896 lines
45 KiB
Fortran
896 lines
45 KiB
Fortran
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief material subroutine for phenomenological crystal plasticity formulation using a powerlaw
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!! fitting
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!--------------------------------------------------------------------------------------------------
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module plastic_phenopowerlaw
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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, target, public :: &
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plastic_phenopowerlaw_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_phenopowerlaw_output !< name of each post result output
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enum, bind(c)
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enumerator :: &
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undefined_ID, &
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resistance_slip_ID, &
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accumulatedshear_slip_ID, &
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shearrate_slip_ID, &
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resolvedstress_slip_ID, &
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totalshear_ID, &
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resistance_twin_ID, &
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accumulatedshear_twin_ID, &
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shearrate_twin_ID, &
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resolvedstress_twin_ID, &
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totalvolfrac_twin_ID
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end enum
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type, private :: tParameters !< container type for internal constitutive parameters
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real(pReal) :: &
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gdot0_slip, & !< reference shear strain rate for slip
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gdot0_twin, & !< reference shear strain rate for twin
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n_slip, & !< stress exponent for slip
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n_twin, & !< stress exponent for twin
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spr, & !< push-up factor for slip saturation due to twinning
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twinB, &
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twinC, &
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twinD, &
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twinE, &
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h0_SlipSlip, & !< reference hardening slip - slip
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h0_TwinSlip, & !< reference hardening twin - slip
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h0_TwinTwin, & !< reference hardening twin - twin
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a_slip, &
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aTolResistance, & ! default absolute tolerance 1 Pa
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aTolShear, & ! default absolute tolerance 1e-6
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aTolTwinfrac ! default absolute tolerance 1e-6
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integer(pInt), dimension(:), allocatable :: &
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Nslip, & !< active number of slip systems per family
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Ntwin !< active number of twin systems per family
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real(pReal), dimension(:), allocatable :: &
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tau0_slip, & !< initial critical shear stress for slip
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tau0_twin, & !< initial critical shear stress for twin
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tausat_slip, & !< maximum critical shear stress for slip
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nonSchmidCoeff, &
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H_int, & !< per family hardening activity (optional)
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interaction_SlipSlip, & !< slip resistance from slip activity
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interaction_SlipTwin, & !< slip resistance from twin activity
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interaction_TwinSlip, & !< twin resistance from slip activity
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interaction_TwinTwin !< twin resistance from twin activity
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real(pReal), dimension(:,:), allocatable :: &
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matrix_SlipSlip, & !< slip resistance from slip activity
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matrix_SlipTwin, & !< slip resistance from twin activity
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matrix_TwinSlip, & !< twin resistance from slip activity
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matrix_TwinTwin !< twin resistance from twin activity
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integer(kind(undefined_ID)), dimension(:), allocatable :: &
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outputID !< ID of each post result output
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end type
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type(tParameters), dimension(:), allocatable, target, private :: param !< containers of constitutive parameters (len Ninstance)
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type, private :: tPhenopowerlawState
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real(pReal), pointer, dimension(:,:) :: &
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s_slip, &
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s_twin, &
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accshear_slip, &
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accshear_twin
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real(pReal), pointer, dimension(:) :: &
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sumGamma, &
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sumF
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end type
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type(tPhenopowerlawState), allocatable, dimension(:), private :: &
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dotState, &
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state
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public :: &
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plastic_phenopowerlaw_init, &
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plastic_phenopowerlaw_LpAndItsTangent, &
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plastic_phenopowerlaw_dotState, &
