969 lines
51 KiB
Fortran
969 lines
51 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Philip Eisenlohr, Michigan State University
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!> @author Zhuowen Zhao, Michigan State University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Introducing Voce-type kinematic hardening rule into crystal plasticity
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!! formulation using a power law fitting
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!--------------------------------------------------------------------------------------------------
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module plastic_kinehardening
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use prec, only: &
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pReal,&
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pInt
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implicit none
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private
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integer(pInt), dimension(:), allocatable, public, protected :: &
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plastic_kinehardening_sizePostResults !< cumulative size of post results
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integer(pInt), dimension(:,:), allocatable, target, public :: &
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plastic_kinehardening_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_kinehardening_output !< name of each post result output
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integer(pInt), dimension(:), allocatable, target, public :: &
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plastic_kinehardening_Noutput !< number of outputs per instance
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integer(pInt), dimension(:), allocatable, public, protected :: &
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plastic_kinehardening_totalNslip !< no. of slip system used in simulation
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integer(pInt), dimension(:,:), allocatable, private :: &
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plastic_kinehardening_Nslip !< active number of slip systems per family (input parameter, per family)
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enum, bind(c)
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enumerator :: undefined_ID, &
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crss_ID, & !< critical resolved stress
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crss_back_ID, & !< critical resolved back stress
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sense_ID, & !< sense of acting shear stress (-1 or +1)
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chi0_ID, & !< backstress at last switch of stress sense (positive?)
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gamma0_ID, & !< accumulated shear at last switch of stress sense (at current switch?)
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accshear_ID, &
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sumGamma_ID, &
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shearrate_ID, &
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resolvedstress_ID
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end enum
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type, private :: tParameters !< container type for internal constitutive parameters
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integer(kind(undefined_ID)), dimension(:), allocatable, private :: &
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outputID !< ID of each post result output
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real(pReal) :: &
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gdot0, & !< reference shear strain rate for slip (input parameter)
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n_slip, & !< stress exponent for slip (input parameter)
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aTolResistance, &
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aTolShear
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real(pReal), dimension(:), allocatable, private :: &
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crss0, & !< initial critical shear stress for slip (input parameter, per family)
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theta0, & !< initial hardening rate of forward stress for each slip
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theta1, & !< asymptotic hardening rate of forward stress for each slip >
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theta0_b, & !< initial hardening rate of back stress for each slip >
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theta1_b, & !< asymptotic hardening rate of back stress for each slip >
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tau1, &
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tau1_b, &
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interaction_slipslip, & !< latent hardening matrix
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nonSchmidCoeff
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real(pReal), dimension(:,:), allocatable, private :: &
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hardeningMatrix_SlipSlip
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end type
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type, private :: tKinehardeningState
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real(pReal), pointer, dimension(:,:) :: & !< vectors along NipcMyInstance
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crss, & !< critical resolved stress
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crss_back, & !< critical resolved back stress
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sense, & !< sense of acting shear stress (-1 or +1)
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chi0, & !< backstress at last switch of stress sense
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gamma0, & !< accumulated shear at last switch of stress sense
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accshear !< accumulated (absolute) shear
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real(pReal), pointer, dimension(:) :: & !< scalars along NipcMyInstance
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sumGamma !< accumulated shear across all systems
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end type
