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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 parallelization
use HDF5_utilities
use DAMASK_interface
use results
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implicit none
private
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enum , bind ( c ) ; enumerator :: &
PLASTICITY_UNDEFINED_ID , &
PLASTICITY_NONE_ID , &
PLASTICITY_ISOTROPIC_ID , &
PLASTICITY_PHENOPOWERLAW_ID , &
PLASTICITY_KINEHARDENING_ID , &
PLASTICITY_DISLOTWIN_ID , &
PLASTICITY_DISLOTUNGSTEN_ID , &
PLASTICITY_NONLOCAL_ID , &
SOURCE_UNDEFINED_ID , &
SOURCE_THERMAL_DISSIPATION_ID , &
SOURCE_THERMAL_EXTERNALHEAT_ID , &
SOURCE_DAMAGE_ISOBRITTLE_ID , &
SOURCE_DAMAGE_ISODUCTILE_ID , &
SOURCE_DAMAGE_ANISOBRITTLE_ID , &
SOURCE_DAMAGE_ANISODUCTILE_ID , &
KINEMATICS_UNDEFINED_ID , &
KINEMATICS_CLEAVAGE_OPENING_ID , &
KINEMATICS_SLIPPLANE_OPENING_ID , &
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KINEMATICS_THERMAL_EXPANSION_ID
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end enum
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real ( pReal ) , dimension ( : , : , : ) , allocatable :: &
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crystallite_subdt !< substepped time increment of each grain
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type ( rotation ) , dimension ( : , : , : ) , allocatable :: &
crystallite_orientation !< current orientation
real ( pReal ) , dimension ( : , : , : , : , : ) , allocatable :: &
crystallite_F0 , & !< def grad at start of FE inc
crystallite_Fe , & !< current "elastic" def grad (end of converged time step)
crystallite_subFp0 , & !< plastic def grad at start of crystallite inc
crystallite_subFi0 , & !< intermediate def grad at start of crystallite inc
crystallite_Lp0 , & !< plastic velocitiy grad at start of FE inc
crystallite_partitionedLp0 , & !< plastic velocity grad at start of homog inc
crystallite_S0 , & !< 2nd Piola-Kirchhoff stress vector at start of FE inc
crystallite_partitionedS0 !< 2nd Piola-Kirchhoff stress vector at start of homog inc
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real ( pReal ) , dimension ( : , : , : , : , : ) , allocatable , public :: &
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crystallite_P , & !< 1st Piola-Kirchhoff stress per grain
crystallite_Lp , & !< current plastic velocitiy grad (end of converged time step)
crystallite_S , & !< current 2nd Piola-Kirchhoff stress vector (end of converged time step)
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crystallite_partitionedF0 , & !< def grad at start of homog inc
crystallite_F !< def grad to be reached at end of homog inc
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type :: tTensorContainer
real ( pReal ) , dimension ( : , : , : ) , allocatable :: data
end type
type ( tTensorContainer ) , dimension ( : ) , allocatable :: &
constitutive_mech_Fi , &
constitutive_mech_Fi0 , &
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constitutive_mech_partitionedFi0 , &
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constitutive_mech_Li , &
constitutive_mech_Li0 , &
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constitutive_mech_partitionedLi0 , &
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constitutive_mech_Fp , &
constitutive_mech_Fp0 , &
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constitutive_mech_partitionedFp0
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type :: tNumerics
integer :: &
iJacoLpresiduum , & !< frequency of Jacobian update of residuum in Lp
nState , & !< state loop limit
nStress !< stress loop limit
real ( pReal ) :: &
subStepMinCryst , & !< minimum (relative) size of sub-step allowed during cutback
subStepSizeCryst , & !< size of first substep when cutback
subStepSizeLp , & !< size of first substep when cutback in Lp calculation
subStepSizeLi , & !< size of first substep when cutback in Li calculation
stepIncreaseCryst , & !< increase of next substep size when previous substep converged
rtol_crystalliteState , & !< relative tolerance in state loop
rtol_crystalliteStress , & !< relative tolerance in stress loop
atol_crystalliteStress !< absolute tolerance in stress loop
end type tNumerics
type ( tNumerics ) :: num ! numerics parameters. Better name?
type :: tDebugOptions
logical :: &
basic , &
extensive , &
selective
integer :: &
element , &
ip , &
grain
end type tDebugOptions
type ( tDebugOptions ) :: debugCrystallite
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integer ( kind ( PLASTICITY_undefined_ID ) ) , dimension ( : ) , allocatable , public :: &
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phase_plasticity !< plasticity of each phase
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integer ( kind ( SOURCE_undefined_ID ) ) , dimension ( : , : ) , allocatable :: &
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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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integer , dimension ( : ) , allocatable , public :: & !< ToDo: should be protected (bug in Intel compiler)
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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
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logical , dimension ( : ) , allocatable , public :: & ! ToDo: should be protected (bug in Intel Compiler)
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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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! == cleaned:begin =================================================================================
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module subroutine mech_init
end subroutine mech_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 subroutine mech_results ( group , ph )
character ( len = * ) , intent ( in ) :: group
integer , intent ( in ) :: ph
end subroutine mech_results
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module subroutine damage_results ( group , ph )
character ( len = * ) , intent ( in ) :: group
integer , intent ( in ) :: ph
end subroutine damage_results
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module subroutine mech_restart_read ( fileHandle )
integer ( HID_T ) , intent ( in ) :: fileHandle
end subroutine mech_restart_read
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module subroutine mech_initializeRestorationPoints ( ph , me )
integer , intent ( in ) :: ph , me
end subroutine mech_initializeRestorationPoints
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module subroutine constitutive_mech_windForward ( ph , me )
integer , intent ( in ) :: ph , me
end subroutine constitutive_mech_windForward
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module subroutine constitutive_mech_forward
end subroutine constitutive_mech_forward
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module subroutine mech_restore ( ip , el , includeL )
integer , intent ( in ) :: &
ip , &
el
logical , intent ( in ) :: &
includeL
end subroutine mech_restore
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! == cleaned:end ===================================================================================
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module function crystallite_stress ( dt , co , ip , el ) result ( converged_ )
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real ( pReal ) , intent ( in ) :: dt
integer , intent ( in ) :: co , ip , el
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logical :: converged_
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end function crystallite_stress
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module function constitutive_homogenizedC ( co , ip , el ) result ( C )
integer , intent ( in ) :: co , ip , el
real ( pReal ) , dimension ( 6 , 6 ) :: C
end function constitutive_homogenizedC
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module subroutine source_damage_anisoBrittle_dotState ( S , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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ip , & !< integration point
el !< element
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real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
end subroutine source_damage_anisoBrittle_dotState
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module subroutine source_damage_anisoDuctile_dotState ( co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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ip , & !< integration point
el !< element
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end subroutine source_damage_anisoDuctile_dotState
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module subroutine source_damage_isoDuctile_dotState ( co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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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 subroutine plastic_nonlocal_updateCompatibility ( orientation , instance , i , e )
integer , intent ( in ) :: &
instance , &
i , &
e
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type ( rotation ) , dimension ( 1 , discretization_nIPs , discretization_Nelems ) , intent ( in ) :: &
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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 , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< grain number
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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