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plastic_phenopowerlaw_postResults
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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_phenopowerlaw_init
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#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
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use, intrinsic :: iso_fortran_env, only: &
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compiler_version, &
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compiler_options
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#endif
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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_warning, &
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IO_error, &
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IO_timeStamp
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use material, only: &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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PLASTICITY_PHENOPOWERLAW_label, &
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PLASTICITY_PHENOPOWERLAW_ID, &
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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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phaseConfig
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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) :: &
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maxNinstance, &
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instance,phase,j,k, f,o, i,&
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NipcMyPhase, outputSize, &
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offset_slip, index_myFamily, index_otherFamily, &
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sizeState,sizeDotState, &
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startIndex, endIndex
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integer(pInt), dimension(0), parameter :: emptyInt = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyReal = [real(pReal)::]
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type(tParameters), pointer :: prm
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integer(kind(undefined_ID)) :: &
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outputID !< ID of each post result output
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character(len=512) :: &
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extmsg = ''
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character(len=64), dimension(:), allocatable :: outputs
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_PHENOPOWERLAW_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_PHENOPOWERLAW_ID),pInt)
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
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write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
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allocate(plastic_phenopowerlaw_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
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allocate(plastic_phenopowerlaw_output(maxval(phase_Noutput),maxNinstance))
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plastic_phenopowerlaw_output = ''
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allocate(param(maxNinstance)) ! one container of parameters per instance
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allocate(state(maxNinstance))
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allocate(dotState(maxNinstance))
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do phase = 1_pInt, size(phase_plasticityInstance)
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if (phase_plasticity(phase) == PLASTICITY_PHENOPOWERLAW_ID) then
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instance = phase_plasticityInstance(phase)
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prm => param(instance)
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prm%Nslip = phaseConfig(phase)%getInts('nslip',defaultVal=emptyInt)
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!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
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if (sum(prm%Nslip) > 0_pInt) then
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prm%tau0_slip = phaseConfig(phase)%getFloats('tau0_slip')
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prm%tausat_slip = phaseConfig(phase)%getFloats('tausat_slip')
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prm%interaction_SlipSlip = phaseConfig(phase)%getFloats('interaction_slipslip')
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prm%H_int = phaseConfig(phase)%getFloats('h_int',&
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defaultVal=[(0.0_pReal,i=1_pInt,size(prm%Nslip))])
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prm%nonSchmidCoeff = phaseConfig(phase)%getFloats('nonschmid_coefficients',&
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defaultVal = [real(pReal)::1] )
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prm%gdot0_slip = phaseConfig(phase)%getFloat('gdot0_slip')
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prm%n_slip = phaseConfig(phase)%getFloat('n_slip')
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prm%a_slip = phaseConfig(phase)%getFloat('a_slip')
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prm%h0_SlipSlip = phaseConfig(phase)%getFloat('h0_slipslip')
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endif
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prm%Ntwin = phaseConfig(phase)%getInts('ntwin', defaultVal=emptyInt)
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!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
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if (sum(prm%Ntwin) > 0_pInt) then
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prm%tau0_twin = phaseConfig(phase)%getFloats('tau0_twin')
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prm%interaction_TwinTwin = phaseConfig(phase)%getFloats('interaction_twintwin')
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prm%gdot0_twin = phaseConfig(phase)%getFloat('gdot0_twin')
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prm%n_twin = phaseConfig(phase)%getFloat('n_twin')
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prm%spr = phaseConfig(phase)%getFloat('s_pr')
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prm%twinB = phaseConfig(phase)%getFloat('twin_b')
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prm%twinC = phaseConfig(phase)%getFloat('twin_c')
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prm%twinD = phaseConfig(phase)%getFloat('twin_d')
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prm%twinE = phaseConfig(phase)%getFloat('twin_e')
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prm%h0_TwinTwin = phaseConfig(phase)%getFloat('h0_twintwin')
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endif
