DAMASK_EICMD/src/constitutive.f90

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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
!--------------------------------------------------------------------------------------------------
module constitutive
use prec
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use math
use rotations
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use IO
use config
use material
use results
use lattice
use discretization
use parallelization
use HDF5_utilities
use DAMASK_interface
use FEsolving
use results
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implicit none
private
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real(pReal), dimension(:,:,:), allocatable, public :: &
crystallite_dt !< requested time increment of each grain
real(pReal), dimension(:,:,:), allocatable :: &
crystallite_subdt, & !< substepped time increment of each grain
crystallite_subStep !< size of next integration step
type(rotation), dimension(:,:,:), allocatable :: &
crystallite_orientation !< current orientation
real(pReal), dimension(:,:,:,:,:), allocatable :: &
crystallite_F0, & !< def grad at start of FE inc
crystallite_subF, & !< def grad to be reached at end of crystallite inc
crystallite_subF0, & !< def grad at start of crystallite 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 :: &
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)
crystallite_partitionedF0 !< def grad at start of homog inc
real(pReal), dimension(:,:,:,:,:), allocatable, public :: &
crystallite_partitionedF !< def grad to be reached at end of homog inc
logical, dimension(:,:,:), allocatable, public :: &
crystallite_requested !< used by upper level (homogenization) to request crystallite calculation
logical, dimension(:,:,:), allocatable :: &
crystallite_converged !< convergence flag
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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_partionedFi0, &
constitutive_mech_Li, &
constitutive_mech_Li0, &
constitutive_mech_partionedLi0, &
constitutive_mech_Fp, &
constitutive_mech_Fp0, &
constitutive_mech_partionedFp0
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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
procedure(integrateStateFPI), pointer :: integrateState
integer(kind(PLASTICITY_undefined_ID)), dimension(:), allocatable :: &
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phase_plasticity !< plasticity of each phase
integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: &
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phase_source, & !< active sources mechanisms of each phase
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
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
interface
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! == cleaned:begin =================================================================================
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module subroutine mech_init
end subroutine mech_init
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
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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! == cleaned:end ===================================================================================
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module subroutine source_damage_anisoBrittle_dotState(S, co, ip, el)
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
end subroutine source_damage_anisoBrittle_dotState
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module subroutine source_damage_anisoDuctile_dotState(co, ip, el)
integer, intent(in) :: &
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co, & !< component-ID of integration point
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ip, & !< integration point
el !< element
end subroutine source_damage_anisoDuctile_dotState
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module subroutine source_damage_isoDuctile_dotState(co, ip, el)
integer, intent(in) :: &
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co, & !< component-ID of integration point
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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 subroutine constitutive_damage_getRateAndItsTangents(phiDot, dPhiDot_dPhi, phi, ip, el)
integer, intent(in) :: &
ip, & !< integration point number
el !< element number
real(pReal), intent(in) :: &
phi !< damage parameter
real(pReal), intent(inout) :: &
phiDot, &
dPhiDot_dPhi
end subroutine constitutive_damage_getRateAndItsTangents
module subroutine constitutive_thermal_getRateAndItsTangents(TDot, dTDot_dT, T, S, Lp, ip, el)
integer, intent(in) :: &
ip, & !< integration point number
el !< element number
real(pReal), intent(in) :: &
T
real(pReal), intent(in), dimension(:,:,:,:,:) :: &
S, & !< current 2nd Piola Kitchoff stress vector
Lp !< plastic velocity gradient
real(pReal), intent(inout) :: &
TDot, &
dTDot_dT
end subroutine constitutive_thermal_getRateAndItsTangents
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module function plastic_dislotwin_homogenizedC(co,ip,el) result(homogenizedC)
real(pReal), dimension(6,6) :: &
homogenizedC
integer, intent(in) :: &
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co, & !< component-ID of integration point
ip, & !< integration point
el !< element
end function plastic_dislotwin_homogenizedC
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module subroutine plastic_nonlocal_updateCompatibility(orientation,instance,i,e)
integer, intent(in) :: &
instance, &
i, &
e
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)
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) :: &
Mi !< Mandel stress
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)
integer, intent(in) :: &
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co, & !< grain number
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ip, & !< integration point number
el !< element number
real(pReal), intent(in), dimension(3,3) :: &
S
real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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)
end subroutine kinematics_cleavage_opening_LiAndItsTangent
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module subroutine kinematics_slipplane_opening_LiAndItsTangent(Ld, dLd_dTstar, S, co, ip, el)
integer, intent(in) :: &
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co, & !< grain number
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ip, & !< integration point number
el !< element number
real(pReal), intent(in), dimension(3,3) :: &
S
real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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)
end subroutine kinematics_slipplane_opening_LiAndItsTangent
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module subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar, co, ip, el)
integer, intent(in) :: &
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co, & !< grain number
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ip, & !< integration point number
el !< element number
real(pReal), intent(out), dimension(3,3) :: &
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Li !< thermal velocity gradient
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)
end subroutine kinematics_thermal_expansion_LiAndItsTangent
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module subroutine source_damage_isoBrittle_deltaState(C, Fe, co, ip, el)