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module subroutine kinematics_slipplane_opening_LiAndItsTangent ( Ld , dLd_dTstar , S , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< grain number
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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
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module subroutine kinematics_thermal_expansion_LiAndItsTangent ( Li , dLi_dTstar , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< grain number
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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 source_damage_isoBrittle_deltaState ( C , Fe , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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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 constitutive_plastic_LpAndItsTangents ( Lp , dLp_dS , dLp_dFi , &
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S , Fi , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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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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module subroutine constitutive_plastic_dependentState ( F , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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ip , & !< integration point
el !< element
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
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F !< elastic deformation gradient
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end subroutine constitutive_plastic_dependentState
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module subroutine constitutive_hooke_SandItsTangents ( S , dS_dFe , dS_dFi , Fe , Fi , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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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
end subroutine constitutive_hooke_SandItsTangents
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end interface
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type ( tDebugOptions ) :: debugConstitutive
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public :: &
constitutive_init , &
constitutive_homogenizedC , &
constitutive_LiAndItsTangents , &
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constitutive_damage_getRateAndItsTangents , &
constitutive_thermal_getRateAndItsTangents , &
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constitutive_results , &
constitutive_allocateState , &
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constitutive_forward , &
constitutive_restore , &
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plastic_nonlocal_updateCompatibility , &
source_active , &
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kinematics_active , &
converged , &
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crystallite_init , &
crystallite_stress , &
crystallite_stressTangent , &
crystallite_orientations , &
crystallite_push33ToRef , &
crystallite_restartWrite , &
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integrateSourceState , &
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crystallite_restartRead , &
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constitutive_initializeRestorationPoints , &
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constitutive_windForward , &
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PLASTICITY_UNDEFINED_ID , &
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PLASTICITY_NONE_ID , &
PLASTICITY_ISOTROPIC_ID , &
PLASTICITY_PHENOPOWERLAW_ID , &
PLASTICITY_KINEHARDENING_ID , &
PLASTICITY_DISLOTWIN_ID , &
PLASTICITY_DISLOTUNGSTEN_ID , &
PLASTICITY_NONLOCAL_ID , &
SOURCE_UNDEFINED_ID , &
SOURCE_THERMAL_DISSIPATION_ID , &
SOURCE_THERMAL_EXTERNALHEAT_ID , &
SOURCE_DAMAGE_ISOBRITTLE_ID , &
SOURCE_DAMAGE_ISODUCTILE_ID , &
SOURCE_DAMAGE_ANISOBRITTLE_ID , &
SOURCE_DAMAGE_ANISODUCTILE_ID , &
KINEMATICS_UNDEFINED_ID , &
KINEMATICS_CLEAVAGE_OPENING_ID , &
KINEMATICS_SLIPPLANE_OPENING_ID , &
KINEMATICS_THERMAL_EXPANSION_ID
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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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ph , & !< counter in phase loop
so !< counter in source loop
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class ( tNode ) , pointer :: &
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debug_constitutive , &
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phases
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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 constitutive laws
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print '(/,a)' , ' <<<+- constitutive init -+>>>' ; flush ( IO_STDOUT )
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call mech_init
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call damage_init
call thermal_init
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phases = > config_material % get ( 'phase' )
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constitutive_source_maxSizeDotState = 0
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PhaseLoop2 : do ph = 1 , phases % length
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!--------------------------------------------------------------------------------------------------
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! partition and initialize state
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plasticState ( ph ) % partitionedState0 = plasticState ( ph ) % state0
plasticState ( ph ) % state = plasticState ( ph ) % partitionedState0
forall ( so = 1 : phase_Nsources ( ph ) )
sourceState ( ph ) % p ( so ) % partitionedState0 = sourceState ( ph ) % p ( so ) % state0
sourceState ( ph ) % p ( so ) % state = sourceState ( ph ) % p ( so ) % partitionedState0
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end forall
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constitutive_source_maxSizeDotState = max ( constitutive_source_maxSizeDotState , &
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maxval ( sourceState ( ph ) % 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
!--------------------------------------------------------------------------------------------------
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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
!--------------------------------------------------------------------------------------------------
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function kinematics_active ( kinematics_label , kinematics_length ) result ( active_kinematics )
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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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!--------------------------------------------------------------------------------------------------
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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 , &
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S , Fi , co , ip , el )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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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 ( co , el ) ) )
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case ( PLASTICITY_isotropic_ID ) plasticityType
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of = material_phasememberAt ( co , ip , el )
instance = phase_plasticityInstance ( material_phaseAt ( co , 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 ( co , el ) )
kinematicsType : select case ( phase_kinematics ( k , material_phaseAt ( co , el ) ) )
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case ( KINEMATICS_cleavage_opening_ID ) kinematicsType
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call kinematics_cleavage_opening_LiAndItsTangent ( my_Li , my_dLi_dS , S , co , ip , el )
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case ( KINEMATICS_slipplane_opening_ID ) kinematicsType
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call kinematics_slipplane_opening_LiAndItsTangent ( my_Li , my_dLi_dS , S , co , ip , el )
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case ( KINEMATICS_thermal_expansion_ID ) kinematicsType
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call kinematics_thermal_expansion_LiAndItsTangent ( my_Li , my_dLi_dS , co , ip , el )
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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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!--------------------------------------------------------------------------------------------------
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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function constitutive_damage_collectDotState ( S , co , ip , el , ph , of ) result ( broken )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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ip , & !< integration point
el , & !< element
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ph , &
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of
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S !< 2nd Piola Kirchhoff stress (vector notation)
integer :: &
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so !< counter in source loop
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logical :: broken
broken = . false .