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if (sum(prm%Nslip) > 0_pInt .and. sum(prm%Ntwin) > 0_pInt) then
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prm%interaction_SlipTwin = phaseConfig(phase)%getFloats('interaction_sliptwin')
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prm%interaction_TwinSlip = phaseConfig(phase)%getFloats('interaction_twinslip')
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prm%h0_TwinSlip = phaseConfig(phase)%getFloat('h0_twinslip')
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endif
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allocate(prm%matrix_SlipSlip(sum(prm%Nslip),sum(prm%Nslip)),source =0.0_pReal)
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allocate(prm%matrix_SlipTwin(sum(prm%Nslip),sum(prm%Ntwin)),source =0.0_pReal)
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allocate(prm%matrix_TwinSlip(sum(prm%Ntwin),sum(prm%Nslip)),source =0.0_pReal)
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allocate(prm%matrix_TwinTwin(sum(prm%Ntwin),sum(prm%Ntwin)),source =0.0_pReal)
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prm%aTolResistance = phaseConfig(phase)%getFloat('atol_resistance',defaultVal=1.0_pReal)
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prm%aTolShear = phaseConfig(phase)%getFloat('atol_shear',defaultVal=1.0e-6_pReal)
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prm%aTolTwinfrac = phaseConfig(phase)%getFloat('atol_twinfrac',defaultVal=1.0e-6_pReal)
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outputs = phaseConfig(phase)%getStrings('(output)')
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allocate(prm%outputID(0))
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do i=1_pInt, size(outputs)
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outputID = undefined_ID
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select case(outputs(i))
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case ('resistance_slip')
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outputID = resistance_slip_ID
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outputSize = sum(prm%Nslip)
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case ('acumulatedshear_slip','accumulated_shear_slip')
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outputID = accumulatedshear_slip_ID
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outputSize = sum(prm%Nslip)
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case ('shearrate_slip')
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outputID = shearrate_slip_ID
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outputSize = sum(prm%Nslip)
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case ('resolvedstress_slip')
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outputID = resolvedstress_slip_ID
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outputSize = sum(prm%Nslip)
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case ('resistance_twin')
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outputID = resistance_twin_ID
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outputSize = sum(prm%Ntwin)
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case ('accumulatedshear_twin','accumulated_shear_twin')
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outputID = accumulatedshear_twin_ID
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outputSize = sum(prm%Ntwin)
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case ('shearrate_twin')
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outputID = shearrate_twin_ID
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outputSize = sum(prm%Ntwin)
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case ('resolvedstress_twin')
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outputID = resolvedstress_twin_ID
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outputSize = sum(prm%Ntwin)
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case ('totalvolfrac_twin')
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outputID = totalvolfrac_twin_ID
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outputSize = 1_pInt
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case ('totalshear')
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outputID = totalshear_ID
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outputSize = 1_pInt
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end select
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if (outputID /= undefined_ID) then
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plastic_phenopowerlaw_output(i,instance) = outputs(i)
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plastic_phenopowerlaw_sizePostResult(i,instance) = outputSize
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prm%outputID = [prm%outputID , outputID]
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endif
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end do
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extmsg = ''
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if (sum(prm%Nslip) > 0_pInt) then
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if (size(prm%tau0_slip) /= size(prm%nslip)) extmsg = trim(extmsg)//" shape(tau0_slip) "
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if (size(prm%tausat_slip) /= size(prm%nslip)) extmsg = trim(extmsg)//" shape(tausat_slip) "
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if (size(prm%H_int) /= size(prm%nslip)) extmsg = trim(extmsg)//" shape(h_int) "
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if (any(prm%tau0_slip < 0.0_pReal .and. prm%Nslip > 0_pInt)) &
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extmsg = trim(extmsg)//" 'tau0_slip' "
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if (any(prm%tausat_slip < prm%tau0_slip .and. prm%Nslip > 0_pInt)) &
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extmsg = trim(extmsg)//" 'tausat_slip' "
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if (prm%gdot0_slip <= 0.0_pReal) extmsg = trim(extmsg)//" 'gdot0_slip' "
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if (dEq0(prm%a_slip)) extmsg = trim(extmsg)//" a_slip " ! ToDo: negative values ok?
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if (dEq0(prm%n_slip)) extmsg = trim(extmsg)//" n_slip " ! ToDo: negative values ok?
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endif
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if (sum(prm%Ntwin) > 0_pInt) then
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if (size(prm%tau0_twin) /= size(prm%ntwin)) extmsg = trim(extmsg)//" shape(tau0_twin) "
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if (any(prm%tau0_twin < 0.0_pReal .and. prm%Ntwin > 0_pInt)) &
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extmsg = trim(extmsg)//" 'tau0_twin' "
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if (prm%gdot0_twin <= 0.0_pReal) extmsg = trim(extmsg)//" 'gdot0_twin' "
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if (dEq0(prm%n_twin)) extmsg = trim(extmsg)//" n_twin " ! ToDo: negative values ok?
