666 lines
35 KiB
Fortran
666 lines
35 KiB
Fortran
! Copyright 2011-13 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!--------------------------------------------------------------------------------------------------
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! $Id$
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!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief material subroutine for isotropic (J2) plasticity
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!> @details Isotropic (J2) Plasticity which resembles the phenopowerlaw plasticity without
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!! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an
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!! untextured polycrystal
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!--------------------------------------------------------------------------------------------------
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module constitutive_j2
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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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character (len=*), parameter, public :: &
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CONSTITUTIVE_J2_label = 'j2' !< label for this constitutive model
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integer(pInt), dimension(:), allocatable, public, protected :: &
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constitutive_j2_sizeDotState, & !< number of dotStates
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constitutive_j2_sizeState, & !< total number of microstructural variables
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constitutive_j2_sizePostResults !< cumulative size of post results
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integer(pInt), dimension(:,:), allocatable, target, public :: &
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constitutive_j2_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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constitutive_j2_output !< name of each post result output
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character(len=32), dimension(:), allocatable, private :: &
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constitutive_j2_structureName !< name of the lattice structure
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integer(pInt), dimension(:), allocatable, private :: &
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constitutive_j2_Noutput !< number of outputs per instance
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real(pReal), dimension(:), allocatable, private :: &
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constitutive_j2_fTaylor, & !< Taylor factor
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constitutive_j2_tau0, & !< initial plastic stress
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constitutive_j2_gdot0, & !< reference velocity
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constitutive_j2_n, & !< Visco-plastic parameter
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!--------------------------------------------------------------------------------------------------
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! h0 as function of h0 = A + B log (gammadot)
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constitutive_j2_h0, &
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constitutive_j2_h0_slopeLnRate, &
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constitutive_j2_tausat, & !< final plastic stress
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constitutive_j2_a, &
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constitutive_j2_aTolResistance, &
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!--------------------------------------------------------------------------------------------------
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! tausat += (asinh((gammadot / SinhFitA)**(1 / SinhFitD)))**(1 / SinhFitC) / (SinhFitB * (gammadot / gammadot0)**(1/n))
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constitutive_j2_tausat_SinhFitA, & !< fitting parameter for normalized strain rate vs. stress function
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constitutive_j2_tausat_SinhFitB, & !< fitting parameter for normalized strain rate vs. stress function
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constitutive_j2_tausat_SinhFitC, & !< fitting parameter for normalized strain rate vs. stress function
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constitutive_j2_tausat_SinhFitD !< fitting parameter for normalized strain rate vs. stress function
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real(pReal), dimension(:,:,:), allocatable, private :: &
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constitutive_j2_Cslip_66
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public :: &
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constitutive_j2_init, &
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constitutive_j2_stateInit, &
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constitutive_j2_aTolState, &
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constitutive_j2_homogenizedC, &
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constitutive_j2_microstructure, &
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constitutive_j2_LpAndItsTangent, &
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constitutive_j2_dotState, &
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constitutive_j2_deltaState, &
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constitutive_j2_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 constitutive_j2_init(myFile)
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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 math, only: &
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math_Mandel3333to66, &
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math_Voigt66to3333
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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_error, &
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IO_timeStamp
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use material
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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 lattice, only: &
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lattice_symmetrizeC66
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implicit none
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integer(pInt), intent(in) :: myFile
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integer(pInt), parameter :: MAXNCHUNKS = 7_pInt
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integer(pInt), dimension(1_pInt+2_pInt*MAXNCHUNKS) :: positions
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integer(pInt) :: section = 0_pInt, maxNinstance, i,o, mySize
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character(len=65536) :: &
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tag = '', &
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line = '' ! to start initialized
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write(6,'(/,a)') ' <<<+- constitutive_'//CONSTITUTIVE_J2_label//' init -+>>>'
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write(6,'(a)') ' $Id$'
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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 == CONSTITUTIVE_J2_label),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,'(a16,1x,i5,/)') '# instances:',maxNinstance
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allocate(constitutive_j2_sizeDotState(maxNinstance))
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constitutive_j2_sizeDotState = 0_pInt
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allocate(constitutive_j2_sizeState(maxNinstance))
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constitutive_j2_sizeState = 0_pInt
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allocate(constitutive_j2_sizePostResults(maxNinstance))
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constitutive_j2_sizePostResults = 0_pInt
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allocate(constitutive_j2_sizePostResult(maxval(phase_Noutput), maxNinstance))
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constitutive_j2_sizePostResult = 0_pInt
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allocate(constitutive_j2_output(maxval(phase_Noutput), maxNinstance))
