949 lines
48 KiB
Fortran
949 lines
48 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief elasticity, plasticity, damage & thermal internal microstructure state
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!--------------------------------------------------------------------------------------------------
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module constitutive
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use prec
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use math
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use rotations
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use IO
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use config
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use material
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use results
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use lattice
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use discretization
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use geometry_plastic_nonlocal, only: &
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geometry_plastic_nonlocal_disable
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implicit none
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private
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integer(kind(ELASTICITY_undefined_ID)), dimension(:), allocatable, protected :: &
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phase_elasticity !< elasticity of each phase
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integer(kind(PLASTICITY_undefined_ID)), dimension(:), allocatable :: & !ToDo: old intel compiler complains about protected
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phase_plasticity !< plasticity of each phase
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integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: & ! ToDo: old intel compiler complains about protected
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phase_source, & !< active sources mechanisms of each phase
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phase_kinematics, & !< active kinematic mechanisms of each phase
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phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase
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integer, dimension(:), allocatable, public :: & ! ToDo: old intel compiler complains about protected
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phase_Nsources, & !< number of source mechanisms active in each phase
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phase_Nkinematics, & !< number of kinematic mechanisms active in each phase
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phase_NstiffnessDegradations, & !< number of stiffness degradation mechanisms active in each phase
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phase_plasticityInstance, & !< instance of particular plasticity of each phase
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phase_elasticityInstance !< instance of particular elasticity of each phase
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logical, dimension(:), allocatable, public :: & ! ToDo: old intel compiler complains about protected
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phase_localPlasticity !< flags phases with local constitutive law
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type(tPlasticState), allocatable, dimension(:), public :: &
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plasticState
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type(tSourceState), allocatable, dimension(:), public :: &
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sourceState
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integer, public, protected :: &
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constitutive_plasticity_maxSizeDotState, &
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constitutive_source_maxSizeDotState
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interface
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module subroutine plastic_init
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end subroutine plastic_init
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module subroutine damage_init
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end subroutine damage_init
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module subroutine thermal_init
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end subroutine thermal_init
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module function plastic_active(plastic_label) result(active_plastic)
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character(len=*), intent(in) :: plastic_label
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logical, dimension(:), allocatable :: active_plastic
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end function plastic_active
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module function source_active(source_label,src_length) result(active_source)
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character(len=*), intent(in) :: source_label
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integer, intent(in) :: src_length
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logical, dimension(:,:), allocatable :: active_source
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end function source_active
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module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics)
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character(len=*), intent(in) :: kinematics_label
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integer, intent(in) :: kinematics_length
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logical, dimension(:,:), allocatable :: active_kinematics
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end function kinematics_active
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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_maxNgrains,discretization_nIP,discretization_nElem), 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 source_damage_anisoBrittle_dotState(S, 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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S
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end subroutine source_damage_anisoBrittle_dotState
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module subroutine source_damage_anisoDuctile_dotState(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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end subroutine source_damage_anisoDuctile_dotState
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module subroutine source_damage_isoDuctile_dotState(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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end subroutine source_damage_isoDuctile_dotState
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module subroutine source_thermal_externalheat_dotState(phase, of)
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integer, intent(in) :: &
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phase, &
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of
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end subroutine source_thermal_externalheat_dotState
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module subroutine constitutive_damage_getRateAndItsTangents(phiDot, dPhiDot_dPhi, phi, ip, el)
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integer, intent(in) :: &
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in) :: &
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phi !< damage parameter
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real(pReal), intent(inout) :: &
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phiDot, &
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dPhiDot_dPhi
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end subroutine constitutive_damage_getRateAndItsTangents
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module subroutine constitutive_thermal_getRateAndItsTangents(TDot, dTDot_dT, T, S, Lp, ip, el)
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integer, intent(in) :: &
