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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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!--------------------------------------------------------------------------------------------------
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
use config
use material
use results
use lattice
use discretization
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use geometry_plastic_nonlocal , only : &
geometry_plastic_nonlocal_disable
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implicit none
private
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integer ( kind ( ELASTICITY_undefined_ID ) ) , dimension ( : ) , allocatable , protected :: &
phase_elasticity !< elasticity of each phase
integer ( kind ( PLASTICITY_undefined_ID ) ) , dimension ( : ) , allocatable :: & !ToDo: old intel compiler complains about protected
phase_plasticity !< plasticity of each phase
integer ( kind ( SOURCE_undefined_ID ) ) , dimension ( : , : ) , allocatable :: & ! ToDo: old intel compiler complains about protected
phase_source , & !< active sources mechanisms of each phase
phase_kinematics , & !< active kinematic mechanisms of each phase
phase_stiffnessDegradation !< active stiffness degradation mechanisms of each phase
integer , dimension ( : ) , allocatable , public :: & ! ToDo: old intel compiler complains about protected
phase_Nsources , & !< number of source mechanisms active in each phase
phase_Nkinematics , & !< number of kinematic mechanisms active in each phase
phase_NstiffnessDegradations , & !< number of stiffness degradation mechanisms active in each phase
phase_plasticityInstance , & !< instance of particular plasticity of each phase
phase_elasticityInstance !< instance of particular elasticity of each phase
logical , dimension ( : ) , allocatable , public :: & ! ToDo: old intel compiler complains about protected
phase_localPlasticity !< flags phases with local constitutive law
type ( tPlasticState ) , allocatable , dimension ( : ) , public :: &
plasticState
type ( tSourceState ) , allocatable , dimension ( : ) , public :: &
sourceState
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integer , public , protected :: &
constitutive_plasticity_maxSizeDotState , &
constitutive_source_maxSizeDotState
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interface
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module subroutine plastic_init
end subroutine plastic_init
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module subroutine damage_init
end subroutine damage_init
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module subroutine thermal_init
end subroutine thermal_init
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module function plastic_active ( plastic_label ) result ( active_plastic )
character ( len = * ) , intent ( in ) :: plastic_label
logical , dimension ( : ) , allocatable :: active_plastic
end function plastic_active
module function source_active ( source_label , src_length ) result ( active_source )
character ( len = * ) , intent ( in ) :: source_label
integer , intent ( in ) :: src_length
logical , dimension ( : , : ) , allocatable :: active_source
end function source_active
module function kinematics_active ( kinematics_label , kinematics_length ) result ( active_kinematics )
character ( len = * ) , intent ( in ) :: kinematics_label
integer , intent ( in ) :: kinematics_length
logical , dimension ( : , : ) , allocatable :: active_kinematics
end function kinematics_active
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module subroutine plastic_isotropic_dotState ( Mp , instance , of )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
integer , intent ( in ) :: &
instance , &
of
end subroutine plastic_isotropic_dotState
module subroutine plastic_phenopowerlaw_dotState ( Mp , instance , of )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
integer , intent ( in ) :: &
instance , &
of
end subroutine plastic_phenopowerlaw_dotState
module subroutine plastic_kinehardening_dotState ( Mp , instance , of )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
integer , intent ( in ) :: &
instance , &
of
end subroutine plastic_kinehardening_dotState
module subroutine plastic_dislotwin_dotState ( Mp , T , instance , of )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
real ( pReal ) , intent ( in ) :: &
T
integer , intent ( in ) :: &
instance , &
of
end subroutine plastic_dislotwin_dotState
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module subroutine plastic_disloTungsten_dotState ( Mp , T , instance , of )
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
Mp !< Mandel stress
real ( pReal ) , intent ( in ) :: &
T
integer , intent ( in ) :: &
instance , &
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 )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
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Mp !< MandelStress
real ( pReal ) , dimension ( 3 , 3 , homogenization_maxNgrains , discretization_nIP , discretization_nElem ) , intent ( in ) :: &
F , & !< deformation gradient
Fp !< plastic deformation gradient
real ( pReal ) , intent ( in ) :: &
Temperature , & !< temperature
timestep !< substepped crystallite time increment
integer , intent ( in ) :: &
instance , &
of , &
ip , & !< current integration point
el !< current element number
end subroutine plastic_nonlocal_dotState
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module subroutine source_damage_anisoBrittle_dotState ( S , ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
end subroutine source_damage_anisoBrittle_dotState