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
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) :: &
F !< elastic deformation gradient
end subroutine constitutive_plastic_dependentState
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module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, co, ip, el)
integer, intent(in) :: &
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co, & !< 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
end subroutine constitutive_hooke_SandItsTangents
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module subroutine integrateStateFPI(co,ip,el)
integer, intent(in) :: co, ip, el
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end subroutine integrateStateFPI
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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, &
crystallite_init, &
crystallite_stress, &
crystallite_stressTangent, &
crystallite_orientations, &
crystallite_push33ToRef, &
crystallite_restartWrite, &
crystallite_restartRead, &
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constitutive_initializeRestorationPoints, &
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constitutive_windForward, &
crystallite_restore
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contains
!--------------------------------------------------------------------------------------------------
!> @brief Initialze constitutive models for individual physics
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_init
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integer :: &
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p, & !< counter in phase loop
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s !< counter in source loop
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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')
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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call mech_init
call damage_init
call thermal_init
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print'(/,a)', ' <<<+- constitutive init -+>>>'; flush(IO_STDOUT)
phases => config_material%get('phase')
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constitutive_source_maxSizeDotState = 0
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PhaseLoop2:do p = 1,phases%length
!--------------------------------------------------------------------------------------------------
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! partition and initialize state
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plasticState(p)%partitionedState0 = plasticState(p)%state0
plasticState(p)%state = plasticState(p)%partitionedState0
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forall(s = 1:phase_Nsources(p))
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sourceState(p)%p(s)%partitionedState0 = sourceState(p)%p(s)%state0
sourceState(p)%p(s)%state = sourceState(p)%p(s)%partitionedState0
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end forall
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constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, &
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maxval(sourceState(p)%p%sizeDotState))
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enddo PhaseLoop2
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constitutive_plasticity_maxSizeDotState = maxval(plasticState%sizeDotState)
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, &
src
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integer :: p,s
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, &
kinematics_type
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integer :: p,k
phases => config_material%get('phase')
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allocate(active_kinematics(kinematics_length,phases%length), source = .false. )
do p = 1, phases%length
phase => phases%get(p)
kinematics => phase%get('kinematics',defaultVal=emptyList)
do k = 1, kinematics%length
kinematics_type => kinematics%get(k)
if(kinematics_type%get_asString('type') == kinematics_label) active_kinematics(k,p) = .true.
enddo
enddo
end function kinematics_active
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!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenize elasticity matrix
!> ToDo: homogenizedC66 would be more consistent
!--------------------------------------------------------------------------------------------------
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function constitutive_homogenizedC(co,ip,el)
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real(pReal), dimension(6,6) :: &
constitutive_homogenizedC
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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plasticityType: select case (phase_plasticity(material_phaseAt(co,el)))
case (PLASTICITY_DISLOTWIN_ID) plasticityType
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constitutive_homogenizedC = plastic_dislotwin_homogenizedC(co,ip,el)
case default plasticityType
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constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(co,el))
end select plasticityType
end function constitutive_homogenizedC
!--------------------------------------------------------------------------------------------------
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!> @brief contains the constitutive equation for calculating the velocity gradient
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! ToDo: MD: S is Mi?
!--------------------------------------------------------------------------------------------------
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
!--------------------------------------------------------------------------------------------------
!> @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,phase,of) result(broken)
integer, intent(in) :: &
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co, & !< component-ID of integration point
ip, & !< integration point
el, & !< element
phase, &
of
real(pReal), intent(in), dimension(3,3) :: &
S !< 2nd Piola Kirchhoff stress (vector notation)
integer :: &
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i !< counter in source loop
logical :: broken
broken = .false.
SourceLoop: do i = 1, phase_Nsources(phase)
sourceType: select case (phase_source(i,phase))
case (SOURCE_damage_anisoBrittle_ID) sourceType
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call source_damage_anisoBrittle_dotState(S, co, ip, el) ! correct stress?
case (SOURCE_damage_isoDuctile_ID) sourceType
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call source_damage_isoDuctile_dotState(co, ip, el)
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
broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%dotState(:,of)))
enddo SourceLoop
end function constitutive_damage_collectDotState
!--------------------------------------------------------------------------------------------------
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
function constitutive_thermal_collectDotState(ph,me) result(broken)
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integer, intent(in) :: ph, me
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logical :: broken
integer :: i
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broken = .false.