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in) :: &
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T
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real(pReal), intent(in), dimension(:,:,:,:,:) :: &
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S, & !< current 2nd Piola Kitchoff stress vector
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Lp !< plastic velocity gradient
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real(pReal), intent(inout) :: &
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TDot, &
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dTDot_dT
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end subroutine constitutive_thermal_getRateAndItsTangents
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module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
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real(pReal), dimension(6,6) :: &
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homogenizedC
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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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end function plastic_dislotwin_homogenizedC
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pure module function kinematics_thermal_expansion_initialStrain(homog,phase,offset) result(initialStrain)
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integer, intent(in) :: &
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phase, &
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homog, &
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offset
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real(pReal), dimension(3,3) :: &
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initialStrain
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end function kinematics_thermal_expansion_initialStrain
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module subroutine plastic_nonlocal_updateCompatibility(orientation,instance,i,e)
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integer, intent(in) :: &
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instance, &
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i, &
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e
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type(rotation), dimension(1,discretization_nIP,discretization_nElem), intent(in) :: &
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orientation !< crystal orientation
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end subroutine plastic_nonlocal_updateCompatibility
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module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Li !< inleastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLi_dMi !< derivative of Li with respect to Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mi !< 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_LiAndItsTangent
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module subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in), dimension(3,3) :: &
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S
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real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
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end subroutine kinematics_cleavage_opening_LiAndItsTangent
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module subroutine kinematics_slipplane_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in), dimension(3,3) :: &
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S
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real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
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end subroutine kinematics_slipplane_opening_LiAndItsTangent
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module subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(out), dimension(3,3) :: &
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Li !< thermal velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLi_dTstar !< derivative of Li with respect to Tstar (4th-order tensor defined to be zero)
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end subroutine kinematics_thermal_expansion_LiAndItsTangent
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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 source_damage_isoBrittle_deltaState(C, Fe, 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
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real(pReal), intent(in), dimension(6,6) :: &
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C
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end subroutine source_damage_isoBrittle_deltaState
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module subroutine plastic_results
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end subroutine plastic_results
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module subroutine damage_results
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end subroutine damage_results
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end interface
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interface constitutive_LpAndItsTangents
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module subroutine constitutive_plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, &
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S, 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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S, & !< 2nd Piola-Kirchhoff stress
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Fi !< intermediate deformation gradient
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real(pReal), intent(out), dimension(3,3) :: &
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Lp !< plastic velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLp_dS, &
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dLp_dFi !< derivative of Lp with respect to Fi
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end subroutine constitutive_plastic_LpAndItsTangents
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end interface constitutive_LpAndItsTangents
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interface constitutive_dependentState
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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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end subroutine constitutive_plastic_dependentState
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end interface constitutive_dependentState
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type :: tDebugOptions
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logical :: &
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basic, &
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extensive, &
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selective
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integer :: &
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element, &
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ip, &
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grain
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end type tDebugOptions
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type(tDebugOptions) :: debugConstitutive
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public :: &
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constitutive_init, &
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constitutive_homogenizedC, &
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constitutive_LpAndItsTangents, &
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constitutive_dependentState, &
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constitutive_LiAndItsTangents, &
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constitutive_initialFi, &
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constitutive_SandItsTangents, &
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constitutive_collectDotState, &
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constitutive_deltaState, &
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constitutive_damage_getRateAndItsTangents, &
