DAMASK_EICMD/code/constitutive_nonlocal.f90

3750 lines
187 KiB
Fortran

! Copyright 2011-13 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##############################################################
!* $Id$
!************************************
!* Module: CONSTITUTIVE_NONLOCAL *
!************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!************************************
MODULE constitutive_nonlocal
!* Include other modules
use prec, only: &
pReal, &
pInt, &
p_vec
implicit none
private
!* Definition of parameters
character (len=*), parameter, public :: &
CONSTITUTIVE_NONLOCAL_LABEL = 'nonlocal'
character(len=22), dimension(11), parameter, private :: &
BASICSTATES = (/'rhoSglEdgePosMobile ', &
'rhoSglEdgeNegMobile ', &
'rhoSglScrewPosMobile ', &
'rhoSglScrewNegMobile ', &
'rhoSglEdgePosImmobile ', &
'rhoSglEdgeNegImmobile ', &
'rhoSglScrewPosImmobile', &
'rhoSglScrewNegImmobile', &
'rhoDipEdge ', &
'rhoDipScrew ', &
'accumulatedshear ' /) !< list of "basic" microstructural state variables that are independent from other state variables
character(len=16), dimension(3), parameter, private :: &
DEPENDENTSTATES = (/'rhoForest ', &
'tauThreshold ', &
'tauBack ' /) !< list of microstructural state variables that depend on other state variables
character(len=20), dimension(6), parameter, private :: &
OTHERSTATES = (/'velocityEdgePos ', &
'velocityEdgeNeg ', &
'velocityScrewPos ', &
'velocityScrewNeg ', &
'maxDipoleHeightEdge ', &
'maxDipoleHeightScrew' /) !< list of other dependent state variables that are not updated by microstructure
real(pReal), parameter, private :: &
KB = 1.38e-23_pReal !< Physical parameter, Boltzmann constant in J/Kelvin
!* Definition of global variables
integer(pInt), dimension(:), allocatable, public :: &
constitutive_nonlocal_sizeDotState, & !< number of dotStates = number of basic state variables
constitutive_nonlocal_sizeDependentState, & !< number of dependent state variables
constitutive_nonlocal_sizeState, & !< total number of state variables
constitutive_nonlocal_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
constitutive_nonlocal_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
constitutive_nonlocal_output !< name of each post result output
integer(pInt), dimension(:), allocatable, private :: &
Noutput !< number of outputs per instance of this plasticity
integer(pInt), dimension(:,:), allocatable, private :: &
iGamma, & !< state indices for accumulated shear
iRhoF, & !< state indices for forest density
iTauF, & !< state indices for critical resolved shear stress
iTauB !< state indices for backstress
integer(pInt), dimension(:,:,:), allocatable, private :: &
iRhoU, & !< state indices for unblocked density
iRhoB, & !< state indices for blocked density
iRhoD, & !< state indices for dipole density
iV, & !< state indices for dislcation velocities
iD !< state indices for stable dipole height
character(len=32), dimension(:), allocatable, public :: &
constitutive_nonlocal_structureName !< name of the lattice structure
integer(pInt), dimension(:), allocatable, public :: &
constitutive_nonlocal_structure !< number representing the kind of lattice structure
integer(pInt), dimension(:), allocatable, private :: &
totalNslip !< total number of active slip systems for each instance
integer(pInt), dimension(:,:), allocatable, private :: &
Nslip, & !< number of active slip systems for each family and instance
slipFamily, & !< lookup table relating active slip system to slip family for each instance
slipSystemLattice, & !< lookup table relating active slip system index to lattice slip system index for each instance
colinearSystem !< colinear system to the active slip system (only valid for fcc!)
real(pReal), dimension(:), allocatable, private :: &
CoverA, & !< c/a ratio for hex type lattice
mu, & !< shear modulus
nu, & !< poisson's ratio
atomicVolume, & !< atomic volume
Dsd0, & !< prefactor for self-diffusion coefficient
selfDiffusionEnergy, & !< activation enthalpy for diffusion
aTolRho, & !< absolute tolerance for dislocation density in state integration
aTolShear, & !< absolute tolerance for accumulated shear in state integration
significantRho, & !< density considered significant
significantN, & !< number of dislocations considered significant
cutoffRadius, & !< cutoff radius for dislocation stress
doublekinkwidth, & !< width of a doubkle kink in multiples of the burgers vector length b
solidSolutionEnergy, & !< activation energy for solid solution in J
solidSolutionSize, & !< solid solution obstacle size in multiples of the burgers vector length
solidSolutionConcentration, & !< concentration of solid solution in atomic parts
pParam, & !< parameter for kinetic law (Kocks,Argon,Ashby)
qParam, & !< parameter for kinetic law (Kocks,Argon,Ashby)
viscosity, & !< viscosity for dislocation glide in Pa s
fattack, & !< attack frequency in Hz
rhoSglScatter, & !< standard deviation of scatter in initial dislocation density
surfaceTransmissivity, & !< transmissivity at free surface
grainboundaryTransmissivity, & !< transmissivity at grain boundary (identified by different texture)
CFLfactor, & !< safety factor for CFL flux condition
fEdgeMultiplication, & !< factor that determines how much edge dislocations contribute to multiplication (0...1)
rhoSglRandom, &
rhoSglRandomBinning, &
linetensionEffect, &
edgeJogFactor
real(pReal), dimension(:,:), allocatable, private :: &
rhoSglEdgePos0, & !< initial edge_pos dislocation density per slip system for each family and instance
rhoSglEdgeNeg0, & !< initial edge_neg dislocation density per slip system for each family and instance
rhoSglScrewPos0, & !< initial screw_pos dislocation density per slip system for each family and instance
rhoSglScrewNeg0, & !< initial screw_neg dislocation density per slip system for each family and instance
rhoDipEdge0, & !< initial edge dipole dislocation density per slip system for each family and instance
rhoDipScrew0, & !< initial screw dipole dislocation density per slip system for each family and instance
lambda0PerSlipFamily, & !< mean free path prefactor for each family and instance
lambda0, & !< mean free path prefactor for each slip system and instance
burgersPerSlipFamily, & !< absolute length of burgers vector [m] for each family and instance
burgers, & !< absolute length of burgers vector [m] for each slip system and instance
interactionSlipSlip !< coefficients for slip-slip interaction for each interaction type and instance
real(pReal), dimension(:,:,:), allocatable, private :: &
Cslip66, & !< elasticity matrix in Mandel notation for each instance
minDipoleHeightPerSlipFamily, & !< minimum stable edge/screw dipole height for each family and instance
minDipoleHeight, & !< minimum stable edge/screw dipole height for each slip system and instance
peierlsStressPerSlipFamily, & !< Peierls stress (edge and screw)
peierlsStress, & !< Peierls stress (edge and screw)
forestProjectionEdge, & !< matrix of forest projections of edge dislocations for each instance
forestProjectionScrew, & !< matrix of forest projections of screw dislocations for each instance
interactionMatrixSlipSlip !< interaction matrix of the different slip systems for each instance
real(pReal), dimension(:,:,:,:), allocatable, private :: &
lattice2slip, & !< orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!)
rhoDotEdgeJogsOutput, &
sourceProbability
real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
Cslip3333, & !< elasticity matrix for each instance
rhoDotFluxOutput, &
rhoDotMultiplicationOutput, &
rhoDotSingle2DipoleGlideOutput, &
rhoDotAthermalAnnihilationOutput, &
rhoDotThermalAnnihilationOutput
real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: &
compatibility !< slip system compatibility between me and my neighbors
real(pReal), dimension(:,:), allocatable, private :: &
nonSchmidCoeff
logical, dimension(:), allocatable, private :: &
shortRangeStressCorrection, & !< flag indicating the use of the short range stress correction by a excess density gradient term
deadZoneScaling, &
probabilisticMultiplication
public :: &
constitutive_nonlocal_init, &
constitutive_nonlocal_stateInit, &
constitutive_nonlocal_aTolState, &
constitutive_nonlocal_homogenizedC, &
constitutive_nonlocal_microstructure, &
constitutive_nonlocal_LpAndItsTangent, &
constitutive_nonlocal_dotState, &
constitutive_nonlocal_deltaState, &
constitutive_nonlocal_dotTemperature, &
constitutive_nonlocal_updateCompatibility, &
constitutive_nonlocal_postResults
private :: &
constitutive_nonlocal_kinetics, &
constitutive_nonlocal_dislocationstress
CONTAINS
!**************************************
!* Module initialization *
!**************************************
subroutine constitutive_nonlocal_init(myFile)
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use math, only: math_Mandel3333to66, &
math_Voigt66to3333, &
math_mul3x3, &
math_transpose33
use IO, only: IO_read, &
IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_intValue, &
IO_error, &
IO_timeStamp
use debug, only: debug_level, &
debug_constitutive, &
debug_levelBasic
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_maxNipNeighbors
use material, only: homogenization_maxNgrains, &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput
use lattice
!*** output variables
!*** input variables
integer(pInt), intent(in) :: myFile
!*** local variables
integer(pInt), parameter :: maxNchunks = 21_pInt
integer(pInt), &
dimension(1_pInt+2_pInt*maxNchunks) :: positions
integer(pInt), dimension(6) :: configNchunks
integer(pInt) :: section = 0_pInt, &
maxNinstance, &
maxTotalNslip, &
myStructure, &
f, & ! index of my slip family
i, & ! index of my instance of this plasticity
l, &
ns, & ! short notation for total number of active slip systems for the current instance
o, & ! index of my output
s, & ! index of my slip system
s1, & ! index of my slip system
s2, & ! index of my slip system
it, & ! index of my interaction type
t, & ! index of dislocation type
c, & ! index of dislocation character
Nchunks_SlipSlip = 0_pInt, &
Nchunks_SlipFamilies = 0_pInt, &
mySize = 0_pInt ! to suppress warnings, safe as init is called only once
character(len=65536) tag
character(len=65536) :: line = '' ! to start initialized
write(6,*)
write(6,*) '<<<+- constitutive_',trim(CONSTITUTIVE_NONLOCAL_LABEL),' init -+>>>'
write(6,*) '$Id$'
write(6,'(a16,a)') ' Current time : ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == CONSTITUTIVE_NONLOCAL_LABEL),pInt)
if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) then
write(6,'(a16,1x,i5)') '# instances:',maxNinstance
write(6,*)
endif
!*** memory allocation for global variables
allocate(constitutive_nonlocal_sizeDotState(maxNinstance))
allocate(constitutive_nonlocal_sizeDependentState(maxNinstance))
allocate(constitutive_nonlocal_sizeState(maxNinstance))
allocate(constitutive_nonlocal_sizePostResults(maxNinstance))
allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance))
allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance))
allocate(Noutput(maxNinstance))
constitutive_nonlocal_sizeDotState = 0_pInt
constitutive_nonlocal_sizeDependentState = 0_pInt
constitutive_nonlocal_sizeState = 0_pInt
constitutive_nonlocal_sizePostResults = 0_pInt
constitutive_nonlocal_sizePostResult = 0_pInt
constitutive_nonlocal_output = ''
Noutput = 0_pInt
allocate(constitutive_nonlocal_structureName(maxNinstance))
allocate(constitutive_nonlocal_structure(maxNinstance))
allocate(Nslip(lattice_maxNslipFamily, maxNinstance))
allocate(slipFamily(lattice_maxNslip, maxNinstance))
allocate(slipSystemLattice(lattice_maxNslip, maxNinstance))
allocate(totalNslip(maxNinstance))
constitutive_nonlocal_structureName = ''
constitutive_nonlocal_structure = 0_pInt
Nslip = 0_pInt
slipFamily = 0_pInt
slipSystemLattice = 0_pInt
totalNslip = 0_pInt
allocate(CoverA(maxNinstance))
allocate(mu(maxNinstance))
allocate(nu(maxNinstance))
allocate(atomicVolume(maxNinstance))
allocate(Dsd0(maxNinstance))
allocate(selfDiffusionEnergy(maxNinstance))
allocate(aTolRho(maxNinstance))
allocate(aTolShear(maxNinstance))
allocate(significantRho(maxNinstance))
allocate(significantN(maxNinstance))
allocate(Cslip66(6,6,maxNinstance))
allocate(Cslip3333(3,3,3,3,maxNinstance))
allocate(cutoffRadius(maxNinstance))
allocate(doublekinkwidth(maxNinstance))
allocate(solidSolutionEnergy(maxNinstance))
allocate(solidSolutionSize(maxNinstance))
allocate(solidSolutionConcentration(maxNinstance))
allocate(pParam(maxNinstance))
allocate(qParam(maxNinstance))
allocate(viscosity(maxNinstance))
allocate(fattack(maxNinstance))
allocate(rhoSglScatter(maxNinstance))
allocate(rhoSglRandom(maxNinstance))
allocate(rhoSglRandomBinning(maxNinstance))
allocate(surfaceTransmissivity(maxNinstance))
allocate(grainboundaryTransmissivity(maxNinstance))
allocate(shortRangeStressCorrection(maxNinstance))
allocate(deadZoneScaling(maxNinstance))
allocate(probabilisticMultiplication(maxNinstance))
allocate(CFLfactor(maxNinstance))
allocate(fEdgeMultiplication(maxNinstance))
allocate(linetensionEffect(maxNinstance))
allocate(edgeJogFactor(maxNinstance))
CoverA = 0.0_pReal
mu = 0.0_pReal
atomicVolume = 0.0_pReal
Dsd0 = -1.0_pReal
selfDiffusionEnergy = 0.0_pReal
aTolRho = 0.0_pReal
aTolShear = 0.0_pReal
significantRho = 0.0_pReal
significantN = 0.0_pReal
nu = 0.0_pReal
Cslip66 = 0.0_pReal
Cslip3333 = 0.0_pReal
cutoffRadius = -1.0_pReal
doublekinkwidth = 0.0_pReal
solidSolutionEnergy = 0.0_pReal
solidSolutionSize = 0.0_pReal
solidSolutionConcentration = 0.0_pReal
pParam = 1.0_pReal
qParam = 1.0_pReal
viscosity = 0.0_pReal
fattack = 0.0_pReal
rhoSglScatter = 0.0_pReal
rhoSglRandom = 0.0_pReal
rhoSglRandomBinning = 1.0_pReal
surfaceTransmissivity = 1.0_pReal
grainboundaryTransmissivity = -1.0_pReal
CFLfactor = 2.0_pReal
fEdgeMultiplication = 0.0_pReal
linetensionEffect = 0.0_pReal
edgeJogFactor = 1.0_pReal
shortRangeStressCorrection = .false.