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SourceLoop : do so = 1 , phase_Nsources ( ph )
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sourceType : select case ( phase_source ( so , ph ) )
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case ( SOURCE_damage_anisoBrittle_ID ) sourceType
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call source_damage_anisoBrittle_dotState ( S , co , ip , el ) ! correct stress?
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case ( SOURCE_damage_isoDuctile_ID ) sourceType
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call source_damage_isoDuctile_dotState ( co , ip , el )
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case ( SOURCE_damage_anisoDuctile_ID ) sourceType
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call source_damage_anisoDuctile_dotState ( co , ip , el )
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end select sourceType
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broken = broken . or . any ( IEEE_is_NaN ( sourceState ( ph ) % p ( so ) % dotState ( : , of ) ) )
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enddo SourceLoop
end function constitutive_damage_collectDotState
!--------------------------------------------------------------------------------------------------
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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function constitutive_thermal_collectDotState ( ph , me ) result ( broken )
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integer , intent ( in ) :: ph , me
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logical :: broken
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integer :: i
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broken = . false .
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SourceLoop : do i = 1 , phase_Nsources ( ph )
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if ( phase_source ( i , ph ) == SOURCE_thermal_externalheat_ID ) &
call source_thermal_externalheat_dotState ( ph , me )
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broken = broken . or . any ( IEEE_is_NaN ( sourceState ( ph ) % p ( i ) % dotState ( : , me ) ) )
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enddo SourceLoop
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end function constitutive_thermal_collectDotState
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!--------------------------------------------------------------------------------------------------
!> @brief for constitutive models having an instantaneous change of state
!> will return false if delta state is not needed/supported by the constitutive model
!--------------------------------------------------------------------------------------------------
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function constitutive_damage_deltaState ( Fe , co , ip , el , ph , of ) result ( broken )
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integer , intent ( in ) :: &
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co , & !< component-ID of integration point
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ip , & !< integration point
el , & !< element
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ph , &
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of
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
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Fe !< elastic deformation gradient
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integer :: &
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so , &
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myOffset , &
mySize
logical :: &
broken
broken = . false .
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sourceLoop : do so = 1 , phase_Nsources ( ph )
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sourceType : select case ( phase_source ( so , ph ) )
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case ( SOURCE_damage_isoBrittle_ID ) sourceType
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call source_damage_isoBrittle_deltaState ( constitutive_homogenizedC ( co , ip , el ) , Fe , &
co , ip , el )
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broken = any ( IEEE_is_NaN ( sourceState ( ph ) % p ( so ) % deltaState ( : , of ) ) )
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if ( . not . broken ) then
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myOffset = sourceState ( ph ) % p ( so ) % offsetDeltaState
mySize = sourceState ( ph ) % p ( so ) % sizeDeltaState
sourceState ( ph ) % p ( so ) % state ( myOffset + 1 : myOffset + mySize , of ) = &
sourceState ( ph ) % p ( so ) % state ( myOffset + 1 : myOffset + mySize , of ) + sourceState ( ph ) % p ( so ) % deltaState ( 1 : mySize , of )
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endif
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end select sourceType
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enddo SourceLoop
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end function constitutive_damage_deltaState
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!--------------------------------------------------------------------------------------------------
!> @brief Allocate the components of the state structure for a given phase
!--------------------------------------------------------------------------------------------------
subroutine constitutive_allocateState ( state , &
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Nconstituents , sizeState , sizeDotState , sizeDeltaState )
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class ( tState ) , intent ( out ) :: &
state
integer , intent ( in ) :: &
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Nconstituents , &
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sizeState , &
sizeDotState , &
sizeDeltaState
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state % sizeState = sizeState
state % sizeDotState = sizeDotState
state % sizeDeltaState = sizeDeltaState
state % offsetDeltaState = sizeState - sizeDeltaState ! deltaState occupies latter part of state by definition
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allocate ( state % atol ( sizeState ) , source = 0.0_pReal )
allocate ( state % state0 ( sizeState , Nconstituents ) , source = 0.0_pReal )
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allocate ( state % partitionedState0 ( sizeState , Nconstituents ) , source = 0.0_pReal )
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allocate ( state % subState0 ( sizeState , Nconstituents ) , source = 0.0_pReal )
allocate ( state % state ( sizeState , Nconstituents ) , source = 0.0_pReal )
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allocate ( state % dotState ( sizeDotState , Nconstituents ) , source = 0.0_pReal )
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allocate ( state % deltaState ( sizeDeltaState , Nconstituents ) , source = 0.0_pReal )
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end subroutine constitutive_allocateState
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!--------------------------------------------------------------------------------------------------
!> @brief Restore data after homog cutback.
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_restore ( ip , el , includeL )
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logical , intent ( in ) :: includeL
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integer , intent ( in ) :: &
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ip , & !< integration point number
el !< element number
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integer :: &
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co , & !< constituent number
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so
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do co = 1 , homogenization_Nconstituents ( material_homogenizationAt ( el ) )
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do so = 1 , phase_Nsources ( material_phaseAt ( co , el ) )
sourceState ( material_phaseAt ( co , el ) ) % p ( so ) % state ( : , material_phasememberAt ( co , ip , el ) ) = &
sourceState ( material_phaseAt ( co , el ) ) % p ( so ) % partitionedState0 ( : , material_phasememberAt ( co , ip , el ) )
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enddo
enddo
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call mech_restore ( ip , el , includeL )
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end subroutine constitutive_restore
!--------------------------------------------------------------------------------------------------
!> @brief Forward data after successful increment.