module subroutine source_damage_anisoDuctile_dotState ( ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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end subroutine source_damage_anisoDuctile_dotState
module subroutine source_damage_isoDuctile_dotState ( ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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end subroutine source_damage_isoDuctile_dotState
module subroutine source_thermal_externalheat_dotState ( phase , of )
integer , intent ( in ) :: &
phase , &
of
end subroutine source_thermal_externalheat_dotState
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module subroutine constitutive_damage_getRateAndItsTangents ( phiDot , dPhiDot_dPhi , phi , ip , el )
integer , intent ( in ) :: &
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( in ) :: &
phi !< damage parameter
real ( pReal ) , intent ( inout ) :: &
phiDot , &
dPhiDot_dPhi
end subroutine constitutive_damage_getRateAndItsTangents
module subroutine constitutive_thermal_getRateAndItsTangents ( TDot , dTDot_dT , T , S , Lp , ip , el )
integer , intent ( in ) :: &
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( in ) :: &
T
real ( pReal ) , intent ( in ) , dimension ( : , : , : , : , : ) :: &
S , & !< current 2nd Piola Kitchoff stress vector
Lp !< plastic velocity gradient
real ( pReal ) , intent ( inout ) :: &
TDot , &
dTDot_dT
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 ) :: &
homogenizedC
integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
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 )
integer , intent ( in ) :: &
phase , &
homog , &
offset
real ( pReal ) , dimension ( 3 , 3 ) :: &
initialStrain
end function kinematics_thermal_expansion_initialStrain
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module subroutine plastic_nonlocal_updateCompatibility ( orientation , instance , i , e )
integer , intent ( in ) :: &
instance , &
i , &
e
type ( rotation ) , dimension ( 1 , discretization_nIP , discretization_nElem ) , intent ( in ) :: &
orientation !< crystal orientation
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 ) :: &
Li !< inleastic velocity gradient
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( out ) :: &
dLi_dMi !< derivative of Li with respect to Mandel stress
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
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Mi !< Mandel stress
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integer , intent ( in ) :: &
instance , &
of
end subroutine plastic_isotropic_LiAndItsTangent
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module subroutine kinematics_cleavage_opening_LiAndItsTangent ( Ld , dLd_dTstar , S , ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< grain number
ip , & !< integration point number
el !< element number
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
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
module subroutine kinematics_slipplane_opening_LiAndItsTangent ( Ld , dLd_dTstar , S , ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< grain number
ip , & !< integration point number
el !< element number
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
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
module subroutine kinematics_thermal_expansion_LiAndItsTangent ( Li , dLi_dTstar , ipc , ip , el )
integer , intent ( in ) :: &
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ipc , & !< grain number
ip , & !< integration point number
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 ) :: &
Mp !< Mandel stress
integer , intent ( in ) :: &
instance , &
of
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 ) :: &
Mp
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integer , intent ( in ) :: &
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instance , &
of , &
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ip , &
el
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
ip , & !< integration point
el !< element
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
Fe
real ( pReal ) , intent ( in ) , dimension ( 6 , 6 ) :: &
C
end subroutine source_damage_isoBrittle_deltaState
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module subroutine plastic_results
end subroutine plastic_results
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module subroutine damage_results
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 , &
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
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 )
integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
F , & !< elastic deformation gradient
Fp !< plastic deformation gradient
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end subroutine constitutive_plastic_dependentState
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end interface constitutive_dependentState
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type :: tDebugOptions
logical :: &
basic , &
extensive , &
selective
integer :: &
element , &
ip , &
grain
end type tDebugOptions
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type ( tDebugOptions ) :: debugConstitutive
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public :: &
constitutive_init , &
constitutive_homogenizedC , &
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constitutive_LpAndItsTangents , &
constitutive_dependentState , &
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constitutive_LiAndItsTangents , &
constitutive_initialFi , &
constitutive_SandItsTangents , &
constitutive_collectDotState , &
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constitutive_deltaState , &
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constitutive_damage_getRateAndItsTangents , &
