefined_ID)
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allocate(phase_plasticityInstance(phases%length),source = 0)
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allocate(phase_localPlasticity(phases%length), source=.true.)
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where(plastic_none_init()) phase_plasticity = PLASTICITY_NONE_ID
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where(plastic_isotropic_init()) phase_plasticity = PLASTICITY_ISOTROPIC_ID
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where(plastic_phenopowerlaw_init()) phase_plasticity = PLASTICITY_PHENOPOWERLAW_ID
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where(plastic_kinehardening_init()) phase_plasticity = PLASTICITY_KINEHARDENING_ID
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where(plastic_dislotwin_init()) phase_plasticity = PLASTICITY_DISLOTWIN_ID
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where(plastic_dislotungsten_init()) phase_plasticity = PLASTICITY_DISLOTUNGSTEN_ID
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where(plastic_nonlocal_init()) phase_plasticity = PLASTICITY_NONLOCAL_ID
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do p = 1, phases%length
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phase_elasticityInstance(p) = count(phase_elasticity(1:p) == phase_elasticity(p))
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phase_plasticityInstance(p) = count(phase_plasticity(1:p) == phase_plasticity(p))
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enddo
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end subroutine mech_init
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!--------------------------------------------------------------------------------------------------
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!> @brief checks if a plastic module is active or not
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!--------------------------------------------------------------------------------------------------
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module function plastic_active(plastic_label) result(active_plastic)
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character(len=*), intent(in) :: plastic_label !< type of plasticity model
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logical, dimension(:), allocatable :: active_plastic
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class(tNode), pointer :: &
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phases, &
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phase, &
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mech, &
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pl
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integer :: p
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phases => config_material%get('phase')
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allocate(active_plastic(phases%length), source = .false. )
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do p = 1, phases%length
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phase => phases%get(p)
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mech => phase%get('mechanics')
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pl => mech%get('plasticity')
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if(pl%get_asString('type') == plastic_label) active_plastic(p) = .true.
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enddo
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end function plastic_active
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!--------------------------------------------------------------------------------------------------
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!> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
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!> the elastic and intermediate deformation gradients using Hooke's law
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!--------------------------------------------------------------------------------------------------
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module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
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Fe, Fi, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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Fe, & !< elastic deformation gradient
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Fi !< intermediate deformation gradient
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real(pReal), intent(out), dimension(3,3) :: &
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S !< 2nd Piola-Kirchhoff stress tensor in lattice configuration
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
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dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
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real(pReal), dimension(3,3) :: E
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real(pReal), dimension(3,3,3,3) :: C
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integer :: &
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ho, & !< homogenization
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d !< counter in degradation loop
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integer :: &
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i, j
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ho = material_homogenizationAt(el)
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C = math_66toSym3333(constitutive_homogenizedC(ipc,ip,el))
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DegradationLoop: do d = 1, phase_NstiffnessDegradations(material_phaseAt(ipc,el))
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degradationType: select case(phase_stiffnessDegradation(d,material_phaseAt(ipc,el)))
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case (STIFFNESS_DEGRADATION_damage_ID) degradationType
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C = C * damage(ho)%p(material_homogenizationMemberAt(ip,el))**2
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end select degradationType
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enddo DegradationLoop
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E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration
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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
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do i =1, 3;do j=1,3
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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
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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
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enddo; enddo
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end subroutine constitutive_hooke_SandItsTangents
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!--------------------------------------------------------------------------------------------------
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!> @brief calls microstructure function of the different plasticity constitutive models
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!--------------------------------------------------------------------------------------------------
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module subroutine constitutive_plastic_dependentState(F, Fp, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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F, & !< elastic deformation gradient
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Fp !< plastic deformation gradient
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integer :: &
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ho, & !< homogenization
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tme, & !< thermal member position
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instance, of
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ho = material_homogenizationAt(el)
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tme = material_homogenizationMemberAt(ip,el)
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of = material_phasememberAt(ipc,ip,el)
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instance = phase_plasticityInstance(material_phaseAt(ipc,el))
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plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
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case (PLASTICITY_DISLOTWIN_ID) plasticityType
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call plastic_dislotwin_dependentState(temperature(ho)%p(tme),instance,of)
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case (PLASTICITY_DISLOTUNGSTEN_ID) plasticityType
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call plastic_dislotungsten_dependentState(instance,of)
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case (PLASTICITY_NONLOCAL_ID) plasticityType
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call plastic_nonlocal_dependentState (F,Fp,instance,of,ip,el)
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end select plasticityType
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end subroutine constitutive_plastic_dependentState
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|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the velocity gradient
|
|
! ToDo: Discuss whether it makes sense if crystallite handles the configuration conversion, i.e.