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type(tParameters), dimension(:), allocatable, private :: &
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param !< containers of constitutive parameters (len Ninstance)
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type(tKinehardeningState), allocatable, dimension(:), private :: &
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dotState, &
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deltaState, &
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state, &
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state0
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public :: &
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plastic_kinehardening_init, &
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plastic_kinehardening_LpAndItsTangent, &
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plastic_kinehardening_dotState, &
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plastic_kinehardening_deltaState, &
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plastic_kinehardening_postResults
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private :: &
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plastic_kinehardening_shearRates
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief module initialization
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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subroutine plastic_kinehardening_init(fileUnit)
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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use prec, only: &
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dEq0
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use debug, only: &
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debug_level, &
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debug_constitutive,&
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debug_levelBasic
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use math, only: &
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math_Mandel3333to66, &
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math_Voigt66to3333, &
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math_expand
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use IO, only: &
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IO_read, &
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IO_lc, &
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IO_getTag, &
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IO_isBlank, &
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IO_stringPos, &
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IO_stringValue, &
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IO_floatValue, &
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IO_intValue, &
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IO_warning, &
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IO_error, &
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IO_timeStamp, &
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IO_EOF
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use material, only: &
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PLASTICITY_kinehardening_label, &
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PLASTICITY_kinehardening_ID, &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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material_phase, &
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plasticState
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use config, only: &
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MATERIAL_partPhase
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use lattice
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use numerics,only: &
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numerics_integrator
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implicit none
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integer(pInt), intent(in) :: fileUnit
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integer(pInt), allocatable, dimension(:) :: chunkPos
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integer(kind(undefined_ID)) :: &
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output_ID
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integer(pInt) :: &
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o, j, k, f, &
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phase, &
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instance, &
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maxNinstance, &
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NipcMyPhase, &
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Nchunks_SlipSlip = 0_pInt, Nchunks_SlipFamilies = 0_pInt, &
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Nchunks_nonSchmid = 0_pInt, &
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offset_slip, index_myFamily, index_otherFamily, &
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startIndex, endIndex, &
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mySize, nSlip, nSlipFamilies, &
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sizeDotState, &
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sizeState, &
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sizeDeltaState
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real(pReal), dimension(:), allocatable :: tempPerSlip
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character(len=65536) :: &
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tag = '', &
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line = '', &
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extmsg = ''
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_KINEHARDENING_label//' init -+>>>'
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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#include "compilation_info.f90"
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maxNinstance = int(count(phase_plasticity == PLASTICITY_KINEHARDENING_ID),pInt)
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if (maxNinstance == 0_pInt) return
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
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write(6,'(a,1x,i5,/)') '# instances:',maxNinstance
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allocate(plastic_kinehardening_sizePostResults(maxNinstance), source=0_pInt)
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allocate(plastic_kinehardening_sizePostResult(maxval(phase_Noutput),maxNinstance), &