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constitutive_thermal_getRateAndItsTangents, &
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constitutive_results, &
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constitutive_allocateState, &
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plastic_nonlocal_updateCompatibility, &
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plastic_active, &
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source_active, &
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kinematics_active
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Initialze constitutive models for individual physics
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_init
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integer :: &
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p, & !< counter in phase loop
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s, & !< counter in source loop
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stiffDegradationCtr
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class (tNode), pointer :: &
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debug_constitutive, &
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phases, &
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phase, &
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elastic, &
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stiffDegradation
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debug_constitutive => debug_root%get('constitutive', defaultVal=emptyList)
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debugConstitutive%basic = debug_constitutive%contains('basic')
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debugConstitutive%extensive = debug_constitutive%contains('extensive')
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debugConstitutive%selective = debug_constitutive%contains('selective')
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debugConstitutive%element = debug_root%get_asInt('element',defaultVal = 1)
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debugConstitutive%ip = debug_root%get_asInt('integrationpoint',defaultVal = 1)
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debugConstitutive%grain = debug_root%get_asInt('grain',defaultVal = 1)
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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 => material_root%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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elastic => phase%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 => phase%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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stiffDegradation => phase%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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do p = 1, phases%length
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phase_elasticityInstance(p) = count(phase_elasticity(1:p) == phase_elasticity(p))
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enddo
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!--------------------------------------------------------------------------------------------------
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! initialize constitutive laws
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call plastic_init
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call damage_init
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call thermal_init
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write(6,'(/,a)') ' <<<+- constitutive init -+>>>'; flush(6)
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constitutive_source_maxSizeDotState = 0
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PhaseLoop2:do p = 1,phases%length
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!--------------------------------------------------------------------------------------------------
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! partition and initialize state
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plasticState(p)%partionedState0 = plasticState(p)%state0
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plasticState(p)%state = plasticState(p)%partionedState0
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forall(s = 1:phase_Nsources(p))
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sourceState(p)%p(s)%partionedState0 = sourceState(p)%p(s)%state0
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sourceState(p)%p(s)%state = sourceState(p)%p(s)%partionedState0
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end forall
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constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, &
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maxval(sourceState(p)%p%sizeDotState))
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enddo PhaseLoop2
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constitutive_plasticity_maxSizeDotState = maxval(plasticState%sizeDotState)
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end subroutine constitutive_init
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!--------------------------------------------------------------------------------------------------
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!> @brief checks if a source mechanism is active or not
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!--------------------------------------------------------------------------------------------------
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module function source_active(source_label,src_length) result(active_source)
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character(len=*), intent(in) :: source_label !< name of source mechanism
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integer, intent(in) :: src_length !< max. number of sources in system
|
|
logical, dimension(:,:), allocatable :: active_source
|
|
|
|
class(tNode), pointer :: &
|
|
phases, &
|
|
phase, &
|
|
sources, &
|
|
src
|
|
integer :: p,s
|
|
|
|
phases => material_root%get('phase')
|
|
allocate(active_source(src_length,phases%length), source = .false. )
|
|
do p = 1, phases%length
|
|
phase => phases%get(p)
|
|
sources => phase%get('source',defaultVal=emptyList)
|
|
do s = 1, sources%length
|
|
src => sources%get(s)
|
|
if(src%get_asString('type') == source_label) active_source(s,p) = .true.
|
|
enddo
|
|
enddo
|
|
|
|
|
|
end function source_active
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief checks if a kinematic mechanism is active or not
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics)
|
|
|
|
character(len=*), intent(in) :: kinematics_label !< name of kinematic mechanism
|
|
integer, intent(in) :: kinematics_length !< max. number of kinematics in system
|
|
logical, dimension(:,:), allocatable :: active_kinematics
|
|
|
|
class(tNode), pointer :: &
|
|
phases, &
|
|
phase, &
|
|
kinematics, &
|
|
kinematics_type
|
|
integer :: p,k
|
|
|
|
phases => material_root%get('phase')
|
|
allocate(active_kinematics(kinematics_length,phases%length), source = .false. )
|
|
do p = 1, phases%length
|
|
phase => phases%get(p)
|
|
kinematics => phase%get('kinematics',defaultVal=emptyList)
|
|
do k = 1, kinematics%length
|
|
kinematics_type => kinematics%get(k)
|
|
if(kinematics_type%get_asString('type') == kinematics_label) active_kinematics(k,p) = .true.
|
|
enddo
|
|
enddo
|
|
|
|
|
|
end function kinematics_active
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief returns the homogenize elasticity matrix
|
|
!> ToDo: homogenizedC66 would be more consistent
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_homogenizedC(ipc,ip,el)
|
|
|
|
real(pReal), dimension(6,6) :: &
|
|
constitutive_homogenizedC
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
|
|
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
|
|
case (PLASTICITY_DISLOTWIN_ID) plasticityType
|
|
constitutive_homogenizedC = plastic_dislotwin_homogenizedC(ipc,ip,el)
|
|
case default plasticityType
|
|
constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(ipc,el))
|
|
end select plasticityType
|
|
|
|
end function constitutive_homogenizedC
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the velocity gradient
|
|
! ToDo: MD: S is Mi?