|
|
! Mp in, dLp_dMp out
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine constitutive_plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, &
|
|
S, Fi, ipc, ip, el)
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
S, & !< 2nd Piola-Kirchhoff stress
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(out), dimension(3,3) :: &
|
|
Lp !< plastic velocity gradient
|
|
real(pReal), intent(out), dimension(3,3,3,3) :: &
|
|
dLp_dS, &
|
|
dLp_dFi !< derivative of Lp with respect to Fi
|
|
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
dLp_dMp !< derivative of Lp with respect to Mandel stress
|
|
real(pReal), dimension(3,3) :: &
|
|
Mp !< Mandel stress work conjugate with Lp
|
|
integer :: &
|
|
ho, & !< homogenization
|
|
tme !< thermal member position
|
|
integer :: &
|
|
i, j, instance, of
|
|
|
|
ho = material_homogenizationAt(el)
|
|
tme = material_homogenizationMemberAt(ip,el)
|
|
|
|
Mp = matmul(matmul(transpose(Fi),Fi),S)
|
|
of = material_phasememberAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
|
|
|
|
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
|
|
|
|
case (PLASTICITY_NONE_ID) plasticityType
|
|
Lp = 0.0_pReal
|
|
dLp_dMp = 0.0_pReal
|
|
|
|
case (PLASTICITY_ISOTROPIC_ID) plasticityType
|
|
call plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
|
|
|
|
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
|
|
call plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
|
|
|
|
case (PLASTICITY_KINEHARDENING_ID) plasticityType
|
|
call plastic_kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
|
|
|
|
case (PLASTICITY_NONLOCAL_ID) plasticityType
|
|
call plastic_nonlocal_LpAndItsTangent(Lp,dLp_dMp,Mp, temperature(ho)%p(tme),instance,of,ip,el)
|
|
|
|
case (PLASTICITY_DISLOTWIN_ID) plasticityType
|
|
call plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of)
|
|
|
|
case (PLASTICITY_DISLOTUNGSTEN_ID) plasticityType
|
|
call plastic_dislotungsten_LpAndItsTangent(Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of)
|
|
|
|
end select plasticityType
|
|
|
|
do i=1,3; do j=1,3
|
|
dLp_dFi(i,j,1:3,1:3) = matmul(matmul(Fi,S),transpose(dLp_dMp(i,j,1:3,1:3))) + &
|
|
matmul(matmul(Fi,dLp_dMp(i,j,1:3,1:3)),S)
|
|
dLp_dS(i,j,1:3,1:3) = matmul(matmul(transpose(Fi),Fi),dLp_dMp(i,j,1:3,1:3)) ! ToDo: @PS: why not: dLp_dMp:(FiT Fi)
|
|
enddo; enddo
|
|
|
|
end subroutine constitutive_plastic_LpAndItsTangents
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
module function constitutive_collectDotState(S, FArray, Fi, FpArray, subdt, ipc, ip, el,phase,of) result(broken)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el, & !< element
|
|
phase, &
|
|
of
|
|
real(pReal), intent(in) :: &
|
|
subdt !< timestep
|
|
real(pReal), intent(in), dimension(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: &
|
|
FArray, & !< elastic deformation gradient