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SourceLoop: do i = 1, phase_Nsources(ph)
if (phase_source(i,ph) == SOURCE_thermal_externalheat_ID) &
call source_thermal_externalheat_dotState(ph,me)
broken = broken .or. any(IEEE_is_NaN(sourceState(ph)%p(i)%dotState(:,me)))
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, phase, of) result(broken)
integer, intent(in) :: &
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co, & !< component-ID of integration point
ip, & !< integration point
el, & !< element
phase, &
of
real(pReal), intent(in), dimension(3,3) :: &
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Fe !< elastic deformation gradient
integer :: &
i, &
myOffset, &
mySize
logical :: &
broken
broken = .false.
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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
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call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(co,ip,el), Fe, &
co, ip, el)
broken = any(IEEE_is_NaN(sourceState(phase)%p(i)%deltaState(:,of)))
if(.not. broken) then
myOffset = sourceState(phase)%p(i)%offsetDeltaState
mySize = sourceState(phase)%p(i)%sizeDeltaState
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) = &
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) + sourceState(phase)%p(i)%deltaState(1:mySize,of)
endif
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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, &
Nconstituents,sizeState,sizeDotState,sizeDeltaState)
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class(tState), intent(out) :: &
state
integer, intent(in) :: &
Nconstituents, &
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sizeState, &
sizeDotState, &
sizeDeltaState
state%sizeState = sizeState
state%sizeDotState = sizeDotState
state%sizeDeltaState = sizeDeltaState
state%offsetDeltaState = sizeState-sizeDeltaState ! deltaState occupies latter part of state by definition
allocate(state%atol (sizeState), source=0.0_pReal)
allocate(state%state0 (sizeState,Nconstituents), source=0.0_pReal)
allocate(state%partitionedState0(sizeState,Nconstituents), source=0.0_pReal)
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)
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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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s
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do co = 1,homogenization_Nconstituents(material_homogenizationAt(el))
do s = 1, phase_Nsources(material_phaseAt(co,el))
sourceState(material_phaseAt(co,el))%p(s)%state( :,material_phasememberAt(co,ip,el)) = &
sourceState(material_phaseAt(co,el))%p(s)%partitionedState0(:,material_phasememberAt(co,ip,el))
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enddo
enddo
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_partitionedF
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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!--------------------------------------------------------------------------------------------------
!> @brief writes constitutive results to HDF5 output file
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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, &
p, &
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m, &
c, & !< counter in integration point component loop
i, & !< counter in integration point loop
e, & !< counter in element loop
cMax, & !< maximum number of integration point components
iMax, & !< maximum number of integration points
eMax !< maximum number of elements
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
allocate(crystallite_partitionedF(3,3,cMax,iMax,eMax),source=0.0_pReal)
allocate(crystallite_S0, &
crystallite_F0,crystallite_Lp0, &
crystallite_partitionedS0, &
crystallite_partitionedF0,&
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crystallite_partitionedLp0, &
crystallite_S,crystallite_P, &
crystallite_Fe,crystallite_Lp, &
crystallite_subF,crystallite_subF0, &
crystallite_subFp0,crystallite_subFi0, &
source = crystallite_partitionedF)
allocate(crystallite_dt(cMax,iMax,eMax),source=0.0_pReal)
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allocate(crystallite_subdt,crystallite_subStep, &
source = crystallite_dt)
allocate(crystallite_orientation(cMax,iMax,eMax))
allocate(crystallite_requested(cMax,iMax,eMax), source=.false.)
allocate(crystallite_converged(cMax,iMax,eMax), source=.true.)
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))
allocate(constitutive_mech_partionedFi0(phases%length))
allocate(constitutive_mech_Fp(phases%length))
allocate(constitutive_mech_Fp0(phases%length))
allocate(constitutive_mech_partionedFp0(phases%length))
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allocate(constitutive_mech_Li(phases%length))
allocate(constitutive_mech_Li0(phases%length))
allocate(constitutive_mech_partionedLi0(phases%length))
do p = 1, phases%length
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Nconstituents = count(material_phaseAt == p) * discretization_nIPs
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allocate(constitutive_mech_Fi(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_Fi0(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_partionedFi0(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_Fp(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_Fp0(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_partionedFp0(p)%data(3,3,Nconstituents))
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allocate(constitutive_mech_Li(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_Li0(p)%data(3,3,Nconstituents))
allocate(constitutive_mech_partionedLi0(p)%data(3,3,Nconstituents))
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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!$OMP PARALLEL DO PRIVATE(p,m)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
do i = FEsolving_execIP(1), FEsolving_execIP(2); do c = 1, homogenization_Nconstituents(material_homogenizationAt(e))
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p = material_phaseAt(c,e)
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m = material_phaseMemberAt(c,i,e)
constitutive_mech_Fp0(p)%data(1:3,1:3,m) = material_orientation0(c,i,e)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005)
constitutive_mech_Fp0(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m) &
/ math_det33(constitutive_mech_Fp0(p)%data(1:3,1:3,m))**(1.0_pReal/3.0_pReal)
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constitutive_mech_Fi0(p)%data(1:3,1:3,m) = math_I3
crystallite_F0(1:3,1:3,c,i,e) = math_I3
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crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(matmul(constitutive_mech_Fi0(p)%data(1:3,1:3,m), &
constitutive_mech_Fp0(p)%data(1:3,1:3,m))) ! assuming that euler angles are given in internal strain free configuration
constitutive_mech_Fp(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m)
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constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m)
constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m)
constitutive_mech_partionedFp0(p)%data(1:3,1:3,m) = constitutive_mech_Fp0(p)%data(1:3,1:3,m)
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crystallite_requested(c,i,e) = .true.