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constitutive_j2_output = ''
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allocate(constitutive_j2_Noutput(maxNinstance))
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constitutive_j2_Noutput = 0_pInt
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allocate(constitutive_j2_structureName(maxNinstance))
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constitutive_j2_structureName = ''
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allocate(constitutive_j2_Cslip_66(6,6,maxNinstance))
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constitutive_j2_Cslip_66 = 0.0_pReal
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allocate(constitutive_j2_fTaylor(maxNinstance))
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constitutive_j2_fTaylor = 0.0_pReal
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allocate(constitutive_j2_tau0(maxNinstance))
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constitutive_j2_tau0 = 0.0_pReal
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allocate(constitutive_j2_gdot0(maxNinstance))
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constitutive_j2_gdot0 = 0.0_pReal
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allocate(constitutive_j2_n(maxNinstance))
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constitutive_j2_n = 0.0_pReal
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allocate(constitutive_j2_h0(maxNinstance))
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constitutive_j2_h0 = 0.0_pReal
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allocate(constitutive_j2_h0_slopeLnRate(maxNinstance))
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constitutive_j2_h0_slopeLnRate = 0.0_pReal
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allocate(constitutive_j2_tausat(maxNinstance))
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constitutive_j2_tausat = 0.0_pReal
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allocate(constitutive_j2_a(maxNinstance))
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constitutive_j2_a = 0.0_pReal
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allocate(constitutive_j2_aTolResistance(maxNinstance))
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constitutive_j2_aTolResistance = 0.0_pReal
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allocate(constitutive_j2_tausat_SinhFitA(maxNinstance))
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constitutive_j2_tausat_SinhFitA = 0.0_pReal
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allocate(constitutive_j2_tausat_SinhFitB(maxNinstance))
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constitutive_j2_tausat_SinhFitB = 0.0_pReal
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allocate(constitutive_j2_tausat_SinhFitC(maxNinstance))
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constitutive_j2_tausat_SinhFitC = 0.0_pReal
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allocate(constitutive_j2_tausat_SinhFitD(maxNinstance))
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constitutive_j2_tausat_SinhFitD = 0.0_pReal
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rewind(myFile)
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do while (trim(line) /= '#EOF#' .and. IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
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line = IO_read(myFile)
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enddo
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do while (trim(line) /= '#EOF#') ! read through sections of phase part
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line = IO_read(myFile)
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
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if (IO_getTag(line,'[',']') /= '') then ! next section
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section = section + 1_pInt ! advance section counter
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cycle ! skip to next line
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endif
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if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if-statement). It's not safe in Fortran
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if (trim(phase_plasticity(section)) == CONSTITUTIVE_J2_label) then ! one of my sections
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i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
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positions = IO_stringPos(line,MAXNCHUNKS)
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tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
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select case(tag)
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case ('plasticity','elasticity')
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cycle
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case ('(output)')
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constitutive_j2_Noutput(i) = constitutive_j2_Noutput(i) + 1_pInt
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constitutive_j2_output(constitutive_j2_Noutput(i),i) = &
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IO_lc(IO_stringValue(line,positions,2_pInt))
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case ('lattice_structure')
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constitutive_j2_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
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case ('c11')
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constitutive_j2_Cslip_66(1,1,i) = IO_floatValue(line,positions,2_pInt)
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case ('c12')
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constitutive_j2_Cslip_66(1,2,i) = IO_floatValue(line,positions,2_pInt)
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case ('c13')
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constitutive_j2_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt)
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case ('c22')
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constitutive_j2_Cslip_66(2,2,i) = IO_floatValue(line,positions,2_pInt)
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case ('c23')
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constitutive_j2_Cslip_66(2,3,i) = IO_floatValue(line,positions,2_pInt)
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case ('c33')
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constitutive_j2_Cslip_66(3,3,i) = IO_floatValue(line,positions,2_pInt)
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case ('c44')
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constitutive_j2_Cslip_66(4,4,i) = IO_floatValue(line,positions,2_pInt)
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case ('c55')
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constitutive_j2_Cslip_66(5,5,i) = IO_floatValue(line,positions,2_pInt)
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case ('c66')
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constitutive_j2_Cslip_66(6,6,i) = IO_floatValue(line,positions,2_pInt)
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case ('tau0')
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constitutive_j2_tau0(i) = IO_floatValue(line,positions,2_pInt)
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case ('gdot0')
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constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2_pInt)
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case ('n')
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constitutive_j2_n(i) = IO_floatValue(line,positions,2_pInt)
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case ('h0')
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constitutive_j2_h0(i) = IO_floatValue(line,positions,2_pInt)
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case ('h0_slope','slopelnrate')
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constitutive_j2_h0_slopeLnRate(i) = IO_floatValue(line,positions,2_pInt)
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case ('tausat')
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constitutive_j2_tausat(i) = IO_floatValue(line,positions,2_pInt)
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case ('tausat_sinhfita')