deadZoneScaling = .false.
probabilisticMultiplication = .false.
allocate(rhoSglEdgePos0(lattice_maxNslipFamily,maxNinstance))
allocate(rhoSglEdgeNeg0(lattice_maxNslipFamily,maxNinstance))
allocate(rhoSglScrewPos0(lattice_maxNslipFamily,maxNinstance))
allocate(rhoSglScrewNeg0(lattice_maxNslipFamily,maxNinstance))
allocate(rhoDipEdge0(lattice_maxNslipFamily,maxNinstance))
allocate(rhoDipScrew0(lattice_maxNslipFamily,maxNinstance))
allocate(burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
allocate(lambda0PerSlipFamily(lattice_maxNslipFamily,maxNinstance))
allocate(interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
rhoSglEdgePos0 = -1.0_pReal
rhoSglEdgeNeg0 = -1.0_pReal
rhoSglScrewPos0 = -1.0_pReal
rhoSglScrewNeg0 = -1.0_pReal
rhoDipEdge0 = -1.0_pReal
rhoDipScrew0 = -1.0_pReal
burgersPerSlipFamily = 0.0_pReal
lambda0PerSlipFamily = 0.0_pReal
interactionSlipSlip = 0.0_pReal
allocate(minDipoleHeightPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance))
allocate(peierlsStressPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance))
minDipoleHeightPerSlipFamily = -1.0_pReal
peierlsStressPerSlipFamily = 0.0_pReal
allocate(nonSchmidCoeff(lattice_maxNonSchmid,maxNinstance))
nonSchmidCoeff = 0.0_pReal
!*** readout data from material.config file
rewind(myFile)
do while (trim(line) /= '#EOF#' .and. IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
line = IO_read(myFile)
enddo
do while (trim(line) /= '#EOF#') ! read thru sections of phase part
line = IO_read(myFile)
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1_pInt ! advance section counter
cycle
endif
if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if statemen). It's not safe in Fortran
if (phase_plasticity(section) == CONSTITUTIVE_NONLOCAL_LABEL) then ! one of my sections
i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case('plasticity','elasticity','/nonlocal/')
cycle
case ('(output)')
Noutput(i) = Noutput(i) + 1_pInt
constitutive_nonlocal_output(Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('lattice_structure')
constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
configNchunks = lattice_configNchunks(constitutive_nonlocal_structureName(i))
Nchunks_SlipFamilies = configNchunks(1)
Nchunks_SlipSlip = configNchunks(3)
case ('c/a_ratio','covera_ratio')
CoverA(i) = IO_floatValue(line,positions,2_pInt)
case ('c11')
Cslip66(1,1,i) = IO_floatValue(line,positions,2_pInt)
case ('c12')
Cslip66(1,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c13')
Cslip66(1,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c22')
Cslip66(2,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c23')
Cslip66(2,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c33')
Cslip66(3,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c44')
Cslip66(4,4,i) = IO_floatValue(line,positions,2_pInt)
case ('c55')
Cslip66(5,5,i) = IO_floatValue(line,positions,2_pInt)
case ('c66')
Cslip66(6,6,i) = IO_floatValue(line,positions,2_pInt)
case ('nslip')
do f = 1_pInt, Nchunks_SlipFamilies
Nslip(f,i) = IO_intValue(line,positions,1_pInt+f)
enddo
case ('rhosgledgepos0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoSglEdgePos0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('rhosgledgeneg0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoSglEdgeNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('rhosglscrewpos0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoSglScrewPos0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('rhosglscrewneg0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoSglScrewNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('rhodipedge0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoDipEdge0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('rhodipscrew0')
do f = 1_pInt, Nchunks_SlipFamilies
rhoDipScrew0(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('lambda0')
do f = 1_pInt, Nchunks_SlipFamilies
lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case ('burgers')
do f = 1_pInt, Nchunks_SlipFamilies
burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('cutoffradius','r')
cutoffRadius(i) = IO_floatValue(line,positions,2_pInt)
case('minimumdipoleheightedge','ddipminedge')
do f = 1_pInt, Nchunks_SlipFamilies
minDipoleHeightPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('minimumdipoleheightscrew','ddipminscrew')
do f = 1_pInt, Nchunks_SlipFamilies
minDipoleHeightPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('atomicvolume')
atomicVolume(i) = IO_floatValue(line,positions,2_pInt)
case('selfdiffusionprefactor','dsd0')
Dsd0(i) = IO_floatValue(line,positions,2_pInt)
case('selfdiffusionenergy','qsd')
selfDiffusionEnergy(i) = IO_floatValue(line,positions,2_pInt)
case('atol_rho','atol_density','absolutetolerancedensity','absolutetolerance_density')
aTolRho(i) = IO_floatValue(line,positions,2_pInt)
case('atol_shear','atol_plasticshear','atol_accumulatedshear','absolutetoleranceshear','absolutetolerance_shear')
aTolShear(i) = IO_floatValue(line,positions,2_pInt)
case('significantrho','significant_rho','significantdensity','significant_density')
significantRho(i) = IO_floatValue(line,positions,2_pInt)
case('significantn','significant_n','significantdislocations','significant_dislcations')
significantN(i) = IO_floatValue(line,positions,2_pInt)
case ('interaction_slipslip')
do it = 1_pInt, Nchunks_SlipSlip
interactionSlipSlip(it,i) = IO_floatValue(line,positions,1_pInt+it)
enddo
case('linetension','linetensioneffect','linetension_effect')
linetensionEffect(i) = IO_floatValue(line,positions,2_pInt)
case('edgejog','edgejogs','edgejogeffect','edgejog_effect')
edgeJogFactor(i) = IO_floatValue(line,positions,2_pInt)
case('peierlsstressedge','peierlsstress_edge')
do f = 1_pInt, Nchunks_SlipFamilies
peierlsStressPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('peierlsstressscrew','peierlsstress_screw')
do f = 1_pInt, Nchunks_SlipFamilies
peierlsStressPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('doublekinkwidth')
doublekinkwidth(i) = IO_floatValue(line,positions,2_pInt)
case('solidsolutionenergy')
solidSolutionEnergy(i) = IO_floatValue(line,positions,2_pInt)
case('solidsolutionsize')
solidSolutionSize(i) = IO_floatValue(line,positions,2_pInt)
case('solidsolutionconcentration')
solidSolutionConcentration(i) = IO_floatValue(line,positions,2_pInt)
case('p')
pParam(i) = IO_floatValue(line,positions,2_pInt)
case('q')
qParam(i) = IO_floatValue(line,positions,2_pInt)
case('viscosity','glideviscosity')
viscosity(i) = IO_floatValue(line,positions,2_pInt)
case('attackfrequency','fattack')
fattack(i) = IO_floatValue(line,positions,2_pInt)
case('rhosglscatter')
rhoSglScatter(i) = IO_floatValue(line,positions,2_pInt)
case('rhosglrandom')
rhoSglRandom(i) = IO_floatValue(line,positions,2_pInt)
case('rhosglrandombinning')
rhoSglRandomBinning(i) = IO_floatValue(line,positions,2_pInt)
case('surfacetransmissivity')
surfaceTransmissivity(i) = IO_floatValue(line,positions,2_pInt)
case('grainboundarytransmissivity')
grainboundaryTransmissivity(i) = IO_floatValue(line,positions,2_pInt)
case('cflfactor')
CFLfactor(i) = IO_floatValue(line,positions,2_pInt)
case('fedgemultiplication','edgemultiplicationfactor','edgemultiplication')
fEdgeMultiplication(i) = IO_floatValue(line,positions,2_pInt)
case('shortrangestresscorrection')
shortRangeStressCorrection(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
case ('nonschmid_coefficients')
do f = 1_pInt, lattice_maxNonSchmid
nonSchmidCoeff(f,i) = IO_floatValue(line,positions,1_pInt+f)
enddo
case('deadzonescaling','deadzone','deadscaling')
deadZoneScaling(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
case('probabilisticmultiplication','randomsources','randommultiplication','discretesources')
probabilisticMultiplication(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
case default
call IO_error(210_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
end select
endif
endif
enddo
do i = 1_pInt,maxNinstance
constitutive_nonlocal_structure(i) = &
lattice_initializeStructure(constitutive_nonlocal_structureName(i), CoverA(i)) ! our lattice structure is defined in the material.config file by the structureName (and the c/a ratio)
myStructure = constitutive_nonlocal_structure(i)
!*** sanity checks
if (myStructure < 1_pInt) &
call IO_error(205_pInt,e=i)
if (sum(Nslip(:,i)) <= 0_pInt) &
call IO_error(211_pInt,ext_msg='Nslip ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
do o = 1_pInt,maxval(phase_Noutput)
if(len(constitutive_nonlocal_output(o,i)) > 64_pInt) &
call IO_error(666_pInt)
enddo
do f = 1_pInt,lattice_maxNslipFamily
if (Nslip(f,i) > 0_pInt) then
if (rhoSglEdgePos0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglEdgePos0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglEdgeNeg0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglEdgeNeg0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglScrewPos0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglScrewPos0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglScrewNeg0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglScrewNeg0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoDipEdge0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoDipEdge0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoDipScrew0(f,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoDipScrew0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (burgersPerSlipFamily(f,i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='Burgers ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (lambda0PerSlipFamily(f,i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='lambda0 ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (minDipoleHeightPerSlipFamily(f,1,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='minimumDipoleHeightEdge ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (minDipoleHeightPerSlipFamily(f,2,i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='minimumDipoleHeightScrew ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (peierlsStressPerSlipFamily(f,1,i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='peierlsStressEdge ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (peierlsStressPerSlipFamily(f,2,i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='peierlsStressScrew ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
endif
enddo
if (any(interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) &