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source=0_pInt)
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allocate(plastic_kinehardening_output(maxval(phase_Noutput),maxNinstance))
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plastic_kinehardening_output = ''
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allocate(plastic_kinehardening_Noutput(maxNinstance), source=0_pInt)
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allocate(plastic_kinehardening_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
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allocate(plastic_kinehardening_totalNslip(maxNinstance), source=0_pInt)
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allocate(param(maxNinstance)) ! one container of parameters per instance
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rewind(fileUnit)
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phase = 0_pInt
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do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= material_partPhase) ! wind forward to <phase>
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line = IO_read(fileUnit)
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enddo
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parsingFile: do while (trim(line) /= IO_EOF) ! read through sections of phase part
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line = IO_read(fileUnit)
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') then ! stop at next part
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line = IO_read(fileUnit, .true.) ! reset IO_read
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exit
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endif
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if (IO_getTag(line,'[',']') /= '') then ! next phase
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phase = phase + 1_pInt ! advance phase section counter
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if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then
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instance = phase_plasticityInstance(phase) ! count instances of my constitutive law
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Nchunks_SlipFamilies = count(lattice_NslipSystem(:,phase) > 0_pInt) ! maximum number of slip families according to lattice type of current phase
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Nchunks_SlipSlip = maxval(lattice_interactionSlipSlip(:,:,phase))
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Nchunks_nonSchmid = lattice_NnonSchmid(phase)
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allocate(param(instance)%crss0 (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%tau1 (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%tau1_b (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%theta0 (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%theta1 (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%theta0_b(Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%theta1_b(Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%interaction_slipslip(Nchunks_SlipSlip), source=0.0_pReal)
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allocate(param(instance)%nonSchmidCoeff(Nchunks_nonSchmid), source=0.0_pReal)
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if(allocated(tempPerSlip)) deallocate(tempPerSlip)
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allocate(tempPerSlip(Nchunks_SlipFamilies))
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allocate(param(instance)%outputID(0))
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endif
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cycle ! skip to next line
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endif
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if (phase > 0_pInt ) then; if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then ! one of my phases. Do not short-circuit here (.and. between if-statements), it's not safe in Fortran
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chunkPos = IO_stringPos(line)
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tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key
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select case(tag)
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case ('(output)')
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output_ID = undefined_ID
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select case(IO_lc(IO_stringValue(line,chunkPos,2_pInt)))
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case ('resistance')
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output_ID = crss_ID
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case ('backstress')
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output_ID = crss_back_ID
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case ('sense')
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output_ID = sense_ID
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case ('chi0')
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output_ID = chi0_ID
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case ('gamma0')
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output_ID = gamma0_ID
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case ('accumulatedshear')
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output_ID = accshear_ID
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case ('totalshear')
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output_ID = sumGamma_ID
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case ('shearrate')
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output_ID = shearrate_ID
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case ('resolvedstress')
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output_ID = resolvedstress_ID
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end select
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if (output_ID /= undefined_ID) then
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plastic_kinehardening_Noutput(instance) = plastic_kinehardening_Noutput(instance) + 1_pInt
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plastic_kinehardening_output(plastic_kinehardening_Noutput(instance),instance) = &
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IO_lc(IO_stringValue(line,chunkPos,2_pInt))
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param(instance)%outputID = [param(instance)%outputID, output_ID]