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constitutive_j2_tausat_SinhFitA(i) = IO_floatValue(line,positions,2_pInt)
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case ('tausat_sinhfitb')
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constitutive_j2_tausat_SinhFitB(i) = IO_floatValue(line,positions,2_pInt)
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case ('tausat_sinhfitc')
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constitutive_j2_tausat_SinhFitC(i) = IO_floatValue(line,positions,2_pInt)
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case ('tausat_sinhfitd')
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constitutive_j2_tausat_SinhFitD(i) = IO_floatValue(line,positions,2_pInt)
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case ('a', 'w0')
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constitutive_j2_a(i) = IO_floatValue(line,positions,2_pInt)
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case ('taylorfactor')
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constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2_pInt)
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case ('atol_resistance')
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constitutive_j2_aTolResistance(i) = IO_floatValue(line,positions,2_pInt)
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case default
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call IO_error(210_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_J2_label//')')
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end select
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endif
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endif
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enddo
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sanityChecks: do i = 1_pInt,maxNinstance
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if (constitutive_j2_structureName(i) == '') call IO_error(205_pInt,el=i)
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if (constitutive_j2_tau0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='tau0 (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='gdot0 (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='n (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_tausat(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='tausat (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_a(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='a (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='taylorfactor (' &
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//CONSTITUTIVE_J2_label//')')
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if (constitutive_j2_aTolResistance(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_resistance (' &
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//CONSTITUTIVE_J2_label//')')
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enddo sanityChecks
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instancesLoop: do i = 1_pInt,maxNinstance
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outputsLoop: do o = 1_pInt,constitutive_j2_Noutput(i)
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select case(constitutive_j2_output(o,i))
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case('flowstress')
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mySize = 1_pInt
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case('strainrate')
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mySize = 1_pInt
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case default
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call IO_error(212_pInt,ext_msg=constitutive_j2_output(o,i)//' ('//CONSTITUTIVE_J2_label//')')
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end select
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if (mySize > 0_pInt) then ! any meaningful output found
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constitutive_j2_sizePostResult(o,i) = mySize
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constitutive_j2_sizePostResults(i) = &
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constitutive_j2_sizePostResults(i) + mySize
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endif
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enddo outputsLoop
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constitutive_j2_sizeDotState(i) = 1_pInt
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constitutive_j2_sizeState(i) = 1_pInt
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constitutive_j2_Cslip_66(1:6,1:6,i) = lattice_symmetrizeC66(constitutive_j2_structureName(i),&
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constitutive_j2_Cslip_66(1:6,1:6,i))
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constitutive_j2_Cslip_66(1:6,1:6,i) = &
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math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(1:6,1:6,i))) ! Literature data is Voigt, DAMASK uses Mandel
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enddo instancesLoop
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end subroutine constitutive_j2_init
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!--------------------------------------------------------------------------------------------------
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!> @brief sets the initial microstructural state for a given instance of this plasticity
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!> @details initial microstructural state is set to the value specified by tau0
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_stateInit(matID)
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implicit none
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real(pReal), dimension(1) :: constitutive_j2_stateInit
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integer(pInt), intent(in) :: matID !< number specifying the instance of the plasticity
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constitutive_j2_stateInit = constitutive_j2_tau0(matID)
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end function constitutive_j2_stateInit
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!--------------------------------------------------------------------------------------------------
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!> @brief sets the relevant state values for a given instance of this plasticity
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_aTolState(matID)
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implicit none
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integer(pInt), intent(in) :: matID !< number specifying the instance of the plasticity
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real(pReal), dimension(constitutive_j2_sizeState(matID)) :: &
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constitutive_j2_aTolState
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constitutive_j2_aTolState = constitutive_j2_aTolResistance(matID)
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end function constitutive_j2_aTolState
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!--------------------------------------------------------------------------------------------------
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!> @brief returns the homogenized elasticity matrix
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_homogenizedC(state,ipc,ip,el)
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use prec, only: &
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p_vec
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains,&
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material_phase, &
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phase_plasticityInstance
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implicit none
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real(pReal), dimension(6,6) :: &
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constitutive_j2_homogenizedC
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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
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(1:6,1:6,&
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phase_plasticityInstance(material_phase(ipc,ip,el)))
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end function constitutive_j2_homogenizedC
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates derived quantities from state