! ToDo: Any guessing for the current states possible?
!--------------------------------------------------------------------------------------------------
subroutine constitutive_forward
integer :: i , j
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crystallite_F0 = crystallite_F
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crystallite_Lp0 = crystallite_Lp
crystallite_S0 = crystallite_S
call constitutive_mech_forward ( )
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do i = 1 , size ( sourceState )
do j = 1 , phase_Nsources ( i )
sourceState ( i ) % p ( j ) % state0 = sourceState ( i ) % p ( j ) % state
enddo ; enddo
end subroutine constitutive_forward
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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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integer :: ph
character ( len = : ) , allocatable :: group
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call results_closeGroup ( results_addGroup ( '/current/phase/' ) )
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do ph = 1 , size ( material_name_phase )
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group = '/current/phase/' / / trim ( material_name_phase ( ph ) ) / / '/'
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call results_closeGroup ( results_addGroup ( group ) )
call mech_results ( group , ph )
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call damage_results ( group , ph )
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enddo
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end subroutine constitutive_results
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!--------------------------------------------------------------------------------------------------
!> @brief allocates and initialize per grain variables
!--------------------------------------------------------------------------------------------------
subroutine crystallite_init
integer :: &
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Nconstituents , &
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ph , &
me , &
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co , & !< counter in integration point component loop
ip , & !< counter in integration point loop
el , & !< counter in element loop
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cMax , & !< maximum number of integration point components
iMax , & !< maximum number of integration points
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eMax , & !< maximum number of elements
so
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class ( tNode ) , pointer :: &
num_crystallite , &
debug_crystallite , & ! pointer to debug options for crystallite
phases , &
phase , &
mech
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print '(/,a)' , ' <<<+- crystallite init -+>>>'
debug_crystallite = > config_debug % get ( 'crystallite' , defaultVal = emptyList )
debugCrystallite % extensive = debug_crystallite % contains ( 'extensive' )
cMax = homogenization_maxNconstituents
iMax = discretization_nIPs
eMax = discretization_Nelems
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allocate ( crystallite_F ( 3 , 3 , cMax , iMax , eMax ) , source = 0.0_pReal )
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allocate ( crystallite_S0 , &
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crystallite_F0 , crystallite_Lp0 , &
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crystallite_partitionedS0 , &
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crystallite_partitionedF0 , &
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crystallite_partitionedLp0 , &
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crystallite_S , crystallite_P , &
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crystallite_Fe , crystallite_Lp , &
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crystallite_subFp0 , crystallite_subFi0 , &
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source = crystallite_F )
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allocate ( crystallite_subdt ( cMax , iMax , eMax ) , source = 0.0_pReal )
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allocate ( crystallite_orientation ( cMax , iMax , eMax ) )
num_crystallite = > config_numerics % get ( 'crystallite' , defaultVal = emptyDict )
num % subStepMinCryst = num_crystallite % get_asFloat ( 'subStepMin' , defaultVal = 1.0e-3_pReal )
num % subStepSizeCryst = num_crystallite % get_asFloat ( 'subStepSize' , defaultVal = 0.25_pReal )
num % stepIncreaseCryst = num_crystallite % get_asFloat ( 'stepIncrease' , defaultVal = 1.5_pReal )
num % subStepSizeLp = num_crystallite % get_asFloat ( 'subStepSizeLp' , defaultVal = 0.5_pReal )
num % subStepSizeLi = num_crystallite % get_asFloat ( 'subStepSizeLi' , defaultVal = 0.5_pReal )
num % rtol_crystalliteState = num_crystallite % get_asFloat ( 'rtol_State' , defaultVal = 1.0e-6_pReal )
num % rtol_crystalliteStress = num_crystallite % get_asFloat ( 'rtol_Stress' , defaultVal = 1.0e-6_pReal )
num % atol_crystalliteStress = num_crystallite % get_asFloat ( 'atol_Stress' , defaultVal = 1.0e-8_pReal )
num % iJacoLpresiduum = num_crystallite % get_asInt ( 'iJacoLpresiduum' , defaultVal = 1 )
num % nState = num_crystallite % get_asInt ( 'nState' , defaultVal = 20 )
num % nStress = num_crystallite % get_asInt ( 'nStress' , defaultVal = 40 )
if ( num % subStepMinCryst < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'subStepMinCryst' )
if ( num % subStepSizeCryst < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'subStepSizeCryst' )
if ( num % stepIncreaseCryst < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'stepIncreaseCryst' )
if ( num % subStepSizeLp < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'subStepSizeLp' )
if ( num % subStepSizeLi < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'subStepSizeLi' )
if ( num % rtol_crystalliteState < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'rtol_crystalliteState' )
if ( num % rtol_crystalliteStress < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'rtol_crystalliteStress' )
if ( num % atol_crystalliteStress < = 0.0_pReal ) call IO_error ( 301 , ext_msg = 'atol_crystalliteStress' )
if ( num % iJacoLpresiduum < 1 ) call IO_error ( 301 , ext_msg = 'iJacoLpresiduum' )
if ( num % nState < 1 ) call IO_error ( 301 , ext_msg = 'nState' )
if ( num % nStress < 1 ) call IO_error ( 301 , ext_msg = 'nStress' )
phases = > config_material % get ( 'phase' )
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allocate ( constitutive_mech_Fi ( phases % length ) )
allocate ( constitutive_mech_Fi0 ( phases % length ) )
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allocate ( constitutive_mech_partitionedFi0 ( phases % length ) )
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allocate ( constitutive_mech_Fp ( phases % length ) )
allocate ( constitutive_mech_Fp0 ( phases % length ) )
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allocate ( constitutive_mech_partitionedFp0 ( phases % length ) )
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allocate ( constitutive_mech_Li ( phases % length ) )
allocate ( constitutive_mech_Li0 ( phases % length ) )
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allocate ( constitutive_mech_partitionedLi0 ( phases % length ) )
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do ph = 1 , phases % length
Nconstituents = count ( material_phaseAt == ph ) * discretization_nIPs
allocate ( constitutive_mech_Fi ( ph ) % data ( 3 , 3 , Nconstituents ) )
allocate ( constitutive_mech_Fi0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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allocate ( constitutive_mech_partitionedFi0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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allocate ( constitutive_mech_Fp ( ph ) % data ( 3 , 3 , Nconstituents ) )