constitutive_thermal_getRateAndItsTangents , &
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constitutive_results , &
constitutive_allocateState , &
plastic_nonlocal_updateCompatibility , &
plastic_active , &
source_active , &
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
s , & !< counter in source loop
stiffDegradationCtr
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class ( tNode ) , pointer :: &
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debug_constitutive , &
phases , &
phase , &
elastic , &
stiffDegradation
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debug_constitutive = > config_debug % get ( 'constitutive' , defaultVal = emptyList )
debugConstitutive % basic = debug_constitutive % contains ( 'basic' )
debugConstitutive % extensive = debug_constitutive % contains ( 'extensive' )
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debugConstitutive % selective = debug_constitutive % contains ( 'selective' )
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debugConstitutive % element = config_debug % get_asInt ( 'element' , defaultVal = 1 )
debugConstitutive % ip = config_debug % get_asInt ( 'integrationpoint' , defaultVal = 1 )
debugConstitutive % grain = config_debug % get_asInt ( 'grain' , defaultVal = 1 )
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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 )
allocate ( phase_elasticityInstance ( phases % length ) , source = 0 )
allocate ( phase_NstiffnessDegradations ( phases % length ) , source = 0 )
do p = 1 , phases % length
phase = > phases % get ( p )
elastic = > phase % get ( 'elasticity' )
if ( elastic % get_asString ( 'type' ) == 'hooke' ) then
phase_elasticity ( p ) = ELASTICITY_HOOKE_ID
else
call IO_error ( 200 , ext_msg = elastic % get_asString ( 'type' ) )
endif
stiffDegradation = > phase % get ( 'stiffness_degradation' , defaultVal = emptyList ) ! check for stiffness degradation mechanisms
phase_NstiffnessDegradations ( p ) = stiffDegradation % length
enddo
allocate ( phase_stiffnessDegradation ( maxval ( phase_NstiffnessDegradations ) , phases % length ) , &
source = STIFFNESS_DEGRADATION_undefined_ID )
if ( maxVal ( phase_NstiffnessDegradations ) / = 0 ) then
do p = 1 , phases % length
phase = > phases % get ( p )
stiffDegradation = > phase % get ( 'stiffness_degradation' , defaultVal = emptyList )
do stiffDegradationCtr = 1 , stiffDegradation % length
if ( stiffDegradation % get_asString ( stiffDegradationCtr ) == 'damage' ) &
phase_stiffnessDegradation ( stiffDegradationCtr , p ) = STIFFNESS_DEGRADATION_damage_ID
enddo
enddo
endif
do p = 1 , phases % length
phase_elasticityInstance ( p ) = count ( phase_elasticity ( 1 : p ) == phase_elasticity ( p ) )
enddo
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!--------------------------------------------------------------------------------------------------
! initialize constitutive laws
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call plastic_init
call damage_init
call thermal_init
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print '(/,a)' , ' <<<+- constitutive init -+>>>' ; flush ( IO_STDOUT )
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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 ) % partitionedState0 = plasticState ( p ) % state0
plasticState ( p ) % state = plasticState ( p ) % partitionedState0
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forall ( s = 1 : phase_Nsources ( p ) )
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sourceState ( p ) % p ( s ) % partitionedState0 = sourceState ( p ) % p ( s ) % state0
sourceState ( p ) % p ( s ) % state = sourceState ( p ) % p ( s ) % partitionedState0
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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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!--------------------------------------------------------------------------------------------------
!> @brief checks if a source mechanism is active or not
!--------------------------------------------------------------------------------------------------
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 , &
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src
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integer :: p , s
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phases = > config_material % get ( 'phase' )
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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 , &
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kinematics_type
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integer :: p , k
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phases = > config_material % get ( 'phase' )
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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
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!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenize elasticity matrix
!> ToDo: homogenizedC66 would be more consistent
!--------------------------------------------------------------------------------------------------
function constitutive_homogenizedC ( ipc , ip , el )
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real ( pReal ) , dimension ( 6 , 6 ) :: &
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constitutive_homogenizedC
integer , intent ( in ) :: &
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ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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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
openmp parallelization working again (at least for j2 and nonlocal constitutive model).
