2359 lines
120 KiB
Fortran
2359 lines
120 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief elasticity, plasticity, damage & thermal internal microstructure state
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!--------------------------------------------------------------------------------------------------
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module constitutive
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use prec
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use math
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use rotations
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use IO
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use config
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use material
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use results
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use lattice
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use discretization
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use parallelization
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use HDF5_utilities
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use DAMASK_interface
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use FEsolving
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use results
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implicit none
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private
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real(pReal), dimension(:,:,:), allocatable, public :: &
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crystallite_dt !< requested time increment of each grain
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real(pReal), dimension(:,:,:), allocatable :: &
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crystallite_subdt, & !< substepped time increment of each grain
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crystallite_subStep !< size of next integration step
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type(rotation), dimension(:,:,:), allocatable :: &
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crystallite_orientation !< current orientation
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real(pReal), dimension(:,:,:,:,:), allocatable :: &
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crystallite_F0, & !< def grad at start of FE inc
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crystallite_subF, & !< def grad to be reached at end of crystallite inc
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crystallite_subF0, & !< def grad at start of crystallite inc
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!
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crystallite_Fe, & !< current "elastic" def grad (end of converged time step)
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!
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crystallite_Fp, & !< current plastic def grad (end of converged time step)
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crystallite_Fp0, & !< plastic def grad at start of FE inc
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crystallite_partitionedFp0,& !< plastic def grad at start of homog inc
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crystallite_subFp0,& !< plastic def grad at start of crystallite inc
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!
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crystallite_subFi0,& !< intermediate def grad at start of crystallite inc
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!
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crystallite_Lp0, & !< plastic velocitiy grad at start of FE inc
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crystallite_partitionedLp0, & !< plastic velocity grad at start of homog inc
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!
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crystallite_Li, & !< current intermediate velocitiy grad (end of converged time step)
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crystallite_Li0, & !< intermediate velocitiy grad at start of FE inc
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crystallite_partitionedLi0, & !< intermediate velocity grad at start of homog inc
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!
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crystallite_S0, & !< 2nd Piola-Kirchhoff stress vector at start of FE inc
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crystallite_partitionedS0 !< 2nd Piola-Kirchhoff stress vector at start of homog inc
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real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: &
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crystallite_P, & !< 1st Piola-Kirchhoff stress per grain
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crystallite_Lp, & !< current plastic velocitiy grad (end of converged time step)
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crystallite_S, & !< current 2nd Piola-Kirchhoff stress vector (end of converged time step)
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crystallite_partitionedF0 !< def grad at start of homog inc
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real(pReal), dimension(:,:,:,:,:), allocatable, public :: &
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crystallite_partitionedF !< def grad to be reached at end of homog inc
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logical, dimension(:,:,:), allocatable, public :: &
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crystallite_requested !< used by upper level (homogenization) to request crystallite calculation
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logical, dimension(:,:,:), allocatable :: &
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crystallite_converged !< convergence flag
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type :: tOutput !< new requested output (per phase)
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character(len=pStringLen), allocatable, dimension(:) :: &
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label
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end type tOutput
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type(tOutput), allocatable, dimension(:) :: output_constituent
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type :: tTensorContainer
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real(pReal), dimension(:,:,:), allocatable :: data
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end type
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type(tTensorContainer), dimension(:), allocatable :: &
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constitutive_mech_Fi, &
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constitutive_mech_Fi0, &
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constitutive_mech_partionedFi0
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type :: tNumerics
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integer :: &
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iJacoLpresiduum, & !< frequency of Jacobian update of residuum in Lp
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nState, & !< state loop limit
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nStress !< stress loop limit
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real(pReal) :: &
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subStepMinCryst, & !< minimum (relative) size of sub-step allowed during cutback
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subStepSizeCryst, & !< size of first substep when cutback
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subStepSizeLp, & !< size of first substep when cutback in Lp calculation
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subStepSizeLi, & !< size of first substep when cutback in Li calculation
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stepIncreaseCryst, & !< increase of next substep size when previous substep converged
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rtol_crystalliteState, & !< relative tolerance in state loop
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rtol_crystalliteStress, & !< relative tolerance in stress loop
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atol_crystalliteStress !< absolute tolerance in stress loop
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end type tNumerics
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type(tNumerics) :: num ! numerics parameters. Better name?
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type :: tDebugOptions
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logical :: &
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basic, &
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extensive, &
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selective
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integer :: &
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element, &
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ip, &
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grain
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end type tDebugOptions
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type(tDebugOptions) :: debugCrystallite
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procedure(integrateStateFPI), pointer :: integrateState
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integer(kind(PLASTICITY_undefined_ID)), dimension(:), allocatable :: &
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phase_plasticity !< plasticity of each phase
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integer(kind(SOURCE_undefined_ID)), dimension(:,:), allocatable :: &
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phase_source, & !< active sources mechanisms of each phase
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phase_kinematics !< active kinematic mechanisms of each phase
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integer, dimension(:), allocatable, public :: & !< ToDo: should be protected (bug in Intel compiler)
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phase_Nsources, & !< number of source mechanisms active in each phase
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phase_Nkinematics, & !< number of kinematic mechanisms active in each phase
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phase_NstiffnessDegradations, & !< number of stiffness degradation mechanisms active in each phase
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phase_plasticityInstance, & !< instance of particular plasticity of each phase
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phase_elasticityInstance !< instance of particular elasticity of each phase
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logical, dimension(:), allocatable, public :: & ! ToDo: should be protected (bug in Intel Compiler)
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phase_localPlasticity !< flags phases with local constitutive law
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type(tPlasticState), allocatable, dimension(:), public :: &
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plasticState
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type(tSourceState), allocatable, dimension(:), public :: &
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sourceState
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integer, public, protected :: &
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constitutive_plasticity_maxSizeDotState, &
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constitutive_source_maxSizeDotState
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interface
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module subroutine mech_init
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end subroutine mech_init
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module subroutine damage_init
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end subroutine damage_init
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module subroutine thermal_init
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end subroutine thermal_init
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module function constitutive_collectDotState(S, FArray, Fi, FpArray, subdt, ipc, ip, el,phase,of) result(broken)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el, & !< element
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phase, &
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of
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real(pReal), intent(in) :: &
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subdt !< timestep
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real(pReal), intent(in), dimension(3,3,homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: &
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FArray, & !< elastic deformation gradient
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FpArray !< plastic deformation gradient
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real(pReal), intent(in), dimension(3,3) :: &
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Fi !< intermediate deformation gradient
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real(pReal), intent(in), dimension(3,3) :: &
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S !< 2nd Piola Kirchhoff stress (vector notation)
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logical :: broken
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end function constitutive_collectDotState
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module function constitutive_deltaState(S, Fi, ipc, ip, el, phase, of) result(broken)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el, & !< element
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phase, &
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of
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real(pReal), intent(in), dimension(3,3) :: &
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S, & !< 2nd Piola Kirchhoff stress
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Fi !< intermediate deformation gradient
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logical :: &
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broken
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end function constitutive_deltaState
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module function plastic_active(plastic_label) result(active_plastic)
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character(len=*), intent(in) :: plastic_label
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logical, dimension(:), allocatable :: active_plastic
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end function plastic_active
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module function source_active(source_label,src_length) result(active_source)
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character(len=*), intent(in) :: source_label
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integer, intent(in) :: src_length
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logical, dimension(:,:), allocatable :: active_source
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end function source_active
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module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics)
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character(len=*), intent(in) :: kinematics_label
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integer, intent(in) :: kinematics_length
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logical, dimension(:,:), allocatable :: active_kinematics
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end function kinematics_active
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module subroutine source_damage_anisoBrittle_dotState(S, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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S
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end subroutine source_damage_anisoBrittle_dotState
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module subroutine source_damage_anisoDuctile_dotState(ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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end subroutine source_damage_anisoDuctile_dotState
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module subroutine source_damage_isoDuctile_dotState(ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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end subroutine source_damage_isoDuctile_dotState
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module subroutine source_thermal_externalheat_dotState(phase, of)
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integer, intent(in) :: &
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phase, &
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of