|
|
FpArray !< plastic deformation gradient
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
S !< 2nd Piola Kirchhoff stress (vector notation)
|
|
real(pReal), dimension(3,3) :: &
|
|
Mp
|
|
integer :: &
|
|
ho, & !< homogenization
|
|
tme, & !< thermal member position
|
|
i, & !< counter in source loop
|
|
instance
|
|
logical :: broken
|
|
|
|
ho = material_homogenizationAt(el)
|
|
tme = material_homogenizationMemberAt(ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
|
|
Mp = matmul(matmul(transpose(Fi),Fi),S)
|
|
|
|
plasticityType: select case (phase_plasticity(phase))
|
|
|
|
case (PLASTICITY_ISOTROPIC_ID) plasticityType
|
|
call plastic_isotropic_dotState(Mp,instance,of)
|
|
|
|
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
|
|
call plastic_phenopowerlaw_dotState(Mp,instance,of)
|
|
|
|
case (PLASTICITY_KINEHARDENING_ID) plasticityType
|
|
call plastic_kinehardening_dotState(Mp,instance,of)
|
|
|
|
case (PLASTICITY_DISLOTWIN_ID) plasticityType
|
|
call plastic_dislotwin_dotState(Mp,temperature(ho)%p(tme),instance,of)
|
|
|
|
case (PLASTICITY_DISLOTUNGSTEN_ID) plasticityType
|
|
call plastic_disloTungsten_dotState(Mp,temperature(ho)%p(tme),instance,of)
|
|
|
|
case (PLASTICITY_NONLOCAL_ID) plasticityType
|
|
call plastic_nonlocal_dotState(Mp,FArray,FpArray,temperature(ho)%p(tme),subdt, &
|
|
instance,of,ip,el)
|
|
end select plasticityType
|
|
broken = any(IEEE_is_NaN(plasticState(phase)%dotState(:,of)))
|
|
|
|
|
|
end function constitutive_collectDotState
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief for constitutive models having an instantaneous change of state
|
|
!> will return false if delta state is not needed/supported by the constitutive model
|
|
!--------------------------------------------------------------------------------------------------
|
|
module function constitutive_deltaState(S, Fi, ipc, ip, el, phase, of) result(broken)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el, & !< element
|
|
phase, &
|
|
of
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
S, & !< 2nd Piola Kirchhoff stress
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), dimension(3,3) :: &
|
|
Mp
|
|
integer :: &
|
|
instance, &
|
|
myOffset, &
|
|
mySize
|
|
logical :: &
|
|
broken
|
|
|
|
Mp = matmul(matmul(transpose(Fi),Fi),S)
|
|
instance = phase_plasticityInstance(phase)
|
|
|
|
plasticityType: select case (phase_plasticity(phase))
|
|
|
|
case (PLASTICITY_KINEHARDENING_ID) plasticityType
|
|
call plastic_kinehardening_deltaState(Mp,instance,of)
|
|
broken = any(IEEE_is_NaN(plasticState(phase)%deltaState(:,of)))
|
|
|
|
case (PLASTICITY_NONLOCAL_ID) plasticityType
|
|
call plastic_nonlocal_deltaState(Mp,instance,of,ip,el)
|
|
broken = any(IEEE_is_NaN(plasticState(phase)%deltaState(:,of)))
|
|
|
|
case default
|
|
broken = .false.