enddo; enddo
enddo
!$OMP END PARALLEL DO
crystallite_partitionedF0 = crystallite_F0
crystallite_partitionedF = crystallite_F0
call crystallite_orientations()
!$OMP PARALLEL DO PRIVATE(p,m)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
do i = FEsolving_execIP(1),FEsolving_execIP(2)
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
p = material_phaseAt(c,e)
m = material_phaseMemberAt(c,i,e)
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call constitutive_plastic_dependentState(crystallite_partitionedF0(1:3,1:3,c,i,e), &
c,i,e) ! update dependent state variables to be consistent with basic states
enddo
enddo
enddo
!$OMP END PARALLEL DO
end subroutine crystallite_init
!--------------------------------------------------------------------------------------------------
!> @brief calculate stress (P)
!--------------------------------------------------------------------------------------------------
function crystallite_stress()
logical, dimension(discretization_nIPs,discretization_Nelems) :: crystallite_stress
real(pReal) :: &
formerSubStep
integer :: &
NiterationCrystallite, & ! number of iterations in crystallite loop
c, & !< counter in integration point component loop
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ip, & !< counter in integration point loop
el, & !< counter in element loop
s, ph, me
logical, dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: todo !ToDo: need to set some values to false for different Ngrains
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real(pReal), dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: subFrac !ToDo: need to set some values to false for different Ngrains
real(pReal), dimension(:,:,:,:,:), allocatable :: &
subLp0,& !< plastic velocity grad at start of crystallite inc
subLi0 !< intermediate velocity grad at start of crystallite inc
todo = .false.
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allocate(subLi0(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems))
subLp0 = crystallite_partitionedLp0
!--------------------------------------------------------------------------------------------------
! initialize to starting condition
crystallite_subStep = 0.0_pReal
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!$OMP PARALLEL DO PRIVATE(ph,me)
elementLooping1: do el = FEsolving_execElem(1),FEsolving_execElem(2)
do ip = FEsolving_execIP(1),FEsolving_execIP(2); do c = 1,homogenization_Nconstituents(material_homogenizationAt(el))
ph = material_phaseAt(c,el)
me = material_phaseMemberAt(c,ip,el)
subLi0(1:3,1:3,c,ip,el) = constitutive_mech_partionedLi0(ph)%data(1:3,1:3,me)
homogenizationRequestsCalculation: if (crystallite_requested(c,ip,el)) then
plasticState (material_phaseAt(c,el))%subState0( :,material_phaseMemberAt(c,ip,el)) = &
plasticState (material_phaseAt(c,el))%partitionedState0(:,material_phaseMemberAt(c,ip,el))
do s = 1, phase_Nsources(material_phaseAt(c,el))
sourceState(material_phaseAt(c,el))%p(s)%subState0( :,material_phaseMemberAt(c,ip,el)) = &
sourceState(material_phaseAt(c,el))%p(s)%partitionedState0(:,material_phaseMemberAt(c,ip,el))
enddo
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crystallite_subFp0(1:3,1:3,c,ip,el) = constitutive_mech_partionedFp0(ph)%data(1:3,1:3,me)
crystallite_subFi0(1:3,1:3,c,ip,el) = constitutive_mech_partionedFi0(ph)%data(1:3,1:3,me)
crystallite_subF0(1:3,1:3,c,ip,el) = crystallite_partitionedF0(1:3,1:3,c,ip,el)
subFrac(c,ip,el) = 0.0_pReal
crystallite_subStep(c,ip,el) = 1.0_pReal/num%subStepSizeCryst
todo(c,ip,el) = .true.