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end subroutine source_thermal_externalheat_dotState
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module subroutine constitutive_damage_getRateAndItsTangents(phiDot, dPhiDot_dPhi, phi, ip, el)
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integer, intent(in) :: &
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in) :: &
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phi !< damage parameter
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real(pReal), intent(inout) :: &
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phiDot, &
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dPhiDot_dPhi
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end subroutine constitutive_damage_getRateAndItsTangents
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module subroutine constitutive_thermal_getRateAndItsTangents(TDot, dTDot_dT, T, S, Lp, ip, el)
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integer, intent(in) :: &
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in) :: &
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T
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real(pReal), intent(in), dimension(:,:,:,:,:) :: &
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S, & !< current 2nd Piola Kitchoff stress vector
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Lp !< plastic velocity gradient
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real(pReal), intent(inout) :: &
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TDot, &
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dTDot_dT
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end subroutine constitutive_thermal_getRateAndItsTangents
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module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
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real(pReal), dimension(6,6) :: &
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homogenizedC
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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end function plastic_dislotwin_homogenizedC
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module subroutine plastic_nonlocal_updateCompatibility(orientation,instance,i,e)
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integer, intent(in) :: &
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instance, &
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i, &
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e
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type(rotation), dimension(1,discretization_nIPs,discretization_Nelems), intent(in) :: &
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orientation !< crystal orientation
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end subroutine plastic_nonlocal_updateCompatibility
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module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,instance,of)
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real(pReal), dimension(3,3), intent(out) :: &
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Li !< inleastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLi_dMi !< derivative of Li with respect to Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mi !< Mandel stress
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integer, intent(in) :: &
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instance, &
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of
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end subroutine plastic_isotropic_LiAndItsTangent
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module subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in), dimension(3,3) :: &
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S
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real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
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end subroutine kinematics_cleavage_opening_LiAndItsTangent
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module subroutine kinematics_slipplane_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(in), dimension(3,3) :: &
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S
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real(pReal), intent(out), dimension(3,3) :: &
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Ld !< damage velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLd_dTstar !< derivative of Ld with respect to Tstar (4th-order tensor)
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end subroutine kinematics_slipplane_opening_LiAndItsTangent
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module subroutine kinematics_thermal_expansion_LiAndItsTangent(Li, dLi_dTstar, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< grain number
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ip, & !< integration point number
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el !< element number
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real(pReal), intent(out), dimension(3,3) :: &
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Li !< thermal velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLi_dTstar !< derivative of Li with respect to Tstar (4th-order tensor defined to be zero)
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end subroutine kinematics_thermal_expansion_LiAndItsTangent
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module subroutine source_damage_isoBrittle_deltaState(C, Fe, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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Fe
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real(pReal), intent(in), dimension(6,6) :: &
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C
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end subroutine source_damage_isoBrittle_deltaState
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module subroutine plastic_results
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end subroutine plastic_results
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module subroutine damage_results
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end subroutine damage_results
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module subroutine constitutive_plastic_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, &
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S, Fi, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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S, & !< 2nd Piola-Kirchhoff stress
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Fi !< intermediate deformation gradient
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real(pReal), intent(out), dimension(3,3) :: &
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Lp !< plastic velocity gradient
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dLp_dS, &
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dLp_dFi !< derivative of Lp with respect to Fi
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end subroutine constitutive_plastic_LpAndItsTangents
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module subroutine constitutive_plastic_dependentState(F, Fp, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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F, & !< elastic deformation gradient
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Fp !< plastic deformation gradient
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end subroutine constitutive_plastic_dependentState
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module subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el)
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integer, intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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real(pReal), intent(in), dimension(3,3) :: &
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Fe, & !< elastic deformation gradient
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Fi !< intermediate deformation gradient
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real(pReal), intent(out), dimension(3,3) :: &
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S !< 2nd Piola-Kirchhoff stress tensor
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real(pReal), intent(out), dimension(3,3,3,3) :: &
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dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
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dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
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end subroutine constitutive_hooke_SandItsTangents
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end interface
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type(tDebugOptions) :: debugConstitutive
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public :: &
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constitutive_init, &
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constitutive_homogenizedC, &
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constitutive_LiAndItsTangents, &
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constitutive_collectDotState, &
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constitutive_collectDotState_source, &
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constitutive_deltaState, &
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constitutive_deltaState_source, &
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constitutive_damage_getRateAndItsTangents, &
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constitutive_thermal_getRateAndItsTangents, &
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constitutive_results, &
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constitutive_allocateState, &
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constitutive_forward, &
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constitutive_restore, &
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plastic_nonlocal_updateCompatibility, &
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plastic_active, &
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source_active, &
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kinematics_active
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public :: &
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crystallite_init, &
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crystallite_stress, &
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crystallite_stressTangent, &
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crystallite_orientations, &
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crystallite_push33ToRef, &
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crystallite_results, &
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crystallite_restartWrite, &
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crystallite_restartRead, &
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crystallite_forward, &
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crystallite_initializeRestorationPoints, &
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crystallite_windForward, &
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crystallite_restore
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Initialze constitutive models for individual physics
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_init
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integer :: &
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p, & !< counter in phase loop
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s !< counter in source loop
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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)
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debugConstitutive%basic = debug_constitutive%contains('basic')
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debugConstitutive%extensive = debug_constitutive%contains('extensive')
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debugConstitutive%selective = debug_constitutive%contains('selective')
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debugConstitutive%element = config_debug%get_asInt('element',defaultVal = 1)
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debugConstitutive%ip = config_debug%get_asInt('integrationpoint',defaultVal = 1)
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debugConstitutive%grain = config_debug%get_asInt('grain',defaultVal = 1)
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!--------------------------------------------------------------------------------------------------
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! initialize constitutive laws
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call mech_init
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call damage_init
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call thermal_init
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print'(/,a)', ' <<<+- constitutive init -+>>>'; flush(IO_STDOUT)
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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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!--------------------------------------------------------------------------------------------------
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! partition and initialize state
|
|
plasticState(p)%partitionedState0 = plasticState(p)%state0
|
|
plasticState(p)%state = plasticState(p)%partitionedState0
|
|
forall(s = 1:phase_Nsources(p))
|
|
sourceState(p)%p(s)%partitionedState0 = sourceState(p)%p(s)%state0
|
|
sourceState(p)%p(s)%state = sourceState(p)%p(s)%partitionedState0
|
|
end forall
|
|
|
|
constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, &
|
|
maxval(sourceState(p)%p%sizeDotState))
|
|
enddo PhaseLoop2
|
|
constitutive_plasticity_maxSizeDotState = maxval(plasticState%sizeDotState)
|
|
|
|
end subroutine constitutive_init
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief checks if a source mechanism is active or not
|
|
!--------------------------------------------------------------------------------------------------
|
|
module function source_active(source_label,src_length) result(active_source)
|
|
|
|
character(len=*), intent(in) :: source_label !< name of source mechanism
|
|
integer, intent(in) :: src_length !< max. number of sources in system
|
|
logical, dimension(:,:), allocatable :: active_source
|
|
|
|
class(tNode), pointer :: &
|
|
phases, &
|
|
phase, &
|
|
sources, &
|
|
src
|
|
integer :: p,s
|
|
|
|
phases => config_material%get('phase')
|
|
allocate(active_source(src_length,phases%length), source = .false. )
|
|
do p = 1, phases%length
|
|
phase => phases%get(p)
|
|
sources => phase%get('source',defaultVal=emptyList)
|
|
do s = 1, sources%length
|
|
src => sources%get(s)
|
|
if(src%get_asString('type') == source_label) active_source(s,p) = .true.
|
|
enddo
|
|
enddo
|
|
|
|
|
|
end function source_active
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief checks if a kinematic mechanism is active or not
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
module function kinematics_active(kinematics_label,kinematics_length) result(active_kinematics)
|
|
|
|
character(len=*), intent(in) :: kinematics_label !< name of kinematic mechanism
|
|
integer, intent(in) :: kinematics_length !< max. number of kinematics in system
|
|
logical, dimension(:,:), allocatable :: active_kinematics
|
|
|
|
class(tNode), pointer :: &
|
|
phases, &
|
|
phase, &
|
|
kinematics, &
|
|
kinematics_type
|
|
integer :: p,k
|
|
|
|
phases => config_material%get('phase')
|
|
allocate(active_kinematics(kinematics_length,phases%length), source = .false. )
|
|
do p = 1, phases%length
|
|
phase => phases%get(p)
|
|
kinematics => phase%get('kinematics',defaultVal=emptyList)
|
|
do k = 1, kinematics%length
|
|
kinematics_type => kinematics%get(k)
|
|
if(kinematics_type%get_asString('type') == kinematics_label) active_kinematics(k,p) = .true.
|
|
enddo
|
|
enddo
|
|
|
|
|
|
end function kinematics_active
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief returns the homogenize elasticity matrix
|
|
!> ToDo: homogenizedC66 would be more consistent
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_homogenizedC(ipc,ip,el)
|
|
|
|
real(pReal), dimension(6,6) :: &
|
|
constitutive_homogenizedC
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
|
|
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
|
|
case (PLASTICITY_DISLOTWIN_ID) plasticityType
|
|
constitutive_homogenizedC = plastic_dislotwin_homogenizedC(ipc,ip,el)
|
|
case default plasticityType
|
|
constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(ipc,el))
|
|
end select plasticityType
|
|
|
|
end function constitutive_homogenizedC
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the velocity gradient
|
|
! ToDo: MD: S is Mi?