|
|
|
|
end select plasticityType
|
|
|
|
if(.not. broken) then
|
|
select case(phase_plasticity(phase))
|
|
case (PLASTICITY_NONLOCAL_ID,PLASTICITY_KINEHARDENING_ID)
|
|
|
|
myOffset = plasticState(phase)%offsetDeltaState
|
|
mySize = plasticState(phase)%sizeDeltaState
|
|
plasticState(phase)%state(myOffset + 1:myOffset + mySize,of) = &
|
|
plasticState(phase)%state(myOffset + 1:myOffset + mySize,of) + plasticState(phase)%deltaState(1:mySize,of)
|
|
end select
|
|
endif
|
|
|
|
end function constitutive_deltaState
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------
|
|
!> @brief writes plasticity constitutive results to HDF5 output file
|
|
!--------------------------------------------------------------------------------------------
|
|
module subroutine plastic_results
|
|
|
|
integer :: p
|
|
character(len=:), allocatable :: group
|
|
|
|
plasticityLoop: do p=1,size(material_name_phase)
|
|
group = '/current/phase/'//trim(material_name_phase(p))
|
|
call results_closeGroup(results_addGroup(group))
|
|
|
|
group = trim(group)//'/plastic'
|
|
|
|
call results_closeGroup(results_addGroup(group))
|
|
select case(phase_plasticity(p))
|
|
|
|
case(PLASTICITY_ISOTROPIC_ID)
|
|
call plastic_isotropic_results(phase_plasticityInstance(p),group)
|
|
|
|
case(PLASTICITY_PHENOPOWERLAW_ID)
|
|
call plastic_phenopowerlaw_results(phase_plasticityInstance(p),group)
|
|
|
|
case(PLASTICITY_KINEHARDENING_ID)
|
|
call plastic_kinehardening_results(phase_plasticityInstance(p),group)
|
|
|
|
case(PLASTICITY_DISLOTWIN_ID)
|
|
call plastic_dislotwin_results(phase_plasticityInstance(p),group)
|
|
|
|
case(PLASTICITY_DISLOTUNGSTEN_ID)
|
|
call plastic_dislotungsten_results(phase_plasticityInstance(p),group)
|
|
|
|
case(PLASTICITY_NONLOCAL_ID)
|
|
call plastic_nonlocal_results(phase_plasticityInstance(p),group)
|
|
end select
|
|
|
|
enddo plasticityLoop
|
|
|
|
end subroutine plastic_results
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculation of stress (P) with time integration based on a residuum in Lp and
|
|
!> intermediate acceleration of the Newton-Raphson correction
|
|
!--------------------------------------------------------------------------------------------------
|
|
function integrateStress(ipc,ip,el,timeFraction) result(broken)
|
|
|
|
integer, intent(in):: el, & ! element index
|
|
ip, & ! integration point index
|
|
ipc ! grain index
|
|
real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep
|
|
|
|
real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep
|
|
Fp_new, & ! plastic deformation gradient at end of timestep
|
|
invFp_new, & ! inverse of Fp_new
|
|
invFp_current, & ! inverse of Fp_current
|
|
Lpguess, & ! current guess for plastic velocity gradient
|
|
Lpguess_old, & ! known last good guess for plastic velocity gradient
|
|
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
|
|
residuumLp, & ! current residuum of plastic velocity gradient
|
|
residuumLp_old, & ! last residuum of plastic velocity gradient
|
|
deltaLp, & ! direction of next guess
|
|
Fi_new, & ! gradient of intermediate deformation stages
|
|
invFi_new, &
|
|
invFi_current, & ! inverse of Fi_current
|
|
Liguess, & ! current guess for intermediate velocity gradient
|
|
Liguess_old, & ! known last good guess for intermediate velocity gradient
|
|
Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law
|
|
residuumLi, & ! current residuum of intermediate velocity gradient
|
|
residuumLi_old, & ! last residuum of intermediate velocity gradient
|
|
deltaLi, & ! direction of next guess
|
|
Fe, & ! elastic deformation gradient
|
|
S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration
|
|
A, &
|
|
B, &
|
|
temp_33
|
|
real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK
|
|
integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK
|
|
real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme)
|
|
dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme)
|
|
real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress
|
|
dS_dFi, &
|
|
dFe_dLp, & ! partial derivative of elastic deformation gradient
|
|
dFe_dLi, &
|
|
dFi_dLi, &
|
|
dLp_dFi, &
|
|
dLi_dFi, &
|
|
dLp_dS, &
|
|
dLi_dS
|
|
real(pReal) steplengthLp, &
|
|
steplengthLi, &
|
|
dt, & ! time increment
|
|
atol_Lp, &
|
|
atol_Li, &
|
|
devNull
|
|
integer NiterationStressLp, & ! number of stress integrations
|
|
NiterationStressLi, & ! number of inner stress integrations
|
|
ierr, & ! error indicator for LAPACK
|
|
o, &
|
|
p, &
|
|
m, &
|
|
jacoCounterLp, &
|
|
jacoCounterLi ! counters to check for Jacobian update
|
|
logical :: error,broken
|
|
|
|
broken = .true.