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endif
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if (prm%aTolResistance <= 0.0_pReal) extmsg = trim(extmsg)//" 'aTolresistance' "
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if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//" 'aTolShear' "
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if (prm%aTolTwinfrac <= 0.0_pReal) extmsg = trim(extmsg)//" 'atoltwinfrac' "
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if (extmsg /= '') call IO_error(211_pInt,ip=instance,&
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ext_msg=trim(extmsg)//'('//PLASTICITY_PHENOPOWERLAW_label//')')
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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NipcMyPhase = count(material_phase == phase) ! number of IPCs containing my phase
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sizeState = size(['tau_slip ','accshear_slip']) * sum(prm%nslip) &
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+ size(['tau_twin ','accshear_twin']) * sum(prm%ntwin) &
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+ size(['sum(gamma)', 'sum(f) '])
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sizeDotState = sizeState
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plasticState(phase)%sizeState = sizeState
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plasticState(phase)%sizeDotState = sizeDotState
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plasticState(phase)%nSlip = sum(prm%Nslip)
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plasticState(phase)%nTwin = sum(prm%Ntwin)
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allocate(plasticState(phase)%aTolState ( sizeState), source=0.0_pReal)
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allocate(plasticState(phase)%state0 ( sizeState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%partionedState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%subState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%state ( sizeState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%deltaState (0_pInt,NipcMyPhase), source=0.0_pReal)
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if (any(numerics_integrator == 1_pInt)) then
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allocate(plasticState(phase)%previousDotState (sizeDotState,NipcMyPhase),source=0.0_pReal)
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allocate(plasticState(phase)%previousDotState2(sizeDotState,NipcMyPhase),source=0.0_pReal)
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endif
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if (any(numerics_integrator == 4_pInt)) &
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allocate(plasticState(phase)%RK4dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
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if (any(numerics_integrator == 5_pInt)) &
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allocate(plasticState(phase)%RKCK45dotState (6,sizeDotState,NipcMyPhase), source=0.0_pReal)
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!--------------------------------------------------------------------------------------------------
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! calculate hardening matrices
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mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1) ! >>> interaction slip -- X
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index_myFamily = sum(prm%Nslip(1:f-1_pInt))
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mySlipSystems: do j = 1_pInt,prm%Nslip(f)
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otherSlipFamilies: do o = 1_pInt,size(prm%Nslip,1)
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index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
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otherSlipSystems: do k = 1_pInt,prm%Nslip(o)
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prm%matrix_SlipSlip(index_myFamily+j,index_otherFamily+k) = &
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prm%interaction_SlipSlip(lattice_interactionSlipSlip( &
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sum(lattice_NslipSystem(1:f-1,phase))+j, &
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sum(lattice_NslipSystem(1:o-1,phase))+k, &
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phase))
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enddo otherSlipSystems; enddo otherSlipFamilies
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twinFamilies: do o = 1_pInt,size(prm%Ntwin,1)
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index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
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twinSystems: do k = 1_pInt,prm%Ntwin(o)
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prm%matrix_SlipTwin(index_myFamily+j,index_otherFamily+k) = &
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prm%interaction_SlipTwin(lattice_interactionSlipTwin( &
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sum(lattice_NslipSystem(1:f-1_pInt,phase))+j, &
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sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
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phase))
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enddo twinSystems; enddo twinFamilies
