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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, internal microstructure state
!--------------------------------------------------------------------------------------------------
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 debug
use numerics
use IO
use config
use material
use results
use lattice
use discretization
use geometry_plastic_nonlocal
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implicit none
private
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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 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
module subroutine plastic_disloUCLA_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_disloUCLA_dotState
module subroutine plastic_nonlocal_dotState ( Mp , F , Fp , Temperature , timestep , &
instance , of , ip , el )
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
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
module subroutine source_damage_anisoBrittle_dotState ( S , 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
end subroutine source_damage_anisoBrittle_dotState
module subroutine source_damage_anisoDuctile_dotState ( ipc , ip , el )
integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
end subroutine source_damage_anisoDuctile_dotState
module subroutine source_damage_isoDuctile_dotState ( ipc , ip , el )
integer , intent ( in ) :: &
ipc , & !< component-ID of integration point
ip , & !< integration point
el !< element
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 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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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
end subroutine constitutive_plastic_dependentState
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
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
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
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
real ( pReal ) , intent ( inout ) :: &
phiDot , &
dPhiDot_dPhi
end subroutine constitutive_damage_getRateAndItsTangents
module subroutine constitutive_thermal_getRateAndItsTangents ( TDot , dTDot_dT , T , Tstar , Lp , ip , el )
integer , intent ( in ) :: &
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( in ) :: &
T
real ( pReal ) , intent ( in ) , dimension ( : , : , : , : , : ) :: &
Tstar , &
Lp
real ( pReal ) , intent ( inout ) :: &
TDot , &
dTDot_dT
end subroutine constitutive_thermal_getRateAndItsTangents
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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
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: &
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Mi !< Mandel stress
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integer , intent ( in ) :: &
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 ) :: &
ipc , & !< grain number
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 ) :: &
Ld !< damage velocity gradient
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 , 3 , 3 ) :: &
dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
end subroutine kinematics_cleavage_opening_LiAndItsTangent
module subroutine kinematics_slipplane_opening_LiAndItsTangent ( Ld , dLd_dTstar , S , ipc , ip , el )
integer , intent ( in ) :: &
ipc , & !< grain number
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( in ) , dimension ( 3 , 3 ) :: &
S
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 ) :: &
Ld !< damage velocity gradient
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 , 3 , 3 ) :: &
dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
end subroutine kinematics_slipplane_opening_LiAndItsTangent
module subroutine kinematics_thermal_expansion_LiAndItsTangent ( Li , dLi_dTstar , ipc , ip , el )
integer , intent ( in ) :: &
ipc , & !< grain number
ip , & !< integration point number
el !< element number
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 ) :: &
Li !< thermal velocity gradient
real ( pReal ) , intent ( out ) , dimension ( 3 , 3 , 3 , 3 ) :: &
dLi_dTstar !< derivative of Li with respect to Tstar (4th-order tensor defined to be zero)
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
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_isotropic_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
end subroutine plastic_isotropic_results
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module subroutine plastic_phenopowerlaw_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
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end subroutine plastic_phenopowerlaw_results
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module subroutine plastic_kinehardening_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
end subroutine plastic_kinehardening_results
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module subroutine plastic_dislotwin_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
end subroutine plastic_dislotwin_results
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module subroutine plastic_disloUCLA_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
end subroutine plastic_disloUCLA_results
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module subroutine plastic_nonlocal_results ( instance , group )
integer , intent ( in ) :: instance
character ( len = * ) , intent ( in ) :: group
end subroutine plastic_nonlocal_results
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module subroutine source_damage_anisoBrittle_results ( phase , group )
integer , intent ( in ) :: phase
character ( len = * ) , intent ( in ) :: group
end subroutine source_damage_anisoBrittle_results
module subroutine source_damage_anisoDuctile_results ( phase , group )
integer , intent ( in ) :: phase
character ( len = * ) , intent ( in ) :: group
