1770 lines
94 KiB
Fortran
1770 lines
94 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
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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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!> @author Christoph Kords, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Chen Zhang, Michigan State University
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!> @brief crystallite state integration functions and reporting of results
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!--------------------------------------------------------------------------------------------------
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module crystallite
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use prec
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use parallelization
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use IO
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use HDF5_utilities
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use DAMASK_interface
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use config
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use rotations
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use math
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use FEsolving
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use material
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use constitutive
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use discretization
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use lattice
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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_subFrac, & !< already calculated fraction of increment
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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_partionedFp0,& !< 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_Fi, & !< current intermediate def grad (end of converged time step)
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crystallite_Fi0, & !< intermediate def grad at start of FE inc
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crystallite_partionedFi0,& !< intermediate def grad at start of homog inc
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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_partionedLp0, & !< plastic velocity grad at start of homog inc
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crystallite_subLp0,& !< plastic velocity grad at start of crystallite 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_partionedLi0, & !< intermediate velocity grad at start of homog inc
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crystallite_subLi0, & !< intermediate velocity grad at start of crystallite 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_partionedS0 !< 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_partionedF0 !< def grad at start of homog inc
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real(pReal), dimension(:,:,:,:,:), allocatable, public :: &
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crystallite_partionedF !< def grad to be reached at end of homog inc
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable, public, protected :: &
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crystallite_dPdF !< current individual dPdF per grain (end of converged time step)
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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 :: 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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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 allocates and initialize per grain variables
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!--------------------------------------------------------------------------------------------------
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subroutine crystallite_init
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logical, dimension(discretization_nIP,discretization_nElem) :: devNull
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integer :: &
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c, & !< counter in integration point component loop
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i, & !< counter in integration point loop
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e, & !< counter in element loop
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cMax, & !< maximum number of integration point components
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iMax, & !< maximum number of integration points
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eMax !< maximum number of elements
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class(tNode), pointer :: &
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num_crystallite, &
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debug_crystallite, & ! pointer to debug options for crystallite
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phases, &
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phase, &
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generic_param
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print'(/,a)', ' <<<+- crystallite init -+>>>'
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debug_crystallite => config_debug%get('crystallite', defaultVal=emptyList)
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debugCrystallite%basic = debug_crystallite%contains('basic')
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debugCrystallite%extensive = debug_crystallite%contains('extensive')
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debugCrystallite%selective = debug_crystallite%contains('selective')
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debugCrystallite%element = config_debug%get_asInt('element', defaultVal=1)
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debugCrystallite%ip = config_debug%get_asInt('integrationpoint', defaultVal=1)
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debugCrystallite%grain = config_debug%get_asInt('grain', defaultVal=1)
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cMax = homogenization_maxNgrains
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iMax = discretization_nIP
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eMax = discretization_nElem
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allocate(crystallite_partionedF(3,3,cMax,iMax,eMax),source=0.0_pReal)
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allocate(crystallite_S0, &
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crystallite_F0, crystallite_Fi0,crystallite_Fp0, &
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crystallite_Li0,crystallite_Lp0, &
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crystallite_partionedS0, &
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crystallite_partionedF0,crystallite_partionedFp0,crystallite_partionedFi0, &
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crystallite_partionedLp0,crystallite_partionedLi0, &
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crystallite_S,crystallite_P, &
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crystallite_Fe,crystallite_Fi,crystallite_Fp, &
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crystallite_Li,crystallite_Lp, &
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crystallite_subF,crystallite_subF0, &
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crystallite_subFp0,crystallite_subFi0, &
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crystallite_subLi0,crystallite_subLp0, &
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source = crystallite_partionedF)
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allocate(crystallite_dPdF(3,3,3,3,cMax,iMax,eMax),source=0.0_pReal)
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allocate(crystallite_dt(cMax,iMax,eMax),source=0.0_pReal)
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allocate(crystallite_subdt,crystallite_subFrac,crystallite_subStep, &
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source = crystallite_dt)
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allocate(crystallite_orientation(cMax,iMax,eMax))
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allocate(crystallite_requested(cMax,iMax,eMax), source=.false.)
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allocate(crystallite_converged(cMax,iMax,eMax), source=.true.)