crystallite_converged(c,ip,el) = .false. ! pretend failed step of 1/subStepSizeCryst
endif homogenizationRequestsCalculation
enddo; enddo
enddo elementLooping1
!$OMP END PARALLEL DO
NiterationCrystallite = 0
cutbackLooping: do while (any(todo(:,FEsolving_execIP(1):FEsolving_execIP(2),FEsolving_execELem(1):FEsolving_execElem(2))))
NiterationCrystallite = NiterationCrystallite + 1
#ifdef DEBUG
if (debugCrystallite%extensive) &
print'(a,i6)', '<< CRYST stress >> crystallite iteration ',NiterationCrystallite
#endif
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!$OMP PARALLEL DO PRIVATE(formerSubStep,ph,me)
elementLooping3: do el = FEsolving_execElem(1),FEsolving_execElem(2)
do ip = FEsolving_execIP(1),FEsolving_execIP(2)
do c = 1,homogenization_Nconstituents(material_homogenizationAt(el))
ph = material_phaseAt(c,el)
me = material_phaseMemberAt(c,ip,el)
!--------------------------------------------------------------------------------------------------
! wind forward
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if (crystallite_converged(c,ip,el)) then
formerSubStep = crystallite_subStep(c,ip,el)
subFrac(c,ip,el) = subFrac(c,ip,el) + crystallite_subStep(c,ip,el)
crystallite_subStep(c,ip,el) = min(1.0_pReal - subFrac(c,ip,el), &
num%stepIncreaseCryst * crystallite_subStep(c,ip,el))
todo(c,ip,el) = crystallite_subStep(c,ip,el) > 0.0_pReal ! still time left to integrate on?
if (todo(c,ip,el)) then
crystallite_subF0 (1:3,1:3,c,ip,el) = crystallite_subF(1:3,1:3,c,ip,el)
subLp0(1:3,1:3,c,ip,el) = crystallite_Lp (1:3,1:3,c,ip,el)
subLi0(1:3,1:3,c,ip,el) = constitutive_mech_Li(ph)%data(1:3,1:3,me)
crystallite_subFp0(1:3,1:3,c,ip,el) = constitutive_mech_Fp(ph)%data(1:3,1:3,me)
crystallite_subFi0(1:3,1:3,c,ip,el) = constitutive_mech_Fi(ph)%data(1:3,1:3,me)
plasticState( material_phaseAt(c,el))%subState0(:,material_phaseMemberAt(c,ip,el)) &
= plasticState(material_phaseAt(c,el))%state( :,material_phaseMemberAt(c,ip,el))
do s = 1, phase_Nsources(material_phaseAt(c,el))
sourceState( material_phaseAt(c,el))%p(s)%subState0(:,material_phaseMemberAt(c,ip,el)) &
= sourceState(material_phaseAt(c,el))%p(s)%state( :,material_phaseMemberAt(c,ip,el))
enddo
endif
!--------------------------------------------------------------------------------------------------
! cut back (reduced time and restore)
else
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crystallite_subStep(c,ip,el) = num%subStepSizeCryst * crystallite_subStep(c,ip,el)
constitutive_mech_Fp(ph)%data(1:3,1:3,me) = crystallite_subFp0(1:3,1:3,c,ip,el)
constitutive_mech_Fi(ph)%data(1:3,1:3,me) = crystallite_subFi0(1:3,1:3,c,ip,el)
crystallite_S (1:3,1:3,c,ip,el) = crystallite_S0 (1:3,1:3,c,ip,el)
if (crystallite_subStep(c,ip,el) < 1.0_pReal) then ! actual (not initial) cutback
crystallite_Lp (1:3,1:3,c,ip,el) = subLp0(1:3,1:3,c,ip,el)
constitutive_mech_Li(ph)%data(1:3,1:3,me) = subLi0(1:3,1:3,c,ip,el)
endif
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plasticState (material_phaseAt(c,el))%state( :,material_phaseMemberAt(c,ip,el)) &
= plasticState(material_phaseAt(c,el))%subState0(:,material_phaseMemberAt(c,ip,el))
do s = 1, phase_Nsources(material_phaseAt(c,el))
sourceState( material_phaseAt(c,el))%p(s)%state( :,material_phaseMemberAt(c,ip,el)) &
= sourceState(material_phaseAt(c,el))%p(s)%subState0(:,material_phaseMemberAt(c,ip,el))
enddo
! cant restore dotState here, since not yet calculated in first cutback after initialization
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todo(c,ip,el) = crystallite_subStep(c,ip,el) > num%subStepMinCryst ! still on track or already done (beyond repair)
endif
!--------------------------------------------------------------------------------------------------
! prepare for integration
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if (todo(c,ip,el)) then
crystallite_subF(1:3,1:3,c,ip,el) = crystallite_subF0(1:3,1:3,c,ip,el) &
+ crystallite_subStep(c,ip,el) *( crystallite_partitionedF (1:3,1:3,c,ip,el) &
-crystallite_partitionedF0(1:3,1:3,c,ip,el))
crystallite_Fe(1:3,1:3,c,ip,el) = matmul(crystallite_subF(1:3,1:3,c,ip,el), &
math_inv33(matmul(constitutive_mech_Fi(ph)%data(1:3,1:3,me), &
constitutive_mech_Fp(ph)%data(1:3,1:3,me))))
crystallite_subdt(c,ip,el) = crystallite_subStep(c,ip,el) * crystallite_dt(c,ip,el)
crystallite_converged(c,ip,el) = .false.