end subroutine source_damage_anisoDuctile_results
module subroutine source_damage_isoBrittle_results ( phase , group )
integer , intent ( in ) :: phase
character ( len = * ) , intent ( in ) :: group
end subroutine source_damage_isoBrittle_results
module subroutine source_damage_isoDuctile_results ( phase , group )
integer , intent ( in ) :: phase
character ( len = * ) , intent ( in ) :: group
end subroutine source_damage_isoDuctile_results
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end interface
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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_plastic_LpAndItsTangents , &
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constitutive_plastic_dependentState , &
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constitutive_LiAndItsTangents , &
constitutive_initialFi , &
constitutive_SandItsTangents , &
constitutive_collectDotState , &
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constitutive_deltaState , &
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plastic_nonlocal_updateCompatibility , &
constitutive_damage_getRateAndItsTangents , &
constitutive_thermal_getRateAndItsTangents , &
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constitutive_results
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contains
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!--------------------------------------------------------------------------------------------------
!> @brief allocates arrays pointing to array of the various constitutive modules
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_init
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integer :: &
ph , & !< counter in phase loop
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s !< counter in source loop
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class ( tNode ) , pointer :: &
debug_constitutive
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debug_constitutive = > debug_root % get ( 'constitutive' , defaultVal = emptyList )
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debugConstitutive % basic = debug_constitutive % contains ( 'basic' )
debugConstitutive % extensive = debug_constitutive % contains ( 'extensive' )
debugConstitutive % selective = debug_constitutive % contains ( 'selective' )
debugConstitutive % element = debug_root % get_asInt ( 'element' , defaultVal = 1 )
debugConstitutive % ip = debug_root % get_asInt ( 'integrationpoint' , defaultVal = 1 )
debugConstitutive % grain = debug_root % get_asInt ( 'grain' , defaultVal = 1 )
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!--------------------------------------------------------------------------------------------------
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! initialized plasticity
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call plastic_init
call damage_init
call thermal_init
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write ( 6 , '(/,a)' ) ' <<<+- constitutive init -+>>>' ; flush ( 6 )
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constitutive_source_maxSizeDotState = 0
PhaseLoop2 : do ph = 1 , material_Nphase
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!--------------------------------------------------------------------------------------------------
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! partition and initialize state
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plasticState ( ph ) % partionedState0 = plasticState ( ph ) % state0
plasticState ( ph ) % state = plasticState ( ph ) % partionedState0
forall ( s = 1 : phase_Nsources ( ph ) )
sourceState ( ph ) % p ( s ) % partionedState0 = sourceState ( ph ) % p ( s ) % state0
sourceState ( ph ) % p ( s ) % state = sourceState ( ph ) % p ( s ) % partionedState0
end forall
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!--------------------------------------------------------------------------------------------------
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! determine max size of source state
constitutive_source_maxSizeDotState = max ( constitutive_source_maxSizeDotState , &
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 returns the homogenize elasticity matrix
!> ToDo: homogenizedC66 would be more consistent
!--------------------------------------------------------------------------------------------------
function constitutive_homogenizedC ( ipc , ip , el )
real ( pReal ) , dimension ( 6 , 6 ) :: &
constitutive_homogenizedC
integer , intent ( in ) :: &
ipc , &
ip , &
el
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
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 :: &
ho , &
tme , &
i , &
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
call plastic_isotropic_dotState ( Mp , instance , of )
case ( PLASTICITY_PHENOPOWERLAW_ID ) plasticityType
call plastic_phenopowerlaw_dotState ( Mp , instance , of )
case ( PLASTICITY_KINEHARDENING_ID ) plasticityType
call plastic_kinehardening_dotState ( Mp , instance , of )
case ( PLASTICITY_DISLOTWIN_ID ) plasticityType
call plastic_dislotwin_dotState ( Mp , temperature ( ho ) % p ( tme ) , instance , of )
case ( PLASTICITY_DISLOUCLA_ID ) plasticityType
call plastic_disloucla_dotState ( Mp , temperature ( ho ) % p ( tme ) , instance , of )
case ( PLASTICITY_NONLOCAL_ID ) plasticityType
call plastic_nonlocal_dotState ( Mp , FArray , FpArray , temperature ( ho ) % p ( tme ) , subdt , &
instance , of , ip , el )
end select plasticityType
broken = any ( IEEE_is_NaN ( plasticState ( phase ) % dotState ( : , of ) ) )
SourceLoop : do i = 1 , phase_Nsources ( phase )
sourceType : select case ( phase_source ( i , phase ) )
case ( SOURCE_damage_anisoBrittle_ID ) sourceType
call source_damage_anisoBrittle_dotState ( S , ipc , ip , el ) !< correct stress?