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!> @details dummy subroutine, does nothing
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!--------------------------------------------------------------------------------------------------
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pure subroutine constitutive_j2_microstructure(temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains
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implicit none
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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
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real(pReal), intent(in) :: &
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temperature !< temperature at IP
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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end subroutine constitutive_j2_microstructure
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates plastic velocity gradient and its tangent
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!--------------------------------------------------------------------------------------------------
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pure subroutine constitutive_j2_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,&
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temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec
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use math, only: &
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math_mul6x6, &
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math_Mandel6to33, &
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math_Plain3333to99, &
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math_deviatoric33, &
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math_mul33xx33
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance
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implicit none
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(9,9), intent(out) :: &
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dLp_dTstar99 !< derivative of Lp with respect to 2nd Piola Kirchhoff stress
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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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real(pReal), intent(in) :: &
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temperature !< temperature at IP
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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
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(3,3) :: &
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Tstar_dev_33 !< deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
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real(pReal), dimension(3,3,3,3) :: &
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dLp_dTstar_3333 !< derivative of Lp with respect to Tstar as 4th order tensor
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real(pReal) :: &
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gamma_dot, & !< strainrate
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norm_Tstar_dev, & !< euclidean norm of Tstar_dev
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squarenorm_Tstar_dev !< square of the euclidean norm of Tstar_dev
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integer(pInt) :: &
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matID, &
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k, l, m, n
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matID = phase_plasticityInstance(material_phase(ipc,ip,el))
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Tstar_dev_33 = math_deviatoric33(math_Mandel6to33(Tstar_v)) ! deviatoric part of 2nd Piola-Kirchhoff stress
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squarenorm_Tstar_dev = math_mul33xx33(Tstar_dev_33,Tstar_dev_33)
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norm_Tstar_dev = sqrt(squarenorm_Tstar_dev)
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if (norm_Tstar_dev <= 0.0_pReal) then ! Tstar == 0 --> both Lp and dLp_dTstar are zero
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Lp = 0.0_pReal
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dLp_dTstar99 = 0.0_pReal
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else
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gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
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/ &!----------------------------------------------------------------------------------
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(constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) **constitutive_j2_n(matID)
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Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID)
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!--------------------------------------------------------------------------------------------------
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! Calculation of the tangent of Lp
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forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
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dLp_dTstar_3333(k,l,m,n) = (constitutive_j2_n(matID)-1.0_pReal) * &
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Tstar_dev_33(k,l)*Tstar_dev_33(m,n) / squarenorm_Tstar_dev
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forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
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dLp_dTstar_3333(k,l,k,l) = dLp_dTstar_3333(k,l,k,l) + 1.0_pReal
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dLp_dTstar99 = math_Plain3333to99(gamma_dot / constitutive_j2_fTaylor(matID) * &
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dLp_dTstar_3333 / norm_Tstar_dev)
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end if
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end subroutine constitutive_j2_LpAndItsTangent
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates the rate of change of microstructure
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_dotState(Tstar_v,temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec
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use math, only: &
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math_mul6x6
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance
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implicit none
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real(pReal), dimension(1) :: &
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constitutive_j2_dotState
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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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real(pReal), intent(in) :: &
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temperature !< temperature at integration point
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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
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(6) :: &
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Tstar_dev_v !< deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
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real(pReal) :: &
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gamma_dot, & !< strainrate
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hardening, & !< hardening coefficient
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saturation, & !< saturation resistance
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norm_Tstar_dev !< euclidean norm of Tstar_dev
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integer(pInt) :: &
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matID
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matID = phase_plasticityInstance(material_phase(ipc,ip,el))
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!--------------------------------------------------------------------------------------------------
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! norm of deviatoric part of 2nd Piola-Kirchhoff stress
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Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal
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Tstar_dev_v(4:6) = Tstar_v(4:6)
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norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