|
|
|
|
if (present(timeFraction)) then
|
|
dt = crystallite_subdt(ipc,ip,el) * timeFraction
|
|
F = crystallite_subF0(1:3,1:3,ipc,ip,el) &
|
|
+ (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction
|
|
else
|
|
dt = crystallite_subdt(ipc,ip,el)
|
|
F = crystallite_subF(1:3,1:3,ipc,ip,el)
|
|
endif
|
|
|
|
call constitutive_plastic_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), &
|
|
crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el)
|
|
|
|
p = material_phaseAt(ipc,el)
|
|
m = material_phaseMemberAt(ipc,ip,el)
|
|
|
|
Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess
|
|
Liguess = constitutive_mech_Li(p)%data(1:3,1:3,m) ! take as first guess
|
|
|
|
call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el))
|
|
if (error) return ! error
|
|
call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el))
|
|
if (error) return ! error
|
|
|
|
A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp
|
|
|
|
jacoCounterLi = 0
|
|
steplengthLi = 1.0_pReal
|
|
residuumLi_old = 0.0_pReal
|
|
Liguess_old = Liguess
|
|
|
|
NiterationStressLi = 0
|
|
LiLoop: do
|
|
NiterationStressLi = NiterationStressLi + 1
|
|
if (NiterationStressLi>num%nStress) return ! error
|
|
|
|
invFi_new = matmul(invFi_current,math_I3 - dt*Liguess)
|
|
Fi_new = math_inv33(invFi_new)
|
|
|
|
jacoCounterLp = 0
|
|
steplengthLp = 1.0_pReal
|
|
residuumLp_old = 0.0_pReal
|
|
Lpguess_old = Lpguess
|
|
|
|
NiterationStressLp = 0
|
|
LpLoop: do
|
|
NiterationStressLp = NiterationStressLp + 1
|
|
if (NiterationStressLp>num%nStress) return ! error
|
|
|
|
B = math_I3 - dt*Lpguess
|
|
Fe = matmul(matmul(A,B), invFi_new)
|
|
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
Fe, Fi_new, ipc, ip, el)
|
|
|
|
call constitutive_plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, &
|
|
S, Fi_new, ipc, ip, el)
|
|
|
|
!* update current residuum and check for convergence of loop
|
|
atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
residuumLp = Lpguess - Lp_constitutive
|
|
|
|
if (any(IEEE_is_NaN(residuumLp))) then
|
|
return ! error
|
|
elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance
|
|
exit LpLoop
|
|
elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
residuumLp_old = residuumLp ! ...remember old values and...
|
|
Lpguess_old = Lpguess
|
|
steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
else ! not converged and residuum not improved...
|
|
steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction
|
|
Lpguess = Lpguess_old &
|
|
+ deltaLp * stepLengthLp
|
|
cycle LpLoop
|
|
endif
|
|
|
|
calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then
|
|
jacoCounterLp = jacoCounterLp + 1
|
|
|
|
do o=1,3; do p=1,3
|
|
dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
enddo; enddo
|
|
dRLp_dLp = math_eye(9) &
|
|
- math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp))
|
|
temp_9 = math_33to9(residuumLp)
|
|
call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp
|
|
if (ierr /= 0) return ! error
|
|
deltaLp = - math_9to33(temp_9)
|
|
endif calculateJacobiLi
|
|
|
|
Lpguess = Lpguess &
|
|
+ deltaLp * steplengthLp
|
|
enddo LpLoop
|
|
|
|
call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, &
|
|
S, Fi_new, ipc, ip, el)
|
|
|
|
!* update current residuum and check for convergence of loop
|
|
atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
residuumLi = Liguess - Li_constitutive
|
|
if (any(IEEE_is_NaN(residuumLi))) then
|
|
return ! error
|
|
elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance
|
|
exit LiLoop
|
|
elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
residuumLi_old = residuumLi ! ...remember old values and...