call IO_error(211_pInt,ext_msg='interaction_SlipSlip ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (linetensionEffect(i) < 0.0_pReal .or. linetensionEffect(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='linetension ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (edgeJogFactor(i) < 0.0_pReal .or. edgeJogFactor(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='edgejog ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (cutoffRadius(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='r ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (atomicVolume(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='atomicVolume ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (Dsd0(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='selfDiffusionPrefactor ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (selfDiffusionEnergy(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='selfDiffusionEnergy ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (aTolRho(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='aTol_rho ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (aTolShear(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='aTol_shear ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (significantRho(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='significantRho ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (significantN(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='significantN ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (doublekinkwidth(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='doublekinkwidth ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (solidSolutionEnergy(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='solidSolutionEnergy ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (solidSolutionSize(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='solidSolutionSize ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (solidSolutionConcentration(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='solidSolutionConcentration ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (pParam(i) <= 0.0_pReal .or. pParam(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='p ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (qParam(i) < 1.0_pReal .or. qParam(i) > 2.0_pReal) &
call IO_error(211_pInt,ext_msg='q ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (viscosity(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='viscosity ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (fattack(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='attackFrequency ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglScatter(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglScatter ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglRandom(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglRandom ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (rhoSglRandomBinning(i) <= 0.0_pReal) &
call IO_error(211_pInt,ext_msg='rhoSglRandomBinning ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (surfaceTransmissivity(i) < 0.0_pReal .or. surfaceTransmissivity(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='surfaceTransmissivity ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (grainboundaryTransmissivity(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='grainboundaryTransmissivity ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (CFLfactor(i) < 0.0_pReal) &
call IO_error(211_pInt,ext_msg='CFLfactor ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
if (fEdgeMultiplication(i) < 0.0_pReal .or. fEdgeMultiplication(i) > 1.0_pReal) &
call IO_error(211_pInt,ext_msg='edgemultiplicationfactor ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
!*** determine total number of active slip systems
Nslip(1:lattice_maxNslipFamily,i) = min(lattice_NslipSystem(1:lattice_maxNslipFamily,myStructure), &
Nslip(1:lattice_maxNslipFamily,i) ) ! we can't use more slip systems per family than specified in lattice
totalNslip(i) = sum(Nslip(1:lattice_maxNslipFamily,i))
enddo
!*** allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(totalNslip)
allocate(iRhoU(maxTotalNslip,4,maxNinstance))
allocate(iRhoB(maxTotalNslip,4,maxNinstance))
allocate(iRhoD(maxTotalNslip,2,maxNinstance))
allocate(iV(maxTotalNslip,4,maxNinstance))
allocate(iD(maxTotalNslip,2,maxNinstance))
allocate(iGamma(maxTotalNslip,maxNinstance))
allocate(iRhoF(maxTotalNslip,maxNinstance))
allocate(iTauF(maxTotalNslip,maxNinstance))
allocate(iTauB(maxTotalNslip,maxNinstance))
iRhoU = 0_pInt
iRhoB = 0_pInt
iRhoD = 0_pInt
iV = 0_pInt
iD = 0_pInt
iGamma = 0_pInt
iRhoF = 0_pInt
iTauF = 0_pInt
iTauB = 0_pInt
allocate(burgers(maxTotalNslip, maxNinstance))
burgers = 0.0_pReal
allocate(lambda0(maxTotalNslip, maxNinstance))
lambda0 = 0.0_pReal
allocate(minDipoleHeight(maxTotalNslip,2,maxNinstance))
minDipoleHeight = -1.0_pReal
allocate(forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance))
forestProjectionEdge = 0.0_pReal
allocate(forestProjectionScrew(maxTotalNslip, maxTotalNslip, maxNinstance))
forestProjectionScrew = 0.0_pReal
allocate(interactionMatrixSlipSlip(maxTotalNslip, maxTotalNslip, maxNinstance))
interactionMatrixSlipSlip = 0.0_pReal
allocate(lattice2slip(1:3, 1:3, maxTotalNslip, maxNinstance))
lattice2slip = 0.0_pReal
allocate(sourceProbability(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
sourceProbability = 2.0_pReal
allocate(rhoDotFluxOutput(maxTotalNslip, 8, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(rhoDotMultiplicationOutput(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(rhoDotSingle2DipoleGlideOutput(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(rhoDotAthermalAnnihilationOutput(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(rhoDotThermalAnnihilationOutput(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(rhoDotEdgeJogsOutput(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
rhoDotFluxOutput = 0.0_pReal
rhoDotMultiplicationOutput = 0.0_pReal
rhoDotSingle2DipoleGlideOutput = 0.0_pReal
rhoDotAthermalAnnihilationOutput = 0.0_pReal
rhoDotThermalAnnihilationOutput = 0.0_pReal
rhoDotEdgeJogsOutput = 0.0_pReal
allocate(compatibility(2,maxTotalNslip, maxTotalNslip, mesh_maxNipNeighbors, mesh_maxNips, mesh_NcpElems))
compatibility = 0.0_pReal
allocate(peierlsStress(maxTotalNslip,2,maxNinstance))
peierlsStress = 0.0_pReal
allocate(colinearSystem(maxTotalNslip,maxNinstance))
colinearSystem = 0_pInt
do i = 1,maxNinstance
myStructure = constitutive_nonlocal_structure(i) ! lattice structure of this instance
!*** Inverse lookup of my slip system family and the slip system in lattice
l = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily
do s = 1_pInt,Nslip(f,i)
l = l + 1_pInt
slipFamily(l,i) = f
slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1_pInt, myStructure)) + s
enddo; enddo
!*** determine size of state array
ns = totalNslip(i)
constitutive_nonlocal_sizeDotState(i) = int(size(BASICSTATES),pInt) * ns
constitutive_nonlocal_sizeDependentState(i) = int(size(DEPENDENTSTATES),pInt) * ns
constitutive_nonlocal_sizeState(i) = constitutive_nonlocal_sizeDotState(i) &
+ constitutive_nonlocal_sizeDependentState(i) &
+ int(size(OTHERSTATES),pInt) * ns
!*** determine indices to state array
l = 0_pInt
do t = 1_pInt,4_pInt
do s = 1_pInt,ns
l = l + 1_pInt
iRhoU(s,t,i) = l
enddo
enddo
do t = 1_pInt,4_pInt
do s = 1_pInt,ns
l = l + 1_pInt
iRhoB(s,t,i) = l
enddo
enddo
do c = 1_pInt,2_pInt
do s = 1_pInt,ns
l = l + 1_pInt
iRhoD(s,c,i) = l
enddo
enddo
do s = 1_pInt,ns
l = l + 1_pInt
iGamma(s,i) = l
enddo
do s = 1_pInt,ns
l = l + 1_pInt
iRhoF(s,i) = l
enddo
do s = 1_pInt,ns
l = l + 1_pInt
iTauF(s,i) = l
enddo
do s = 1_pInt,ns
l = l + 1_pInt
iTauB(s,i) = l
enddo
do t = 1_pInt,4_pInt
do s = 1_pInt,ns
l = l + 1_pInt
iV(s,t,i) = l
enddo
enddo
do c = 1_pInt,2_pInt
do s = 1_pInt,ns
l = l + 1_pInt
iD(s,c,i) = l
enddo
enddo
if (iD(ns,2,i) /= constitutive_nonlocal_sizeState(i)) & ! check if last index is equal to size of state
call IO_error(0_pInt, ext_msg = 'state indices not properly set ('//CONSTITUTIVE_NONLOCAL_LABEL//')')
!*** determine size of postResults array
do o = 1_pInt,Noutput(i)
select case(constitutive_nonlocal_output(o,i))
case( 'rho', &
'delta', &
'rho_edge', &
'rho_screw', &
'rho_sgl', &
'delta_sgl', &
'rho_sgl_edge', &
'rho_sgl_edge_pos', &
'rho_sgl_edge_neg', &
'rho_sgl_screw', &
'rho_sgl_screw_pos', &
'rho_sgl_screw_neg', &
'rho_sgl_mobile', &
'rho_sgl_edge_mobile', &
'rho_sgl_edge_pos_mobile', &
'rho_sgl_edge_neg_mobile', &
'rho_sgl_screw_mobile', &
'rho_sgl_screw_pos_mobile', &
'rho_sgl_screw_neg_mobile', &
'rho_sgl_immobile', &
'rho_sgl_edge_immobile', &
'rho_sgl_edge_pos_immobile', &
'rho_sgl_edge_neg_immobile', &
'rho_sgl_screw_immobile', &
'rho_sgl_screw_pos_immobile', &
'rho_sgl_screw_neg_immobile', &
'rho_dip', &
'delta_dip', &
'rho_dip_edge', &
'rho_dip_screw', &
'excess_rho', &
'excess_rho_edge', &
'excess_rho_screw', &
'rho_forest', &
'shearrate', &
'resolvedstress', &
'resolvedstress_external', &
'resolvedstress_back', &
'resistance', &
'rho_dot', &
'rho_dot_sgl', &
'rho_dot_dip', &
'rho_dot_gen', &
'rho_dot_gen_edge', &
'rho_dot_gen_screw', &
'rho_dot_sgl2dip', &
'rho_dot_sgl2dip_edge', &
'rho_dot_sgl2dip_screw', &
'rho_dot_ann_ath', &
'rho_dot_ann_the', &
'rho_dot_ann_the_edge', &
'rho_dot_ann_the_screw', &
'rho_dot_edgejogs', &
'rho_dot_flux', &
'rho_dot_flux_edge', &
'rho_dot_flux_screw', &
'velocity_edge_pos', &
'velocity_edge_neg', &
'velocity_screw_pos', &
'velocity_screw_neg', &
'slipdirection.x', &
'slipdirection.y', &
'slipdirection.z', &
'slipnormal.x', &
'slipnormal.y', &
'slipnormal.z', &
'fluxdensity_edge_pos.x', &
'fluxdensity_edge_pos.y', &
'fluxdensity_edge_pos.z', &
'fluxdensity_edge_neg.x', &
'fluxdensity_edge_neg.y', &
'fluxdensity_edge_neg.z', &
'fluxdensity_screw_pos.x', &
'fluxdensity_screw_pos.y', &
'fluxdensity_screw_pos.z', &
'fluxdensity_screw_neg.x', &
'fluxdensity_screw_neg.y', &
'fluxdensity_screw_neg.z', &
'maximumdipoleheight_edge', &
'maximumdipoleheight_screw', &
'accumulatedshear', &
'boundarylayer' )
mySize = totalNslip(i)
case('dislocationstress')
mySize = 6_pInt
case default
call IO_error(212_pInt,ext_msg=constitutive_nonlocal_output(o,i)//'&
('//CONSTITUTIVE_NONLOCAL_LABEL//')')
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_nonlocal_sizePostResult(o,i) = mySize
constitutive_nonlocal_sizePostResults(i) = constitutive_nonlocal_sizePostResults(i) + mySize
endif
enddo
!*** elasticity matrix and shear modulus according to material.config
Cslip66(:,:,i) = lattice_symmetrizeC66(constitutive_nonlocal_structureName(i), Cslip66(:,:,i))
mu(i) = 0.2_pReal * ( Cslip66(1,1,i) - Cslip66(1,2,i) + 3.0_pReal*Cslip66(4,4,i)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
nu(i) = (Cslip66(1,1,i) + 4.0_pReal*Cslip66(1,2,i) - 2.0_pReal*Cslip66(4,4,i)) &
/ (4.0_pReal*Cslip66(1,1,i) + 6.0_pReal*Cslip66(1,2,i) + 2.0_pReal*Cslip66(4,4,i)) ! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
Cslip66(1:6,1:6,i) = math_Mandel3333to66(math_Voigt66to3333(Cslip66(1:6,1:6,i)))
Cslip3333(1:3,1:3,1:3,1:3,i) = math_Voigt66to3333(Cslip66(1:6,1:6,i))
do s1 = 1_pInt,ns
f = slipFamily(s1,i)
!*** burgers vector, mean free path prefactor and minimum dipole distance for each slip system
burgers(s1,i) = burgersPerSlipFamily(f,i)