allocate ( constitutive_mech_Fp0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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allocate ( constitutive_mech_partitionedFp0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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allocate ( constitutive_mech_Li ( ph ) % data ( 3 , 3 , Nconstituents ) )
allocate ( constitutive_mech_Li0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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allocate ( constitutive_mech_partitionedLi0 ( ph ) % data ( 3 , 3 , Nconstituents ) )
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enddo
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print '(a42,1x,i10)' , ' # of elements: ' , eMax
print '(a42,1x,i10)' , ' # of integration points/element: ' , iMax
print '(a42,1x,i10)' , 'max # of constituents/integration point: ' , cMax
flush ( IO_STDOUT )
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!$OMP PARALLEL DO PRIVATE(ph,me)
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do el = 1 , size ( material_phaseMemberAt , 3 ) ; do ip = 1 , size ( material_phaseMemberAt , 2 )
do co = 1 , homogenization_Nconstituents ( material_homogenizationAt ( el ) )
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ph = material_phaseAt ( co , el )
me = material_phaseMemberAt ( co , ip , el )
constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = material_orientation0 ( co , ip , el ) % asMatrix ( ) ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005)
constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) &
/ math_det33 ( constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) ) ** ( 1.0_pReal / 3.0_pReal )
constitutive_mech_Fi0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = math_I3
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crystallite_F0 ( 1 : 3 , 1 : 3 , co , ip , el ) = math_I3
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crystallite_Fe ( 1 : 3 , 1 : 3 , co , ip , el ) = math_inv33 ( matmul ( constitutive_mech_Fi0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) , &
constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) ) ) ! assuming that euler angles are given in internal strain free configuration
constitutive_mech_Fp ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me )
constitutive_mech_Fi ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = constitutive_mech_Fi0 ( ph ) % data ( 1 : 3 , 1 : 3 , me )
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constitutive_mech_partitionedFi0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = constitutive_mech_Fi0 ( ph ) % data ( 1 : 3 , 1 : 3 , me )
constitutive_mech_partitionedFp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me ) = constitutive_mech_Fp0 ( ph ) % data ( 1 : 3 , 1 : 3 , me )
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enddo
enddo ; enddo
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!$OMP END PARALLEL DO
crystallite_partitionedF0 = crystallite_F0
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crystallite_F = crystallite_F0
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!$OMP PARALLEL DO PRIVATE(ph,me)
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do el = 1 , size ( material_phaseMemberAt , 3 )
do ip = 1 , size ( material_phaseMemberAt , 2 )
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do co = 1 , homogenization_Nconstituents ( material_homogenizationAt ( el ) )
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ph = material_phaseAt ( co , el )
me = material_phaseMemberAt ( co , ip , el )
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call crystallite_orientations ( co , ip , el )
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call constitutive_plastic_dependentState ( crystallite_partitionedF0 ( 1 : 3 , 1 : 3 , co , ip , el ) , co , ip , el ) ! update dependent state variables to be consistent with basic states
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enddo
enddo
enddo
!$OMP END PARALLEL DO
end subroutine crystallite_init
!--------------------------------------------------------------------------------------------------
!> @brief Backup data for homog cutback.
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_initializeRestorationPoints ( ip , el )
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integer , intent ( in ) :: &
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ip , & !< integration point number
el !< element number
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integer :: &
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co , & !< constituent number
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so , ph , me
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do co = 1 , homogenization_Nconstituents ( material_homogenizationAt ( el ) )
ph = material_phaseAt ( co , el )
me = material_phaseMemberAt ( co , ip , el )
crystallite_partitionedLp0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_Lp0 ( 1 : 3 , 1 : 3 , co , ip , el )
crystallite_partitionedF0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_F0 ( 1 : 3 , 1 : 3 , co , ip , el )
crystallite_partitionedS0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_S0 ( 1 : 3 , 1 : 3 , co , ip , el )
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call mech_initializeRestorationPoints ( ph , me )
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do so = 1 , phase_Nsources ( material_phaseAt ( co , el ) )
sourceState ( material_phaseAt ( co , el ) ) % p ( so ) % partitionedState0 ( : , material_phasememberAt ( co , ip , el ) ) = &
sourceState ( material_phaseAt ( co , el ) ) % p ( so ) % state0 ( : , material_phasememberAt ( co , ip , el ) )
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enddo
enddo
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end subroutine constitutive_initializeRestorationPoints
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!--------------------------------------------------------------------------------------------------
!> @brief Wind homog inc forward.
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_windForward ( ip , el )
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integer , intent ( in ) :: &
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ip , & !< integration point number
el !< element number
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integer :: &
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co , & !< constituent number
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so , ph , me
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do co = 1 , homogenization_Nconstituents ( material_homogenizationAt ( el ) )
ph = material_phaseAt ( co , el )
me = material_phaseMemberAt ( co , ip , el )
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crystallite_partitionedF0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el )
crystallite_partitionedLp0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_Lp ( 1 : 3 , 1 : 3 , co , ip , el )
crystallite_partitionedS0 ( 1 : 3 , 1 : 3 , co , ip , el ) = crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el )
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call constitutive_mech_windForward ( ph , me )
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do so = 1 , phase_Nsources ( material_phaseAt ( co , el ) )
sourceState ( ph ) % p ( so ) % partitionedState0 ( : , me ) = sourceState ( ph ) % p ( so ) % state ( : , me )
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enddo
enddo
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end subroutine constitutive_windForward
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!--------------------------------------------------------------------------------------------------
!> @brief Calculate tangent (dPdF).