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_LiAndItsTangents(Li, dLi_dS, dLi_dFi, &
|
|
S, Fi, ipc, ip, el)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
S !< 2nd Piola-Kirchhoff stress
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fi !< intermediate deformation gradient
|
|
real(pReal), intent(out), dimension(3,3) :: &
|
|
Li !< intermediate velocity gradient
|
|
real(pReal), intent(out), dimension(3,3,3,3) :: &
|
|
dLi_dS, & !< derivative of Li with respect to S
|
|
dLi_dFi
|
|
|
|
real(pReal), dimension(3,3) :: &
|
|
my_Li, & !< intermediate velocity gradient
|
|
FiInv, &
|
|
temp_33
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
my_dLi_dS
|
|
real(pReal) :: &
|
|
detFi
|
|
integer :: &
|
|
k, i, j, &
|
|
instance, of
|
|
|
|
Li = 0.0_pReal
|
|
dLi_dS = 0.0_pReal
|
|
dLi_dFi = 0.0_pReal
|
|
|
|
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
|
|
case (PLASTICITY_isotropic_ID) plasticityType
|
|
of = material_phasememberAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
|
|
call plastic_isotropic_LiAndItsTangent(my_Li, my_dLi_dS, S ,instance,of)
|
|
case default plasticityType
|
|
my_Li = 0.0_pReal
|
|
my_dLi_dS = 0.0_pReal
|
|
end select plasticityType
|
|
|
|
Li = Li + my_Li
|
|
dLi_dS = dLi_dS + my_dLi_dS
|
|
|
|
KinematicsLoop: do k = 1, phase_Nkinematics(material_phaseAt(ipc,el))
|
|
kinematicsType: select case (phase_kinematics(k,material_phaseAt(ipc,el)))
|
|
case (KINEMATICS_cleavage_opening_ID) kinematicsType
|
|
call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
|
|
case (KINEMATICS_slipplane_opening_ID) kinematicsType
|
|
call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
|
|
case (KINEMATICS_thermal_expansion_ID) kinematicsType
|
|
call kinematics_thermal_expansion_LiAndItsTangent(my_Li, my_dLi_dS, ipc, ip, el)
|
|
case default kinematicsType
|
|
my_Li = 0.0_pReal
|
|
my_dLi_dS = 0.0_pReal
|
|
end select kinematicsType
|
|
Li = Li + my_Li
|
|
dLi_dS = dLi_dS + my_dLi_dS
|
|
enddo KinematicsLoop
|
|
|
|
FiInv = math_inv33(Fi)
|
|
detFi = math_det33(Fi)
|
|
Li = matmul(matmul(Fi,Li),FiInv)*detFi !< push forward to intermediate configuration
|
|
temp_33 = matmul(FiInv,Li)
|
|
|
|
do i = 1,3; do j = 1,3
|
|
dLi_dS(1:3,1:3,i,j) = matmul(matmul(Fi,dLi_dS(1:3,1:3,i,j)),FiInv)*detFi
|
|
dLi_dFi(1:3,1:3,i,j) = dLi_dFi(1:3,1:3,i,j) + Li*FiInv(j,i)
|
|
dLi_dFi(1:3,i,1:3,j) = dLi_dFi(1:3,i,1:3,j) + math_I3*temp_33(j,i) + Li*FiInv(j,i)
|
|
enddo; enddo
|
|
|
|
end subroutine constitutive_LiAndItsTangents
|
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_collectDotState_source(S, ipc, ip, el,phase,of) result(broken)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el, & !< element
|
|
phase, &
|
|
of
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
S !< 2nd Piola Kirchhoff stress (vector notation)
|
|
integer :: &
|
|
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
|
|
call source_damage_anisoBrittle_dotState(S, ipc, ip, el) ! correct stress?
|
|
|
|
case (SOURCE_damage_isoDuctile_ID) sourceType
|
|
call source_damage_isoDuctile_dotState(ipc, ip, el)
|
|
|
|
case (SOURCE_damage_anisoDuctile_ID) sourceType
|
|
call source_damage_anisoDuctile_dotState(ipc, ip, el)
|
|
|
|
case (SOURCE_thermal_externalheat_ID) sourceType
|
|
call source_thermal_externalheat_dotState(phase,of)
|
|
|
|
end select sourceType
|
|
|
|
broken = broken .or. any(IEEE_is_NaN(sourceState(phase)%p(i)%dotState(:,of)))
|
|
|
|
enddo SourceLoop
|
|
|
|
end function constitutive_collectDotState_source
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief for constitutive models having an instantaneous change of state
|
|
!> will return false if delta state is not needed/supported by the constitutive model
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_deltaState_source(Fe, ipc, ip, el, phase, of) result(broken)
|
|
|
|
integer, intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el, & !< element
|
|
phase, &
|
|
of
|
|
real(pReal), intent(in), dimension(3,3) :: &
|
|
Fe !< elastic deformation gradient
|
|
integer :: &
|
|
i, &
|
|
myOffset, &
|
|
mySize
|
|
logical :: &
|
|
broken
|
|
|
|
|
|
broken = .false.
|
|
|
|
sourceLoop: do i = 1, phase_Nsources(phase)
|
|
|
|
sourceType: select case (phase_source(i,phase))
|
|
|
|
case (SOURCE_damage_isoBrittle_ID) sourceType
|
|
call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(ipc,ip,el), Fe, &
|
|
ipc, ip, el)
|
|
broken = any(IEEE_is_NaN(sourceState(phase)%p(i)%deltaState(:,of)))
|
|
if(.not. broken) then
|
|
myOffset = sourceState(phase)%p(i)%offsetDeltaState
|
|
mySize = sourceState(phase)%p(i)%sizeDeltaState
|
|
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) = &
|
|
sourceState(phase)%p(i)%state(myOffset + 1: myOffset + mySize,of) + sourceState(phase)%p(i)%deltaState(1:mySize,of)
|
|
endif
|
|
|
|
end select sourceType
|
|
|
|
enddo SourceLoop
|
|
|
|
end function constitutive_deltaState_source
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Allocate the components of the state structure for a given phase
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_allocateState(state, &
|
|
Nconstituents,sizeState,sizeDotState,sizeDeltaState)
|
|
|
|
class(tState), intent(out) :: &
|
|
state
|
|
integer, intent(in) :: &
|
|
Nconstituents, &
|
|
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)
|
|
|
|
allocate(state%dotState (sizeDotState,Nconstituents), source=0.0_pReal)
|
|
|
|
allocate(state%deltaState(sizeDeltaState,Nconstituents), source=0.0_pReal)
|
|
|
|
|
|
end subroutine constitutive_allocateState
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Restore data after homog cutback.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_restore(i,e)
|
|
|
|
integer, intent(in) :: &
|
|
i, & !< integration point number
|
|
e !< element number
|
|
integer :: &
|
|
c, & !< constituent number
|
|
s
|
|
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState(material_phaseAt(c,e))%p(s)%state( :,material_phasememberAt(c,i,e)) = &
|
|
sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e))
|
|
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
|
|
|
|
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
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief writes constitutive results to HDF5 output file
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_results
|
|
|
|
call plastic_results
|
|
call damage_results
|
|
|
|
end subroutine constitutive_results
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief allocates and initialize per grain variables
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_init
|
|
|
|
integer :: &
|
|
Nconstituents, &
|
|
p, &
|
|
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
|
|
|
|
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_Fp0, &
|
|
crystallite_Li0,crystallite_Lp0, &
|
|
crystallite_partitionedS0, &
|
|
crystallite_partitionedF0,crystallite_partitionedFp0,&
|
|
crystallite_partitionedLp0,crystallite_partitionedLi0, &
|
|
crystallite_S,crystallite_P, &
|
|
crystallite_Fe,crystallite_Fp, &
|
|
crystallite_Li,crystallite_Lp, &
|
|
crystallite_subF,crystallite_subF0, &
|
|
crystallite_subFp0,crystallite_subFi0, &
|
|
source = crystallite_partitionedF)
|
|
|
|
allocate(crystallite_dt(cMax,iMax,eMax),source=0.0_pReal)
|
|
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')
|
|
|
|
select case(num_crystallite%get_asString('integrator',defaultVal='FPI'))
|
|
case('FPI')
|
|
integrateState => integrateStateFPI
|
|
case('Euler')
|
|
integrateState => integrateStateEuler
|
|
case('AdaptiveEuler')
|
|
integrateState => integrateStateAdaptiveEuler
|
|
case('RK4')
|
|
integrateState => integrateStateRK4
|
|
case('RKCK45')
|
|
integrateState => integrateStateRKCK45
|
|