|
|
Liguess_old = Liguess
|
|
steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
else ! not converged and residuum not improved...
|
|
steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction
|
|
Liguess = Liguess_old &
|
|
+ deltaLi * steplengthLi
|
|
cycle LiLoop
|
|
endif
|
|
|
|
calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then
|
|
jacoCounterLi = jacoCounterLi + 1
|
|
|
|
temp_33 = matmul(matmul(A,B),invFi_current)
|
|
do o=1,3; do p=1,3
|
|
dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current
|
|
enddo; enddo
|
|
do o=1,3; do p=1,3
|
|
dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new)
|
|
enddo; enddo
|
|
dRLi_dLi = math_eye(9) &
|
|
- math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) &
|
|
+ math_mul3333xx3333(dS_dFi, dFi_dLi))) &
|
|
- math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi))
|
|
temp_9 = math_33to9(residuumLi)
|
|
call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li
|
|
if (ierr /= 0) return ! error
|
|
deltaLi = - math_9to33(temp_9)
|
|
endif calculateJacobiLp
|
|
|
|
Liguess = Liguess &
|
|
+ deltaLi * steplengthLi
|
|
enddo LiLoop
|
|
|
|
invFp_new = matmul(invFp_current,B)
|
|
call math_invert33(Fp_new,devNull,error,invFp_new)
|
|
if (error) return ! error
|
|
|
|
p = material_phaseAt(ipc,el)
|
|
m = material_phaseMemberAt(ipc,ip,el)
|
|
|
|
crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new)))
|
|
crystallite_S (1:3,1:3,ipc,ip,el) = S
|
|
crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess
|
|
constitutive_mech_Li(p)%data(1:3,1:3,m) = Liguess
|
|
crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = Fi_new
|
|
crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new)
|
|
broken = .false.
|
|
|
|
end function integrateStress
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
|
!> using Fixed Point Iteration to adapt the stepsize
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine integrateStateFPI(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
NiterationState, & !< number of iterations in state loop
|
|
p, &
|
|
c, &
|
|
s, &
|
|
size_pl
|
|
integer, dimension(maxval(phase_Nsources)) :: &
|
|
size_so
|
|
real(pReal) :: &
|
|
zeta
|
|
real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: &
|
|
r ! state residuum
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,2) :: &
|
|
plastic_dotState
|
|
real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState
|
|
logical :: &
|
|
broken
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
size_pl = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) &
|
|
+ plasticState(p)%dotState (1:size_pl,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
plastic_dotState(1:size_pl,2) = 0.0_pReal
|
|
|
|
iteration: do NiterationState = 1, num%nState
|
|
|
|
if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1)
|
|
plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c)
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken) exit iteration
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) exit iteration
|
|
|
|
zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),&
|
|
plastic_dotState(1:size_pl,2))
|
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta &
|
|
+ plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta)
|
|
r(1:size_pl) = plasticState(p)%state (1:size_pl,c) &
|
|
- plasticState(p)%subState0(1:size_pl,c) &
|
|
- plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e)
|
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) &
|
|
- r(1:size_pl)
|
|
crystallite_converged(g,i,e) = converged(r(1:size_pl), &
|
|
plasticState(p)%state(1:size_pl,c), &
|
|
plasticState(p)%atol(1:size_pl))
|
|
|
|
if(crystallite_converged(g,i,e)) then
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
exit iteration
|
|
endif
|
|
|
|
enddo iteration
|
|
|
|
|
|
contains
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate the damping for correction of state and dot state
|
|
!--------------------------------------------------------------------------------------------------
|
|
real(pReal) pure function damper(current,previous,previous2)
|
|
|
|
real(pReal), dimension(:), intent(in) ::&
|
|
current, previous, previous2
|
|
|
|
real(pReal) :: dot_prod12, dot_prod22
|
|
|
|
dot_prod12 = dot_product(current - previous, previous - previous2)
|
|
dot_prod22 = dot_product(previous - previous2, previous - previous2)
|
|
if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then
|
|
damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22)
|
|
else
|
|
damper = 1.0_pReal
|