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num_crystallite => config_numerics%get('crystallite',defaultVal=emptyDict)
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num%subStepMinCryst = num_crystallite%get_asFloat ('subStepMin', defaultVal=1.0e-3_pReal)
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num%subStepSizeCryst = num_crystallite%get_asFloat ('subStepSize', defaultVal=0.25_pReal)
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num%stepIncreaseCryst = num_crystallite%get_asFloat ('stepIncrease', defaultVal=1.5_pReal)
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num%subStepSizeLp = num_crystallite%get_asFloat ('subStepSizeLp', defaultVal=0.5_pReal)
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num%subStepSizeLi = num_crystallite%get_asFloat ('subStepSizeLi', defaultVal=0.5_pReal)
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num%rtol_crystalliteState = num_crystallite%get_asFloat ('rtol_State', defaultVal=1.0e-6_pReal)
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num%rtol_crystalliteStress = num_crystallite%get_asFloat ('rtol_Stress', defaultVal=1.0e-6_pReal)
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num%atol_crystalliteStress = num_crystallite%get_asFloat ('atol_Stress', defaultVal=1.0e-8_pReal)
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num%iJacoLpresiduum = num_crystallite%get_asInt ('iJacoLpresiduum', defaultVal=1)
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num%nState = num_crystallite%get_asInt ('nState', defaultVal=20)
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num%nStress = num_crystallite%get_asInt ('nStress', defaultVal=40)
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if(num%subStepMinCryst <= 0.0_pReal) call IO_error(301,ext_msg='subStepMinCryst')
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if(num%subStepSizeCryst <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeCryst')
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if(num%stepIncreaseCryst <= 0.0_pReal) call IO_error(301,ext_msg='stepIncreaseCryst')
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if(num%subStepSizeLp <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeLp')
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if(num%subStepSizeLi <= 0.0_pReal) call IO_error(301,ext_msg='subStepSizeLi')
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if(num%rtol_crystalliteState <= 0.0_pReal) call IO_error(301,ext_msg='rtol_crystalliteState')
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if(num%rtol_crystalliteStress <= 0.0_pReal) call IO_error(301,ext_msg='rtol_crystalliteStress')
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if(num%atol_crystalliteStress <= 0.0_pReal) call IO_error(301,ext_msg='atol_crystalliteStress')
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if(num%iJacoLpresiduum < 1) call IO_error(301,ext_msg='iJacoLpresiduum')
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if(num%nState < 1) call IO_error(301,ext_msg='nState')
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if(num%nStress< 1) call IO_error(301,ext_msg='nStress')
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select case(num_crystallite%get_asString('integrator',defaultVal='FPI'))
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case('FPI')
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integrateState => integrateStateFPI
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case('Euler')
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integrateState => integrateStateEuler
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case('AdaptiveEuler')
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integrateState => integrateStateAdaptiveEuler
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case('RK4')
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integrateState => integrateStateRK4
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case('RKCK45')
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integrateState => integrateStateRKCK45
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case default
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call IO_error(301,ext_msg='integrator')
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end select
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phases => config_material%get('phase')
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allocate(output_constituent(phases%length))
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do c = 1, phases%length
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phase => phases%get(c)
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generic_param => phase%get('generic',defaultVal = emptyDict)
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#if defined(__GFORTRAN__)
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output_constituent(c)%label = output_asStrings(generic_param)
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#else
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output_constituent(c)%label = generic_param%get_asStrings('output',defaultVal=emptyStringArray)
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#endif
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enddo
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!--------------------------------------------------------------------------------------------------
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! initialize
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!$OMP PARALLEL DO PRIVATE(i,c)
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do e = FEsolving_execElem(1),FEsolving_execElem(2)
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do i = FEsolving_execIP(1), FEsolving_execIP(2); do c = 1, homogenization_Ngrains(material_homogenizationAt(e))
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crystallite_Fp0(1:3,1:3,c,i,e) = material_orientation0(c,i,e)%asMatrix() ! Fp reflects initial orientation (see 10.1016/j.actamat.2006.01.005)
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crystallite_Fp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e) &
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/ math_det33(crystallite_Fp0(1:3,1:3,c,i,e))**(1.0_pReal/3.0_pReal)
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crystallite_Fi0(1:3,1:3,c,i,e) = constitutive_initialFi(c,i,e)
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crystallite_F0(1:3,1:3,c,i,e) = math_I3
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crystallite_Fe(1:3,1:3,c,i,e) = math_inv33(matmul(crystallite_Fi0(1:3,1:3,c,i,e), &
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crystallite_Fp0(1:3,1:3,c,i,e))) ! assuming that euler angles are given in internal strain free configuration
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crystallite_Fp(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e)
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crystallite_Fi(1:3,1:3,c,i,e) = crystallite_Fi0(1:3,1:3,c,i,e)
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crystallite_requested(c,i,e) = .true.