case default
|
|
call IO_error(301,ext_msg='integrator')
|
|
end select
|
|
|
|
phases => config_material%get('phase')
|
|
|
|
allocate(output_constituent(phases%length))
|
|
allocate(constitutive_mech_Fi(phases%length))
|
|
allocate(constitutive_mech_Fi0(phases%length))
|
|
allocate(constitutive_mech_partionedFi0(phases%length))
|
|
do p = 1, phases%length
|
|
Nconstituents = count(material_phaseAt == p) * discretization_nIPs
|
|
phase => phases%get(p)
|
|
mech => phase%get('mechanics',defaultVal = emptyDict)
|
|
#if defined(__GFORTRAN__)
|
|
output_constituent(p)%label = output_asStrings(mech)
|
|
#else
|
|
output_constituent(p)%label = mech%get_asStrings('output',defaultVal=emptyStringArray)
|
|
#endif
|
|
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))
|
|
enddo
|
|
|
|
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)
|
|
|
|
!$OMP PARALLEL DO PRIVATE(p,m)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1), FEsolving_execIP(2); do c = 1, homogenization_Nconstituents(material_homogenizationAt(e))
|
|
|
|
p = material_phaseAt(i,e)
|
|
m = material_phaseMemberAt(c,i,e)
|
|
crystallite_Fp0(1:3,1:3,c,i,e) = material_orientation0(c,i,e)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005)
|
|
crystallite_Fp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) &
|
|
/ math_det33(crystallite_Fp0(1:3,1:3,c,i,e))**(1.0_pReal/3.0_pReal)
|
|
constitutive_mech_Fi0(p)%data(1:3,1:3,m) = math_I3
|
|
|
|
crystallite_F0(1:3,1:3,c,i,e) = math_I3
|
|
|
|
crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(matmul(constitutive_mech_Fi0(p)%data(1:3,1:3,m), &
|
|
crystallite_Fp0(1:3,1:3,c,i,e))) ! assuming that euler angles are given in internal strain free configuration
|
|
crystallite_Fp(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e)
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m)
|
|
|
|
constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m)
|
|
|
|
|
|
crystallite_requested(c,i,e) = .true.
|
|
enddo; enddo
|
|
enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
|
|
crystallite_partitionedFp0 = crystallite_Fp0
|
|
crystallite_partitionedF0 = crystallite_F0
|
|
crystallite_partitionedF = crystallite_F0
|
|
|
|
call crystallite_orientations()
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
call constitutive_plastic_dependentState(crystallite_partitionedF0(1:3,1:3,c,i,e), &
|
|
crystallite_partitionedFp0(1:3,1:3,c,i,e), &
|
|
c,i,e) ! update dependent state variables to be consistent with basic states
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$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
|
|
i, & !< counter in integration point loop
|
|
e, & !< counter in element loop
|
|
s, p, m
|
|
logical, dimension(homogenization_maxNconstituents,discretization_nIPs,discretization_Nelems) :: todo !ToDo: need to set some values to false for different Ngrains
|
|
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.
|
|
|
|
subLp0 = crystallite_partitionedLp0
|
|
subLi0 = crystallite_partitionedLi0
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! initialize to starting condition
|
|
crystallite_subStep = 0.0_pReal
|
|
!$OMP PARALLEL DO PRIVATE(p,m)
|
|
elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2); do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
homogenizationRequestsCalculation: if (crystallite_requested(c,i,e)) then
|
|
p = material_phaseAt(i,e)
|
|
m = material_phaseMemberAt(c,i,e)
|
|
plasticState (material_phaseAt(c,e))%subState0( :,material_phaseMemberAt(c,i,e)) = &
|
|
plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phaseMemberAt(c,i,e))
|
|
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState(material_phaseAt(c,e))%p(s)%subState0( :,material_phaseMemberAt(c,i,e)) = &
|
|
sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phaseMemberAt(c,i,e))
|
|
enddo
|
|
crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_partitionedFp0(1:3,1:3,c,i,e)
|
|
crystallite_subFi0(1:3,1:3,c,i,e) = constitutive_mech_partionedFi0(p)%data(1:3,1:3,m)
|
|
crystallite_subF0(1:3,1:3,c,i,e) = crystallite_partitionedF0(1:3,1:3,c,i,e)
|
|
subFrac(c,i,e) = 0.0_pReal
|
|
crystallite_subStep(c,i,e) = 1.0_pReal/num%subStepSizeCryst
|
|
todo(c,i,e) = .true.
|
|
crystallite_converged(c,i,e) = .false. ! pretend failed step of 1/subStepSizeCryst
|
|
endif homogenizationRequestsCalculation
|
|
enddo; enddo
|
|
enddo elementLooping1
|
|
!$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
|
|
!$OMP PARALLEL DO PRIVATE(formerSubStep,p,m)
|
|
elementLooping3: 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(i,e)
|
|
m = material_phaseMemberAt(c,i,e)
|
|
!--------------------------------------------------------------------------------------------------
|
|
! wind forward
|
|
if (crystallite_converged(c,i,e)) then
|
|
formerSubStep = crystallite_subStep(c,i,e)
|
|
subFrac(c,i,e) = subFrac(c,i,e) + crystallite_subStep(c,i,e)
|
|
crystallite_subStep(c,i,e) = min(1.0_pReal - subFrac(c,i,e), &
|
|
num%stepIncreaseCryst * crystallite_subStep(c,i,e))
|
|
|
|
todo(c,i,e) = crystallite_subStep(c,i,e) > 0.0_pReal ! still time left to integrate on?
|
|
|
|
if (todo(c,i,e)) then
|
|
crystallite_subF0 (1:3,1:3,c,i,e) = crystallite_subF(1:3,1:3,c,i,e)
|
|
subLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e)
|
|
subLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e)
|
|
crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e)
|
|
crystallite_subFi0(1:3,1:3,c,i,e) = constitutive_mech_Fi(p)%data(1:3,1:3,m)
|
|
plasticState( material_phaseAt(c,e))%subState0(:,material_phaseMemberAt(c,i,e)) &
|
|
= plasticState(material_phaseAt(c,e))%state( :,material_phaseMemberAt(c,i,e))
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState( material_phaseAt(c,e))%p(s)%subState0(:,material_phaseMemberAt(c,i,e)) &
|
|
= sourceState(material_phaseAt(c,e))%p(s)%state( :,material_phaseMemberAt(c,i,e))
|
|
enddo
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! cut back (reduced time and restore)
|
|
else
|
|
crystallite_subStep(c,i,e) = num%subStepSizeCryst * crystallite_subStep(c,i,e)
|
|
crystallite_Fp (1:3,1:3,c,i,e) = crystallite_subFp0(1:3,1:3,c,i,e)
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = crystallite_subFi0(1:3,1:3,c,i,e)
|
|
crystallite_S (1:3,1:3,c,i,e) = crystallite_S0 (1:3,1:3,c,i,e)
|
|
if (crystallite_subStep(c,i,e) < 1.0_pReal) then ! actual (not initial) cutback
|
|
crystallite_Lp (1:3,1:3,c,i,e) = subLp0(1:3,1:3,c,i,e)
|
|
crystallite_Li (1:3,1:3,c,i,e) = subLi0(1:3,1:3,c,i,e)
|
|
endif
|
|
plasticState (material_phaseAt(c,e))%state( :,material_phaseMemberAt(c,i,e)) &
|
|
= plasticState(material_phaseAt(c,e))%subState0(:,material_phaseMemberAt(c,i,e))
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState( material_phaseAt(c,e))%p(s)%state( :,material_phaseMemberAt(c,i,e)) &
|
|
= sourceState(material_phaseAt(c,e))%p(s)%subState0(:,material_phaseMemberAt(c,i,e))
|
|
enddo
|
|
|
|
! cant restore dotState here, since not yet calculated in first cutback after initialization
|
|
todo(c,i,e) = crystallite_subStep(c,i,e) > num%subStepMinCryst ! still on track or already done (beyond repair)
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! prepare for integration
|
|
if (todo(c,i,e)) then
|
|
crystallite_subF(1:3,1:3,c,i,e) = crystallite_subF0(1:3,1:3,c,i,e) &
|
|
+ crystallite_subStep(c,i,e) *( crystallite_partitionedF (1:3,1:3,c,i,e) &
|
|
-crystallite_partitionedF0(1:3,1:3,c,i,e))
|
|
crystallite_Fe(1:3,1:3,c,i,e) = matmul(crystallite_subF(1:3,1:3,c,i,e), &
|
|
math_inv33(matmul(constitutive_mech_Fi(p)%data(1:3,1:3,m), &
|
|
crystallite_Fp(1:3,1:3,c,i,e))))
|
|
crystallite_subdt(c,i,e) = crystallite_subStep(c,i,e) * crystallite_dt(c,i,e)
|
|
crystallite_converged(c,i,e) = .false.