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endif
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!--------------------------------------------------------------------------------------------------
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! parameters depending on number of slip families
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case ('nslip')
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if (chunkPos(1) < Nchunks_SlipFamilies + 1_pInt) &
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call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
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if (chunkPos(1) > Nchunks_SlipFamilies + 1_pInt) &
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call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
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Nchunks_SlipFamilies = chunkPos(1) - 1_pInt ! user specified number of (possibly) active slip families (e.g. 6 0 6 --> 3)
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do j = 1_pInt, Nchunks_SlipFamilies
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plastic_kinehardening_Nslip(j,instance) = IO_intValue(line,chunkPos,1_pInt+j)
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enddo
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case ('crss0','tau1','tau1_b','theta0','theta1','theta0_b','theta1_b')
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tempPerSlip = 0.0_pReal
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do j = 1_pInt, Nchunks_SlipFamilies
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if (plastic_kinehardening_Nslip(j,instance) > 0_pInt) &
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tempPerSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
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enddo
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select case(tag)
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case ('crss0')
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param(instance)%crss0(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('tau1')
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param(instance)%tau1(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('tau1_b')
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param(instance)%tau1_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('theta0')
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param(instance)%theta0(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('theta1')
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param(instance)%theta1(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('theta0_b')
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param(instance)%theta0_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('theta1_b')
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param(instance)%theta1_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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end select
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!--------------------------------------------------------------------------------------------------
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! parameters depending on number of interactions
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case ('interaction_slipslip')
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if (chunkPos(1) < 1_pInt + Nchunks_SlipSlip) &
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call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
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do j = 1_pInt, Nchunks_SlipSlip
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param(instance)%interaction_slipslip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
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enddo
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case ('nonschmidcoeff')
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if (chunkPos(1) < 1_pInt + Nchunks_nonSchmid) &
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call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
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do j = 1_pInt,Nchunks_nonSchmid
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param(instance)%nonSchmidCoeff(j) = IO_floatValue(line,chunkPos,1_pInt+j)
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enddo
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!--------------------------------------------------------------------------------------------------
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case ('gdot0')
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param(instance)%gdot0 = IO_floatValue(line,chunkPos,2_pInt)
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case ('n_slip')
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param(instance)%n_slip = IO_floatValue(line,chunkPos,2_pInt)
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case ('atol_resistance')
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param(instance)%aTolResistance = IO_floatValue(line,chunkPos,2_pInt)
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case ('atol_shear')
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param(instance)%aTolShear = IO_floatValue(line,chunkPos,2_pInt)
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case default
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end select
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endif; endif
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enddo parsingFile
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!--------------------------------------------------------------------------------------------------
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! allocation of variables whose size depends on the total number of active slip systems
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allocate(state(maxNinstance))
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allocate(state0(maxNinstance))
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allocate(dotState(maxNinstance))
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allocate(deltaState(maxNinstance))
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initializeInstances: do phase = 1_pInt, size(phase_plasticity) ! loop through all phases in material.config
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myPhase2: if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then ! only consider my phase