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enddo; enddo
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enddo
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!$OMP END PARALLEL DO
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crystallite_partionedFp0 = crystallite_Fp0
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crystallite_partionedFi0 = crystallite_Fi0
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crystallite_partionedF0 = crystallite_F0
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crystallite_partionedF = crystallite_F0
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call crystallite_orientations()
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!$OMP PARALLEL DO
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do e = FEsolving_execElem(1),FEsolving_execElem(2)
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do i = FEsolving_execIP(1),FEsolving_execIP(2)
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do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
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call constitutive_dependentState(crystallite_partionedF0(1:3,1:3,c,i,e), &
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crystallite_partionedFp0(1:3,1:3,c,i,e), &
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c,i,e) ! update dependent state variables to be consistent with basic states
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enddo
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enddo
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enddo
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!$OMP END PARALLEL DO
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devNull = crystallite_stress()
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call crystallite_stressTangent
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#ifdef DEBUG
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if (debugCrystallite%basic) then
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print'(a42,1x,i10)', ' # of elements: ', eMax
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print'(a42,1x,i10)', ' # of integration points/element: ', iMax
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print'(a42,1x,i10)', 'max # of constituents/integration point: ', cMax
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flush(IO_STDOUT)
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endif
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#endif
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end subroutine crystallite_init
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!--------------------------------------------------------------------------------------------------
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!> @brief calculate stress (P)
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!--------------------------------------------------------------------------------------------------
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function crystallite_stress()
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logical, dimension(discretization_nIP,discretization_nElem) :: crystallite_stress
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real(pReal) :: &
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formerSubStep
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integer :: &
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NiterationCrystallite, & ! number of iterations in crystallite loop
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c, & !< counter in integration point component loop
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i, & !< counter in integration point loop
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e, & !< counter in element loop
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startIP, endIP, &
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s
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logical, dimension(homogenization_maxNgrains,discretization_nIP,discretization_nElem) :: todo !ToDo: need to set some values to false for different Ngrains
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todo = .false.
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#ifdef DEBUG
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if (debugCrystallite%selective &
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.and. FEsolving_execElem(1) <= debugCrystallite%element &
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.and. debugCrystallite%element <= FEsolving_execElem(2)) then
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print'(/,a,i8,1x,i2,1x,i3)', '<< CRYST stress >> boundary and initial values at el ip ipc ', &
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debugCrystallite%element,debugCrystallite%ip, debugCrystallite%grain
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> F ', &
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transpose(crystallite_partionedF(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> F0 ', &
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transpose(crystallite_partionedF0(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> Fp0', &
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transpose(crystallite_partionedFp0(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> Fi0', &
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transpose(crystallite_partionedFi0(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> Lp0', &
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transpose(crystallite_partionedLp0(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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print'(a,/,3(12x,3(f14.9,1x)/))', '<< CRYST stress >> Li0', &
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transpose(crystallite_partionedLi0(1:3,1:3,debugCrystallite%grain, &
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debugCrystallite%ip,debugCrystallite%element))
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endif
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#endif
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!--------------------------------------------------------------------------------------------------
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! initialize to starting condition
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crystallite_subStep = 0.0_pReal
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!$OMP PARALLEL DO
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elementLooping1: do e = FEsolving_execElem(1),FEsolving_execElem(2)
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do i = FEsolving_execIP(1),FEsolving_execIP(2); do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
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homogenizationRequestsCalculation: if (crystallite_requested(c,i,e)) then
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plasticState (material_phaseAt(c,e))%subState0( :,material_phaseMemberAt(c,i,e)) = &
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plasticState (material_phaseAt(c,e))%partionedState0(:,material_phaseMemberAt(c,i,e))
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do s = 1, phase_Nsources(material_phaseAt(c,e))
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sourceState(material_phaseAt(c,e))%p(s)%subState0( :,material_phaseMemberAt(c,i,e)) = &
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sourceState(material_phaseAt(c,e))%p(s)%partionedState0(:,material_phaseMemberAt(c,i,e))
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enddo
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crystallite_subFp0(1:3,1:3,c,i,e) = crystallite_partionedFp0(1:3,1:3,c,i,e)
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crystallite_subLp0(1:3,1:3,c,i,e) = crystallite_partionedLp0(1:3,1:3,c,i,e)
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crystallite_subFi0(1:3,1:3,c,i,e) = crystallite_partionedFi0(1:3,1:3,c,i,e)
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crystallite_subLi0(1:3,1:3,c,i,e) = crystallite_partionedLi0(1:3,1:3,c,i,e)
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crystallite_subF0(1:3,1:3,c,i,e) = crystallite_partionedF0(1:3,1:3,c,i,e)
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crystallite_subFrac(c,i,e) = 0.0_pReal
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crystallite_subStep(c,i,e) = 1.0_pReal/num%subStepSizeCryst
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todo(c,i,e) = .true.