!--------------------------------------------------------------------------------------------------
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function crystallite_stressTangent ( co , ip , el ) result ( dPdF )
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: dPdF
integer , intent ( in ) :: &
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co , & !< counter in constituent loop
ip , & !< counter in integration point loop
el !< counter in element loop
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integer :: &
o , &
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p , ph , me
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real ( pReal ) , dimension ( 3 , 3 ) :: devNull , &
invSubFp0 , invSubFi0 , invFp , invFi , &
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temp_33_1 , temp_33_2 , temp_33_3
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: dSdFe , &
dSdF , &
dSdFi , &
dLidS , & ! tangent in lattice configuration
dLidFi , &
dLpdS , &
dLpdFi , &
dFidS , &
dFpinvdF , &
rhs_3333 , &
lhs_3333 , &
temp_3333
real ( pReal ) , dimension ( 9 , 9 ) :: temp_99
logical :: error
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ph = material_phaseAt ( co , el )
me = material_phaseMemberAt ( co , ip , el )
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call constitutive_hooke_SandItsTangents ( devNull , dSdFe , dSdFi , &
crystallite_Fe ( 1 : 3 , 1 : 3 , co , ip , el ) , &
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constitutive_mech_Fi ( ph ) % data ( 1 : 3 , 1 : 3 , me ) , co , ip , el )
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call constitutive_LiAndItsTangents ( devNull , dLidS , dLidFi , &
crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) , &
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constitutive_mech_Fi ( ph ) % data ( 1 : 3 , 1 : 3 , me ) , &
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co , ip , el )
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invFp = math_inv33 ( constitutive_mech_Fp ( ph ) % data ( 1 : 3 , 1 : 3 , me ) )
invFi = math_inv33 ( constitutive_mech_Fi ( ph ) % data ( 1 : 3 , 1 : 3 , me ) )
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invSubFp0 = math_inv33 ( crystallite_subFp0 ( 1 : 3 , 1 : 3 , co , ip , el ) )
invSubFi0 = math_inv33 ( crystallite_subFi0 ( 1 : 3 , 1 : 3 , co , ip , el ) )
if ( sum ( abs ( dLidS ) ) < tol_math_check ) then
dFidS = 0.0_pReal
else
lhs_3333 = 0.0_pReal ; rhs_3333 = 0.0_pReal
do o = 1 , 3 ; do p = 1 , 3
lhs_3333 ( 1 : 3 , 1 : 3 , o , p ) = lhs_3333 ( 1 : 3 , 1 : 3 , o , p ) &
+ crystallite_subdt ( co , ip , el ) * matmul ( invSubFi0 , dLidFi ( 1 : 3 , 1 : 3 , o , p ) )
lhs_3333 ( 1 : 3 , o , 1 : 3 , p ) = lhs_3333 ( 1 : 3 , o , 1 : 3 , p ) &
+ invFi * invFi ( p , o )
rhs_3333 ( 1 : 3 , 1 : 3 , o , p ) = rhs_3333 ( 1 : 3 , 1 : 3 , o , p ) &
- crystallite_subdt ( co , ip , el ) * matmul ( invSubFi0 , dLidS ( 1 : 3 , 1 : 3 , o , p ) )
enddo ; enddo
call math_invert ( temp_99 , error , math_3333to99 ( lhs_3333 ) )
if ( error ) then
call IO_warning ( warning_ID = 600 , el = el , ip = ip , g = co , &
ext_msg = 'inversion error in analytic tangent calculation' )
dFidS = 0.0_pReal
else
dFidS = math_mul3333xx3333 ( math_99to3333 ( temp_99 ) , rhs_3333 )
endif
dLidS = math_mul3333xx3333 ( dLidFi , dFidS ) + dLidS
endif
call constitutive_plastic_LpAndItsTangents ( devNull , dLpdS , dLpdFi , &
crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) , &
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constitutive_mech_Fi ( ph ) % data ( 1 : 3 , 1 : 3 , me ) , co , ip , el )
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dLpdS = math_mul3333xx3333 ( dLpdFi , dFidS ) + dLpdS
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!--------------------------------------------------------------------------------------------------
! calculate dSdF
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temp_33_1 = transpose ( matmul ( invFp , invFi ) )
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temp_33_2 = matmul ( crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el ) , invSubFp0 )
temp_33_3 = matmul ( matmul ( crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el ) , invFp ) , invSubFi0 )
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do o = 1 , 3 ; do p = 1 , 3
rhs_3333 ( p , o , 1 : 3 , 1 : 3 ) = matmul ( dSdFe ( p , o , 1 : 3 , 1 : 3 ) , temp_33_1 )
temp_3333 ( 1 : 3 , 1 : 3 , p , o ) = matmul ( matmul ( temp_33_2 , dLpdS ( 1 : 3 , 1 : 3 , p , o ) ) , invFi ) &
+ matmul ( temp_33_3 , dLidS ( 1 : 3 , 1 : 3 , p , o ) )
enddo ; enddo
lhs_3333 = crystallite_subdt ( co , ip , el ) * math_mul3333xx3333 ( dSdFe , temp_3333 ) &
+ math_mul3333xx3333 ( dSdFi , dFidS )
call math_invert ( temp_99 , error , math_eye ( 9 ) + math_3333to99 ( lhs_3333 ) )
if ( error ) then
call IO_warning ( warning_ID = 600 , el = el , ip = ip , g = co , &
ext_msg = 'inversion error in analytic tangent calculation' )
dSdF = rhs_3333
else
dSdF = math_mul3333xx3333 ( math_99to3333 ( temp_99 ) , rhs_3333 )
endif
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!--------------------------------------------------------------------------------------------------
! calculate dFpinvdF
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temp_3333 = math_mul3333xx3333 ( dLpdS , dSdF )
do o = 1 , 3 ; do p = 1 , 3
dFpinvdF ( 1 : 3 , 1 : 3 , p , o ) = - crystallite_subdt ( co , ip , el ) &
* matmul ( invSubFp0 , matmul ( temp_3333 ( 1 : 3 , 1 : 3 , p , o ) , invFi ) )
enddo ; enddo
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!--------------------------------------------------------------------------------------------------
! assemble dPdF
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temp_33_1 = matmul ( crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) , transpose ( invFp ) )
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temp_33_2 = matmul ( crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el ) , invFp )
temp_33_3 = matmul ( temp_33_2 , crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) )
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dPdF = 0.0_pReal
do p = 1 , 3
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dPdF ( p , 1 : 3 , p , 1 : 3 ) = transpose ( matmul ( invFp , temp_33_1 ) )
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enddo
do o = 1 , 3 ; do p = 1 , 3
dPdF ( 1 : 3 , 1 : 3 , p , o ) = dPdF ( 1 : 3 , 1 : 3 , p , o ) &
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+ matmul ( matmul ( crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el ) , &
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dFpinvdF ( 1 : 3 , 1 : 3 , p , o ) ) , temp_33_1 ) &
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+ matmul ( matmul ( temp_33_2 , dSdF ( 1 : 3 , 1 : 3 , p , o ) ) , &
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transpose ( invFp ) ) &