lambda0(s1,i) = lambda0PerSlipFamily(f,i)
minDipoleHeight(s1,1:2,i) = minDipoleHeightPerSlipFamily(f,1:2,i)
peierlsStress(s1,1:2,i) = peierlsStressPerSlipFamily(f,1:2,i)
do s2 = 1_pInt,ns
!*** calculation of forest projections for edge and screw dislocations. s2 acts as forest for s1
forestProjectionEdge(s1,s2,i) &
= abs(math_mul3x3(lattice_sn(1:3,slipSystemLattice(s1,i),myStructure), &
lattice_st(1:3,slipSystemLattice(s2,i),myStructure))) ! forest projection of edge dislocations is the projection of (t = b x n) onto the slip normal of the respective slip plane
forestProjectionScrew(s1,s2,i) &
= abs(math_mul3x3(lattice_sn(1:3,slipSystemLattice(s1,i),myStructure), &
lattice_sd(1:3,slipSystemLattice(s2,i),myStructure))) ! forest projection of screw dislocations is the projection of b onto the slip normal of the respective splip plane
!*** calculation of interaction matrices
interactionMatrixSlipSlip(s1,s2,i) &
= interactionSlipSlip(lattice_interactionSlipSlip(slipSystemLattice(s1,i), &
slipSystemLattice(s2,i), &
myStructure), i)
!*** colinear slip system (only makes sense for fcc like it is defined here)
if (lattice_interactionSlipSlip(slipSystemLattice(s1,i), &
slipSystemLattice(s2,i), &
myStructure) == 3_pInt) then
colinearSystem(s1,i) = s2
endif
enddo
!*** rotation matrix from lattice configuration to slip system
lattice2slip(1:3,1:3,s1,i) &
= math_transpose33( reshape([ lattice_sd(1:3, slipSystemLattice(s1,i), myStructure), &
-lattice_st(1:3, slipSystemLattice(s1,i), myStructure), &
lattice_sn(1:3, slipSystemLattice(s1,i), myStructure)], [3,3]))
enddo
enddo
endsubroutine
!*********************************************************************
!* initial microstructural state (just the "basic" states) *
!*********************************************************************
subroutine constitutive_nonlocal_stateInit(state)
use IO, only: IO_error
use lattice, only: lattice_maxNslipFamily
use math, only: math_sampleGaussVar
use mesh, only: mesh_ipVolume, &
mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
FE_Nips, &
FE_geomtype
use material, only: material_phase, &
phase_plasticityInstance, &
phase_plasticity, &
homogenization_Ngrains
implicit none
!*** input/output variables
type(p_vec), dimension(1,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! microstructural state
!*** local variables
integer(pInt) el, &
ip, &
e, &
i, &
idx, &
ns, & ! short notation for total number of active slip systems
f, & ! index of lattice family
from, &
upto, &
s, & ! index of slip system
t, &
j, &
myInstance, &
maxNinstance
real(pReal), dimension(2) :: noise
real(pReal), dimension(4) :: rnd
real(pReal) meanDensity, &
totalVolume, &
densityBinning, &
minimumIpVolume
maxNinstance = int(count(phase_plasticity == CONSTITUTIVE_NONLOCAL_LABEL),pInt)
! ititalize all states to zero
do e = 1_pInt,mesh_NcpElems
do i = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,e)))
if (CONSTITUTIVE_NONLOCAL_LABEL == phase_plasticity(material_phase(1,i,e))) &
state(1,i,e)%p = 0.0_pReal
enddo
enddo
do myInstance = 1_pInt,maxNinstance
ns = totalNslip(myInstance)
! randomly distribute dislocation segments on random slip system and of random type in the volume
if (rhoSglRandom(myInstance) > 0.0_pReal) then
! get the total volume of the instance
minimumIpVolume = 1e99_pReal
totalVolume = 0.0_pReal
do e = 1_pInt,mesh_NcpElems
do i = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,e)))
if (CONSTITUTIVE_NONLOCAL_LABEL == phase_plasticity(material_phase(1,i,e)) &
.and. myInstance == phase_plasticityInstance(material_phase(1,i,e))) then
totalVolume = totalVolume + mesh_ipVolume(i,e)
minimumIpVolume = min(minimumIpVolume, mesh_ipVolume(i,e))
endif
enddo
enddo
densityBinning = rhoSglRandomBinning(myInstance) / minimumIpVolume ** (2.0_pReal / 3.0_pReal)
! subsequently fill random ips with dislocation segments until we reach the desired overall density
meanDensity = 0.0_pReal
do while(meanDensity < rhoSglRandom(myInstance))
call random_number(rnd)
el = nint(rnd(1)*real(mesh_NcpElems,pReal)+0.5_pReal,pInt)
ip = nint(rnd(2)*real(FE_Nips(FE_geomtype(mesh_element(2,el))),pReal)+0.5_pReal,pInt)
if (CONSTITUTIVE_NONLOCAL_LABEL == phase_plasticity(material_phase(1,ip,el)) &
.and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then
s = nint(rnd(3)*real(ns,pReal)+0.5_pReal,pInt)
t = nint(rnd(4)*4.0_pReal+0.5_pReal,pInt)
meanDensity = meanDensity + densityBinning * mesh_ipVolume(ip,el) / totalVolume
state(1,ip,el)%p(iRhoU(s,t,myInstance)) = state(1,ip,el)%p(iRhoU(s,t,myInstance)) + densityBinning
endif
enddo
! homogeneous distribution of density with some noise
else
do e = 1_pInt,mesh_NcpElems
do i = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,e)))
if (CONSTITUTIVE_NONLOCAL_LABEL == phase_plasticity(material_phase(1,i,e)) &
.and. myInstance == phase_plasticityInstance(material_phase(1,i,e))) then
do f = 1_pInt,lattice_maxNslipFamily
from = 1_pInt + sum(Nslip(1:f-1_pInt,myInstance))
upto = sum(Nslip(1:f,myInstance))
do s = from,upto
do j = 1_pInt,2_pInt
noise(j) = math_sampleGaussVar(0.0_pReal, rhoSglScatter(myInstance))
enddo
state(1,i,e)%p(iRhoU(s,1,myInstance)) = rhoSglEdgePos0(f, myInstance) + noise(1)
state(1,i,e)%p(iRhoU(s,2,myInstance)) = rhoSglEdgeNeg0(f, myInstance) + noise(1)
state(1,i,e)%p(iRhoU(s,3,myInstance)) = rhoSglScrewPos0(f, myInstance) + noise(2)
state(1,i,e)%p(iRhoU(s,4,myInstance)) = rhoSglScrewNeg0(f, myInstance) + noise(2)
enddo
state(1,i,e)%p(iRhoD(from:upto,1,myInstance)) = rhoDipEdge0(f, myInstance)
state(1,i,e)%p(iRhoD(from:upto,2,myInstance)) = rhoDipScrew0(f, myInstance)
enddo
endif
enddo
enddo
endif
enddo
endsubroutine
!*********************************************************************
!* absolute state tolerance *
!*********************************************************************
pure function constitutive_nonlocal_aTolState(myInstance)
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the plasticity
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
constitutive_nonlocal_aTolState ! absolute state tolerance for the current instance of this plasticity
!*** local variables
integer(pInt) :: ns, t, c
ns = totalNslip(myInstance)
constitutive_nonlocal_aTolState = 0.0_pReal
forall (t = 1_pInt:4_pInt)
constitutive_nonlocal_aTolState(iRhoU(1:ns,t,myInstance)) = aTolRho(myInstance)
constitutive_nonlocal_aTolState(iRhoB(1:ns,t,myInstance)) = aTolRho(myInstance)
endforall
forall (c = 1_pInt:2_pInt) &
constitutive_nonlocal_aTolState(iRhoD(1:ns,c,myInstance)) = aTolRho(myInstance)
constitutive_nonlocal_aTolState(iGamma(1:ns,myInstance)) = aTolShear(myInstance)
endfunction
!*********************************************************************
!* calculates homogenized elacticity matrix *
!*********************************************************************
pure function constitutive_nonlocal_homogenizedC(state,g,ip,el)
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! microstructural state
!*** output variables
real(pReal), dimension(6,6) :: constitutive_nonlocal_homogenizedC ! homogenized elasticity matrix
!*** local variables
integer(pInt) myInstance ! current instance of this plasticity
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
constitutive_nonlocal_homogenizedC = Cslip66(1:6,1:6,myInstance)
endfunction
!*********************************************************************
!* calculates quantities characterizing the microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, Fp, gr, ip, el)
use IO, only: &
IO_error
use math, only: &
pi, &
math_mul33x3, &
math_mul3x3, &
math_norm3, &
math_invert33, &
math_transpose33
use debug, only: &
debug_level, &
debug_constitutive, &
debug_levelBasic, &
debug_levelExtensive, &
debug_levelSelective, &
debug_g, &
debug_i, &
debug_e
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
mesh_ipNeighborhood, &
mesh_ipCoordinates, &
mesh_ipVolume, &
mesh_ipAreaNormal, &
mesh_ipArea, &
FE_NipNeighbors, &
mesh_maxNipNeighbors, &
FE_geomtype, &
FE_celltype
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_localPlasticity, &
phase_plasticityInstance
use lattice, only: &
lattice_sd, &
lattice_st, &
lattice_interactionSlipSlip
implicit none
!*** input variables
integer(pInt), intent(in) :: gr, & ! current grain ID
ip, & ! current integration point
el ! current element
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(3,3), intent(in) :: &
Fe, & ! elastic deformation gradient
Fp ! elastic deformation gradient
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! microstructural state
!*** output variables
!*** local variables
integer(pInt) neighboring_el, & ! element number of neighboring material point
neighboring_ip, & ! integration point of neighboring material point
instance, & ! my instance of this plasticity
neighboring_instance, & ! instance of this plasticity of neighboring material point
latticeStruct, & ! my lattice structure
neighboring_latticeStruct, & ! lattice structure of neighboring material point
phase, &
neighboring_phase, &
ns, & ! total number of active slip systems at my material point
neighboring_ns, & ! total number of active slip systems at neighboring material point
c, & ! index of dilsocation character (edge, screw)
s, & ! slip system index
s2, & ! slip system index
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
dir, &
n, &
nRealNeighbors, & ! number of really existing neighbors
interactionCoefficient
integer(pInt), dimension(2) :: neighbor
real(pReal) detFe, &
detFp, &
FVsize, &
temp, &
correction, &
myRhoForest
real(pReal), dimension(2) :: rhoExcessGradient, &
rhoExcessGradient_over_rho, &
rhoTotal
real(pReal), dimension(3) :: rhoExcessDifferences, &
normal_latticeConf
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(gr,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauBack, & ! back stress from pileup on same slip system
tauThreshold ! threshold shear stress
real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient
invFp, & ! inverse of plastic deformation gradient
connections, &
invConnections
real(pReal), dimension(3,mesh_maxNipNeighbors) :: &
connection_latticeConf
real(pReal), dimension(2,totalNslip(phase_plasticityInstance(material_phase(gr,ip,el)))) :: &
rhoExcess
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(gr,ip,el))),2) :: &
rhoDip ! dipole dislocation density (edge, screw)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(gr,ip,el))),8) :: &
rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(gr,ip,el))), &
totalNslip(phase_plasticityInstance(material_phase(gr,ip,el)))) :: &
myInteractionMatrix ! corrected slip interaction matrix
real(pReal), dimension(2,maxval(totalNslip),mesh_maxNipNeighbors) :: &
neighboring_rhoExcess, & ! excess density at neighboring material point
neighboring_rhoTotal ! total density at neighboring material point
real(pReal), dimension(3,totalNslip(phase_plasticityInstance(material_phase(gr,ip,el))),2) :: &