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crystallite_converged(c,i,e) = .false. ! pretend failed step of 1/subStepSizeCryst
|
|
endif homogenizationRequestsCalculation
|
|
enddo; enddo
|
|
enddo elementLooping1
|
|
!$OMP END PARALLEL DO
|
|
|
|
singleRun: if (FEsolving_execELem(1) == FEsolving_execElem(2) .and. &
|
|
FEsolving_execIP (1) == FEsolving_execIP (2)) then
|
|
startIP = FEsolving_execIP(1)
|
|
endIP = startIP
|
|
else singleRun
|
|
startIP = 1
|
|
endIP = discretization_nIP
|
|
endif singleRun
|
|
|
|
NiterationCrystallite = 0
|
|
cutbackLooping: do while (any(todo(:,startIP:endIP,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)
|
|
elementLooping3: do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
!--------------------------------------------------------------------------------------------------
|
|
! wind forward
|
|
if (crystallite_converged(c,i,e)) then
|
|
formerSubStep = crystallite_subStep(c,i,e)
|
|
crystallite_subFrac(c,i,e) = crystallite_subFrac(c,i,e) + crystallite_subStep(c,i,e)
|
|
crystallite_subStep(c,i,e) = min(1.0_pReal - crystallite_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)
|
|
crystallite_subLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e)
|
|
crystallite_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) = crystallite_Fi (1:3,1:3,c,i,e)
|
|
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)
|
|
crystallite_Fi (1:3,1:3,c,i,e) = 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) = crystallite_subLp0(1:3,1:3,c,i,e)
|
|
crystallite_Li (1:3,1:3,c,i,e) = crystallite_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_partionedF (1:3,1:3,c,i,e) &
|
|
-crystallite_partionedF0(1:3,1:3,c,i,e))
|
|
crystallite_Fe(1:3,1:3,c,i,e) = matmul(matmul(crystallite_subF(1:3,1:3,c,i,e), &
|
|
math_inv33(crystallite_Fp(1:3,1:3,c,i,e))), &
|
|
math_inv33(crystallite_Fi(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.
|
|
endif
|
|
|
|
enddo
|
|
enddo
|
|
enddo elementLooping3
|
|
!$OMP END PARALLEL DO
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! integrate --- requires fully defined state array (basic + dependent state)
|
|
if (any(todo)) call integrateState(todo) ! TODO: unroll into proper elementloop to avoid N^2 for single point evaluation
|
|
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
|
|
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
crystallite_partionedFp0(1:3,1:3,c,i,e) = crystallite_Fp0(1:3,1:3,c,i,e)
|
|
crystallite_partionedLp0(1:3,1:3,c,i,e) = crystallite_Lp0(1:3,1:3,c,i,e)
|
|
crystallite_partionedFi0(1:3,1:3,c,i,e) = crystallite_Fi0(1:3,1:3,c,i,e)
|
|
crystallite_partionedLi0(1:3,1:3,c,i,e) = crystallite_Li0(1:3,1:3,c,i,e)
|
|
crystallite_partionedF0(1:3,1:3,c,i,e) = crystallite_F0(1:3,1:3,c,i,e)
|
|
crystallite_partionedS0(1:3,1:3,c,i,e) = crystallite_S0(1:3,1:3,c,i,e)
|
|
|
|
plasticState(material_phaseAt(c,e))%partionedState0(:,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)%partionedState0(:,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
|
|
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
crystallite_partionedF0 (1:3,1:3,c,i,e) = crystallite_partionedF(1:3,1:3,c,i,e)
|
|
crystallite_partionedFp0(1:3,1:3,c,i,e) = crystallite_Fp (1:3,1:3,c,i,e)
|
|
crystallite_partionedLp0(1:3,1:3,c,i,e) = crystallite_Lp (1:3,1:3,c,i,e)
|
|
crystallite_partionedFi0(1:3,1:3,c,i,e) = crystallite_Fi (1:3,1:3,c,i,e)
|
|
crystallite_partionedLi0(1:3,1:3,c,i,e) = crystallite_Li (1:3,1:3,c,i,e)
|
|
crystallite_partionedS0 (1:3,1:3,c,i,e) = crystallite_S (1:3,1:3,c,i,e)
|
|
|
|
plasticState (material_phaseAt(c,e))%partionedState0(:,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)%partionedState0(:,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, & !< constituent number
|
|
s
|
|
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
if (includeL) then
|
|
crystallite_Lp(1:3,1:3,c,i,e) = crystallite_partionedLp0(1:3,1:3,c,i,e)
|
|
crystallite_Li(1:3,1:3,c,i,e) = crystallite_partionedLi0(1:3,1:3,c,i,e)
|
|
endif ! maybe protecting everything from overwriting makes more sense
|
|
crystallite_Fp(1:3,1:3,c,i,e) = crystallite_partionedFp0(1:3,1:3,c,i,e)
|
|
crystallite_Fi(1:3,1:3,c,i,e) = crystallite_partionedFi0(1:3,1:3,c,i,e)
|
|
crystallite_S (1:3,1:3,c,i,e) = crystallite_partionedS0 (1:3,1:3,c,i,e)
|
|
|
|
plasticState (material_phaseAt(c,e))%state( :,material_phasememberAt(c,i,e)) = &
|
|
plasticState (material_phaseAt(c,e))%partionedState0(:,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)%partionedState0(:,material_phasememberAt(c,i,e))
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine crystallite_restore
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief Calculate tangent (dPdF).