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+ matmul ( temp_33_3 , transpose ( dFpinvdF ( 1 : 3 , 1 : 3 , p , o ) ) )
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enddo ; enddo
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end function crystallite_stressTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates orientations
!--------------------------------------------------------------------------------------------------
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subroutine crystallite_orientations ( co , ip , el )
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integer , intent ( in ) :: &
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co , & !< counter in integration point component loop
ip , & !< counter in integration point loop
el !< counter in element loop
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call crystallite_orientation ( co , ip , el ) % fromMatrix ( transpose ( math_rotationalPart ( crystallite_Fe ( 1 : 3 , 1 : 3 , co , ip , el ) ) ) )
if ( plasticState ( material_phaseAt ( 1 , el ) ) % nonlocal ) &
call plastic_nonlocal_updateCompatibility ( crystallite_orientation , &
phase_plasticityInstance ( material_phaseAt ( 1 , el ) ) , ip , el )
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end subroutine crystallite_orientations
!--------------------------------------------------------------------------------------------------
!> @brief Map 2nd order tensor to reference config
!--------------------------------------------------------------------------------------------------
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function crystallite_push33ToRef ( co , ip , el , tensor33 )
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: tensor33
real ( pReal ) , dimension ( 3 , 3 ) :: T
integer , intent ( in ) :: &
el , &
ip , &
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co
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real ( pReal ) , dimension ( 3 , 3 ) :: crystallite_push33ToRef
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T = matmul ( material_orientation0 ( co , ip , el ) % asMatrix ( ) , & ! ToDo: initial orientation correct?
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transpose ( math_inv33 ( crystallite_F ( 1 : 3 , 1 : 3 , co , ip , el ) ) ) )
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crystallite_push33ToRef = matmul ( transpose ( T ) , matmul ( tensor33 , T ) )
end function crystallite_push33ToRef
!--------------------------------------------------------------------------------------------------
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
!> using Fixed Point Iteration to adapt the stepsize
!--------------------------------------------------------------------------------------------------
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function integrateSourceState ( dt , co , ip , el ) result ( broken )
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real ( pReal ) , intent ( in ) :: dt
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integer , intent ( in ) :: &
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el , & !< element index in element loop
ip , & !< integration point index in ip loop
co !< grain index in grain loop
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integer :: &
NiterationState , & !< number of iterations in state loop
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ph , &
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me , &
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so
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integer , dimension ( maxval ( phase_Nsources ) ) :: &
size_so
real ( pReal ) :: &
zeta
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real ( pReal ) , dimension ( constitutive_source_maxSizeDotState ) :: &
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r ! state residuum
real ( pReal ) , dimension ( constitutive_source_maxSizeDotState , 2 , maxval ( phase_Nsources ) ) :: source_dotState
logical :: &
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broken , converged_
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ph = material_phaseAt ( co , el )
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me = material_phaseMemberAt ( co , ip , el )
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converged_ = . true .
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broken = constitutive_thermal_collectDotState ( ph , me )
broken = broken . or . constitutive_damage_collectDotState ( crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) , co , ip , el , ph , me )
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if ( broken ) return
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do so = 1 , phase_Nsources ( ph )
size_so ( so ) = sourceState ( ph ) % p ( so ) % sizeDotState
sourceState ( ph ) % p ( so ) % state ( 1 : size_so ( so ) , me ) = sourceState ( ph ) % p ( so ) % subState0 ( 1 : size_so ( so ) , me ) &
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+ sourceState ( ph ) % p ( so ) % dotState ( 1 : size_so ( so ) , me ) * dt
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source_dotState ( 1 : size_so ( so ) , 2 , so ) = 0.0_pReal
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enddo
iteration : do NiterationState = 1 , num % nState
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do so = 1 , phase_Nsources ( ph )
if ( nIterationState > 1 ) source_dotState ( 1 : size_so ( so ) , 2 , so ) = source_dotState ( 1 : size_so ( so ) , 1 , so )
source_dotState ( 1 : size_so ( so ) , 1 , so ) = sourceState ( ph ) % p ( so ) % dotState ( : , me )
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enddo
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broken = constitutive_thermal_collectDotState ( ph , me )
broken = broken . or . constitutive_damage_collectDotState ( crystallite_S ( 1 : 3 , 1 : 3 , co , ip , el ) , co , ip , el , ph , me )
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if ( broken ) exit iteration
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do so = 1 , phase_Nsources ( ph )
zeta = damper ( sourceState ( ph ) % p ( so ) % dotState ( : , me ) , &
source_dotState ( 1 : size_so ( so ) , 1 , so ) , &
source_dotState ( 1 : size_so ( so ) , 2 , so ) )
sourceState ( ph ) % p ( so ) % dotState ( : , me ) = sourceState ( ph ) % p ( so ) % dotState ( : , me ) * zeta &
+ source_dotState ( 1 : size_so ( so ) , 1 , so ) * ( 1.0_pReal - zeta )
r ( 1 : size_so ( so ) ) = sourceState ( ph ) % p ( so ) % state ( 1 : size_so ( so ) , me ) &
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- sourceState ( ph ) % p ( so ) % subState0 ( 1 : size_so ( so ) , me ) &
- sourceState ( ph ) % p ( so ) % dotState ( 1 : size_so ( so ) , me ) * dt
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sourceState ( ph ) % p ( so ) % state ( 1 : size_so ( so ) , me ) = sourceState ( ph ) % p ( so ) % state ( 1 : size_so ( so ) , me ) &
- r ( 1 : size_so ( so ) )