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NipcMyPhase = count(material_phase == phase) ! number of IPCs containing my phase
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instance = phase_plasticityInstance(phase) ! which instance of my phase
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plastic_kinehardening_Nslip(1:lattice_maxNslipFamily,instance) = &
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min(lattice_NslipSystem(1:lattice_maxNslipFamily,phase),& ! limit active slip systems per family to min of available and requested
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plastic_kinehardening_Nslip(1:lattice_maxNslipFamily,instance))
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plastic_kinehardening_totalNslip(instance) = sum(plastic_kinehardening_Nslip(:,instance)) ! how many slip systems altogether
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nSlipFamilies = count(plastic_kinehardening_Nslip(:,instance) > 0_pInt)
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nSlip = plastic_kinehardening_totalNslip(instance) ! total number of active slip systems
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!--------------------------------------------------------------------------------------------------
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! sanity checks
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if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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.and. param(instance)%crss0 (1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' crss0'
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if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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.and. param(instance)%tau1 (1:nSlipFamilies) <= 0.0_pReal)) extmsg = trim(extmsg)//' tau1'
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if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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.and. param(instance)%tau1_b(1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' tau1_b'
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if (param(instance)%gdot0 <= 0.0_pReal) extmsg = trim(extmsg)//' gdot0'
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if (param(instance)%n_slip <= 0.0_pReal) extmsg = trim(extmsg)//' n_slip'
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if (param(instance)%aTolResistance <= 0.0_pReal) param(instance)%aTolResistance = 1.0_pReal ! default absolute tolerance 1 Pa
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if (param(instance)%aTolShear <= 0.0_pReal) param(instance)%aTolShear = 1.0e-6_pReal ! default absolute tolerance 1e-6
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if (extmsg /= '') then
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extmsg = trim(extmsg)//' ('//PLASTICITY_KINEHARDENING_label//')' ! prepare error message identifier
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call IO_error(211_pInt,ip=instance,ext_msg=extmsg)
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endif
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!--------------------------------------------------------------------------------------------------
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! Determine size of postResults array
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outputsLoop: do o = 1_pInt,plastic_kinehardening_Noutput(instance)
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select case(param(instance)%outputID(o))
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case(crss_ID, & !< critical resolved stress
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crss_back_ID, & !< critical resolved back stress
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sense_ID, & !< sense of acting shear stress (-1 or +1)
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chi0_ID, & !< backstress at last switch of stress sense
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gamma0_ID, & !< accumulated shear at last switch of stress sense
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accshear_ID, &
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shearrate_ID, &
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resolvedstress_ID)
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mySize = nSlip
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case(sumGamma_ID)
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mySize = 1_pInt
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case default
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end select
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outputFound: if (mySize > 0_pInt) then
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plastic_kinehardening_sizePostResult(o,instance) = mySize
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plastic_kinehardening_sizePostResults(instance) = plastic_kinehardening_sizePostResults(instance) + mySize
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endif outputFound
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enddo outputsLoop
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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sizeDotState = nSlip & !< crss
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+ nSlip & !< crss_back
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+ nSlip & !< accumulated (absolute) shear
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+ 1_pInt !< sum(gamma)
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sizeDeltaState = nSlip & !< sense of acting shear stress (-1 or +1)
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+ nSlip & !< backstress at last switch of stress sense
|
|
+ nSlip !< accumulated shear at last switch of stress sense
|
|
|
|
sizeState = sizeDotState + sizeDeltaState
|
|
plasticState(phase)%sizeState = sizeState
|
|
plasticState(phase)%sizeDotState = sizeDotState
|
|
plasticState(phase)%sizeDeltaState = sizeDeltaState
|
|
plasticState(phase)%offsetDeltaState = sizeDotState
|
|
plasticState(phase)%sizePostResults = plastic_kinehardening_sizePostResults(instance)
|
|
plasticState(phase)%nSlip = nSlip
|
|
|
|
allocate(plasticState(phase)%state0 ( sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(plasticState(phase)%partionedState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(plasticState(phase)%subState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(plasticState(phase)%state ( sizeState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(plasticState(phase)%aTolState (sizeDotState), source=0.0_pReal)