call integrateState(c,ip,el)
call integrateSourceState(c,ip,el)
endif
enddo
enddo
enddo elementLooping3
!$OMP END PARALLEL DO
!--------------------------------------------------------------------------------------------------
! integrate --- requires fully defined state array (basic + dependent state)
where(.not. crystallite_converged .and. crystallite_subStep > num%subStepMinCryst) & ! do not try non-converged but fully cutbacked any further
todo = .true. ! TODO: again unroll this into proper elementloop to avoid N^2 for single point evaluation
enddo cutbackLooping
! return whether converged or not
crystallite_stress = .false.
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elementLooping5: do el = FEsolving_execElem(1),FEsolving_execElem(2)
do ip = FEsolving_execIP(1),FEsolving_execIP(2)
crystallite_stress(ip,el) = all(crystallite_converged(:,ip,el))
enddo
enddo elementLooping5
end function crystallite_stress
!--------------------------------------------------------------------------------------------------
!> @brief Backup data for homog cutback.
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_initializeRestorationPoints(ip,el)
integer, intent(in) :: &
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ip, & !< integration point number
el !< element number
integer :: &
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co, & !< constituent number
s,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)
call mech_initializeRestorationPoints(ph,me)
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do s = 1, phase_Nsources(material_phaseAt(co,el))
sourceState(material_phaseAt(co,el))%p(s)%partitionedState0(:,material_phasememberAt(co,ip,el)) = &
sourceState(material_phaseAt(co,el))%p(s)%state0( :,material_phasememberAt(co,ip,el))
enddo
enddo
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end subroutine constitutive_initializeRestorationPoints
!--------------------------------------------------------------------------------------------------
!> @brief Wind homog inc forward.
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_windForward(ip,el)
integer, intent(in) :: &
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ip, & !< integration point number
el !< element number
integer :: &
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co, & !< constituent number
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s, 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_partitionedF0 (1:3,1:3,co,ip,el) = crystallite_partitionedF(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 s = 1, phase_Nsources(material_phaseAt(co,el))
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sourceState(ph)%p(s)%partitionedState0(:,me) = sourceState(ph)%p(s)%state(:,me)
enddo
enddo
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end subroutine constitutive_windForward
!--------------------------------------------------------------------------------------------------
!> @brief Restore data after homog cutback.
!--------------------------------------------------------------------------------------------------
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subroutine crystallite_restore(ip,el,includeL)
integer, intent(in) :: &
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ip, & !< integration point number
el !< element number
logical, intent(in) :: &
includeL !< protect agains fake cutback
integer :: &
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co, p, m !< constituent number
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do co = 1,homogenization_Nconstituents(material_homogenizationAt(el))
p = material_phaseAt(co,el)
m = material_phaseMemberAt(co,ip,el)
if (includeL) then
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crystallite_Lp(1:3,1:3,co,ip,el) = crystallite_partitionedLp0(1:3,1:3,co,ip,el)
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constitutive_mech_Li(p)%data(1:3,1:3,m) = constitutive_mech_partionedLi0(p)%data(1:3,1:3,m)
endif ! maybe protecting everything from overwriting makes more sense
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constitutive_mech_Fp(p)%data(1:3,1:3,m) = constitutive_mech_partionedFp0(p)%data(1:3,1:3,m)
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constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_partionedFi0(p)%data(1:3,1:3,m)
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crystallite_S (1:3,1:3,co,ip,el) = crystallite_partitionedS0 (1:3,1:3,co,ip,el)
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plasticState (material_phaseAt(co,el))%state( :,material_phasememberAt(co,ip,el)) = &
plasticState (material_phaseAt(co,el))%partitionedState0(:,material_phasememberAt(co,ip,el))
enddo
end subroutine crystallite_restore
!--------------------------------------------------------------------------------------------------
!> @brief Calculate tangent (dPdF).