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enddo mySlipSystems
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enddo mySlipFamilies
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myTwinFamilies: do f = 1_pInt,size(prm%Ntwin,1) ! >>> interaction twin -- X
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index_myFamily = sum(prm%Ntwin(1:f-1_pInt))
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myTwinSystems: do j = 1_pInt,prm%Ntwin(f)
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slipFamilies: do o = 1_pInt,size(prm%Nslip,1)
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index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
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slipSystems: do k = 1_pInt,prm%Nslip(o)
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prm%matrix_TwinSlip(index_myFamily+j,index_otherFamily+k) = &
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prm%interaction_TwinSlip(lattice_interactionTwinSlip( &
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sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
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sum(lattice_NslipSystem(1:o-1_pInt,phase))+k, &
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phase))
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enddo slipSystems; enddo slipFamilies
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otherTwinFamilies: do o = 1_pInt,size(prm%Ntwin,1)
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index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
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otherTwinSystems: do k = 1_pInt,prm%Ntwin(o)
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prm%matrix_TwinTwin(index_myFamily+j,index_otherFamily+k) = &
|
|
prm%interaction_TwinTwin(lattice_interactionTwinTwin( &
|
|
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
|
|
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
|
|
phase))
|
|
enddo otherTwinSystems; enddo otherTwinFamilies
|
|
enddo myTwinSystems
|
|
enddo myTwinFamilies
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! locally defined state aliases and initialization of state0 and aTolState
|
|
startIndex = 1_pInt
|
|
endIndex = plasticState(phase)%nSlip
|
|
state (instance)%s_slip=>plasticState(phase)%state (startIndex:endIndex,:)
|
|
dotState(instance)%s_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
|
plasticState(phase)%state0(startIndex:endIndex,:) = &
|
|
spread(math_expand(prm%tau0_slip, prm%Nslip), 2, NipcMyPhase)
|
|
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolResistance
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + plasticState(phase)%nTwin
|
|
state (instance)%s_twin=>plasticState(phase)%state (startIndex:endIndex,:)
|
|
dotState(instance)%s_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
|
plasticState(phase)%state0(startIndex:endIndex,:) = &
|
|
spread(math_expand(prm%tau0_twin, prm%Ntwin), 2, NipcMyPhase)
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolResistance
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + 1_pInt
|
|
state (instance)%sumGamma=>plasticState(phase)%state (startIndex,:)
|
|
dotState(instance)%sumGamma=>plasticState(phase)%dotState(startIndex,:)
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + 1_pInt
|
|
state (instance)%sumF=>plasticState(phase)%state (startIndex,:)
|
|
dotState(instance)%sumF=>plasticState(phase)%dotState(startIndex,:)
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + plasticState(phase)%nSlip
|
|
state (instance)%accshear_slip=>plasticState(phase)%state (startIndex:endIndex,:)
|
|
dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
|
|
! global alias
|
|
plasticState(phase)%slipRate =>plasticState(phase)%dotState(startIndex:endIndex,:)
|
|
plasticState(phase)%accumulatedSlip =>plasticState(phase)%state(startIndex:endIndex,:)
|
|
|
|
startIndex = endIndex + 1_pInt
|
|
endIndex = endIndex + plasticState(phase)%nTwin
|
|
state (instance)%accshear_twin=>plasticState(phase)%state (startIndex:endIndex,:)
|
|
dotState(instance)%accshear_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
|
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
|
|
|
|
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)
|
|
|
|
endif
|
|
enddo
|
|
|
|
|
|
end subroutine plastic_phenopowerlaw_init
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates plastic velocity gradient and its tangent
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,ipc,ip,el)
|
|
use prec, only: &
|
|
dNeq0
|
|
use math, only: &
|
|
math_Plain3333to99, &
|
|
math_Mandel6to33
|
|
use lattice, only: &
|
|
lattice_Sslip, &
|
|
lattice_Sslip_v, &
|
|
lattice_Stwin, &
|
|
lattice_Stwin_v, &
|
|
lattice_maxNslipFamily, &
|
|
lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem, &
|
|
lattice_NtwinSystem
|
|
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) :: &
|
|
tau_slip_pos,tau_slip_neg, &
|
|
gdot_slip_pos,gdot_slip_neg, &
|
|
dgdot_dtauslip_pos,dgdot_dtauslip_neg, &
|
|
gdot_twin,dgdot_dtautwin,tau_twin
|
|
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
|
|
|
|
of = phasememberAt(ipc,ip,el)
|
|
ph = phaseAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(ph)
|
|
|
|
Lp = 0.0_pReal
|
|
dLp_dTstar3333 = 0.0_pReal
|
|
dLp_dTstar99 = 0.0_pReal
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Slip part
|
|
j = 0_pInt
|
|
slipFamilies: do f = 1_pInt,size(param(instance)%Nslip,1)