m ! direction of dislocation motion
logical inversionError
phase = material_phase(gr,ip,el)
instance = phase_plasticityInstance(phase)
latticeStruct = constitutive_nonlocal_structure(instance)
ns = totalNslip(instance)
!*** get basic states
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state(gr,ip,el)%p(iRhoU(s,t,instance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state(gr,ip,el)%p(iRhoB(s,t,instance))
endforall
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
rhoDip(s,c) = max(state(gr,ip,el)%p(iRhoD(s,c,instance)), 0.0_pReal) ! ensure positive dipole densities
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(instance) &
.or. abs(rhoSgl) < significantRho(instance)) &
rhoSgl = 0.0_pReal
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(instance) &
.or. abs(rhoDip) < significantRho(instance)) &
rhoDip = 0.0_pReal
!*** calculate the forest dislocation density
!*** (= projection of screw and edge dislocations)
forall (s = 1_pInt:ns) &
rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,[1,2,5,6])),2) + rhoDip(1:ns,1)), &
forestProjectionEdge(s,1:ns,instance)) &
+ dot_product((sum(abs(rhoSgl(1:ns,[3,4,7,8])),2) + rhoDip(1:ns,2)), &
forestProjectionScrew(s,1:ns,instance))
!*** calculate the threshold shear stress for dislocation slip
myInteractionMatrix = 0.0_pReal
myInteractionMatrix(1:ns,1:ns) = interactionMatrixSlipSlip(1:ns,1:ns,instance)
if (latticeStruct == 1_pInt) then ! in case of fcc: coefficients are corrected for the line tension effect (see Kubin,Devincre,Hoc; 2008; Modeling dislocation storage rates and mean free paths in face-centered cubic crystals)
do s = 1_pInt,ns
myRhoForest = max(rhoForest(s),significantRho(instance))
correction = ( 1.0_pReal - linetensionEffect(instance) &
+ linetensionEffect(instance) &
* log(0.35_pReal * burgers(s,instance) * sqrt(myRhoForest)) &
/ log(0.35_pReal * burgers(s,instance) * 1e6_pReal)) ** 2.0_pReal
do s2 = 1_pInt,ns
interactionCoefficient = &
lattice_interactionSlipSlip(slipSystemLattice(s,instance), &
slipSystemLattice(s2,instance), &
latticeStruct)
select case(interactionCoefficient)
case(4_pInt,5_pInt,6_pInt) ! only correct junction forming interactions (4,5,6)
myInteractionMatrix(s,s2) = correction * myInteractionMatrix(s,s2)
endselect
enddo
enddo
endif
forall (s = 1_pInt:ns) &
tauThreshold(s) = mu(instance) * burgers(s,instance) &
* sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), myInteractionMatrix(s,1:ns)))
!*** calculate the dislocation stress of the neighboring excess dislocation densities
!*** zero for material points of local plasticity
tauBack = 0.0_pReal
if (.not. phase_localPlasticity(phase) .and. shortRangeStressCorrection(instance)) then
call math_invert33(Fe, invFe, detFe, inversionError)
call math_invert33(Fp, invFp, detFp, inversionError)
rhoExcess(1,1:ns) = rhoSgl(1:ns,1) - rhoSgl(1:ns,2)
rhoExcess(2,1:ns) = rhoSgl(1:ns,3) - rhoSgl(1:ns,4)
FVsize = mesh_ipVolume(ip,el) ** (1.0_pReal/3.0_pReal)
!* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities
nRealNeighbors = 0_pInt
neighboring_rhoTotal = 0.0_pReal
do n = 1_pInt,FE_NipNeighbors(FE_celltype(FE_geomtype(mesh_element(2,el))))
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
if (neighboring_el > 0 .and. neighboring_ip > 0) then
neighboring_phase = material_phase(gr,neighboring_ip,neighboring_el)
neighboring_instance = phase_plasticityInstance(neighboring_phase)
neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance)
neighboring_ns = totalNslip(neighboring_instance)
if (.not. phase_localPlasticity(neighboring_phase) &
.and. neighboring_latticeStruct == latticeStruct &
.and. neighboring_instance == instance) then
if (neighboring_ns == ns) then
nRealNeighbors = nRealNeighbors + 1_pInt
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt)
neighboring_rhoExcess(c,s,n) = &
max(state(gr,neighboring_ip,neighboring_el)%p(iRhoU(s,2*c-1,neighboring_instance)), 0.0_pReal) &! positive mobiles
- max(state(gr,neighboring_ip,neighboring_el)%p(iRhoU(s,2*c,neighboring_instance)), 0.0_pReal) ! negative mobiles
neighboring_rhoTotal(c,s,n) = &
max(state(gr,neighboring_ip,neighboring_el)%p(iRhoU(s,2*c-1,neighboring_instance)), 0.0_pReal) &! positive mobiles
+ max(state(gr,neighboring_ip,neighboring_el)%p(iRhoU(s,2*c,neighboring_instance)), 0.0_pReal) & ! negative mobiles
+ abs(state(gr,neighboring_ip,neighboring_el)%p(iRhoB(s,2*c-1,neighboring_instance))) & ! positive deads
+ abs(state(gr,neighboring_ip,neighboring_el)%p(iRhoB(s,2*c,neighboring_instance))) & ! negative deads
+ max(state(gr,neighboring_ip,neighboring_el)%p(iRhoD(s,c,neighboring_instance)), 0.0_pReal) ! dipoles
endforall
connection_latticeConf(1:3,n) = &
math_mul33x3(invFe, mesh_ipCoordinates(1:3,neighboring_ip,neighboring_el) &
- mesh_ipCoordinates(1:3,ip,el))
normal_latticeConf = math_mul33x3(math_transpose33(invFp), mesh_ipAreaNormal(1:3,n,ip,el))
if (math_mul3x3(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) then ! neighbor connection points in opposite direction to face normal: must be periodic image
connection_latticeConf(1:3,n) = normal_latticeConf * mesh_ipVolume(ip,el) &
/ mesh_ipArea(n,ip,el) ! instead take the surface normal scaled with the diameter of the cell
endif
else
! different number of active slip systems
call IO_error(-1_pInt,ext_msg='different number of active slip systems in neighboring IPs of same crystal structure')
endif
else
! local neighbor or different lattice structure or different constitution instance -> use central values instead
connection_latticeConf(1:3,n) = 0.0_pReal
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
endif
else
! free surface -> use central values instead
connection_latticeConf(1:3,n) = 0.0_pReal
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
endif
enddo
!* loop through the slip systems and calculate the dislocation gradient by
!* 1. interpolation of the excess density in the neighorhood
!* 2. interpolation of the dead dislocation density in the central volume
m(1:3,1:ns,1) = lattice_sd(1:3,slipSystemLattice(1:ns,instance),latticeStruct)
m(1:3,1:ns,2) = -lattice_st(1:3,slipSystemLattice(1:ns,instance),latticeStruct)
do s = 1_pInt,ns
!* gradient from interpolation of neighboring excess density
do c = 1_pInt,2_pInt
do dir = 1_pInt,3_pInt
neighbor(1) = 2_pInt * dir - 1_pInt
neighbor(2) = 2_pInt * dir
connections(dir,1:3) = connection_latticeConf(1:3,neighbor(1)) &
- connection_latticeConf(1:3,neighbor(2))
rhoExcessDifferences(dir) = neighboring_rhoExcess(c,s,neighbor(1)) &
- neighboring_rhoExcess(c,s,neighbor(2))
enddo
call math_invert33(connections,invConnections,temp,inversionError)
if (inversionError) then
call IO_error(-1_pInt,ext_msg='back stress calculation: inversion error')
endif
rhoExcessGradient(c) = math_mul3x3(m(1:3,s,c), &
math_mul33x3(invConnections,rhoExcessDifferences))
enddo
!* plus gradient from deads
do t = 1_pInt,4_pInt
c = (t - 1_pInt) / 2_pInt + 1_pInt
rhoExcessGradient(c) = rhoExcessGradient(c) + rhoSgl(s,t+4_pInt) / FVsize
enddo
!* normalized with the total density
rhoExcessGradient_over_rho = 0.0_pReal
forall (c = 1_pInt:2_pInt) &
rhoTotal(c) = (sum(abs(rhoSgl(s,[2*c-1,2*c,2*c+3,2*c+4]))) + rhoDip(s,c) + sum(neighboring_rhoTotal(c,s,:))) &
/ real(1_pInt + nRealNeighbors,pReal)
forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) &
rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c)
!* gives the local stress correction when multiplied with a factor
tauBack(s) = - mu(instance) * burgers(s,instance) / (2.0_pReal * pi) &
* (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu(instance)) + rhoExcessGradient_over_rho(2))
enddo
endif
!*** set dependent states
state(gr,ip,el)%p(iRhoF(1:ns,instance)) = rhoForest
state(gr,ip,el)%p(iTauF(1:ns,instance)) = tauThreshold
state(gr,ip,el)%p(iTauB(1:ns,instance)) = tauBack
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == gr)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_microstructure at el ip g',el,ip,gr
write(6,*)
write(6,'(a,/,12x,12(e10.3,1x))') '<< CONST >> rhoForest', rhoForest
write(6,'(a,/,12x,12(f10.5,1x))') '<< CONST >> tauThreshold / MPa', tauThreshold/1e6
write(6,'(a,/,12x,12(f10.5,1x))') '<< CONST >> tauBack / MPa', tauBack/1e6
write(6,*)
endif
#endif
endsubroutine
!*********************************************************************
!* calculates kinetics *
!*********************************************************************
subroutine constitutive_nonlocal_kinetics(v, tau, c, Temperature, state, g, ip, el, dv_dtau)
use debug, only: debug_level, &
debug_constitutive, &
debug_levelBasic, &
debug_levelExtensive, &
debug_levelSelective, &
debug_g, &
debug_i, &
debug_e
use material, only: material_phase, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el, & ! current element number
c ! dislocation character (1:edge, 2:screw)
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
intent(in) :: tau ! resolved external shear stress (for bcc this already contains non Schmid effects)
type(p_vec), intent(in) :: state ! microstructural state
!*** input/output variables
!*** output variables
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
intent(out) :: v ! velocity
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
intent(out), optional :: dv_dtau ! velocity derivative with respect to resolved shear stress
!*** local variables
integer(pInt) :: instance, & ! current instance of this plasticity
ns, & ! short notation for the total number of active slip systems
s ! index of my current slip system
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tauThreshold, & ! threshold shear stress
tauEff ! effective shear stress
real(pReal) tauRel_P, &
tauRel_S, &
tPeierls, & ! waiting time in front of a peierls barriers
tSolidSolution, & ! waiting time in front of a solid solution obstacle
vViscous, & ! viscous glide velocity
dtPeierls_dtau, & ! derivative with respect to resolved shear stress
dtSolidSolution_dtau, & ! derivative with respect to resolved shear stress
meanfreepath_S, & ! mean free travel distance for dislocations between two solid solution obstacles
meanfreepath_P, & ! mean free travel distance for dislocations between two Peierls barriers
jumpWidth_P, & ! depth of activated area
jumpWidth_S, & ! depth of activated area
activationLength_P, & ! length of activated dislocation line
activationLength_S, & ! length of activated dislocation line
activationVolume_P, & ! volume that needs to be activated to overcome barrier
activationVolume_S, & ! volume that needs to be activated to overcome barrier
activationEnergy_P, & ! energy that is needed to overcome barrier
activationEnergy_S, & ! energy that is needed to overcome barrier
criticalStress_P, & ! maximum obstacle strength
criticalStress_S, & ! maximum obstacle strength
mobility ! dislocation mobility
instance = phase_plasticityInstance(material_phase(g,ip,el))
ns = totalNslip(instance)