In order to keep it like that, please follow these simple rules:
DON'T use implicit array subscripts:
example: real, dimension(3,3) :: A,B
A(:,2) = B(:,1) <--- DON'T USE
A(1:3,2) = B(1:3,1) <--- BETTER USE
In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks.
Enclose all write statements with the following:
!$OMP CRITICAL (write2out)
<your write statement>
!$OMP END CRITICAL (write2out)
Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
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!--------------------------------------------------------------------------------------------------
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!> @brief contains the constitutive equation for calculating the velocity gradient
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! ToDo: MD: S is Mi?
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_LiAndItsTangents ( Li , dLi_dS , dLi_dFi , &
S , Fi , ipc , ip , el )
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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
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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
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Li = 0.0_pReal
dLi_dS = 0.0_pReal
dLi_dFi = 0.0_pReal
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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 ) )
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call plastic_isotropic_LiAndItsTangent ( my_Li , my_dLi_dS , S , instance , of )
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case default plasticityType
my_Li = 0.0_pReal
my_dLi_dS = 0.0_pReal
end select plasticityType
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Li = Li + my_Li
dLi_dS = dLi_dS + my_dLi_dS
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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
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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 )
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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 )
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enddo ; enddo
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end subroutine constitutive_LiAndItsTangents
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openmp parallelization working again (at least for j2 and nonlocal constitutive model).
In order to keep it like that, please follow these simple rules:
DON'T use implicit array subscripts:
example: real, dimension(3,3) :: A,B
A(:,2) = B(:,1) <--- DON'T USE
A(1:3,2) = B(1:3,1) <--- BETTER USE
In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks.
Enclose all write statements with the following:
!$OMP CRITICAL (write2out)
<your write statement>
!$OMP END CRITICAL (write2out)
Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
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!--------------------------------------------------------------------------------------------------
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!> @brief collects initial intermediate deformation gradient
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!--------------------------------------------------------------------------------------------------
pure function constitutive_initialFi ( ipc , ip , el )
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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
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constitutive_initialFi = math_I3
phase = material_phaseAt ( ipc , el )
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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 = &
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constitutive_initialFi + kinematics_thermal_expansion_initialStrain ( homog , phase , offset )
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end select kinematicsType
enddo KinematicsLoop
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end function constitutive_initialFi
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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/intermediate deformation gradients depending on the selected elastic law
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!! (so far no case switch because only Hooke is implemented)
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_SandItsTangents ( S , dS_dFe , dS_dFi , Fe , Fi , ipc , ip , el )
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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
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call constitutive_hooke_SandItsTangents ( S , dS_dFe , dS_dFi , Fe , Fi , ipc , ip , el )
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end subroutine constitutive_SandItsTangents
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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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subroutine constitutive_hooke_SandItsTangents ( S , dS_dFe , dS_dFi , &
Fe , Fi , ipc , ip , el )
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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
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ho = material_homogenizationAt ( el )
C = math_66toSym3333 ( constitutive_homogenizedC ( ipc , ip , el ) )
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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
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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
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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
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 contains the constitutive equation for calculating the rate of change of microstructure
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!--------------------------------------------------------------------------------------------------
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function constitutive_collectDotState ( S , FArray , Fi , FpArray , subdt , ipc , ip , el , phase , of ) result ( broken )
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integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
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el , & !< element
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phase , &
of
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real ( pReal ) , intent ( in ) :: &
subdt !< timestep
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 , homogenization_maxNgrains , discretization_nIP , discretization_nElem ) :: &