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converged_ = converged_ . and . converged ( r ( 1 : size_so ( so ) ) , &
sourceState ( ph ) % p ( so ) % state ( 1 : size_so ( so ) , me ) , &
sourceState ( ph ) % p ( so ) % atol ( 1 : size_so ( so ) ) )
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enddo
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if ( converged_ ) then
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broken = constitutive_damage_deltaState ( crystallite_Fe ( 1 : 3 , 1 : 3 , co , ip , el ) , co , ip , el , ph , me )
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exit iteration
endif
enddo iteration
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broken = broken . or . . not . converged_
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contains
!--------------------------------------------------------------------------------------------------
!> @brief calculate the damping for correction of state and dot state
!--------------------------------------------------------------------------------------------------
real ( pReal ) pure function damper ( current , previous , previous2 )
real ( pReal ) , dimension ( : ) , intent ( in ) :: &
current , previous , previous2
real ( pReal ) :: dot_prod12 , dot_prod22
dot_prod12 = dot_product ( current - previous , previous - previous2 )
dot_prod22 = dot_product ( previous - previous2 , previous - previous2 )
if ( ( dot_product ( current , previous ) < 0.0_pReal . or . dot_prod12 < 0.0_pReal ) . and . dot_prod22 > 0.0_pReal ) then
damper = 0.75_pReal + 0.25_pReal * tanh ( 2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22 )
else
damper = 1.0_pReal
endif
end function damper
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end function integrateSourceState
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!--------------------------------------------------------------------------------------------------
!> @brief determines whether a point is converged
!--------------------------------------------------------------------------------------------------
logical pure function converged ( residuum , state , atol )
real ( pReal ) , intent ( in ) , dimension ( : ) :: &
residuum , state , atol
real ( pReal ) :: &
rTol
rTol = num % rTol_crystalliteState
converged = all ( abs ( residuum ) < = max ( atol , rtol * abs ( state ) ) )
end function converged
!--------------------------------------------------------------------------------------------------
!> @brief Write current restart information (Field and constitutive data) to file.
! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively
!--------------------------------------------------------------------------------------------------
subroutine crystallite_restartWrite
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integer :: ph
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integer ( HID_T ) :: fileHandle , groupHandle
character ( len = pStringLen ) :: fileName , datasetName
print * , ' writing field and constitutive data required for restart to file' ; flush ( IO_STDOUT )
write ( fileName , '(a,i0,a)' ) trim ( getSolverJobName ( ) ) / / '_' , worldrank , '.hdf5'
fileHandle = HDF5_openFile ( fileName , 'a' )
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call HDF5_write ( fileHandle , crystallite_F , 'F' )
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call HDF5_write ( fileHandle , crystallite_Lp , 'L_p' )
call HDF5_write ( fileHandle , crystallite_S , 'S' )
groupHandle = HDF5_addGroup ( fileHandle , 'phase' )
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do ph = 1 , size ( material_name_phase )
write ( datasetName , '(i0,a)' ) ph , '_omega'
call HDF5_write ( groupHandle , plasticState ( ph ) % state , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_F_i'
call HDF5_write ( groupHandle , constitutive_mech_Fi ( ph ) % data , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_L_i'
call HDF5_write ( groupHandle , constitutive_mech_Li ( ph ) % data , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_F_p'
call HDF5_write ( groupHandle , constitutive_mech_Fp ( ph ) % data , datasetName )
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enddo
call HDF5_closeGroup ( groupHandle )
groupHandle = HDF5_addGroup ( fileHandle , 'homogenization' )
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do ph = 1 , size ( material_name_homogenization )
write ( datasetName , '(i0,a)' ) ph , '_omega'
call HDF5_write ( groupHandle , homogState ( ph ) % state , datasetName )
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enddo
call HDF5_closeGroup ( groupHandle )
call HDF5_closeFile ( fileHandle )
end subroutine crystallite_restartWrite
!--------------------------------------------------------------------------------------------------
!> @brief Read data for restart
! ToDo: Merge data into one file for MPI, move state to constitutive and homogenization, respectively
!--------------------------------------------------------------------------------------------------
subroutine crystallite_restartRead
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integer :: ph
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integer ( HID_T ) :: fileHandle , groupHandle
character ( len = pStringLen ) :: fileName , datasetName
print '(/,a,i0,a)' , ' reading restart information of increment from file'
write ( fileName , '(a,i0,a)' ) trim ( getSolverJobName ( ) ) / / '_' , worldrank , '.hdf5'
fileHandle = HDF5_openFile ( fileName )
call HDF5_read ( fileHandle , crystallite_F0 , 'F' )
call HDF5_read ( fileHandle , crystallite_Lp0 , 'L_p' )
call HDF5_read ( fileHandle , crystallite_S0 , 'S' )
groupHandle = HDF5_openGroup ( fileHandle , 'phase' )
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do ph = 1 , size ( material_name_phase )
write ( datasetName , '(i0,a)' ) ph , '_omega'
call HDF5_read ( groupHandle , plasticState ( ph ) % state0 , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_F_i'
call HDF5_read ( groupHandle , constitutive_mech_Fi0 ( ph ) % data , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_L_i'
call HDF5_read ( groupHandle , constitutive_mech_Li0 ( ph ) % data , datasetName )
write ( datasetName , '(i0,a)' ) ph , '_F_p'
call HDF5_read ( groupHandle , constitutive_mech_Fp0 ( ph ) % data , datasetName )
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enddo
call HDF5_closeGroup ( groupHandle )
groupHandle = HDF5_openGroup ( fileHandle , 'homogenization' )
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do ph = 1 , size ( material_name_homogenization )
write ( datasetName , '(i0,a)' ) ph , '_omega'
call HDF5_read ( groupHandle , homogState ( ph ) % state0 , datasetName )
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enddo
call HDF5_closeGroup ( groupHandle )
call HDF5_closeFile ( fileHandle )
end subroutine crystallite_restartRead
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end module constitutive