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!--------------------------------------------------------------------------------------------------
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! strain rate
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gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
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/ &!-----------------------------------------------------------------------------------
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(constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
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!--------------------------------------------------------------------------------------------------
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! hardening coefficient
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if (abs(gamma_dot) > 1e-12_pReal) then
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if (constitutive_j2_tausat_SinhFitA(matID) == 0.0_pReal) then
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saturation = constitutive_j2_tausat(matID)
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else
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saturation = ( constitutive_j2_tausat(matID) &
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+ ( log( ( gamma_dot / constitutive_j2_tausat_SinhFitA(matID)&
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)**(1.0_pReal / constitutive_j2_tausat_SinhFitD(matID))&
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+ sqrt( ( gamma_dot / constitutive_j2_tausat_SinhFitA(matID) &
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)**(2.0_pReal / constitutive_j2_tausat_SinhFitD(matID)) &
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+ 1.0_pReal ) &
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) & ! asinh(K) = ln(K + sqrt(K^2 +1))
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)**(1.0_pReal / constitutive_j2_tausat_SinhFitC(matID)) &
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/ ( constitutive_j2_tausat_SinhFitB(matID) &
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* (gamma_dot / constitutive_j2_gdot0(matID))**(1.0_pReal / constitutive_j2_n(matID)) &
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) &
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)
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endif
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hardening = ( constitutive_j2_h0(matID) + constitutive_j2_h0_slopeLnRate(matID) * log(gamma_dot) ) &
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* abs( 1.0_pReal - state(ipc,ip,el)%p(1)/saturation )**constitutive_j2_a(matID) &
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* sign(1.0_pReal, 1.0_pReal - state(ipc,ip,el)%p(1)/saturation)
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else
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hardening = 0.0_pReal
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endif
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constitutive_j2_dotState = hardening * gamma_dot
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end function constitutive_j2_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief (instantaneous) incremental change of microstructure
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!> @details dummy function, returns 0.0
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_deltaState(Tstar_v,temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance
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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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real(pReal), intent(in) :: &
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Temperature !< temperature at integration point
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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
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(constitutive_j2_sizeDotState(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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constitutive_j2_deltaState
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constitutive_j2_deltaState = 0.0_pReal
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end function constitutive_j2_deltaState
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!--------------------------------------------------------------------------------------------------
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!> @brief return array of constitutive results
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_j2_postResults(Tstar_v,temperature,dt,state,ipc,ip,el)
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use prec, only: &
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p_vec
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use math, only: &
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math_mul6x6
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance, &
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phase_Noutput
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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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real(pReal), intent(in) :: &
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temperature, & !< temperature at integration point
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dt
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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
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(constitutive_j2_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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constitutive_j2_postResults
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real(pReal), dimension(6) :: &
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Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
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real(pReal) :: &
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norm_Tstar_dev ! euclidean norm of Tstar_dev
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integer(pInt) :: &
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matID, &
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o, &
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c
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matID = phase_plasticityInstance(material_phase(ipc,ip,el))
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!--------------------------------------------------------------------------------------------------
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! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm
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Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal
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Tstar_dev_v(4:6) = Tstar_v(4:6)
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norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
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c = 0_pInt
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constitutive_j2_postResults = 0.0_pReal
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outputsLoop: do o = 1_pInt,phase_Noutput(material_phase(ipc,ip,el))
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select case(constitutive_j2_output(o,matID))
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case ('flowstress')
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constitutive_j2_postResults(c+1_pInt) = state(ipc,ip,el)%p(1)
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c = c + 1_pInt
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case ('strainrate')
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constitutive_j2_postResults(c+1_pInt) = &
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constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
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/ &!----------------------------------------------------------------------------------
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(constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
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c = c + 1_pInt
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end select
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enddo outputsLoop
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end function constitutive_j2_postResults
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end module constitutive_j2
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