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FArray , & !< elastic deformation gradient
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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)
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real ( pReal ) , dimension ( 3 , 3 ) :: &
Mp
integer :: &
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ho , & !< homogenization
tme , & !< thermal member position
i , & !< counter in source loop
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instance
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logical :: broken
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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
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call plastic_isotropic_dotState ( Mp , instance , of )
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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
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call plastic_dislotwin_dotState ( Mp , temperature ( ho ) % p ( tme ) , instance , of )
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case ( PLASTICITY_DISLOTUNGSTEN_ID ) plasticityType
call plastic_disloTungsten_dotState ( Mp , temperature ( ho ) % p ( tme ) , instance , of )
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case ( PLASTICITY_NONLOCAL_ID ) plasticityType
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call plastic_nonlocal_dotState ( Mp , FArray , FpArray , temperature ( ho ) % p ( tme ) , subdt , &
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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
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call source_damage_anisoBrittle_dotState ( S , ipc , ip , el ) ! correct stress?
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case ( SOURCE_damage_isoDuctile_ID ) sourceType
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call source_damage_isoDuctile_dotState ( ipc , ip , el )
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case ( SOURCE_damage_anisoDuctile_ID ) sourceType
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call source_damage_anisoDuctile_dotState ( ipc , ip , el )
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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
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end function constitutive_collectDotState
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!--------------------------------------------------------------------------------------------------
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!> @brief for constitutive models having an instantaneous change of state
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!> will return false if delta state is not needed/supported by the constitutive model
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!--------------------------------------------------------------------------------------------------
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function constitutive_deltaState ( S , Fe , Fi , ipc , ip , el , phase , of ) result ( broken )
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integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
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el , & !< element
phase , &
of
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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 , &
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instance , &
myOffset , &
mySize
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logical :: &
broken
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Mp = matmul ( matmul ( transpose ( Fi ) , Fi ) , S )
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instance = phase_plasticityInstance ( phase )
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plasticityType : select case ( phase_plasticity ( phase ) )
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case ( PLASTICITY_KINEHARDENING_ID ) plasticityType
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call plastic_kinehardening_deltaState ( Mp , instance , of )
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broken = any ( IEEE_is_NaN ( plasticState ( phase ) % deltaState ( : , of ) ) )
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case ( PLASTICITY_NONLOCAL_ID ) plasticityType
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call plastic_nonlocal_deltaState ( Mp , instance , of , ip , el )
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broken = any ( IEEE_is_NaN ( plasticState ( phase ) % deltaState ( : , of ) ) )
case default
broken = . false .
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end select plasticityType
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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
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sourceLoop : do i = 1 , phase_Nsources ( phase )
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sourceType : select case ( phase_source ( i , phase ) )
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case ( SOURCE_damage_isoBrittle_ID ) sourceType
call source_damage_isoBrittle_deltaState ( constitutive_homogenizedC ( ipc , ip , el ) , Fe , &
ipc , ip , el )
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broken = broken . or . any ( IEEE_is_NaN ( sourceState ( phase ) % p ( i ) % deltaState ( : , of ) ) )
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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
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end select sourceType
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enddo SourceLoop
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end function constitutive_deltaState
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!--------------------------------------------------------------------------------------------------
!> @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 )
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allocate ( state % partitionedState0 ( sizeState , NipcMyPhase ) , source = 0.0_pReal )
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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 )
allocate ( state % deltaState ( sizeDeltaState , NipcMyPhase ) , source = 0.0_pReal )
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
call damage_results
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end subroutine constitutive_results
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end module constitutive