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems: do i = 1_pInt,param(instance)%Nslip(f)
|
|
j = j+1_pInt
|
|
|
|
! Calculation of Lp
|
|
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
|
|
tau_slip_neg = tau_slip_pos
|
|
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,size(param(instance)%nonSchmidCoeff)
|
|
tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
|
|
tau_slip_neg = tau_slip_neg + param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,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
|
|
gdot_slip_pos = 0.5_pReal*param(instance)%gdot0_slip* &
|
|
((abs(tau_slip_pos)/(state(instance)%s_slip(j,of))) &
|
|
**param(instance)%n_slip)*sign(1.0_pReal,tau_slip_pos)
|
|
|
|
gdot_slip_neg = 0.5_pReal*param(instance)%gdot0_slip* &
|
|
((abs(tau_slip_neg)/(state(instance)%s_slip(j,of))) &
|
|
**param(instance)%n_slip)*sign(1.0_pReal,tau_slip_neg)
|
|
|
|
Lp = Lp + (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
|
|
(gdot_slip_pos+gdot_slip_neg)*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
|
|
|
|
! Calculation of the tangent of Lp
|
|
if (dNeq0(gdot_slip_pos)) then
|
|
dgdot_dtauslip_pos = gdot_slip_pos*param(instance)%n_slip/tau_slip_pos
|
|
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_dtauslip_pos*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
|
|
nonSchmid_tensor(m,n,1)
|
|
endif
|
|
|
|
if (dNeq0(gdot_slip_neg)) then
|
|
dgdot_dtauslip_neg = gdot_slip_neg*param(instance)%n_slip/tau_slip_neg
|
|
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_dtauslip_neg*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
|
|
nonSchmid_tensor(m,n,2)
|
|
endif
|
|
enddo slipSystems
|
|
enddo slipFamilies
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Twinning part
|
|
j = 0_pInt
|
|
twinFamilies: do f = 1_pInt,size(param(instance)%Ntwin,1)
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
twinSystems: do i = 1_pInt,param(instance)%Ntwin(f)
|
|
j = j+1_pInt
|
|
|
|
! Calculation of Lp
|
|
tau_twin = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
|
|
gdot_twin = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
|
|
param(instance)%gdot0_twin*&
|
|
(abs(tau_twin)/state(instance)%s_twin(j,of))**&
|
|
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
|
|
Lp = Lp + gdot_twin*lattice_Stwin(1:3,1:3,index_myFamily+i,ph)
|
|
|
|
! Calculation of the tangent of Lp
|
|
if (dNeq0(gdot_twin)) then
|
|
dgdot_dtautwin = gdot_twin*param(instance)%n_twin/tau_twin
|
|
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_dtautwin*lattice_Stwin(k,l,index_myFamily+i,ph)* &
|
|
lattice_Stwin(m,n,index_myFamily+i,ph)
|
|
endif
|
|
enddo twinSystems
|
|
enddo twinFamilies
|
|
|
|
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
|
|
end subroutine plastic_phenopowerlaw_LpAndItsTangent
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates the rate of change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_phenopowerlaw_dotState(Tstar_v,ipc,ip,el)
|
|
use lattice, only: &
|
|
lattice_Sslip_v, &
|
|
lattice_Stwin_v, &
|
|
lattice_maxNslipFamily, &
|
|
lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem, &
|
|
lattice_NtwinSystem, &
|
|
lattice_shearTwin, &
|
|
lattice_NnonSchmid
|
|
use material, only: &
|
|
material_phase, &
|
|
phaseAt, phasememberAt, &
|
|
plasticState, &
|
|
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 !< microstructure state
|
|
|
|
integer(pInt) :: &
|
|
instance,ph, &
|
|
f,i,j,k, &
|
|
index_myFamily, nslip,ntwin,&
|
|
of
|
|
real(pReal) :: &
|
|
c_SlipSlip,c_TwinSlip,c_TwinTwin, &
|
|
ssat_offset, &
|
|
tau_slip_pos,tau_slip_neg,tau_twin
|
|
|
|
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
|
|
gdot_slip,left_SlipSlip,left_SlipTwin,right_SlipSlip,right_TwinSlip
|
|
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: &
|
|
gdot_twin,left_TwinSlip,left_TwinTwin,right_SlipTwin,right_TwinTwin
|
|
|
|
of = phasememberAt(ipc,ip,el)
|
|
ph = phaseAt(ipc,ip,el)
|
|
instance = phase_plasticityInstance(ph)
|
|
|
|
nSlip= sum(param(instance)%nslip)
|
|
nTwin= sum(param(instance)%nTwin)
|
|
|
|
plasticState(ph)%dotState(:,of) = 0.0_pReal
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! system-independent (nonlinear) prefactors to M_Xx (X influenced by x) matrices
|
|
c_SlipSlip = param(instance)%h0_slipslip*&
|
|
(1.0_pReal + param(instance)%twinC*state(instance)%sumF(of)**&
|
|
param(instance)%twinB)
|
|
c_TwinSlip = param(instance)%h0_TwinSlip*&
|
|
state(instance)%sumGamma(of)**param(instance)%twinE
|
|
c_TwinTwin = param(instance)%h0_TwinTwin*&
|
|
state(instance)%sumF(of)**param(instance)%twinD
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate left and right vectors and calculate dot gammas
|
|
ssat_offset = param(instance)%spr*sqrt(state(instance)%sumF(of))
|
|
j = 0_pInt
|
|
slipFamilies1: do f =1_pInt,size(param(instance)%Nslip,1)
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
|
|
j = j+1_pInt
|
|
left_SlipSlip(j) = 1.0_pReal + param(instance)%H_int(f) ! modified no system-dependent left part
|
|
left_SlipTwin(j) = 1.0_pReal ! no system-dependent left part
|
|
right_SlipSlip(j) = abs(1.0_pReal-state(instance)%s_slip(j,of) / &
|
|
(param(instance)%tausat_slip(f)+ssat_offset)) &
|
|
**param(instance)%a_slip&
|
|
*sign(1.0_pReal,1.0_pReal-state(instance)%s_slip(j,of) / &
|
|
(param(instance)%tausat_slip(f)+ssat_offset))
|
|
right_TwinSlip(j) = 1.0_pReal ! no system-dependent part
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Calculation of dot gamma
|
|