tauThreshold = state%p(iTauF(1:ns,instance))
tauEff = abs(tau) - tauThreshold
v = 0.0_pReal
if (present(dv_dtau)) dv_dtau = 0.0_pReal
if (Temperature > 0.0_pReal) then
do s = 1_pInt,ns
if (tauEff(s) > 0.0_pReal) then
!* Peierls contribution
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
meanfreepath_P = burgers(s,instance)
jumpWidth_P = burgers(s,instance)
activationLength_P = doublekinkwidth(instance) * burgers(s,instance)
activationVolume_P = activationLength_P * jumpWidth_P * burgers(s,instance)
criticalStress_P = peierlsStress(s,c,instance)
activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff(s) / criticalStress_P) ! ensure that the activation probability cannot become greater than one
tPeierls = 1.0_pReal / fattack(instance) &
* exp(activationEnergy_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**pParam(instance))**qParam(instance))
if (present(dv_dtau)) then
if (tauEff(s) < criticalStress_P) then
dtPeierls_dtau = tPeierls * pParam(instance) * qParam(instance) * activationVolume_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**pParam(instance))**(qParam(instance)-1.0_pReal) &
* tauRel_P**(pParam(instance)-1.0_pReal)
else
dtPeierls_dtau = 0.0_pReal
endif
endif
!* Contribution from solid solution strengthening
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
meanfreepath_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance))
jumpWidth_S = solidSolutionSize(instance) * burgers(s,instance)
activationLength_S = burgers(s,instance) / sqrt(solidSolutionConcentration(instance))
activationVolume_S = activationLength_S * jumpWidth_S * burgers(s,instance)
activationEnergy_S = solidSolutionEnergy(instance)
criticalStress_S = activationEnergy_S / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff(s) / criticalStress_S) ! ensure that the activation probability cannot become greater than one
tSolidSolution = 1.0_pReal / fattack(instance) &
* exp(activationEnergy_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**pParam(instance))**qParam(instance))
if (present(dv_dtau)) then
if (tauEff(s) < criticalStress_S) then
dtSolidSolution_dtau = tSolidSolution * pParam(instance) * qParam(instance) &
* activationVolume_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**pParam(instance))**(qParam(instance)-1.0_pReal) &
* tauRel_S**(pParam(instance)-1.0_pReal)
else
dtSolidSolution_dtau = 0.0_pReal
endif
endif
!* viscous glide velocity
mobility = burgers(s,instance) / viscosity(instance)
vViscous = mobility * tauEff(s)
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
!* free flight at glide velocity in between.
!* adopt sign from resolved stress
v(s) = sign(1.0_pReal,tau(s)) &
/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
if (present(dv_dtau)) then
dv_dtau(s) = v(s) * v(s) &
* (dtPeierls_dtau / meanfreepath_P &
+ dtSolidSolution_dtau / meanfreepath_S &
+ 1.0_pReal / (mobility * tauEff(s)*tauEff(s)))
endif
endif
enddo
endif
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g
write(6,*)
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauEff / MPa', tauEff / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3
if (present(dv_dtau)) then
write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtau', dv_dtau
endif
endif
#endif
endsubroutine
!*********************************************************************
!* calculates plastic velocity gradient and its tangent *
!*********************************************************************
subroutine constitutive_nonlocal_LpAndItsTangent(Lp, dLp_dTstar99, Tstar_v, Temperature, state, g, ip, el)
use math, only: math_Plain3333to99, &
math_mul6x6, &
math_Mandel6to33
use debug, only: debug_level, &
debug_constitutive, &
debug_levelBasic, &
debug_levelExtensive, &
debug_levelSelective, &
debug_g, &
debug_i, &
debug_e
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
NnonSchmid
use mesh, only: mesh_ipVolume
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
!*** input/output variables
type(p_vec), intent(inout) :: state ! microstructural state
!*** output variables
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 Tstar (9x9 matrix)
!*** local variables
integer(pInt) myInstance, & ! current instance of this plasticity
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
c, &
i, &
j, &
k, &
l, &
t, & ! dislocation type
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix)
real(pReal), dimension(3,3,2,totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
nonSchmidTensor
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl ! single dislocation densities (including blocked)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
v, & ! velocity
tau, & ! resolved shear stress including non Schmid and backstress terms
dgdot_dtau, & ! derivative of the shear rate with respect to the shear stress
dv_dtau ! velocity derivative with respect to the shear stress
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
gdotTotal, & ! shear rate
tauBack, & ! back stress from dislocation gradients on same slip system
deadZoneSize
!*** initialize local variables
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
nonSchmidTensor = 0.0_pReal
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = totalNslip(myInstance)
!*** shortcut to state variables
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state%p(iRhoU(s,t,myInstance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state%p(iRhoB(s,t,myInstance))
endforall
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoSgl) < significantRho(myInstance)) &
rhoSgl = 0.0_pReal
tauBack = state%p(iTauB(1:ns,myInstance))
!*** get effective resolved shear stress
!*** add non schmid contributions to ONLY screw components if present (i.e. if NnonSchmid(myStructure) > 0)
do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance)
tau(s,1:4) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure)) + tauBack(s)
nonSchmidTensor(1:3,1:3,1,s) = lattice_Sslip(1:3,1:3,sLattice,myStructure)
nonSchmidTensor(1:3,1:3,2,s) = nonSchmidTensor(1:3,1:3,1,s)
do k = 1_pInt, NnonSchmid(myStructure)
tau(s,3) = tau(s,3) + nonSchmidCoeff(k,myInstance) &
* math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,2*k,sLattice,myStructure))
tau(s,4) = tau(s,4) + nonSchmidCoeff(k,myInstance) &
* math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,2*k+1,sLattice,myStructure))
nonSchmidTensor(1:3,1:3,1,s) = nonSchmidTensor(1:3,1:3,1,s) &
+ nonSchmidCoeff(k,myInstance) &
* math_Mandel6to33(lattice_Sslip_v(1:6,2*k,sLattice,myStructure))
nonSchmidTensor(1:3,1:3,2,s) = nonSchmidTensor(1:3,1:3,2,s) &
+ nonSchmidCoeff(k,myInstance) &
* math_Mandel6to33(lattice_Sslip_v(1:6,2*k+1,sLattice,myStructure))
enddo
enddo
!*** get dislocation velocity and its tangent and store the velocity in the state array
if (myStructure == 1_pInt .and. NnonSchmid(myStructure) == 0_pInt) then ! for fcc all velcities are equal
call constitutive_nonlocal_kinetics(v(1:ns,1), tau(1:ns,1), 1_pInt, Temperature, state, &
g, ip, el, dv_dtau(1:ns,1))
do t = 1_pInt,4_pInt
v(1:ns,t) = v(1:ns,1)
dv_dtau(1:ns,t) = dv_dtau(1:ns,1)
state%p(iV(1:ns,t,myInstance)) = v(1:ns,1)
enddo
else ! for all other lattice structures the velocities may vary with character and sign
do t = 1_pInt,4_pInt
c = (t-1_pInt)/2_pInt+1_pInt
call constitutive_nonlocal_kinetics(v(1:ns,t), tau(1:ns,t), c, Temperature, state, &
g, ip, el, dv_dtau(1:ns,t))
state%p(iV(1:ns,t,myInstance)) = v(1:ns,t)
enddo
endif
!*** Bauschinger effect
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt, rhoSgl(s,t) * v(s,t-4_pInt) < 0.0_pReal) &
rhoSgl(s,t-4_pInt) = rhoSgl(s,t-4_pInt) + abs(rhoSgl(s,t))
!*** Calculation of gdot and its tangent
deadZoneSize = 0.0_pReal
if (deadZoneScaling(myInstance)) then
forall(s = 1_pInt:ns, sum(abs(rhoSgl(s,1:8))) > 0.0_pReal) &
deadZoneSize(s) = maxval(abs(rhoSgl(s,5:8)) / (rhoSgl(s,1:4) + abs(rhoSgl(s,5:8))))
endif
gdotTotal = sum(rhoSgl(1:ns,1:4) * v, 2) * burgers(1:ns,myInstance) * (1.0_pReal - deadZoneSize)
do t = 1_pInt,4_pInt
dgdot_dtau(:,t) = rhoSgl(1:ns,t) * dv_dtau(1:ns,t) * burgers(1:ns,myInstance) * (1.0_pReal - deadZoneSize)
enddo
!*** Calculation of Lp and its tangent
do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance)
Lp = Lp + gdotTotal(s) * lattice_Sslip(1:3,1:3,sLattice,myStructure)
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) &
+ dgdot_dtau(s,1) * lattice_Sslip(i,j,sLattice,myStructure) * lattice_Sslip(k,l,sLattice,myStructure) &
+ dgdot_dtau(s,2) * lattice_Sslip(i,j,sLattice,myStructure) * lattice_Sslip(k,l,sLattice,myStructure) &
+ dgdot_dtau(s,3) * lattice_Sslip(i,j,sLattice,myStructure) * nonSchmidTensor(k,l,1,s) &
+ dgdot_dtau(s,4) * lattice_Sslip(i,j,sLattice,myStructure) * nonSchmidTensor(k,l,2,s)
enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_LpandItsTangent at el ip g ',el,ip,g
write(6,*)
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> gdot total / 1e-3',gdotTotal*1e3_pReal
write(6,'(a,/,3(12x,3(f12.7,1x),/))') '<< CONST >> Lp',transpose(Lp)
endif
#endif
endsubroutine
!*********************************************************************
!* incremental change of microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_deltaState(deltaState, state, Tstar_v, Temperature, g,ip,el)
use debug, only: debug_level, &
debug_constitutive, &
debug_levelBasic, &
debug_levelExtensive, &
debug_levelSelective, &
debug_g, &
debug_i, &
debug_e
use math, only: pi, &
math_mul6x6
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_ipVolume
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! current microstructural state
!*** output variables
type(p_vec), intent(out) :: deltaState ! change of state variables / microstructure
!*** local variables
integer(pInt) myInstance, & ! current instance of this plasticity
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
c, & ! character of dislocation
t, & ! type of dislocation
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
deltaRho, & ! density increment
deltaRhoRemobilization, & ! density increment by remobilization
deltaRhoDipole2SingleStress ! density increment by dipole dissociation (by stress change)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl ! current single dislocation densities (positive/negative screw and edge without dipoles)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
v ! dislocation glide velocity
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tau, & ! current resolved shear stress
tauBack ! current back stress from pileups on same slip system
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
dLower, & ! minimum stable dipole distance for edges and screws
dUpper, & ! current maximum stable dipole distance for edges and screws
dUpperOld, & ! old maximum stable dipole distance for edges and screws
deltaDUpper ! change in maximum stable dipole distance for edges and screws
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_deltaState at el ip g ',el,ip,g