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_LiAndItsTangents(Li, dLi_dS, dLi_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
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(out), dimension(3,3) :: &
|
|
Li !< intermediate velocity gradient
|
|
real(pReal), intent(out), dimension(3,3,3,3) :: &
|
|
dLi_dS, & !< derivative of Li with respect to S
|
|
dLi_dFi
|
|
|
|
real(pReal), dimension(3,3) :: &
|
|
my_Li, & !< intermediate velocity gradient
|
|
FiInv, &
|
|
temp_33
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
my_dLi_dS
|
|
real(pReal) :: &
|
|
detFi
|
|
integer :: &
|
|
k, i, j, &
|
|
instance, of
|
|
|
|
Li = 0.0_pReal
|
|
dLi_dS = 0.0_pReal
|
|
dLi_dFi = 0.0_pReal
|
|
|
|
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
|
|
case (PLASTICITY_isotropic_ID) plasticityType
|
|
of = material_phasememberAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
|
|
call plastic_isotropic_LiAndItsTangent(my_Li, my_dLi_dS, S ,instance,of)
|
|
case default plasticityType
|
|
my_Li = 0.0_pReal
|
|
my_dLi_dS = 0.0_pReal
|
|
end select plasticityType
|
|
|
|
Li = Li + my_Li
|
|
dLi_dS = dLi_dS + my_dLi_dS
|
|
|
|
KinematicsLoop: do k = 1, phase_Nkinematics(material_phaseAt(ipc,el))
|
|
kinematicsType: select case (phase_kinematics(k,material_phaseAt(ipc,el)))
|
|
case (KINEMATICS_cleavage_opening_ID) kinematicsType
|
|
call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
|
|
case (KINEMATICS_slipplane_opening_ID) kinematicsType
|
|
call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
|
|
case (KINEMATICS_thermal_expansion_ID) kinematicsType
|
|
call kinematics_thermal_expansion_LiAndItsTangent(my_Li, my_dLi_dS, ipc, ip, el)
|
|
case default kinematicsType
|
|
my_Li = 0.0_pReal
|
|
my_dLi_dS = 0.0_pReal
|
|
end select kinematicsType
|
|
Li = Li + my_Li
|
|
dLi_dS = dLi_dS + my_dLi_dS
|
|
enddo KinematicsLoop
|
|
|
|
FiInv = math_inv33(Fi)
|
|
detFi = math_det33(Fi)
|
|
Li = matmul(matmul(Fi,Li),FiInv)*detFi !< push forward to intermediate configuration
|
|
temp_33 = matmul(FiInv,Li)
|
|
|
|
do i = 1,3; do j = 1,3
|
|
dLi_dS(1:3,1:3,i,j) = matmul(matmul(Fi,dLi_dS(1:3,1:3,i,j)),FiInv)*detFi
|
|
dLi_dFi(1:3,1:3,i,j) = dLi_dFi(1:3,1:3,i,j) + Li*FiInv(j,i)
|
|
dLi_dFi(1:3,i,1:3,j) = dLi_dFi(1:3,i,1:3,j) + math_I3*temp_33(j,i) + Li*FiInv(j,i)
|
|
enddo; enddo
|
|
|
|
end subroutine constitutive_LiAndItsTangents
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief collects initial intermediate deformation gradient
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function constitutive_initialFi(ipc, ip, el)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), dimension(3,3) :: &
|
|
constitutive_initialFi !< composite initial intermediate deformation gradient
|
|
integer :: &
|
|
k !< counter in kinematics loop
|
|
integer :: &
|
|
phase, &
|
|
homog, offset
|
|
|
|
constitutive_initialFi = math_I3
|
|
phase = material_phaseAt(ipc,el)
|
|
|
|
KinematicsLoop: do k = 1, phase_Nkinematics(phase) !< Warning: small initial strain assumption
|
|
kinematicsType: select case (phase_kinematics(k,phase))
|
|
case (KINEMATICS_thermal_expansion_ID) kinematicsType
|
|
homog = material_homogenizationAt(el)
|
|
offset = thermalMapping(homog)%p(ip,el)
|
|
constitutive_initialFi = &
|
|
constitutive_initialFi + kinematics_thermal_expansion_initialStrain(homog,phase,offset)
|
|
end select kinematicsType
|
|
enddo KinematicsLoop
|
|
|
|
end function constitutive_initialFi
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
|
|
!> the elastic/intermediate deformation gradients depending on the selected elastic law
|
|
!! (so far no case switch because only Hooke is implemented)
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fe, & !< elastic deformation gradient
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(out), dimension(3,3) :: &
|
|
S !< 2nd Piola-Kirchhoff stress tensor
|
|
real(pReal), intent(out), dimension(3,3,3,3) :: &
|
|
dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
|
|
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
|
|
|
|
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el)
|
|
|
|
|
|
end subroutine constitutive_SandItsTangents
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
|
|
!> the elastic and intermediate deformation gradients using Hooke's law
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
Fe, Fi, ipc, ip, el)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fe, & !< elastic deformation gradient
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(out), dimension(3,3) :: &
|
|
S !< 2nd Piola-Kirchhoff stress tensor in lattice configuration
|
|
real(pReal), intent(out), dimension(3,3,3,3) :: &
|
|
dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
|
|
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
|
|
real(pReal), dimension(3,3) :: E
|
|
real(pReal), dimension(3,3,3,3) :: C
|
|
integer :: &
|
|
ho, & !< homogenization
|
|
d !< counter in degradation loop
|
|
integer :: &
|
|
i, j
|
|
|
|
ho = material_homogenizationAt(el)
|
|