|
|
allocate(plasticState(phase)%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
|
|
allocate(plasticState(phase)%deltaState (sizeDeltaState,NipcMyPhase), source=0.0_pReal) ! allocate space for deltaState
|
|
if (any(numerics_integrator == 1_pInt)) then
|
|
allocate(plasticState(phase)%previousDotState (sizeDotState,NipcMyPhase),source=0.0_pReal)
|
|
allocate(plasticState(phase)%previousDotState2(sizeDotState,NipcMyPhase),source=0.0_pReal)
|
|
endif
|
|
if (any(numerics_integrator == 4_pInt)) &
|
|
allocate(plasticState(phase)%RK4dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
|
|
if (any(numerics_integrator == 5_pInt)) &
|
|
allocate(plasticState(phase)%RKCK45dotState (6,sizeDotState,NipcMyPhase), source=0.0_pReal)
|
|
|
|
offset_slip = plasticState(phase)%nSlip+plasticState(phase)%nTwin+2_pInt
|
|
plasticState(phase)%slipRate => &
|
|
plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
|
|
plasticState(phase)%accumulatedSlip => &
|
|
plasticState(phase)%state(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
|
|
|
|
allocate(param(instance)%hardeningMatrix_SlipSlip(nSlip,nSlip), source=0.0_pReal)
|
|
do f = 1_pInt,lattice_maxNslipFamily ! >>> interaction slip -- X
|
|
index_myFamily = sum(plastic_kinehardening_Nslip(1:f-1_pInt,instance))
|
|
do j = 1_pInt,plastic_kinehardening_Nslip(f,instance) ! loop over (active) systems in my family (slip)
|
|
do o = 1_pInt,lattice_maxNslipFamily
|
|
index_otherFamily = sum(plastic_kinehardening_Nslip(1:o-1_pInt,instance))
|
|
do k = 1_pInt,plastic_kinehardening_Nslip(o,instance) ! loop over (active) systems in other family (slip)
|
|
param(instance)%hardeningMatrix_SlipSlip(index_myFamily+j,index_otherFamily+k) = &
|
|
param(instance)%interaction_SlipSlip(lattice_interactionSlipSlip( &
|
|
sum(lattice_NslipSystem(1:f-1,phase))+j, &
|
|
sum(lattice_NslipSystem(1:o-1,phase))+k, &
|
|
phase))
|
|
enddo; enddo
|
|
enddo; enddo
|
|
|
|
!----------------------------------------------------------------------------------------------
|
|
!locally define dotState alias
|
|
|
|
endindex = 0_pInt
|
|
o = endIndex ! offset of dotstate index relative to state index
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%crss => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%crss => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
dotState(instance)%crss => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%crss = spread(math_expand(param(instance)%crss0,&
|
|
plastic_kinehardening_Nslip(:,instance)), &
|
|
2, NipcMyPhase)
|
|
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolResistance
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%crss_back => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%crss_back => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
dotState(instance)%crss_back => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%crss_back = 0.0_pReal
|
|
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolResistance
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%accshear => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%accshear => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
dotState(instance)%accshear => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%accshear = 0.0_pReal
|
|
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolShear
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + 1_pInt
|
|
state (instance)%sumGamma => plasticState(phase)%state (startIndex ,1:NipcMyPhase)
|
|
state0 (instance)%sumGamma => plasticState(phase)%state0 (startIndex ,1:NipcMyPhase)
|
|
dotState(instance)%sumGamma => plasticState(phase)%dotState (startIndex-o ,1:NipcMyPhase)
|
|
|
|
state0(instance)%sumGamma = 0.0_pReal
|
|
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolShear
|
|
|
|
!----------------------------------------------------------------------------------------------
|
|
!locally define deltaState alias
|
|
o = endIndex
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%sense => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%sense => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
deltaState(instance)%sense => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%sense = 0.0_pReal
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%chi0 => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%chi0 => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
deltaState(instance)%chi0 => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%chi0 = 0.0_pReal
|
|
|
|
! .............................................
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + nSlip
|
|
state (instance)%gamma0 => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
|
|
state0 (instance)%gamma0 => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
|
|
deltaState(instance)%gamma0 => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
|
|
|
|
state0(instance)%gamma0 = 0.0_pReal
|
|
|
|
endif myPhase2
|
|
enddo initializeInstances
|
|
|
|
end subroutine plastic_kinehardening_init
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculation of shear rates (\dot \gamma)
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Tstar_v,ph,instance,of)
|
|
|
|
use lattice, only: &
|
|
lattice_NslipSystem, &
|
|
lattice_Sslip_v, &
|
|
lattice_maxNslipFamily, &
|
|
lattice_NnonSchmid
|
|
|
|
implicit none
|
|
real(pReal), dimension(6), intent(in) :: &
|
|
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
|
integer(pInt), intent(in) :: &
|
|
ph, & !< phase ID
|
|
instance, & !< instance of that phase
|
|
of !< index of phaseMember
|
|
real(pReal), dimension(plastic_kinehardening_totalNslip(instance)), intent(out) :: &
|
|
gdot_pos, & !< shear rates from positive line segments
|
|
gdot_neg, & !< shear rates from negative line segments
|
|
tau_pos, & !< shear stress on positive line segments
|
|
tau_neg !< shear stress on negative line segments
|
|
|
|
integer(pInt) :: &
|
|
index_myFamily, &
|
|
f,i,j,k
|
|
|
|
|
|
j = 0_pInt
|
|
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems: do i = 1_pInt,plastic_kinehardening_Nslip(f,instance)
|
|
j = j + 1_pInt
|
|
tau_pos(j) = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
|
|
tau_neg(j) = tau_pos(j)
|
|
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
|
|
tau_pos(j) = tau_pos(j) + param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+0,index_myFamily+i,ph))
|
|
tau_neg(j) = tau_neg(j) + param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
|
|
enddo nonSchmidSystems
|
|
enddo slipSystems
|
|
enddo slipFamilies