write(6,*)
endif
#endif
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = totalNslip(myInstance)
!*** shortcut to state variables
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state(g,ip,el)%p(iRhoU(s,t,myInstance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state(g,ip,el)%p(iRhoB(s,t,myInstance))
v(s,t) = state(g,ip,el)%p(iV(s,t,myInstance))
endforall
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt)
rhoDip(s,c) = max(state(g,ip,el)%p(iRhoD(s,c,myInstance)), 0.0_pReal) ! ensure positive dipole densities
dUpperOld(s,c) = state(g,ip,el)%p(iD(s,c,myInstance))
endforall
tauBack = state(g,ip,el)%p(iTauB(1:ns,myInstance))
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoSgl) < significantRho(myInstance)) &
rhoSgl = 0.0_pReal
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoDip) < significantRho(myInstance)) &
rhoDip = 0.0_pReal
!****************************************************************************
!*** dislocation remobilization (bauschinger effect)
deltaRhoRemobilization = 0.0_pReal
do t = 1_pInt,4_pInt
do s = 1_pInt,ns
if (rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) then
deltaRhoRemobilization(s,t) = abs(rhoSgl(s,t+4_pInt))
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4_pInt))
deltaRhoRemobilization(s,t+4_pInt) = - rhoSgl(s,t+4_pInt)
rhoSgl(s,t+4_pInt) = 0.0_pReal
endif
enddo
enddo
!****************************************************************************
!*** calculate dipole formation and dissociation by stress change
!*** calculate limits for stable dipole height
do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance)
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure)) + tauBack(s)
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
enddo
dLower = minDipoleHeight(1:ns,1:2,myInstance)
dUpper(1:ns,1) = mu(myInstance) * burgers(1:ns,myInstance) &
/ (8.0_pReal * pi * (1.0_pReal - nu(myInstance)) * abs(tau))
dUpper(1:ns,2) = mu(myInstance) * burgers(1:ns,myInstance) / (4.0_pReal * pi * abs(tau))
forall (c = 1_pInt:2_pInt) &
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
dUpper(1:ns,c))
dUpper = max(dUpper,dLower)
deltaDUpper = dUpper - dUpperOld
!*** dissociation by stress increase
deltaRhoDipole2SingleStress = 0.0_pReal
forall (c=1_pInt:2_pInt, s=1_pInt:ns, deltaDUpper(s,c) < 0.0_pReal) &
deltaRhoDipole2SingleStress(s,8_pInt+c) = rhoDip(s,c) * deltaDUpper(s,c) / (dUpperOld(s,c) - dLower(s,c))
forall (t=1_pInt:4_pInt) &
deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal * deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt)
!*** store new maximum dipole height in state
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
state(g,ip,el)%p(iD(s,c,myInstance)) = dUpper(s,c)
!****************************************************************************
!*** assign the changes in the dislocation densities to deltaState
deltaRho = deltaRhoRemobilization &
+ deltaRhoDipole2SingleStress
deltaState%p = 0.0_pReal
forall (s = 1:ns, t = 1_pInt:4_pInt)
deltaState%p(iRhoU(s,t,myInstance)) = deltaRho(s,t)
deltaState%p(iRhoB(s,t,myInstance)) = deltaRho(s,t+4_pInt)
endforall
forall (s = 1:ns, c = 1_pInt:2_pInt) &
deltaState%p(iRhoD(s,c,myInstance)) = deltaRho(s,c+8_pInt)
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation remobilization', deltaRhoRemobilization(1:ns,1:8)
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole dissociation by stress increase', deltaRhoDipole2SingleStress
write(6,*)
endif
#endif
endsubroutine
!*********************************************************************
!* rate of change of microstructure *
!*********************************************************************
function constitutive_nonlocal_dotState(Tstar_v, Fe, Fp, Temperature, state, state0, timestep, subfrac, g,ip,el)
use prec, only: DAMASK_NaN
use numerics, only: numerics_integrationMode, &
numerics_timeSyncing
use IO, only: IO_error
use debug, only: debug_level, &
debug_constitutive, &
debug_levelBasic, &
debug_levelExtensive, &
debug_levelSelective, &
debug_g, &
debug_i, &
debug_e
use math, only: math_norm3, &
math_mul6x6, &
math_mul3x3, &
math_mul33x3, &
math_mul33x33, &
math_inv33, &
math_det33, &
math_transpose33, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipArea, &
mesh_ipAreaNormal, &
FE_NipNeighbors, &
FE_geomtype, &
FE_celltype
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
phase_localPlasticity, &
phase_plasticity
use lattice, only: lattice_Sslip_v, &
lattice_sd, &
lattice_st
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & !< current grain number
ip, & !< current integration point
el !< current element number
real(pReal), intent(in) :: Temperature, & !< temperature
timestep !< substepped crystallite time increment
real(pReal), dimension(6), intent(in) :: Tstar_v !< current 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
subfrac !< fraction of timestep at the beginning of the substepped crystallite time increment
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & !< elastic deformation gradient
Fp !< plastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state, & !< current microstructural state
state0 !< microstructural state at beginning of crystallite increment
!*** input/output variables
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_nonlocal_dotState !< evolution of state variables / microstructure
!*** local variables
integer(pInt) myInstance, & !< current instance of this plasticity
neighbor_instance, & !< instance of my neighbor's plasticity
myStructure, & !< current lattice structure
ns, & !< short notation for the total number of active slip systems
c, & !< character of dislocation
n, & !< index of my current neighbor
neighbor_el, & !< element number of my neighbor
neighbor_ip, & !< integration point of my neighbor
neighbor_n, & !< neighbor index pointing to me when looking from my neighbor
opposite_neighbor, & !< index of my opposite neighbor
opposite_ip, & !< ip of my opposite neighbor
opposite_el, & !< element index of my opposite neighbor
opposite_n, & !< neighbor index pointing to me when looking from my opposite neighbor
t, & !< type of dislocation
topp, & !< type of dislocation with opposite sign to t
s, & !< index of my current slip system
sLattice, & !< index of my current slip system according to lattice order
deads
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
rhoDot, & !< density evolution
rhoDotMultiplication, & !< density evolution by multiplication
rhoDotFlux, & !< density evolution by flux
rhoDotSingle2DipoleGlide, & !< density evolution by dipole formation (by glide)
rhoDotAthermalAnnihilation, & !< density evolution by athermal annihilation
rhoDotThermalAnnihilation !< density evolution by thermal annihilation
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
rhoSglOriginal, &
neighbor_rhoSgl, & !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
rhoSgl0, & !< single dislocation densities at start of cryst inc (positive/negative screw and edge without dipoles)
my_rhoSgl !< single dislocation densities of central ip (positive/negative screw and edge without dipoles)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
v, & !< current dislocation glide velocity
v0, & !< dislocation glide velocity at start of cryst inc
my_v, & !< dislocation glide velocity of central ip
neighbor_v, & !< dislocation glide velocity of enighboring ip
gdot !< shear rates
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
rhoForest, & !< forest dislocation density
tauThreshold, & !< threshold shear stress
tau, & !< current resolved shear stress
tauBack, & !< current back stress from pileups on same slip system
vClimb, & !< climb velocity of edge dipoles
nSources
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & !< current dipole dislocation densities (screw and edge dipoles)
rhoDipOriginal, &
dLower, & !< minimum stable dipole distance for edges and screws
dUpper !< current maximum stable dipole distance for edges and screws
real(pReal), dimension(3,totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
m !< direction of dislocation motion
real(pReal), dimension(3,3) :: my_F, & !< my total deformation gradient
neighbor_F, & !< total deformation gradient of my neighbor
my_Fe, & !< my elastic deformation gradient
neighbor_Fe, & !< elastic deformation gradient of my neighbor
Favg !< average total deformation gradient of me and my neighbor
real(pReal), dimension(3) :: normal_neighbor2me, & !< interface normal pointing from my neighbor to me in neighbor's lattice configuration
normal_neighbor2me_defConf, & !< interface normal pointing from my neighbor to me in shared deformed configuration
normal_me2neighbor, & !< interface normal pointing from me to my neighbor in my lattice configuration
normal_me2neighbor_defConf !< interface normal pointing from me to my neighbor in shared deformed configuration
real(pReal) area, & !< area of the current interface
transmissivity, & !< overall transmissivity of dislocation flux to neighboring material point
lineLength, & !< dislocation line length leaving the current interface
selfDiffusion, & !< self diffusion
rnd, &
meshlength
logical considerEnteringFlux, &
considerLeavingFlux
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
write(6,*)
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_dotState at el ip g ',el,ip,g
write(6,*)
endif
#endif
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = totalNslip(myInstance)
tau = 0.0_pReal
gdot = 0.0_pReal
!*** shortcut to state variables
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state(g,ip,el)%p(iRhoU(s,t,myInstance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state(g,ip,el)%p(iRhoB(s,t,myInstance))
v(s,t) = state(g,ip,el)%p(iV(s,t,myInstance))
endforall
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt)
rhoDip(s,c) = max(state(g,ip,el)%p(iRhoD(s,c,myInstance)), 0.0_pReal) ! ensure positive dipole densities
endforall
rhoForest = state(g,ip,el)%p(iRhoF(1:ns,myInstance))
tauThreshold = state(g,ip,el)%p(iTauF(1:ns,myInstance))
tauBack = state(g,ip,el)%p(iTauB(1:ns,myInstance))
rhoSglOriginal = rhoSgl
rhoDipOriginal = rhoDip
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoSgl) < significantRho(myInstance)) &
rhoSgl = 0.0_pReal
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoDip) < significantRho(myInstance)) &
rhoDip = 0.0_pReal
if (numerics_timeSyncing) then
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl0(s,t) = max(state0(g,ip,el)%p(iRhoU(s,t,myInstance)), 0.0_pReal)
rhoSgl0(s,t+4_pInt) = state0(g,ip,el)%p(iRhoB(s,t,myInstance))
v0(s,t) = state0(g,ip,el)%p(iV(s,t,myInstance))
endforall
where (abs(rhoSgl0) * mesh_ipVolume(ip,el) ** 0.667_pReal < significantN(myInstance) &
.or. abs(rhoSgl0) < significantRho(myInstance)) &
rhoSgl0 = 0.0_pReal
endif
!*** sanity check for timestep
if (timestep <= 0.0_pReal) then ! if illegal timestep...