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
|
|
tau_slip_neg = tau_slip_pos
|
|
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
|
|
tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k, index_myFamily+i,ph))
|
|
tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
|
|
enddo nonSchmidSystems
|
|
gdot_slip(j) = param(instance)%gdot0_slip*0.5_pReal* &
|
|
((abs(tau_slip_pos)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_slip_pos) &
|
|
+(abs(tau_slip_neg)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_slip_neg))
|
|
enddo slipSystems1
|
|
enddo slipFamilies1
|
|
|
|
|
|
|
|
j = 0_pInt
|
|
twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
|
|
j = j+1_pInt
|
|
left_TwinSlip(j) = 1.0_pReal ! no system-dependent left part
|
|
left_TwinTwin(j) = 1.0_pReal ! no system-dependent left part
|
|
right_SlipTwin(j) = 1.0_pReal ! no system-dependent right part
|
|
right_TwinTwin(j) = 1.0_pReal ! no system-dependent right part
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Calculation of dot vol frac
|
|
tau_twin = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
|
|
gdot_twin(j) = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
|
|
param(instance)%gdot0_twin*&
|
|
(abs(tau_twin)/state(instance)%s_twin(j,of))**&
|
|
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
|
|
enddo twinSystems1
|
|
enddo twinFamilies1
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate the overall hardening based on above
|
|
j = 0_pInt
|
|
slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
|
|
slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
|
|
j = j+1_pInt
|
|
dotState(instance)%s_slip(j,of) = & ! evolution of slip resistance j
|
|
c_SlipSlip * left_SlipSlip(j) * &
|
|
dot_product(param(instance)%matrix_SlipSlip(j,1:nslip), &
|
|
right_SlipSlip*abs(gdot_slip)) + & ! dot gamma_slip modulated by right-side slip factor
|
|
dot_product(param(instance)%matrix_SlipTwin(j,1:ntwin), &
|
|
right_SlipTwin*gdot_twin) ! dot gamma_twin modulated by right-side twin factor
|
|
dotState(instance)%sumGamma(of) = dotState(instance)%sumGamma(of) + &
|
|
abs(gdot_slip(j))
|
|
dotState(instance)%accshear_slip(j,of) = abs(gdot_slip(j))
|
|
enddo slipSystems2
|
|
enddo slipFamilies2
|
|
|
|
j = 0_pInt
|
|
twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
|
|
j = j+1_pInt
|
|
dotState(instance)%s_twin(j,of) = & ! evolution of twin resistance j
|
|
c_TwinSlip * left_TwinSlip(j) * &
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dot_product(param(instance)%matrix_TwinSlip(j,1:nslip), &
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right_TwinSlip*abs(gdot_slip)) + & ! dot gamma_slip modulated by right-side slip factor
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c_TwinTwin * left_TwinTwin(j) * &
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dot_product(param(instance)%matrix_TwinTwin(j,1:ntwin), &
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right_TwinTwin*gdot_twin) ! dot gamma_twin modulated by right-side twin factor
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if (state(instance)%sumF(of) < 0.98_pReal) & ! ensure twin volume fractions stays below 1.0
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dotState(instance)%sumF(of) = dotState(instance)%sumF(of) + &
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gdot_twin(j)/lattice_shearTwin(index_myFamily+i,ph)
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dotState(instance)%accshear_twin(j,of) = abs(gdot_twin(j))
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enddo twinSystems2
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enddo twinFamilies2
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end subroutine plastic_phenopowerlaw_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief return array of constitutive results
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!--------------------------------------------------------------------------------------------------
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function plastic_phenopowerlaw_postResults(Tstar_v,ipc,ip,el)
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use material, only: &
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material_phase, &
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plasticState, &
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phaseAt, phasememberAt, &
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phase_plasticityInstance
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use lattice, only: &
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lattice_Sslip_v, &
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lattice_Stwin_v, &
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lattice_maxNslipFamily, &
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lattice_maxNtwinFamily, &
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lattice_NslipSystem, &
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lattice_NtwinSystem, &
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lattice_NnonSchmid
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implicit none
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real(pReal), dimension(6), intent(in) :: &
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Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
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integer(pInt), intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element !< microstructure state