!--------------------------------------------------------------------------------------------------
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function crystallite_stressTangent(co,ip,el) result(dPdF)
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
integer :: &
o, &
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p, pp, m
real(pReal), dimension(3,3) :: devNull, &
invSubFp0,invSubFi0,invFp,invFi, &
temp_33_1, temp_33_2, temp_33_3, temp_33_4
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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pp = material_phaseAt(co,el)
m = 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), &
constitutive_mech_Fi(pp)%data(1:3,1:3,m),co,ip,el)
call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, &
crystallite_S (1:3,1:3,co,ip,el), &
constitutive_mech_Fi(pp)%data(1:3,1:3,m), &
co,ip,el)
invFp = math_inv33(constitutive_mech_Fp(pp)%data(1:3,1:3,m))
invFi = math_inv33(constitutive_mech_Fi(pp)%data(1:3,1:3,m))
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), &
constitutive_mech_Fi(pp)%data(1:3,1:3,m),co,ip,el)
dLpdS = math_mul3333xx3333(dLpdFi,dFidS) + dLpdS
!--------------------------------------------------------------------------------------------------
! calculate dSdF
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temp_33_1 = transpose(matmul(invFp,invFi))
temp_33_2 = matmul(crystallite_subF(1:3,1:3,co,ip,el),invSubFp0)
temp_33_3 = matmul(matmul(crystallite_subF(1:3,1:3,co,ip,el),invFp), invSubFi0)
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
!--------------------------------------------------------------------------------------------------
! 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
!--------------------------------------------------------------------------------------------------
! assemble dPdF
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temp_33_1 = matmul(crystallite_S(1:3,1:3,co,ip,el),transpose(invFp))
temp_33_2 = matmul(invFp,temp_33_1)
temp_33_3 = matmul(crystallite_subF(1:3,1:3,co,ip,el),invFp)
temp_33_4 = matmul(temp_33_3,crystallite_S(1:3,1:3,co,ip,el))
dPdF = 0.0_pReal
do p=1,3
dPdF(p,1:3,p,1:3) = transpose(temp_33_2)
enddo
do o=1,3; do p=1,3
dPdF(1:3,1:3,p,o) = dPdF(1:3,1:3,p,o) &
+ matmul(matmul(crystallite_subF(1:3,1:3,co,ip,el), &
dFpinvdF(1:3,1:3,p,o)),temp_33_1) &
+ matmul(matmul(temp_33_3,dSdF(1:3,1:3,p,o)), &
transpose(invFp)) &
+ matmul(temp_33_4,transpose(dFpinvdF(1:3,1:3,p,o)))
enddo; enddo
end function crystallite_stressTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates orientations
!--------------------------------------------------------------------------------------------------
subroutine crystallite_orientations
integer &
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co, & !< counter in integration point component loop
ip, & !< counter in integration point loop
el !< counter in element loop
!$OMP PARALLEL DO
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do el = FEsolving_execElem(1),FEsolving_execElem(2)
do ip = FEsolving_execIP(1),FEsolving_execIP(2)
do co = 1,homogenization_Nconstituents(material_homogenizationAt(el))
call crystallite_orientation(co,ip,el)%fromMatrix(transpose(math_rotationalPart(crystallite_Fe(1:3,1:3,co,ip,el))))
enddo; enddo; enddo
!$OMP END PARALLEL DO
nonlocalPresent: if (any(plasticState%nonlocal)) then
!$OMP PARALLEL DO
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do el = FEsolving_execElem(1),FEsolving_execElem(2)
if (plasticState(material_phaseAt(1,el))%nonlocal) then
do ip = FEsolving_execIP(1),FEsolving_execIP(2)
call plastic_nonlocal_updateCompatibility(crystallite_orientation, &
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phase_plasticityInstance(material_phaseAt(1,el)),ip,el)
enddo
endif
enddo
!$OMP END PARALLEL DO
endif nonlocalPresent
end subroutine crystallite_orientations
!--------------------------------------------------------------------------------------------------
!> @brief Map 2nd order tensor to reference config
!--------------------------------------------------------------------------------------------------
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function crystallite_push33ToRef(co,ip,el, tensor33)
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?