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine crystallite_stressTangent
|
|
|
|
integer :: &
|
|
c, & !< counter in constituent loop
|
|
i, & !< counter in integration point loop
|
|
e, & !< counter in element loop
|
|
o, &
|
|
p
|
|
|
|
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
|
|
|
|
!$OMP PARALLEL DO PRIVATE(dSdF,dSdFe,dSdFi,dLpdS,dLpdFi,dFpinvdF,dLidS,dLidFi,dFidS,o,p, &
|
|
!$OMP invSubFp0,invSubFi0,invFp,invFi, &
|
|
!$OMP rhs_3333,lhs_3333,temp_99,temp_33_1,temp_33_2,temp_33_3,temp_33_4,temp_3333,error)
|
|
elementLooping: do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
|
|
call constitutive_SandItsTangents(devNull,dSdFe,dSdFi, &
|
|
crystallite_Fe(1:3,1:3,c,i,e), &
|
|
crystallite_Fi(1:3,1:3,c,i,e),c,i,e)
|
|
call constitutive_LiAndItsTangents(devNull,dLidS,dLidFi, &
|
|
crystallite_S (1:3,1:3,c,i,e), &
|
|
crystallite_Fi(1:3,1:3,c,i,e), &
|
|
c,i,e)
|
|
|
|
invFp = math_inv33(crystallite_Fp(1:3,1:3,c,i,e))
|
|
invFi = math_inv33(crystallite_Fi(1:3,1:3,c,i,e))
|
|
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_LpAndItsTangents(devNull,dLpdS,dLpdFi, &
|
|
crystallite_S (1:3,1:3,c,i,e), &
|
|
crystallite_Fi(1:3,1:3,c,i,e),c,i,e) ! call constitutive law to calculate Lp tangent in lattice configuration
|
|
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))
|
|
|
|
crystallite_dPdF(1:3,1:3,1:3,1:3,c,i,e) = 0.0_pReal
|
|
do p=1,3
|
|
crystallite_dPdF(p,1:3,p,1:3,c,i,e) = transpose(temp_33_2)
|
|
enddo
|
|
do o=1,3; do p=1,3
|
|
crystallite_dPdF(1:3,1:3,p,o,c,i,e) = crystallite_dPdF(1:3,1:3,p,o,c,i,e) &
|
|
+ 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
|
|
|
|
enddo; enddo
|
|
enddo elementLooping
|
|
!$OMP END PARALLEL DO
|
|
|
|
end subroutine 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
|
|
|
|
!$OMP PARALLEL DO
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do c = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
call crystallite_orientation(c,i,e)%fromMatrix(transpose(math_rotationalPart(crystallite_Fe(1:3,1:3,c,i,e))))
|
|
enddo; enddo; enddo
|
|
!$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
|
|
type(rotation), allocatable, dimension(:) :: selected_rotations
|
|
character(len=pStringLen) :: group,structureLabel
|
|
|
|
do p=1,size(material_name_phase)
|
|
group = trim('current/constituent')//'/'//trim(material_name_phase(p))//'/generic'
|
|
|
|
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_partionedF,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'deformation gradient','1')
|
|
case('Fe')
|
|
selected_tensors = select_tensors(crystallite_Fe,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'elastic deformation gradient','1')
|
|
case('Fp')
|
|
selected_tensors = select_tensors(crystallite_Fp,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'plastic deformation gradient','1')
|
|
case('Fi')
|
|
selected_tensors = select_tensors(crystallite_Fi,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'inelastic deformation gradient','1')
|
|
case('Lp')
|
|
selected_tensors = select_tensors(crystallite_Lp,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'plastic velocity gradient','1/s')
|
|
case('Li')
|
|
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-Kirchoff stress','Pa')
|
|
case('S')
|
|
selected_tensors = select_tensors(crystallite_S,p)
|
|
call results_writeDataset(group,selected_tensors,output_constituent(p)%label(o),&
|
|
'Second Piola-Kirchoff stress','Pa')
|
|
case('O')
|
|
select case(lattice_structure(p))
|
|
case(lattice_ISO_ID)
|
|
structureLabel = 'iso'
|
|
case(lattice_FCC_ID)
|
|
structureLabel = 'fcc'
|
|
case(lattice_BCC_ID)
|
|
structureLabel = 'bcc'
|
|
case(lattice_BCT_ID)
|
|
structureLabel = 'bct'
|
|
case(lattice_HEX_ID)
|
|
structureLabel = 'hex'
|
|
case(lattice_ORT_ID)
|
|
structureLabel = 'ort'
|
|
end select
|
|
selected_rotations = select_rotations(crystallite_orientation,p)
|
|
call results_writeDataset(group,selected_rotations,output_constituent(p)%label(o),&
|
|
'crystal orientation as quaternion',structureLabel)
|
|
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_nIP))
|
|
|
|
j=0
|
|
do e = 1, size(material_phaseAt,2)
|
|
do i = 1, discretization_nIP
|
|
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
|
|
type(rotation), allocatable, dimension(:) :: select_rotations
|
|
integer :: e,i,c,j
|
|
|
|
allocate(select_rotations(count(material_phaseAt==instance)*homogenization_maxNgrains*discretization_nIP))
|
|
|
|
j=0
|
|
do e = 1, size(material_phaseAt,2)
|
|