|
endif
|
|
|
|
end function damper
|
|
|
|
end subroutine integrateStateFPI
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate state with 1st order explicit Euler method
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine integrateStateEuler(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
|
|
end subroutine integrateStateEuler
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with 1st order Euler method with adaptive step size
|
|
!--------------------------------------------------------------------------------------------------
|
|
module subroutine integrateStateAdaptiveEuler(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic
|
|
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
|
|
residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e)
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e)
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken) return
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) &
|
|
+ 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), &
|
|
plasticState(p)%state(1:sizeDotState,c), &
|
|
plasticState(p)%atol(1:sizeDotState))
|
|
|
|
end subroutine integrateStateAdaptiveEuler
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
|
|
!---------------------------------------------------------------------------------------------------
|
|
module subroutine integrateStateRK4(g,i,e)
|
|
|
|
integer, intent(in) :: g,i,e
|
|
|
|
real(pReal), dimension(3,3), parameter :: &
|
|
A = reshape([&
|
|
0.5_pReal, 0.0_pReal, 0.0_pReal, &
|
|
0.0_pReal, 0.5_pReal, 0.0_pReal, &
|
|
0.0_pReal, 0.0_pReal, 1.0_pReal],&
|
|
shape(A))
|
|
real(pReal), dimension(3), parameter :: &
|
|
C = [0.5_pReal, 0.5_pReal, 1.0_pReal]
|
|
real(pReal), dimension(4), parameter :: &
|
|
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
|
|
|
|
call integrateStateRK(g,i,e,A,B,C)
|
|
|
|
end subroutine integrateStateRK4
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the Cash-Carp method
|
|
!---------------------------------------------------------------------------------------------------
|
|
module subroutine integrateStateRKCK45(g,i,e)
|
|
|
|
integer, intent(in) :: g,i,e
|
|
|
|
real(pReal), dimension(5,5), parameter :: &
|
|
A = reshape([&
|
|
1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, &
|
|
-11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, &
|
|
1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],&
|
|
shape(A))
|
|
real(pReal), dimension(5), parameter :: &
|
|
C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal]
|
|
real(pReal), dimension(6), parameter :: &
|
|
B = &
|
|
[37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, &
|
|
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], &
|
|
DB = B - &
|
|
[2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,&
|
|
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal]
|
|
|
|
call integrateStateRK(g,i,e,A,B,C,DB)
|
|
|
|
end subroutine integrateStateRKCK45
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
|
|
!! embedded explicit Runge-Kutta method
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRK(g,i,e,A,B,CC,DB)
|
|
|
|
|
|
real(pReal), dimension(:,:), intent(in) :: A
|
|
real(pReal), dimension(:), intent(in) :: B, CC
|
|
real(pReal), dimension(:), intent(in), optional :: DB
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
stage, & ! stage index in integration stage loop
|
|
n, &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
do stage = 1,size(A,1)
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
|
|
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1)
|
|
|
|
do n = 2, stage
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
|
|
+ A(n,stage) * plastic_RKdotState(1:sizeDotState,n)
|
|
enddo
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
|
|
broken = integrateStress(g,i,e,CC(stage))
|
|
if(broken) exit
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
|
|
if(broken) exit
|
|
|
|
enddo
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
|
|
plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c)
|
|
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B)
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
if(present(DB)) &
|
|
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) &
|
|
* crystallite_subdt(g,i,e), &
|
|
plasticState(p)%state(1:sizeDotState,c), &
|
|
plasticState(p)%atol(1:sizeDotState))
|
|
|
|
if(broken) return
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
|
|
|
|
end subroutine integrateStateRK
|
|
|
|
|
|
end submodule constitutive_mech
|
|
|