transpose(math_inv33(crystallite_subF(1:3,1:3,co,ip,el))))
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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subroutine integrateSourceState(co,ip,el)
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, &
c, &
s, &
size_pl
integer, dimension(maxval(phase_Nsources)) :: &
size_so
real(pReal) :: &
zeta
real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: &
r ! state residuum
real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState
logical :: &
broken
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ph = material_phaseAt(co,el)
c = material_phaseMemberAt(co,ip,el)
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broken = constitutive_thermal_collectDotState(ph,c)
broken = broken .or. constitutive_damage_collectDotState(crystallite_S(1:3,1:3,co,ip,el), co,ip,el,ph,c)
if(broken) return
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do s = 1, phase_Nsources(ph)
size_so(s) = sourceState(ph)%p(s)%sizeDotState
sourceState(ph)%p(s)%state(1:size_so(s),c) = sourceState(ph)%p(s)%subState0(1:size_so(s),c) &
+ sourceState(ph)%p(s)%dotState (1:size_so(s),c) &
* crystallite_subdt(co,ip,el)
source_dotState(1:size_so(s),2,s) = 0.0_pReal
enddo
iteration: do NiterationState = 1, num%nState
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do s = 1, phase_Nsources(ph)
if(nIterationState > 1) source_dotState(1:size_so(s),2,s) = source_dotState(1:size_so(s),1,s)
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source_dotState(1:size_so(s),1,s) = sourceState(ph)%p(s)%dotState(:,c)
enddo
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broken = constitutive_thermal_collectDotState(ph,c)
broken = broken .or. constitutive_damage_collectDotState(crystallite_S(1:3,1:3,co,ip,el), co,ip,el,ph,c)
if(broken) exit iteration
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do s = 1, phase_Nsources(ph)
zeta = damper(sourceState(ph)%p(s)%dotState(:,c), &
source_dotState(1:size_so(s),1,s),&
source_dotState(1:size_so(s),2,s))
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sourceState(ph)%p(s)%dotState(:,c) = sourceState(ph)%p(s)%dotState(:,c) * zeta &
+ source_dotState(1:size_so(s),1,s)* (1.0_pReal - zeta)
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r(1:size_so(s)) = sourceState(ph)%p(s)%state (1:size_so(s),c) &
- sourceState(ph)%p(s)%subState0(1:size_so(s),c) &
- sourceState(ph)%p(s)%dotState (1:size_so(s),c) * crystallite_subdt(co,ip,el)
sourceState(ph)%p(s)%state(1:size_so(s),c) = sourceState(ph)%p(s)%state(1:size_so(s),c) &
- r(1:size_so(s))
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crystallite_converged(co,ip,el) = &
crystallite_converged(co,ip,el) .and. converged(r(1:size_so(s)), &
sourceState(ph)%p(s)%state(1:size_so(s),c), &
sourceState(ph)%p(s)%atol(1:size_so(s)))
enddo
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if(crystallite_converged(co,ip,el)) then
broken = constitutive_damage_deltaState(crystallite_Fe(1:3,1:3,co,ip,el),co,ip,el,ph,c)
exit iteration
endif
enddo iteration
contains
!--------------------------------------------------------------------------------------------------
!> @brief calculate the damping for correction of state and dot state
!--------------------------------------------------------------------------------------------------
real(pReal) pure function damper(current,previous,previous2)
real(pReal), dimension(:), intent(in) ::&
current, previous, previous2
real(pReal) :: dot_prod12, dot_prod22
dot_prod12 = dot_product(current - previous, previous - previous2)
dot_prod22 = dot_product(previous - previous2, previous - previous2)
if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then
damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22)
else
damper = 1.0_pReal
endif
end function damper
end subroutine integrateSourceState
!--------------------------------------------------------------------------------------------------
!> @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
integer :: i
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')
call HDF5_write(fileHandle,crystallite_partitionedF,'F')
call HDF5_write(fileHandle,crystallite_Lp, 'L_p')
call HDF5_write(fileHandle,crystallite_S, 'S')
groupHandle = HDF5_addGroup(fileHandle,'phase')
do i = 1,size(material_name_phase)
write(datasetName,'(i0,a)') i,'_omega'
call HDF5_write(groupHandle,plasticState(i)%state,datasetName)
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write(datasetName,'(i0,a)') i,'_F_i'
call HDF5_write(groupHandle,constitutive_mech_Fi(i)%data,datasetName)
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write(datasetName,'(i0,a)') i,'_L_i'
call HDF5_write(groupHandle,constitutive_mech_Li(i)%data,datasetName)
write(datasetName,'(i0,a)') i,'_F_p'
call HDF5_write(groupHandle,constitutive_mech_Fp(i)%data,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_addGroup(fileHandle,'homogenization')
do i = 1, size(material_name_homogenization)
write(datasetName,'(i0,a)') i,'_omega'
call HDF5_write(groupHandle,homogState(i)%state,datasetName)
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
integer :: i
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')
do i = 1,size(material_name_phase)
write(datasetName,'(i0,a)') i,'_omega'
call HDF5_read(groupHandle,plasticState(i)%state0,datasetName)
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write(datasetName,'(i0,a)') i,'_F_i'
call HDF5_read(groupHandle,constitutive_mech_Fi0(i)%data,datasetName)
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write(datasetName,'(i0,a)') i,'_L_i'
call HDF5_read(groupHandle,constitutive_mech_Li0(i)%data,datasetName)
write(datasetName,'(i0,a)') i,'_F_p'
call HDF5_read(groupHandle,constitutive_mech_Fp0(i)%data,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
groupHandle = HDF5_openGroup(fileHandle,'homogenization')
do i = 1,size(material_name_homogenization)
write(datasetName,'(i0,a)') i,'_omega'
call HDF5_read(groupHandle,homogState(i)%state0,datasetName)
enddo
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
end subroutine crystallite_restartRead
end module constitutive