case ( SOURCE_damage_isoDuctile_ID ) sourceType
call source_damage_isoDuctile_dotState ( ipc , ip , el )
case ( SOURCE_damage_anisoDuctile_ID ) sourceType
call source_damage_anisoDuctile_dotState ( ipc , ip , el )
case ( SOURCE_thermal_externalheat_ID ) sourceType
call source_thermal_externalheat_dotState ( phase , of )
end select sourceType
broken = broken . or . any ( IEEE_is_NaN ( sourceState ( phase ) % p ( i ) % dotState ( : , of ) ) )
enddo SourceLoop
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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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!--------------------------------------------------------------------------------------------------
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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 :: p , i
character ( len = pStringLen ) :: group , group_plastic , group_sources
plasticityLoop : do p = 1 , size ( config_name_phase )
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group = trim ( 'current/constituent' ) / / '/' / / trim ( config_name_phase ( p ) )
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call results_closeGroup ( results_addGroup ( group ) )
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group_plastic = trim ( group ) / / '/plastic'
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call results_closeGroup ( results_addGroup ( group_plastic ) )
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select case ( phase_plasticity ( p ) )
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case ( PLASTICITY_ISOTROPIC_ID )
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call plastic_isotropic_results ( phase_plasticityInstance ( p ) , group_plastic )
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case ( PLASTICITY_PHENOPOWERLAW_ID )
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call plastic_phenopowerlaw_results ( phase_plasticityInstance ( p ) , group_plastic )
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case ( PLASTICITY_KINEHARDENING_ID )
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call plastic_kinehardening_results ( phase_plasticityInstance ( p ) , group_plastic )
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case ( PLASTICITY_DISLOTWIN_ID )
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call plastic_dislotwin_results ( phase_plasticityInstance ( p ) , group_plastic )
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case ( PLASTICITY_DISLOUCLA_ID )
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call plastic_disloUCLA_results ( phase_plasticityInstance ( p ) , group_plastic )
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case ( PLASTICITY_NONLOCAL_ID )
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call plastic_nonlocal_results ( phase_plasticityInstance ( p ) , group_plastic )
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end select
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sourceLoop : do i = 1 , phase_Nsources ( p )
group_sources = trim ( group ) / / '/sources'
call results_closeGroup ( results_addGroup ( group_sources ) )
sourceType : select case ( phase_source ( i , p ) )
case ( SOURCE_damage_anisoBrittle_ID ) sourceType
call source_damage_anisoBrittle_results ( p , group_sources )
case ( SOURCE_damage_anisoDuctile_ID ) sourceType
call source_damage_anisoDuctile_results ( p , group_sources )
case ( SOURCE_damage_isoBrittle_ID ) sourceType
call source_damage_isoBrittle_results ( p , group_sources )
case ( SOURCE_damage_isoDuctile_ID ) sourceType
call source_damage_isoDuctile_results ( p , group_sources )
end select sourceType
enddo SourceLoop
enddo plasticityLoop
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end subroutine constitutive_results
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end module constitutive