do i = 1, discretization_nIP
|
|
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(j) = dataset(c,i,e)
|
|
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, &
|
|
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_dependentState(crystallite_partionedF(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_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
Fe, Fi_new, ipc, ip, el)
|
|
|
|
call constitutive_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
|
|
|
|
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
|
|
crystallite_Fi (1:3,1:3,ipc,ip,el) = 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(todo)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
integer :: &
|
|
NiterationState, & !< number of iterations in state loop
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g, & !< grain index in grain 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 :: &
|
|
nonlocalBroken, broken
|
|
|
|
nonlocalBroken = .false.
|
|
!$OMP PARALLEL DO PRIVATE(size_pl,size_so,r,zeta,p,c,plastic_dotState,source_dotState,broken)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do g = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
p = material_phaseAt(g,e)
|
|
if(todo(g,i,e) .and. .not. (nonlocalBroken .and. plasticState(p)%nonlocal)) then
|
|
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
if(broken) cycle
|
|
|
|
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
|
|
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
|
|
|
|
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)
|
|
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 = integrateStress(g,i,e)
|
|
if(broken) exit iteration
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
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))
|
|
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(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_Fe(1:3,1:3,g,i,e), &
|
|
crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c)
|
|
exit iteration
|
|
endif
|
|
|
|
enddo iteration
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
endif
|
|
enddo; enddo; enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
if (nonlocalBroken) call nonlocalConvergenceCheck
|
|
|
|
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 state with 1st order explicit Euler method
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateEuler(todo)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
|
|
integer :: &
|
|
e, & !< element index in element loop
|
|
i, & !< integration point index in ip loop
|
|
g, & !< grain index in grain loop
|
|
p, &
|
|
c, &
|
|
s, &
|
|
sizeDotState
|
|
logical :: &
|
|
nonlocalBroken, broken
|
|
|
|
nonlocalBroken = .false.
|
|
!$OMP PARALLEL DO PRIVATE (sizeDotState,p,c,broken)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do g = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
p = material_phaseAt(g,e)
|
|
if(todo(g,i,e) .and. .not. (nonlocalBroken .and. plasticState(p)%nonlocal)) then
|
|
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
if(broken) cycle
|
|
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
|
|
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
enddo
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_Fe(1:3,1:3,g,i,e), &
|
|
crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c)
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
if(broken) cycle
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
endif
|
|
enddo; enddo; enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
if (nonlocalBroken) call nonlocalConvergenceCheck
|
|
|
|
end subroutine integrateStateEuler
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief integrate stress, state with 1st order Euler method with adaptive step size
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateAdaptiveEuler(todo)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
|
|
integer :: &
|
|
e, & ! element index in element loop
|
|
i, & ! integration point index in ip loop
|
|
g, & ! grain index in grain loop
|
|
p, &
|
|
c, &
|
|
s, &
|
|
sizeDotState
|
|
logical :: &
|
|
nonlocalBroken, broken
|
|
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic
|
|
real(pReal), dimension(constitutive_source_maxSizeDotState,maxval(phase_Nsources)) :: residuum_source
|
|
|
|
nonlocalBroken = .false.
|
|
!$OMP PARALLEL DO PRIVATE(sizeDotState,p,c,residuum_plastic,residuum_source,broken)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do g = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
broken = .false.