|
|
call integrateState(c,i,e)
|
|
call integrateSourceState(c,i,e)
|
|
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.
|
|
elementLooping5: do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
crystallite_stress(i,e) = all(crystallite_converged(:,i,e))
|
|
enddo
|
|
enddo elementLooping5
|
|
|
|
end function crystallite_stress
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Backup data for homog cutback.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_initializeRestorationPoints(i,e)
|
|
|
|
integer, intent(in) :: &
|
|
i, & !< integration point number
|
|
e !< element number
|
|
integer :: &
|
|
c, & !< constituent number
|
|
s,p, m
|
|
|
|
p = material_phaseAt(i,e)
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
m = material_phaseMemberAt(c,i,e)
|
|
crystallite_partitionedFp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e)
|
|
crystallite_partitionedLp0(1:3,1:3,c,i,e) = crystallite_Lp0(1:3,1:3,c,i,e)
|
|
constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) = constitutive_mech_Fi0(p)%data(1:3,1:3,m)
|
|
crystallite_partitionedLi0(1:3,1:3,c,i,e) = crystallite_Li0(1:3,1:3,c,i,e)
|
|
crystallite_partitionedF0(1:3,1:3,c,i,e) = crystallite_F0(1:3,1:3,c,i,e)
|
|
crystallite_partitionedS0(1:3,1:3,c,i,e) = crystallite_S0(1:3,1:3,c,i,e)
|
|
|
|
plasticState(material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e)) = &
|
|
plasticState(material_phaseAt(c,e))%state0( :,material_phasememberAt(c,i,e))
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e)) = &
|
|
sourceState(material_phaseAt(c,e))%p(s)%state0( :,material_phasememberAt(c,i,e))
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine crystallite_initializeRestorationPoints
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Wind homog inc forward.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_windForward(i,e)
|
|
|
|
integer, intent(in) :: &
|
|
i, & !< integration point number
|
|
e !< element number
|
|
integer :: &
|
|
c, & !< constituent number
|
|
s, p, m
|
|
p = material_phaseAt(i,e)
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
m = material_phaseMemberAt(c,i,e)
|
|
crystallite_partitionedF0 (1:3,1:3,c,i,e) = crystallite_partitionedF(1:3,1:3,c,i,e)
|
|
crystallite_partitionedFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e)
|
|
crystallite_partitionedLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e)
|
|
constitutive_mech_partionedFi0(p)%data(1:3,1:3,m) = constitutive_mech_Fi(p)%data(1:3,1:3,m)
|
|
crystallite_partitionedLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e)
|
|
crystallite_partitionedS0 (1:3,1:3,c,i,e) = crystallite_S (1:3,1:3,c,i,e)
|
|
|
|
plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e)) = &
|
|
plasticState (material_phaseAt(c,e))%state (:,material_phasememberAt(c,i,e))
|
|
do s = 1, phase_Nsources(material_phaseAt(c,e))
|
|
sourceState(material_phaseAt(c,e))%p(s)%partitionedState0(:,material_phasememberAt(c,i,e)) = &
|
|
sourceState(material_phaseAt(c,e))%p(s)%state (:,material_phasememberAt(c,i,e))
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine crystallite_windForward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Restore data after homog cutback.
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_restore(i,e,includeL)
|
|
|
|
integer, intent(in) :: &
|
|
i, & !< integration point number
|
|
e !< element number
|
|
logical, intent(in) :: &
|
|
includeL !< protect agains fake cutback
|
|
integer :: &
|
|
c, p, m !< constituent number
|
|
p = material_phaseAt(i,e)
|
|
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
if (includeL) then
|
|
crystallite_Lp(1:3,1:3,c,i,e) = crystallite_partitionedLp0(1:3,1:3,c,i,e)
|
|
crystallite_Li(1:3,1:3,c,i,e) = crystallite_partitionedLi0(1:3,1:3,c,i,e)
|
|
endif ! maybe protecting everything from overwriting makes more sense
|
|
m = material_phaseMemberAt(c,i,e)
|
|
crystallite_Fp(1:3,1:3,c,i,e) = crystallite_partitionedFp0(1:3,1:3,c,i,e)
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = constitutive_mech_partionedFi0(p)%data(1:3,1:3,m)
|
|
crystallite_S (1:3,1:3,c,i,e) = crystallite_partitionedS0 (1:3,1:3,c,i,e)
|
|
|
|
plasticState (material_phaseAt(c,e))%state( :,material_phasememberAt(c,i,e)) = &
|
|
plasticState (material_phaseAt(c,e))%partitionedState0(:,material_phasememberAt(c,i,e))
|
|
enddo
|
|
|
|
end subroutine crystallite_restore
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Calculate tangent (dPdF).