|
|
|
|
gdot_pos = 0.5_pReal * param(instance)%gdot0 * &
|
|
(abs(tau_pos-state(instance)%crss_back(:,of))/ &
|
|
state(instance)%crss(:,of))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_pos-state(instance)%crss_back(:,of))
|
|
gdot_neg = 0.5_pReal * param(instance)%gdot0 * &
|
|
(abs(tau_neg-state(instance)%crss_back(:,of))/ &
|
|
state(instance)%crss(:,of))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_neg-state(instance)%crss_back(:,of))
|
|
|
|
|
|
end subroutine plastic_kinehardening_shearRates
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates plastic velocity gradient and its tangent
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_LpAndItsTangent(Lp,dLp_dTstar99, &
|
|
Tstar_v,ipc,ip,el)
|
|
use prec, only: &
|
|
dNeq0
|
|
use debug, only: &
|
|
debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_e, &
|
|
debug_i, &
|
|
debug_g
|
|
use math, only: &
|
|
math_Plain3333to99, &
|
|
math_Mandel6to33, &
|
|
math_transpose33
|
|
use lattice, only: &
|
|
lattice_Sslip, & !< schmid matrix
|
|
lattice_maxNslipFamily, &
|
|
lattice_NslipSystem, &
|
|
lattice_NnonSchmid
|
|
use material, only: &
|
|
phaseAt, phasememberAt, &
|
|
phase_plasticityInstance
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(out) :: &
|
|
Lp !< plastic velocity gradient
|
|
real(pReal), dimension(9,9), intent(out) :: &
|
|
dLp_dTstar99 !< derivative of Lp with respect to 2nd Piola Kirchhoff stress
|
|
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), dimension(6), intent(in) :: &
|
|
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
|
|
|
integer(pInt) :: &
|
|
instance, &
|
|
index_myFamily, &
|
|
f,i,j,k,l,m,n, &
|
|
of, &
|
|
ph
|
|
|
|
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(phaseAt(ipc,ip,el)))) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg
|
|
real(pReal) :: &
|
|
dgdot_dtau_pos,dgdot_dtau_neg
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
dLp_dTstar3333 !< derivative of Lp with respect to Tstar as 4th order tensor
|
|
real(pReal), dimension(3,3,2) :: &
|
|
nonSchmid_tensor
|
|
|
|
ph = phaseAt(ipc,ip,el) !< figures phase for each material point
|
|
of = phasememberAt(ipc,ip,el) !< index of the positions of each constituent of material point, phasememberAt is a function in material that helps figure them out
|
|
instance = phase_plasticityInstance(ph)
|
|
|
|
Lp = 0.0_pReal
|
|
dLp_dTstar3333 = 0.0_pReal
|
|
dLp_dTstar99 = 0.0_pReal
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Tstar_v,ph,instance,of)
|
|
|
|
|
|
j = 0_pInt ! reading and marking the starting index for each slip family
|
|
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems: do i = 1_pInt,plastic_kinehardening_Nslip(f,instance)
|
|
j = j + 1_pInt
|
|
|
|
! build nonSchmid tensor
|
|
nonSchmid_tensor(1:3,1:3,1) = lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
|
|
nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,1)
|
|
do k = 1,lattice_NnonSchmid(ph)
|
|
nonSchmid_tensor(1:3,1:3,1) = &
|
|
nonSchmid_tensor(1:3,1:3,1) + param(instance)%nonSchmidCoeff(k) * &
|
|
lattice_Sslip(1:3,1:3,2*k,index_myFamily+i,ph)
|
|
nonSchmid_tensor(1:3,1:3,2) = &
|
|
nonSchmid_tensor(1:3,1:3,2) + param(instance)%nonSchmidCoeff(k) * &
|
|
lattice_Sslip(1:3,1:3,2*k+1,index_myFamily+i,ph)
|
|
enddo
|
|
|
|
Lp = Lp + (gdot_pos(j)+gdot_neg(j))*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph) ! sum of all gdot*SchmidTensor gives Lp
|
|
|
|
! Calculation of the tangent of Lp ! sensitivity of Lp
|
|
if (dNeq0(gdot_pos(j))) then
|
|
dgdot_dtau_pos = gdot_pos(j)*param(instance)%n_slip/(tau_pos(j)-state(instance)%crss_back(j,of))
|
|
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
|
dLp_dTstar3333(k,l,m,n) = &
|
|
dLp_dTstar3333(k,l,m,n) + dgdot_dtau_pos*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
|
|
nonSchmid_tensor(m,n,1)
|
|
endif
|
|
|
|
if (dNeq0(gdot_neg(j))) then
|
|
dgdot_dtau_neg = gdot_neg(j)*param(instance)%n_slip/(tau_neg(j)-state(instance)%crss_back(j,of))
|
|
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
|
dLp_dTstar3333(k,l,m,n) = &
|
|
dLp_dTstar3333(k,l,m,n) + dgdot_dtau_neg*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
|
|
nonSchmid_tensor(m,n,2)
|
|
endif
|
|
enddo slipSystems
|
|
enddo slipFamilies
|
|
|
|
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
end subroutine plastic_kinehardening_LpAndItsTangent
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates (instantaneous) incremental change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_deltaState(Tstar_v,ipc,ip,el)
|
|
use prec, only: &
|
|
dNeq, &
|
|
dEq0
|
|
use debug, only: &
|
|
debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_e, &
|
|
debug_i, &
|
|
debug_g
|
|
use material, only: &
|
|
phaseAt, &
|
|
phasememberAt, &
|
|
phase_plasticityInstance
|
|
|
|
implicit none
|
|
real(pReal), dimension(6), intent(in):: &
|
|
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(phaseAt(ipc,ip,el)))) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg, &
|
|
sense
|
|
integer(pInt) :: &
|
|
ph, &
|
|
instance, & !< instance of my instance (unique number of my constitutive model)
|
|
of, &
|
|
j !< shortcut notation for offset position in state array
|
|
|
|
ph = phaseAt(ipc,ip,el)
|
|
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
|
|
instance = phase_plasticityInstance(ph)
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Tstar_v,ph,instance,of)
|
|
sense = merge(state(instance)%sense(:,of), & ! keep existing...
|
|
sign(1.0_pReal,gdot_pos+gdot_neg), & ! ...or have a defined
|
|
dEq0(gdot_pos+gdot_neg,1e-10_pReal)) ! current sense of shear direction
|
|
|
|
#ifdef DEBUG
|
|
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
|
|
.and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
write(6,'(a)') '======= kinehardening delta state ======='
|
|
endif
|
|
#endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! switch in sense of shear?
|
|
do j = 1,plastic_kinehardening_totalNslip(instance)
|
|
#ifdef DEBUG
|
|
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
|
|
.and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
write(6,'(i2,1x,f7.4,1x,f7.4)') j,sense(j),state(instance)%sense(j,of)
|
|
endif
|
|
#endif
|
|
if (dNeq(sense(j),state(instance)%sense(j,of),0.1_pReal)) then
|
|
deltaState(instance)%sense (j,of) = sense(j) - state(instance)%sense(j,of) ! switch sense
|
|
deltaState(instance)%chi0 (j,of) = abs(state(instance)%crss_back(j,of)) - state(instance)%chi0(j,of) ! remember current backstress magnitude
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|