|
|
p = material_phaseAt(g,e)
|
|
if(todo(g,i,e) .and. .not. (nonlocalBroken .and. plasticState(p)%nonlocal)) then
|
|
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) cycle
|
|
|
|
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)
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
|
|
residuum_source(1:sizeDotState,s) = - sourceState(p)%p(s)%dotstate(1:sizeDotState,c) &
|
|
* 0.5_pReal * crystallite_subdt(g,i,e)
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
|
|
+ sourceState(p)%p(s)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e)
|
|
enddo
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_Fe(1:3,1:3,g,i,e), &
|
|
crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c)
|
|
if(broken) cycle
|
|
|
|
broken = integrateStress(g,i,e)
|
|
if(broken) cycle
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) cycle
|
|
|
|
|
|
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))
|
|
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
crystallite_converged(g,i,e) = &
|
|
crystallite_converged(g,i,e) .and. converged(residuum_source(1:sizeDotState,s) &
|
|
+ 0.5_pReal*sourceState(p)%p(s)%dotState(:,c)*crystallite_subdt(g,i,e), &
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c), &
|
|
sourceState(p)%p(s)%atol(1:sizeDotState))
|
|
enddo
|
|
|
|
endif
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
enddo; enddo; enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
if (nonlocalBroken) call nonlocalConvergenceCheck
|
|
|
|
end subroutine integrateStateAdaptiveEuler
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
|
|
!---------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRK4(todo)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
|
|
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(todo,A,B,C)
|
|
|
|
end subroutine integrateStateRK4
|
|
|
|
|
|
!---------------------------------------------------------------------------------------------------
|
|
!> @brief Integrate state (including stress integration) with the Cash-Carp method
|
|
!---------------------------------------------------------------------------------------------------
|
|
subroutine integrateStateRKCK45(todo)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
|
|
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(todo,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(todo,A,B,CC,DB)
|
|
|
|
logical, dimension(:,:,:), intent(in) :: todo
|
|
|
|
real(pReal), dimension(:,:), intent(in) :: A
|
|
real(pReal), dimension(:), intent(in) :: B, CC
|
|
real(pReal), dimension(:), intent(in), optional :: DB
|
|
|
|
integer :: &
|
|
e, & ! element index in element loop
|
|
i, & ! integration point index in ip loop
|
|
g, & ! grain index in grain loop
|
|
stage, & ! stage index in integration stage loop
|
|
n, &
|
|
p, &
|
|
c, &
|
|
s, &
|
|
sizeDotState
|
|
logical :: &
|
|
nonlocalBroken, broken
|
|
real(pReal), dimension(constitutive_source_maxSizeDotState,size(B),maxval(phase_Nsources)) :: source_RKdotState
|
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
|
|
|
|
nonlocalBroken = .false.
|
|
!$OMP PARALLEL DO PRIVATE(sizeDotState,p,c,plastic_RKdotState,source_RKdotState,broken)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
do g = 1,homogenization_Ngrains(material_homogenizationAt(e))
|
|
broken = .false.
|
|
p = material_phaseAt(g,e)
|
|
if(todo(g,i,e) .and. .not. (nonlocalBroken .and. plasticState(p)%nonlocal)) then
|
|
|
|
c = material_phaseMemberAt(g,i,e)
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
if(broken) cycle
|
|
|
|
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 s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
source_RKdotState(1:sizeDotState,stage,s) = sourceState(p)%p(s)%dotState(:,c)
|
|
sourceState(p)%p(s)%dotState(:,c) = A(1,stage) * source_RKdotState(1:sizeDotState,1,s)
|
|
enddo
|
|
|
|
do n = 2, stage
|
|
sizeDotState = plasticState(p)%sizeDotState
|
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
|
|
+ A(n,stage) * plastic_RKdotState(1:sizeDotState,n)
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
sourceState(p)%p(s)%dotState(:,c) = sourceState(p)%p(s)%dotState(:,c) &
|
|
+ A(n,stage) * source_RKdotState(1:sizeDotState,n,s)
|
|
enddo
|
|
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)
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
|
|
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
enddo
|
|
|
|
broken = integrateStress(g,i,e,CC(stage))
|
|
if(broken) exit
|