|
|
!--------------------------------------------------------------------------------------------------
|
|
function crystallite_stressTangent(c,i,e) result(dPdF)
|
|
|
|
real(pReal), dimension(3,3,3,3) :: dPdF
|
|
integer, intent(in) :: &
|
|
c, & !< counter in constituent loop
|
|
i, & !< counter in integration point loop
|
|
e !< counter in element loop
|
|
integer :: &
|
|
o, &
|
|
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
|
|
|
|
pp = material_phaseAt(i,e)
|
|
m = material_phaseMemberAt(c,i,e)
|
|
|
|
call constitutive_hooke_SandItsTangents(devNull,dSdFe,dSdFi, &
|
|
crystallite_Fe(1:3,1:3,c,i,e), &
|
|
constitutive_mech_Fi(pp)%data(1:3,1:3,m),c,i,e)
|
|
call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, &
|
|
crystallite_S (1:3,1:3,c,i,e), &
|
|
constitutive_mech_Fi(pp)%data(1:3,1:3,m), &
|
|
c,i,e)
|
|
|
|
invFp = math_inv33(crystallite_Fp(1:3,1:3,c,i,e))
|
|
invFi = math_inv33(constitutive_mech_Fi(pp)%data(1:3,1:3,m))
|
|
invSubFp0 = math_inv33(crystallite_subFp0(1:3,1:3,c,i,e))
|
|
invSubFi0 = math_inv33(crystallite_subFi0(1:3,1:3,c,i,e))
|
|
|
|
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(c,i,e)*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(c,i,e)*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=e,ip=i,g=c, &
|
|
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,c,i,e), &
|
|
constitutive_mech_Fi(pp)%data(1:3,1:3,m),c,i,e)
|
|
dLpdS = math_mul3333xx3333(dLpdFi,dFidS) + dLpdS
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate dSdF
|
|
temp_33_1 = transpose(matmul(invFp,invFi))
|
|
temp_33_2 = matmul(crystallite_subF(1:3,1:3,c,i,e),invSubFp0)
|
|
temp_33_3 = matmul(matmul(crystallite_subF(1:3,1:3,c,i,e),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(c,i,e)*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=e,ip=i,g=c, &
|
|
ext_msg='inversion error in analytic tangent calculation')
|
|
dSdF = rhs_3333
|
|
else
|
|
dSdF = math_mul3333xx3333(math_99to3333(temp_99),rhs_3333)
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate dFpinvdF
|
|
temp_3333 = math_mul3333xx3333(dLpdS,dSdF)
|
|
do o=1,3; do p=1,3
|
|
dFpinvdF(1:3,1:3,p,o) = -crystallite_subdt(c,i,e) &
|
|
* matmul(invSubFp0, matmul(temp_3333(1:3,1:3,p,o),invFi))
|
|
enddo; enddo
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! assemble dPdF
|
|
temp_33_1 = matmul(crystallite_S(1:3,1:3,c,i,e),transpose(invFp))
|
|
temp_33_2 = matmul(invFp,temp_33_1)
|
|
temp_33_3 = matmul(crystallite_subF(1:3,1:3,c,i,e),invFp)
|
|
temp_33_4 = matmul(temp_33_3,crystallite_S(1:3,1:3,c,i,e))
|
|
|
|
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,c,i,e), &
|
|
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 &
|
|
c, & !< counter in integration point component loop
|
|
i, & !< counter in integration point loop
|
|
e !< counter in element loop
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do c = 1,homogenization_Nconstituents(material_homogenizationAt(e))
|
|
call crystallite_orientation(c,i,e)%fromMatrix(transpose(math_rotationalPart(crystallite_Fe(1:3,1:3,c,i,e))))
|
|
enddo; enddo; enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
nonlocalPresent: if (any(plasticState%nonlocal)) then
|
|
!$OMP PARALLEL DO
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
if (plasticState(material_phaseAt(1,e))%nonlocal) then
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
call plastic_nonlocal_updateCompatibility(crystallite_orientation, &
|
|
phase_plasticityInstance(material_phaseAt(1,e)),i,e)
|
|
enddo
|
|
endif
|
|
enddo
|
|
!$OMP END PARALLEL DO
|
|
endif nonlocalPresent
|
|
|
|
end subroutine crystallite_orientations
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Map 2nd order tensor to reference config
|
|
!--------------------------------------------------------------------------------------------------
|
|
function crystallite_push33ToRef(ipc,ip,el, tensor33)
|
|
|
|
real(pReal), dimension(3,3) :: crystallite_push33ToRef
|
|
real(pReal), dimension(3,3), intent(in) :: tensor33
|
|
real(pReal), dimension(3,3) :: T
|
|
integer, intent(in):: &
|
|
el, &
|
|
ip, &
|
|
ipc
|
|
|
|
T = matmul(material_orientation0(ipc,ip,el)%asMatrix(), & ! ToDo: initial orientation correct?
|
|
transpose(math_inv33(crystallite_subF(1:3,1:3,ipc,ip,el))))
|
|
crystallite_push33ToRef = matmul(transpose(T),matmul(tensor33,T))
|
|
|
|
end function crystallite_push33ToRef
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief writes crystallite results to HDF5 output file
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_results
|
|
|
|
integer :: p,o
|
|
real(pReal), allocatable, dimension(:,:,:) :: selected_tensors
|
|
real(pReal), allocatable, dimension(:,:) :: selected_rotations
|
|
character(len=:), allocatable :: group,structureLabel
|
|
|
|
do p=1,size(material_name_phase)
|
|
group = trim('current/phase')//'/'//trim(material_name_phase(p))//'/mechanics'
|
|
|
|
call results_closeGroup(results_addGroup(group))
|
|
|
|
do o = 1, size(output_constituent(p)%label)
|
|
select case (output_constituent(p)%label(o))
|
|
case('F')
|
|
selected_tensors = select_tensors(crystallite_partitionedF,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'deformation gradient','1')
|
|
case('F_e')
|
|
selected_tensors = select_tensors(crystallite_Fe,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'elastic deformation gradient','1')
|
|
case('F_p')
|
|
selected_tensors = select_tensors(crystallite_Fp,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'plastic deformation gradient','1')
|
|
case('F_i')
|
|
call results_writeDataset(group,constitutive_mech_Fi(p)%data,output_constituent(p)%label(o),&
|
|
'inelastic deformation gradient','1')
|
|
case('L_p')
|
|
selected_tensors = select_tensors(crystallite_Lp,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'plastic velocity gradient','1/s')
|
|
case('L_i')
|
|
selected_tensors = select_tensors(crystallite_Li,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'inelastic velocity gradient','1/s')
|
|
case('P')
|
|
selected_tensors = select_tensors(crystallite_P,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'First Piola-Kirchhoff stress','Pa')
|
|
case('S')
|
|
selected_tensors = select_tensors(crystallite_S,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'Second Piola-Kirchhoff stress','Pa')
|
|
case('O')
|
|
select case(lattice_structure(p))
|
|
case(lattice_ISO_ID)
|
|
structureLabel = 'aP'
|
|
case(lattice_FCC_ID)
|
|
structureLabel = 'cF'
|
|
case(lattice_BCC_ID)
|
|
structureLabel = 'cI'
|
|
case(lattice_BCT_ID)
|
|
structureLabel = 'tI'
|
|
case(lattice_HEX_ID)
|
|
structureLabel = 'hP'
|
|
case(lattice_ORT_ID)
|
|
structureLabel = 'oP'
|
|
end select
|
|
selected_rotations = select_rotations(crystallite_orientation,p)
|
|
call results_writeDataset(group,selected_rotations,output_constituent(p)%label(o),&
|
|
'crystal orientation as quaternion','q_0 <q_1 q_2 q_3>')
|
|
call results_addAttribute('Lattice',structureLabel,group//'/'//output_constituent(p)%label(o))
|
|
end select
|
|
enddo
|
|
enddo
|
|
|
|
contains
|
|
|
|
!------------------------------------------------------------------------------------------------
|
|
!> @brief select tensors for output
|
|
!------------------------------------------------------------------------------------------------
|
|
function select_tensors(dataset,instance)
|
|
|
|
integer, intent(in) :: instance
|
|
real(pReal), dimension(:,:,:,:,:), intent(in) :: dataset
|
|
real(pReal), allocatable, dimension(:,:,:) :: select_tensors
|
|
integer :: e,i,c,j
|
|
|
|
allocate(select_tensors(3,3,count(material_phaseAt==instance)*discretization_nIPs))
|
|
|
|
j=0
|
|
do e = 1, size(material_phaseAt,2)
|
|
do i = 1, discretization_nIPs
|
|
do c = 1, size(material_phaseAt,1) !ToDo: this needs to be changed for varying Ngrains
|
|
if (material_phaseAt(c,e) == instance) then
|
|
j = j + 1
|
|
select_tensors(1:3,1:3,j) = dataset(1:3,1:3,c,i,e)
|
|
endif
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end function select_tensors
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief select rotations for output
|
|
!--------------------------------------------------------------------------------------------------
|
|
function select_rotations(dataset,instance)
|
|
|
|
integer, intent(in) :: instance
|
|
type(rotation), dimension(:,:,:), intent(in) :: dataset
|
|
real(pReal), allocatable, dimension(:,:) :: select_rotations
|
|
integer :: e,i,c,j
|
|
|
|
allocate(select_rotations(4,count(material_phaseAt==instance)*homogenization_maxNconstituents*discretization_nIPs))
|
|
|
|
j=0
|
|
do e = 1, size(material_phaseAt,2)
|
|
do i = 1, discretization_nIPs
|
|
do c = 1, size(material_phaseAt,1) !ToDo: this needs to be changed for varying Ngrains
|
|
if (material_phaseAt(c,e) == instance) then
|
|
j = j + 1
|
|
select_rotations(1:4,j) = dataset(c,i,e)%asQuaternion()
|
|
endif
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end function select_rotations
|
|
|
|
end subroutine crystallite_results
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculation of stress (P) with time integration based on a residuum in Lp and
|
|
!> intermediate acceleration of the Newton-Raphson correction
|
|
!--------------------------------------------------------------------------------------------------
|
|
function integrateStress(ipc,ip,el,timeFraction) result(broken)
|
|
|
|
integer, intent(in):: el, & ! element index
|
|
ip, & ! integration point index
|
|
ipc ! grain index
|
|
real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep
|
|
|
|
real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep
|
|
Fp_new, & ! plastic deformation gradient at end of timestep
|
|
invFp_new, & ! inverse of Fp_new
|
|
invFp_current, & ! inverse of Fp_current
|
|
Lpguess, & ! current guess for plastic velocity gradient
|
|
Lpguess_old, & ! known last good guess for plastic velocity gradient
|
|
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
|
|
residuumLp, & ! current residuum of plastic velocity gradient
|
|
residuumLp_old, & ! last residuum of plastic velocity gradient
|
|
deltaLp, & ! direction of next guess
|
|
Fi_new, & ! gradient of intermediate deformation stages
|
|
invFi_new, &
|
|
invFi_current, & ! inverse of Fi_current
|
|
Liguess, & ! current guess for intermediate velocity gradient
|
|
Liguess_old, & ! known last good guess for intermediate velocity gradient
|
|
Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law
|
|
residuumLi, & ! current residuum of intermediate velocity gradient
|
|
residuumLi_old, & ! last residuum of intermediate velocity gradient
|
|
deltaLi, & ! direction of next guess
|
|
Fe, & ! elastic deformation gradient
|
|
S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration
|
|
A, &
|
|
B, &
|
|
temp_33
|
|
real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK
|
|
integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK
|
|
real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme)
|
|
dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme)
|
|
real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress
|
|
dS_dFi, &
|
|
dFe_dLp, & ! partial derivative of elastic deformation gradient
|
|
dFe_dLi, &
|
|
dFi_dLi, &
|
|
dLp_dFi, &
|
|
dLi_dFi, &
|
|
dLp_dS, &
|
|
dLi_dS
|
|
real(pReal) steplengthLp, &
|
|
steplengthLi, &
|
|
dt, & ! time increment
|
|
atol_Lp, &
|
|
atol_Li, &
|
|
devNull
|
|
integer NiterationStressLp, & ! number of stress integrations
|
|
NiterationStressLi, & ! number of inner stress integrations
|
|
ierr, & ! error indicator for LAPACK
|
|
o, &
|
|
p, &
|
|
m, &
|
|
jacoCounterLp, &
|
|
jacoCounterLi ! counters to check for Jacobian update
|
|
logical :: error,broken
|
|
|
|
broken = .true.