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real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: &
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plastic_phenopowerlaw_postResults
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integer(pInt) :: &
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instance,ph, of, &
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nSlip,nTwin, &
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o,f,i,c,j,k, &
|
|
index_myFamily
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real(pReal) :: &
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tau_slip_pos,tau_slip_neg,tau
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|
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of = phasememberAt(ipc,ip,el)
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ph = phaseAt(ipc,ip,el)
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instance = phase_plasticityInstance(ph)
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nSlip= sum(param(instance)%nslip)
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nTwin= sum(param(instance)%nTwin)
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plastic_phenopowerlaw_postResults = 0.0_pReal
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c = 0_pInt
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outputsLoop: do o = 1_pInt,size(param(instance)%outputID)
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select case(param(instance)%outputID(o))
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case (resistance_slip_ID)
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plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = state(instance)%s_slip(1:nSlip,of)
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c = c + nSlip
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case (accumulatedshear_slip_ID)
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plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = state(instance)%accshear_slip(1:nSlip,of)
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c = c + nSlip
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case (shearrate_slip_ID)
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j = 0_pInt
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slipFamilies1: do f = 1_pInt,size(param(instance)%Nslip,1)
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index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
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slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
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j = j + 1_pInt
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tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
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tau_slip_neg = tau_slip_pos
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do k = 1,lattice_NnonSchmid(ph)
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tau_slip_pos = tau_slip_pos +param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
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tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
|
|
enddo
|
|
plastic_phenopowerlaw_postResults(c+j) = param(instance)%gdot0_slip*0.5_pReal* &
|
|
((abs(tau_slip_pos)/state(instance)%s_slip(j,of))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_slip_pos) &
|
|
+(abs(tau_slip_neg)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
|
|
*sign(1.0_pReal,tau_slip_neg))
|
|
enddo slipSystems1
|
|
enddo slipFamilies1
|
|
c = c + nSlip
|
|
|
|
case (resolvedstress_slip_ID)
|
|
j = 0_pInt
|
|
slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
|
|
j = j + 1_pInt
|
|
plastic_phenopowerlaw_postResults(c+j) = &
|
|
dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
|
|
enddo slipSystems2
|
|
enddo slipFamilies2
|
|
c = c + nSlip
|
|
|
|
case (totalshear_ID)
|
|
plastic_phenopowerlaw_postResults(c+1_pInt) = &
|
|
state(instance)%sumGamma(of)
|
|
c = c + 1_pInt
|
|
|
|
case (resistance_twin_ID)
|
|
plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
|
|
state(instance)%s_twin(1:nTwin,of)
|
|
c = c + nTwin
|
|
|
|
case (accumulatedshear_twin_ID)
|
|
plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
|
|
state(instance)%accshear_twin(1:nTwin,of)
|
|
c = c + nTwin
|
|
case (shearrate_twin_ID)
|
|
j = 0_pInt
|
|
twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
|
|
j = j + 1_pInt
|
|
tau = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
|
|
plastic_phenopowerlaw_postResults(c+j) = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
|
|
param(instance)%gdot0_twin*&
|
|
(abs(tau)/state(instance)%s_twin(j,of))**&
|
|
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau))
|
|
enddo twinSystems1
|
|
enddo twinFamilies1
|
|
c = c + nTwin
|
|
|
|
case (resolvedstress_twin_ID)
|
|
j = 0_pInt
|
|
twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
|
twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
|
|
j = j + 1_pInt
|
|
plastic_phenopowerlaw_postResults(c+j) = &
|
|
dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
|
|
enddo twinSystems2
|
|
enddo twinFamilies2
|
|
c = c + nTwin
|
|
|
|
case (totalvolfrac_twin_ID)
|
|
plastic_phenopowerlaw_postResults(c+1_pInt) = state(instance)%sumF(of)
|
|
c = c + 1_pInt
|
|
|
|
end select
|
|
enddo outputsLoop
|
|
|
|
end function plastic_phenopowerlaw_postResults
|
|
|
|
end module plastic_phenopowerlaw
|