C = math_66toSym3333(constitutive_homogenizedC(ipc,ip,el))
|
|
|
|
DegradationLoop: do d = 1, phase_NstiffnessDegradations(material_phaseAt(ipc,el))
|
|
degradationType: select case(phase_stiffnessDegradation(d,material_phaseAt(ipc,el)))
|
|
case (STIFFNESS_DEGRADATION_damage_ID) degradationType
|
|
C = C * damage(ho)%p(damageMapping(ho)%p(ip,el))**2
|
|
end select degradationType
|
|
enddo DegradationLoop
|
|
|
|
E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration
|
|
S = math_mul3333xx33(C,matmul(matmul(transpose(Fi),E),Fi)) !< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration
|
|
|
|
do i =1, 3;do j=1,3
|
|
dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko
|
|
dS_dFi(i,j,1:3,1:3) = 2.0_pReal*matmul(matmul(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn
|
|
enddo; enddo
|
|
|
|
end subroutine constitutive_hooke_SandItsTangents
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
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_maxNgrains,discretization_nIP,discretization_nElem) :: &
|
|
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 = thermalMapping(ho)%p(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)))
|
|
|
|
SourceLoop: do i = 1, phase_Nsources(phase)
|
|
|
|
sourceType: select case (phase_source(i,phase))
|
|
|
|
case (SOURCE_damage_anisoBrittle_ID) sourceType
|
|
call source_damage_anisoBrittle_dotState(S, ipc, ip, el) ! correct stress?
|
|
|
|
case (SOURCE_damage_isoDuctile_ID) sourceType
|
|
call source_damage_isoDuctile_dotState(ipc, ip, el)
|
|
|
|
case (SOURCE_damage_anisoDuctile_ID) sourceType
|
|
call source_damage_anisoDuctile_dotState(ipc, ip, el)
|
|
|
|
case (SOURCE_thermal_externalheat_ID) sourceType
|
|
call source_thermal_externalheat_dotState(phase,of)
|
|
|
|
end select sourceType
|
|
|
|
broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%dotState(:,of)))
|
|
|
|
enddo SourceLoop
|
|
|
|
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
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_deltaState(S, Fe, 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
|
|
Fe, & !< elastic deformation gradient
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), dimension(3,3) :: &
|
|
Mp
|
|
integer :: &
|
|
i, &
|
|
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
|
|
|
|
|
|
sourceLoop: do i = 1, phase_Nsources(phase)
|
|
|
|
sourceType: select case (phase_source(i,phase))
|
|
|
|
case (SOURCE_damage_isoBrittle_ID) sourceType
|
|
call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(ipc,ip,el), Fe, &
|
|
ipc, ip, el)
|
|
broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%deltaState(:,of)))
|
|
if(.not. broken) then
|
|
myOffset = sourceState(phase)%p(i)%offsetDeltaState
|
|
mySize = sourceState(phase)%p(i)%sizeDeltaState
|
|
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) = &
|
|
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) + sourceState(phase)%p(i)%deltaState(1:mySize,of)
|
|
endif
|
|
|
|
end select sourceType
|
|
|
|
enddo SourceLoop
|
|
|
|
end function constitutive_deltaState
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Allocate the components of the state structure for a given phase
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_allocateState(state, &
|
|
NipcMyPhase,sizeState,sizeDotState,sizeDeltaState)
|
|
|
|
class(tState), intent(out) :: &
|
|
state
|
|
integer, intent(in) :: &
|
|
NipcMyPhase, &
|
|
sizeState, &
|
|
sizeDotState, &
|
|
sizeDeltaState
|
|
|
|
state%sizeState = sizeState
|
|
state%sizeDotState = sizeDotState
|
|
state%sizeDeltaState = sizeDeltaState
|
|
state%offsetDeltaState = sizeState-sizeDeltaState ! deltaState occupies latter part of state by definition
|
|
|
|
allocate(state%atol (sizeState), source=0.0_pReal)
|
|
allocate(state%state0 (sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(state%partionedState0(sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(state%subState0 (sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(state%state (sizeState,NipcMyPhase), source=0.0_pReal)
|
|
|
|
allocate(state%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
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allocate(state%deltaState(sizeDeltaState,NipcMyPhase), source=0.0_pReal)
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end subroutine constitutive_allocateState
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!--------------------------------------------------------------------------------------------------
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!> @brief writes constitutive results to HDF5 output file
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_results
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call plastic_results
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call damage_results
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end subroutine constitutive_results
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end module constitutive
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