|
|
|
|
if (present(timeFraction)) then
|
|
dt = crystallite_subdt(ipc,ip,el) * timeFraction
|
|
F = crystallite_subF0(1:3,1:3,ipc,ip,el) &
|
|
+ (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction
|
|
else
|
|
dt = crystallite_subdt(ipc,ip,el)
|
|
F = crystallite_subF(1:3,1:3,ipc,ip,el)
|
|
endif
|
|
|
|
call constitutive_plastic_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), &
|
|
crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el)
|
|
|
|
Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess
|
|
Liguess = crystallite_Li(1:3,1:3,ipc,ip,el) ! take as first guess
|
|
|
|
call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el))
|
|
if (error) return ! error
|
|
call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el))
|
|
if (error) return ! error
|
|
|
|
A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp
|
|
|
|
jacoCounterLi = 0
|
|
steplengthLi = 1.0_pReal
|
|
residuumLi_old = 0.0_pReal
|
|
Liguess_old = Liguess
|
|
|
|
NiterationStressLi = 0
|
|
LiLoop: do
|
|
NiterationStressLi = NiterationStressLi + 1
|
|
if (NiterationStressLi>num%nStress) return ! error
|
|
|
|
invFi_new = matmul(invFi_current,math_I3 - dt*Liguess)
|
|
Fi_new = math_inv33(invFi_new)
|
|
|
|
jacoCounterLp = 0
|
|
steplengthLp = 1.0_pReal
|
|
residuumLp_old = 0.0_pReal
|
|
Lpguess_old = Lpguess
|
|
|
|
NiterationStressLp = 0
|
|
LpLoop: do
|
|
NiterationStressLp = NiterationStressLp + 1
|
|
if (NiterationStressLp>num%nStress) return ! error
|
|
|
|
B = math_I3 - dt*Lpguess
|
|
Fe = matmul(matmul(A,B), invFi_new)
|
|
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
Fe, Fi_new, ipc, ip, el)
|
|
|
|
call constitutive_plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, &
|
|
S, Fi_new, ipc, ip, el)
|
|
|
|
!* update current residuum and check for convergence of loop
|
|
atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
residuumLp = Lpguess - Lp_constitutive
|
|
|
|
if (any(IEEE_is_NaN(residuumLp))) then
|
|
return ! error
|
|
elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance
|
|
exit LpLoop
|
|
elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
residuumLp_old = residuumLp ! ...remember old values and...
|
|
Lpguess_old = Lpguess
|
|
steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
else ! not converged and residuum not improved...
|
|
steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction
|
|
Lpguess = Lpguess_old &
|
|
+ deltaLp * stepLengthLp
|
|
cycle LpLoop
|
|
endif
|
|
|
|
calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then
|
|
jacoCounterLp = jacoCounterLp + 1
|
|
|
|
do o=1,3; do p=1,3
|
|
dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
enddo; enddo
|
|
dRLp_dLp = math_eye(9) &
|
|
- math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp))
|
|
temp_9 = math_33to9(residuumLp)
|
|
call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp
|
|
if (ierr /= 0) return ! error
|
|
deltaLp = - math_9to33(temp_9)
|
|
endif calculateJacobiLi
|
|
|
|
Lpguess = Lpguess &
|
|
+ deltaLp * steplengthLp
|
|
enddo LpLoop
|
|
|
|
call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, &
|
|
S, Fi_new, ipc, ip, el)
|
|
|
|
!* update current residuum and check for convergence of loop
|
|
atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
residuumLi = Liguess - Li_constitutive
|
|
if (any(IEEE_is_NaN(residuumLi))) then
|
|
return ! error
|
|
elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance
|
|
exit LiLoop
|
|
elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
residuumLi_old = residuumLi ! ...remember old values and...
|
|
Liguess_old = Liguess
|
|
steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
else ! not converged and residuum not improved...
|
|
steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction
|
|
Liguess = Liguess_old &
|
|
+ deltaLi * steplengthLi
|
|
cycle LiLoop
|
|
endif
|
|
|
|
calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then
|
|
jacoCounterLi = jacoCounterLi + 1
|
|
|
|
temp_33 = matmul(matmul(A,B),invFi_current)
|
|
do o=1,3; do p=1,3
|
|
dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current
|
|
enddo; enddo
|
|
do o=1,3; do p=1,3
|
|
dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new)
|
|
enddo; enddo
|
|
dRLi_dLi = math_eye(9) &
|
|
- math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) &
|
|
+ math_mul3333xx3333(dS_dFi, dFi_dLi))) &
|
|
- math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi))
|
|
temp_9 = math_33to9(residuumLi)
|
|
call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li
|
|
if (ierr /= 0) return ! error
|
|
deltaLi = - math_9to33(temp_9)
|
|
endif calculateJacobiLp
|
|
|
|
Liguess = Liguess &
|
|
+ deltaLi * steplengthLi
|
|
enddo LiLoop
|
|
|
|
invFp_new = matmul(invFp_current,B)
|
|
call math_invert33(Fp_new,devNull,error,invFp_new)
|
|
if (error) return ! error
|
|
|
|
p = material_phaseAt(ipc,el)
|
|
m = material_phaseMemberAt(ipc,ip,el)
|
|
|
|
crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new)))
|
|
crystallite_S (1:3,1:3,ipc,ip,el) = S
|
|
crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess
|
|
crystallite_Li (1:3,1:3,ipc,ip,el) = Liguess
|
|
crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = Fi_new
|
|
crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new)
|
|
broken = .false.