deltaState(instance)%gamma0(j,of) = state(instance)%accshear(j,of) - state(instance)%gamma0(j,of) ! remember current accumulated shear
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else
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|
deltaState(instance)%sense (j,of) = 0.0_pReal ! no change
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|
deltaState(instance)%chi0 (j,of) = 0.0_pReal
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|
deltaState(instance)%gamma0(j,of) = 0.0_pReal
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|
endif
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|
enddo
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|
|
|
end subroutine plastic_kinehardening_deltaState
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|
|
|
|
|
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!--------------------------------------------------------------------------------------------------
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|
!> @brief calculates the rate of change of microstructure
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|
!--------------------------------------------------------------------------------------------------
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|
subroutine plastic_kinehardening_dotState(Tstar_v,ipc,ip,el)
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|
use lattice, only: &
|
|
lattice_maxNslipFamily
|
|
use material, only: &
|
|
material_phase, &
|
|
phaseAt, phasememberAt, &
|
|
phase_plasticityInstance
|
|
|
|
implicit none
|
|
real(pReal), dimension(6), intent(in) :: &
|
|
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation, vector form
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element !< microstructure state
|
|
|
|
integer(pInt) :: &
|
|
instance,ph, &
|
|
f,i,j, &
|
|
nSlip, &
|
|
of
|
|
|
|
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg
|
|
|
|
of = phasememberAt(ipc,ip,el)
|
|
ph = phaseAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(ph)
|
|
nSlip = plastic_kinehardening_totalNslip(instance)
|
|
|
|
dotState(instance)%sumGamma(of) = 0.0_pReal
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Tstar_v,ph,instance,of)
|
|
|
|
j = 0_pInt
|
|
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
|
|
slipSystems: do i = 1_pInt,plastic_kinehardening_Nslip(f,instance)
|
|
j = j+1_pInt
|
|
dotState(instance)%crss(j,of) = & ! evolution of slip resistance j
|
|
dot_product(param(instance)%hardeningMatrix_SlipSlip(j,1:nSlip),abs(gdot_pos+gdot_neg)) * &
|
|
( param(instance)%theta1(f) + &
|
|
(param(instance)%theta0(f) - param(instance)%theta1(f) &
|
|
+ param(instance)%theta0(f)*param(instance)%theta1(f)*state(instance)%sumGamma(of)/param(instance)%tau1(f)) &
|
|
*exp(-state(instance)%sumGamma(of)*param(instance)%theta0(f)/param(instance)%tau1(f)) & ! V term depending on the harding law
|
|
)
|
|
dotState(instance)%crss_back(j,of) = & ! evolution of back stress resistance j
|
|
state(instance)%sense(j,of)*abs(gdot_pos(j)+gdot_neg(j)) * &
|
|
( param(instance)%theta1_b(f) + &
|
|
(param(instance)%theta0_b(f) - param(instance)%theta1_b(f) &
|
|
+ param(instance)%theta0_b(f)*param(instance)%theta1_b(f)/(param(instance)%tau1_b(f)+state(instance)%chi0(j,of)) &
|
|
*(state(instance)%accshear(j,of)-state(instance)%gamma0(j,of))) &
|
|
*exp(-(state(instance)%accshear(j,of)-state(instance)%gamma0(j,of)) &
|
|
*param(instance)%theta0_b(f)/(param(instance)%tau1_b(f)+state(instance)%chi0(j,of))) &
|
|
) ! V term depending on the harding law for back stress
|
|
|
|
dotState(instance)%accshear(j,of) = abs(gdot_pos(j)+gdot_neg(j))
|
|
dotState(instance)%sumGamma(of) = dotState(instance)%sumGamma(of) + dotState(instance)%accshear(j,of)
|
|
enddo slipSystems
|
|
enddo slipFamilies
|
|
|
|
end subroutine plastic_kinehardening_dotState
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return array of constitutive results
|
|
!--------------------------------------------------------------------------------------------------
|
|
function plastic_kinehardening_postResults(Tstar_v,ipc,ip,el)
|
|
use material, only: &
|
|
material_phase, &
|
|
phaseAt, phasememberAt, &
|
|
phase_plasticityInstance
|
|
use lattice, only: &
|
|
lattice_Sslip_v, &
|
|
lattice_maxNslipFamily, &
|
|
lattice_NslipSystem
|
|
|
|
implicit none
|
|
real(pReal), dimension(6), intent(in) :: &
|
|
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element !< microstructure state
|
|
|
|
real(pReal), dimension(plastic_kinehardening_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
|
plastic_kinehardening_postResults
|
|
|
|
integer(pInt) :: &
|
|
instance,ph, of, &
|
|
nSlip,&
|
|
o,f,i,c,j,&
|
|
index_myFamily
|
|
|
|
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg
|
|
|
|
of = phasememberAt(ipc,ip,el)
|
|
ph = phaseAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(ph)
|
|
|
|
nSlip = plastic_kinehardening_totalNslip(instance)
|
|
|
|
plastic_kinehardening_postResults = 0.0_pReal
|
|
c = 0_pInt
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Tstar_v,ph,instance,of)
|
|
|
|
outputsLoop: do o = 1_pInt,plastic_kinehardening_Noutput(instance)
|
|
select case(param(instance)%outputID(o))
|
|
case (crss_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%crss(:,of)
|
|
c = c + nSlip
|
|
|
|
case(crss_back_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%crss_back(:,of)
|
|
c = c + nSlip
|
|
|
|
case (sense_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%sense(:,of)
|
|
c = c + nSlip
|
|
|
|
case (chi0_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%chi0(:,of)
|
|
c = c + nSlip
|
|
|
|
case (gamma0_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%gamma0(:,of)
|
|
c = c + nSlip
|
|
|
|
case (accshear_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%accshear(:,of)
|
|
c = c + nSlip
|
|
|
|
case (sumGamma_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt) = state(instance)%sumGamma(of)
|
|
c = c + 1_pInt
|
|
|
|
case (shearrate_ID)
|
|
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = gdot_pos+gdot_neg
|
|
c = c + nSlip
|
|
|
|
case (resolvedstress_ID)
|
|
j = 0_pInt
|
|
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems: do i = 1_pInt,plastic_kinehardening_Nslip(f,instance)
|
|
j = j + 1_pInt
|
|
plastic_kinehardening_postResults(c+j) = &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
|
|
enddo slipSystems
|
|
enddo slipFamilies
|
|
c = c + nSlip
|
|
|
|
end select
|
|
enddo outputsLoop
|
|
|
|
end function plastic_kinehardening_postResults
|
|
|
|
end module plastic_kinehardening
|