|
|
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_partionedF0, &
|
|
crystallite_Fi(1:3,1:3,g,i,e), &
|
|
crystallite_partionedFp0, &
|
|
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
|
|
if(broken) exit
|
|
|
|
enddo
|
|
if(broken) cycle
|
|
|
|
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))
|
|
|
|
do s = 1, phase_Nsources(p)
|
|
sizeDotState = sourceState(p)%p(s)%sizeDotState
|
|
|
|
source_RKdotState(1:sizeDotState,size(B),s) = sourceState(p)%p(s)%dotState(:,c)
|
|
sourceState(p)%p(s)%dotState(:,c) = matmul(source_RKdotState(1:sizeDotState,1:size(B),s),B)
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
|
|
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
|
|
* crystallite_subdt(g,i,e)
|
|
if(present(DB)) &
|
|
broken = broken .or. .not. converged(matmul(source_RKdotState(1:sizeDotState,1:size(DB),s),DB) &
|
|
* crystallite_subdt(g,i,e), &
|
|
sourceState(p)%p(s)%state(1:sizeDotState,c), &
|
|
sourceState(p)%p(s)%atol(1:sizeDotState))
|
|
enddo
|
|
if(broken) cycle
|
|
|
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
crystallite_Fe(1:3,1:3,g,i,e), &
|
|
crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c)
|
|
if(broken) cycle
|
|
|
|
broken = integrateStress(g,i,e)
|
|
crystallite_converged(g,i,e) = .not. broken
|
|
|
|
endif
|
|
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
|
|
enddo; enddo; enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
if(nonlocalBroken) call nonlocalConvergenceCheck
|
|
|
|
end subroutine integrateStateRK
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief sets convergence flag for nonlocal calculations
|
|
!> @details one non-converged nonlocal sets all other nonlocals to non-converged to trigger cut back
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine nonlocalConvergenceCheck
|
|
|
|
integer :: e,i,p
|
|
|
|
!$OMP PARALLEL DO PRIVATE(p)
|
|
do e = FEsolving_execElem(1),FEsolving_execElem(2)
|
|
p = material_phaseAt(1,e)
|
|
do i = FEsolving_execIP(1),FEsolving_execIP(2)
|
|
if(plasticState(p)%nonlocal) crystallite_converged(1,i,e) = .false.
|
|
enddo
|
|
enddo
|
|
!$OMP END PARALLEL DO
|
|
|
|
end subroutine nonlocalConvergenceCheck
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @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_partionedF,'F')
|
|
call HDF5_write(fileHandle,crystallite_Fp, 'Fp')
|
|
call HDF5_write(fileHandle,crystallite_Fi, 'Fi')
|
|
call HDF5_write(fileHandle,crystallite_Lp, 'Lp')
|
|
call HDF5_write(fileHandle,crystallite_Li, 'Li')
|
|
call HDF5_write(fileHandle,crystallite_S, 'S')
|
|
|
|
groupHandle = HDF5_addGroup(fileHandle,'constituent')
|
|
do i = 1,size(material_name_phase)
|
|
write(datasetName,'(i0,a)') i,'_omega_plastic'
|
|
call HDF5_write(groupHandle,plasticState(i)%state,datasetName)
|
|
enddo
|
|
call HDF5_closeGroup(groupHandle)
|
|
|
|
groupHandle = HDF5_addGroup(fileHandle,'materialpoint')
|
|
do i = 1, material_Nhomogenization
|
|
write(datasetName,'(i0,a)') i,'_omega_homogenization'
|
|
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,'Fp')
|
|
call HDF5_read(fileHandle,crystallite_Fi0,'Fi')
|
|
call HDF5_read(fileHandle,crystallite_Lp0,'Lp')
|
|
call HDF5_read(fileHandle,crystallite_Li0,'Li')
|
|
call HDF5_read(fileHandle,crystallite_S0, 'S')
|
|
|
|
groupHandle = HDF5_openGroup(fileHandle,'constituent')
|
|
do i = 1,size(material_name_phase)
|
|
write(datasetName,'(i0,a)') i,'_omega_plastic'
|
|
call HDF5_read(groupHandle,plasticState(i)%state0,datasetName)
|
|
enddo
|
|
call HDF5_closeGroup(groupHandle)
|
|
|
|
groupHandle = HDF5_openGroup(fileHandle,'materialpoint')
|
|
do i = 1, material_Nhomogenization
|
|
write(datasetName,'(i0,a)') i,'_omega_homogenization'
|
|
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_partionedF
|
|
crystallite_Fp0 = crystallite_Fp
|
|
crystallite_Lp0 = crystallite_Lp
|
|
crystallite_Fi0 = crystallite_Fi
|
|
crystallite_Li0 = crystallite_Li
|
|
crystallite_S0 = crystallite_S
|
|
|
|
do i = 1, size(plasticState)
|
|
plasticState(i)%state0 = plasticState(i)%state
|
|
enddo
|
|
do i = 1, size(sourceState)
|
|
do j = 1,phase_Nsources(i)
|
|
sourceState(i)%p(j)%state0 = sourceState(i)%p(j)%state
|
|
enddo; enddo
|
|
do i = 1, material_Nhomogenization
|
|
homogState (i)%state0 = homogState (i)%state
|
|
thermalState(i)%state0 = thermalState(i)%state
|
|
damageState (i)%state0 = damageState (i)%state
|
|
enddo
|
|
|
|
end subroutine crystallite_forward
|
|
|
|
end module crystallite
|