|
|
|
|
end function integrateStress
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
|
!> using Fixed Point Iteration to adapt the stepsize
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateFPI(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
NiterationState, & !< number of iterations in state loop
|
|
p, &
|
|
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_plasticity_maxSizeDotState,2) :: &
|
|
plastic_dotState
|
|
real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState
|
|
logical :: &
|
|
broken
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
size_pl = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) &
|
|
+ plasticState(p)%dotState (1:size_pl,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
plastic_dotState(1:size_pl,2) = 0.0_pReal
|
|
|
|
iteration: do NiterationState = 1, num%nState
|
|
|
|
if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1)
|
|
plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c)
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken) exit iteration
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) exit iteration
|
|
|
|
zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),&
|
|
plastic_dotState(1:size_pl,2))
|
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta &
|
|
+ plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta)
|
|
r(1:size_pl) = plasticState(p)%state (1:size_pl,c) &
|
|
- plasticState(p)%subState0(1:size_pl,c) &
|
|
- plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e)
|
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) &
|
|
- r(1:size_pl)
|
|
crystallite_converged(g,i,e) = converged(r(1:size_pl), &
|
|
plasticState(p)%state(1:size_pl,c), &
|
|
plasticState(p)%atol(1:size_pl))
|
|
|
|
if(crystallite_converged(g,i,e)) then
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,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 integrateStateFPI
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
|
!> using Fixed Point Iteration to adapt the stepsize
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateSourceState(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
NiterationState, & !< number of iterations in state loop
|
|
p, &
|
|
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
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState_source(crystallite_S(1:3,1:3,g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
do s = 1, phase_Nsources(p)
|
|
size_so(s) = sourceState(p)%p(s)%sizeDotState
|
|
sourceState(p)%p(s)%state(1:size_so(s),c) = sourceState(p)%p(s)%subState0(1:size_so(s),c) &
|
|
+ sourceState(p)%p(s)%dotState (1:size_so(s),c) &
|
|
* crystallite_subdt(g,i,e)
|
|
source_dotState(1:size_so(s),2,s) = 0.0_pReal
|
|
enddo
|
|
|
|
iteration: do NiterationState = 1, num%nState
|
|
|
|
do s = 1, phase_Nsources(p)
|
|
if(nIterationState > 1) source_dotState(1:size_so(s),2,s) = source_dotState(1:size_so(s),1,s)
|
|
source_dotState(1:size_so(s),1,s) = sourceState(p)%p(s)%dotState(:,c)
|
|
enddo
|
|
|
|
broken = constitutive_collectDotState_source(crystallite_S(1:3,1:3,g,i,e), g,i,e,p,c)
|
|
if(broken) exit iteration
|
|
|
|
do s = 1, phase_Nsources(p)
|
|
zeta = damper(sourceState(p)%p(s)%dotState(:,c), &
|
|
source_dotState(1:size_so(s),1,s),&
|
|
source_dotState(1:size_so(s),2,s))
|
|
sourceState(p)%p(s)%dotState(:,c) = sourceState(p)%p(s)%dotState(:,c) * zeta &
|
|
+ source_dotState(1:size_so(s),1,s)* (1.0_pReal - zeta)
|
|
r(1:size_so(s)) = sourceState(p)%p(s)%state (1:size_so(s),c) &
|
|
- sourceState(p)%p(s)%subState0(1:size_so(s),c) &
|
|
- sourceState(p)%p(s)%dotState (1:size_so(s),c) * crystallite_subdt(g,i,e)
|
|
sourceState(p)%p(s)%state(1:size_so(s),c) = sourceState(p)%p(s)%state(1:size_so(s),c) &
|
|
- r(1:size_so(s))
|
|
crystallite_converged(g,i,e) = &
|
|
crystallite_converged(g,i,e) .and. converged(r(1:size_so(s)), &
|
|
sourceState(p)%p(s)%state(1:size_so(s),c), &
|
|
sourceState(p)%p(s)%atol(1:size_so(s)))
|
|
enddo
|
|
|
|
if(crystallite_converged(g,i,e)) then
|
|
broken = constitutive_deltaState_source(crystallite_Fe(1:3,1:3,g,i,e),g,i,e,p,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 integrate state with 1st order explicit Euler method
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateEuler(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
|
|
end subroutine integrateStateEuler
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with 1st order Euler method with adaptive step size
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateAdaptiveEuler(g,i,e)
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic
|
|
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
|
|
residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e)
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e)
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken) return
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) &
|
|
+ 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), &
|
|
plasticState(p)%state(1:sizeDotState,c), &
|
|
plasticState(p)%atol(1:sizeDotState))
|
|
|
|
end subroutine integrateStateAdaptiveEuler
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
|
|
!---------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRK4(g,i,e)
|
|
|
|
integer, intent(in) :: g,i,e
|
|
|
|
real(pReal), dimension(3,3), parameter :: &
|
|
A = reshape([&
|
|
0.5_pReal, 0.0_pReal, 0.0_pReal, &
|
|
0.0_pReal, 0.5_pReal, 0.0_pReal, &
|
|
0.0_pReal, 0.0_pReal, 1.0_pReal],&
|
|
shape(A))
|
|
real(pReal), dimension(3), parameter :: &
|
|
C = [0.5_pReal, 0.5_pReal, 1.0_pReal]
|
|
real(pReal), dimension(4), parameter :: &
|
|
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
|
|
|
|
call integrateStateRK(g,i,e,A,B,C)
|
|
|
|
end subroutine integrateStateRK4
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the Cash-Carp method
|
|
!---------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRKCK45(g,i,e)
|
|
|
|
integer, intent(in) :: g,i,e
|
|
|
|
real(pReal), dimension(5,5), parameter :: &
|
|
A = reshape([&
|
|
1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, &
|
|
-11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, &
|
|
1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],&
|
|
shape(A))
|
|
real(pReal), dimension(5), parameter :: &
|
|
C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal]
|
|
real(pReal), dimension(6), parameter :: &
|
|
B = &
|
|
[37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, &
|
|
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], &
|
|
DB = B - &
|
|
[2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,&
|
|
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal]
|
|
|
|
call integrateStateRK(g,i,e,A,B,C,DB)
|
|
|
|
end subroutine integrateStateRKCK45
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
|
|
!! embedded explicit Runge-Kutta method
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRK(g,i,e,A,B,CC,DB)
|
|
|
|
|
|
real(pReal), dimension(:,:), intent(in) :: A
|
|
real(pReal), dimension(:), intent(in) :: B, CC
|
|
real(pReal), dimension(:), intent(in), optional :: DB
|
|
|
|
integer, intent(in) :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g !< grain index in grain loop
|
|
integer :: &
|
|
stage, & ! stage index in integration stage loop
|
|
n, &
|
|
p, &
|
|
c, &
|
|
sizeDotState
|
|
logical :: &
|
|
broken
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
|
|
|
|
p = material_phaseAt(g,e)
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
do stage = 1,size(A,1)
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
|
|
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1)
|
|
|
|
do n = 2, stage
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
|
|
+ A(n,stage) * plastic_RKdotState(1:sizeDotState,n)
|
|
enddo
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
|
|
broken = integrateStress(g,i,e,CC(stage))
|
|
if(broken) exit
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partitionedF0, &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
crystallite_partitionedFp0, &
|
|
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
|
|
if(broken) exit
|
|
|
|
enddo
|
|
if(broken) return
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
|
|
plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c)
|
|
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B)
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
if(present(DB)) &
|
|
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) &
|
|
* crystallite_subdt(g,i,e), &
|
|
plasticState(p)%state(1:sizeDotState,c), &
|
|
plasticState(p)%atol(1:sizeDotState))
|
|
|
|
if(broken) return
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
if(broken) return
|
|
|
|
broken = integrateStress(g,i,e)
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
|
|
|
|
end subroutine integrateStateRK
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @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_Fp, 'F_p')
|
|
call HDF5_write(fileHandle,crystallite_Lp, 'L_p')
|
|
call HDF5_write(fileHandle,crystallite_Li, 'L_i')
|
|
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)
|
|
write(datasetName,'(i0,a)') i,'_F_i'
|
|
call HDF5_write(groupHandle,constitutive_mech_Fi(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_Fp0,'F_p')
|
|
call HDF5_read(fileHandle,crystallite_Lp0,'L_p')
|
|
call HDF5_read(fileHandle,crystallite_Li0,'L_i')
|
|
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)
|
|
write(datasetName,'(i0,a)') i,'_F_i'
|
|
call HDF5_read(groupHandle,constitutive_mech_Fi0(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
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Forward data after successful increment.
|
|
! ToDo: Any guessing for the current states possible?
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_forward
|
|
|
|
integer :: i, j
|
|
|
|
crystallite_F0 = crystallite_partitionedF
|
|
crystallite_Fp0 = crystallite_Fp
|
|
crystallite_Lp0 = crystallite_Lp
|
|
crystallite_Li0 = crystallite_Li
|
|
crystallite_S0 = crystallite_S
|
|
|
|
do i = 1, size(plasticState)
|
|
plasticState(i)%state0 = plasticState(i)%state
|
|
constitutive_mech_Fi0(i) = constitutive_mech_Fi(i)
|
|
enddo
|
|
do i = 1,size(material_name_homogenization)
|
|
homogState (i)%state0 = homogState (i)%state
|
|
damageState (i)%state0 = damageState (i)%state
|
|
enddo
|
|
|
|
end subroutine crystallite_forward
|
|
|
|
end module constitutive
|