constitutive_nonlocal_dotState = 0.0_pReal ! ...return without doing anything (-> zero dotState)
return
endif
!****************************************************************************
!*** Calculate shear rate
forall (t = 1_pInt:4_pInt) &
gdot(1_pInt:ns,t) = rhoSgl(1_pInt:ns,t) * burgers(1:ns,myInstance) * v(1:ns,t)
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> rho / 1/m^2', rhoSgl, rhoDip
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> gdot / 1/s',gdot
endif
#endif
!****************************************************************************
!*** calculate limits for stable dipole height
do s = 1_pInt,ns ! loop over slip systems
sLattice = slipSystemLattice(s,myInstance)
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure)) + tauBack(s)
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
enddo
dLower = minDipoleHeight(1:ns,1:2,myInstance)
dUpper(1:ns,1) = mu(myInstance) * burgers(1:ns,myInstance) &
/ (8.0_pReal * pi * (1.0_pReal - nu(myInstance)) * abs(tau))
dUpper(1:ns,2) = mu(myInstance) * burgers(1:ns,myInstance) &
/ (4.0_pReal * pi * abs(tau))
forall (c = 1_pInt:2_pInt) &
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
dUpper(1:ns,c))
dUpper = max(dUpper,dLower)
!****************************************************************************
!*** calculate dislocation multiplication
rhoDotMultiplication = 0.0_pReal
if (probabilisticMultiplication(myInstance)) then
meshlength = mesh_ipVolume(ip,el)**0.333_pReal
where(sum(rhoSgl(1:ns,1:4),2) > 0.0_pReal)
nSources = (sum(rhoSgl(1:ns,1:2),2) * fEdgeMultiplication(myInstance) + sum(rhoSgl(1:ns,3:4),2)) &
/ sum(rhoSgl(1:ns,1:4),2) * meshlength / lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns))
elsewhere
nSources = meshlength / lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns))
endwhere
do s = 1_pInt,ns
if (nSources(s) < 1.0_pReal) then
if (sourceProbability(s,g,ip,el) > 1.0_pReal) then
call random_number(rnd)
sourceProbability(s,g,ip,el) = rnd
!$OMP FLUSH(sourceProbability)
endif
if (sourceProbability(s,g,ip,el) > 1.0_pReal - nSources(s)) then
rhoDotMultiplication(s,1:4) = sum(rhoSglOriginal(s,1:4) * abs(v(s,1:4))) / meshlength
endif
else
sourceProbability(s,g,ip,el) = 2.0_pReal
rhoDotMultiplication(s,1:4) = &
(sum(abs(gdot(s,1:2))) * fEdgeMultiplication(myInstance) + sum(abs(gdot(s,3:4)))) &
/ burgers(s,myInstance) * sqrt(rhoForest(s)) / lambda0(s,myInstance)
endif
enddo
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,4(12x,12(f12.5,1x),/))') '<< CONST >> sources', nSources
write(6,*)
endif
#endif
else
rhoDotMultiplication(1:ns,1:4) = spread( &
(sum(abs(gdot(1:ns,1:2)),2) * fEdgeMultiplication(myInstance) + sum(abs(gdot(1:ns,3:4)),2)) &
* sqrt(rhoForest(1:ns)) / lambda0(1:ns,myInstance) / burgers(1:ns,myInstance), 2, 4)
endif
!****************************************************************************
!*** calculate dislocation fluxes (only for nonlocal plasticity)
rhoDotFlux = 0.0_pReal
if (.not. phase_localPlasticity(material_phase(g,ip,el))) then ! only for nonlocal plasticity
!*** check CFL (Courant-Friedrichs-Lewy) condition for flux
if (any( abs(gdot) > 0.0_pReal & ! any active slip system ...
.and. CFLfactor(myInstance) * abs(v) * timestep &
> mesh_ipVolume(ip,el) / maxval(mesh_ipArea(:,ip,el)))) then ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt) then
write(6,'(a,i5,a,i2)') '<< CONST >> CFL condition not fullfilled at el ',el,' ip ',ip
write(6,'(a,e10.3,a,e10.3)') '<< CONST >> velocity is at ', &
maxval(abs(v), abs(gdot) > 0.0_pReal &
.and. CFLfactor(myInstance) * abs(v) * timestep &
> mesh_ipVolume(ip,el) / maxval(mesh_ipArea(:,ip,el))), &
' at a timestep of ',timestep
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
endif
#endif
constitutive_nonlocal_dotState = DAMASK_NaN ! -> return NaN and, hence, enforce cutback
return
endif
!*** be aware of the definition of lattice_st = lattice_sd x lattice_sn !!!
!*** opposite sign to our p vector in the (s,p,n) triplet !!!
m(1:3,1:ns,1) = lattice_sd(1:3, slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,2) = -lattice_sd(1:3, slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,3) = -lattice_st(1:3, slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,4) = lattice_st(1:3, slipSystemLattice(1:ns,myInstance), myStructure)
my_Fe = Fe(1:3,1:3,g,ip,el)
my_F = math_mul33x33(my_Fe, Fp(1:3,1:3,g,ip,el))
do n = 1_pInt,FE_NipNeighbors(FE_celltype(FE_geomtype(mesh_element(2,el)))) ! loop through my neighbors
neighbor_el = mesh_ipNeighborhood(1,n,ip,el)
neighbor_ip = mesh_ipNeighborhood(2,n,ip,el)
neighbor_n = mesh_ipNeighborhood(3,n,ip,el)
opposite_neighbor = n + mod(n,2_pInt) - mod(n+1_pInt,2_pInt)
opposite_el = mesh_ipNeighborhood(1,opposite_neighbor,ip,el)
opposite_ip = mesh_ipNeighborhood(2,opposite_neighbor,ip,el)
opposite_n = mesh_ipNeighborhood(3,opposite_neighbor,ip,el)
if (neighbor_n > 0_pInt) then ! if neighbor exists, average deformation gradient
neighbor_instance = phase_plasticityInstance(material_phase(g,neighbor_ip,neighbor_el))
neighbor_Fe = Fe(1:3,1:3,g,neighbor_ip,neighbor_el)
neighbor_F = math_mul33x33(neighbor_Fe, Fp(1:3,1:3,g,neighbor_ip,neighbor_el))
Favg = 0.5_pReal * (my_F + neighbor_F)
else ! if no neighbor, take my value as average
Favg = my_F
endif
!* FLUX FROM MY NEIGHBOR TO ME
!* This is only considered, if I have a neighbor of nonlocal plasticity (also nonlocal constitutive law with local properties) that is at least a little bit compatible.
!* If it's not at all compatible, no flux is arriving, because everything is dammed in front of my neighbor's interface.
!* The entering flux from my neighbor will be distributed on my slip systems according to the compatibility
considerEnteringFlux = .false.
neighbor_v = 0.0_pReal ! needed for check of sign change in flux density below
neighbor_rhoSgl = 0.0_pReal
if (neighbor_n > 0_pInt) then
if (phase_plasticity(material_phase(1,neighbor_ip,neighbor_el)) == CONSTITUTIVE_NONLOCAL_LABEL &
.and. any(compatibility(:,:,:,n,ip,el) > 0.0_pReal)) &
considerEnteringFlux = .true.
endif
if (considerEnteringFlux) then
if(numerics_timeSyncing .and. (subfrac(g,neighbor_ip,neighbor_el) /= subfrac(g,ip,el))) then ! for timesyncing: in case of a timestep at the interface we have to use "state0" to make sure that fluxes n both sides are equal
forall (s = 1:ns, t = 1_pInt:4_pInt)
neighbor_v(s,t) = state0(g,neighbor_ip,neighbor_el)%p(iV(s,t,neighbor_instance))
neighbor_rhoSgl(s,t) = max(state0(g,neighbor_ip,neighbor_el)%p(iRhoU(s,t,neighbor_instance)), 0.0_pReal)
neighbor_rhoSgl(s,t+4_pInt) = state0(g,neighbor_ip,neighbor_el)%p(iRhoB(s,t,neighbor_instance))
endforall
else
forall (s = 1:ns, t = 1_pInt:4_pInt)
neighbor_v(s,t) = state(g,neighbor_ip,neighbor_el)%p(iV(s,t,neighbor_instance))
neighbor_rhoSgl(s,t) = max(state(g,neighbor_ip,neighbor_el)%p(iRhoU(s,t,neighbor_instance)), 0.0_pReal)
neighbor_rhoSgl(s,t+4_pInt) = state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,t,neighbor_instance))
endforall
endif
where (abs(neighbor_rhoSgl) * mesh_ipVolume(neighbor_ip,neighbor_el) ** 0.667_pReal &
< significantN(myInstance) &
.or. abs(neighbor_rhoSgl) < significantRho(myInstance)) &
neighbor_rhoSgl = 0.0_pReal
normal_neighbor2me_defConf = math_det33(Favg) * math_mul33x3(math_inv33(transpose(Favg)), &
mesh_ipAreaNormal(1:3,neighbor_n,neighbor_ip,neighbor_el)) ! calculate the normal of the interface in (average) deformed configuration (now pointing from my neighbor to me!!!)
normal_neighbor2me = math_mul33x3(transpose(neighbor_Fe), normal_neighbor2me_defConf) &
/ math_det33(neighbor_Fe) ! interface normal in the lattice configuration of my neighbor
area = mesh_ipArea(neighbor_n,neighbor_ip,neighbor_el) * math_norm3(normal_neighbor2me)
normal_neighbor2me = normal_neighbor2me / math_norm3(normal_neighbor2me) ! normalize the surface normal to unit length
do s = 1_pInt,ns
do t = 1_pInt,4_pInt
c = (t + 1_pInt) / 2
topp = t + mod(t,2_pInt) - mod(t+1_pInt,2_pInt)
if (neighbor_v(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal & ! flux from my neighbor to me == entering flux for me
.and. v(s,t) * neighbor_v(s,t) > 0.0_pReal ) then ! ... only if no sign change in flux density
do deads = 0_pInt,4_pInt,4_pInt
lineLength = abs(neighbor_rhoSgl(s,t+deads)) * neighbor_v(s,t) &
* math_mul3x3(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
where (compatibility(c,1_pInt:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility...
rhoDotFlux(1_pInt:ns,t) = rhoDotFlux(1_pInt:ns,t) &
+ lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed mobile dislocation type
* compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
where (compatibility(c,1_pInt:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility...
rhoDotFlux(1_pInt:ns,topp) = rhoDotFlux(1_pInt:ns,topp) &
+ lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed mobile dislocation type
* compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
enddo
endif
enddo
enddo
endif
!* FLUX FROM ME TO MY NEIGHBOR
!* This is not considered, if my opposite neighbor has a different constitutive law than nonlocal (still considered for nonlocal law with lcal properties).
!* Then, we assume, that the opposite(!) neighbor sends an equal amount of dislocations to me.
!* So the net flux in the direction of my neighbor is equal to zero:
!* leaving flux to neighbor == entering flux from opposite neighbor
!* In case of reduced transmissivity, part of the leaving flux is stored as dead dislocation density.
!* That means for an interface of zero transmissivity the leaving flux is fully converted to dead dislocations.
considerLeavingFlux = .true.
if (opposite_n > 0_pInt) then
if (phase_plasticity(material_phase(1,opposite_ip,opposite_el)) /= CONSTITUTIVE_NONLOCAL_LABEL) &
considerLeavingFlux = .false.
endif
if (considerLeavingFlux) then
!* timeSyncing mode: If the central ip has zero subfraction, always use "state0". This is needed in case of
!* a synchronization step for the central ip, because then "state" contains the values at the end of the
!* previously converged full time step. Also, if either me or my neighbor has zero subfraction, we have to
!* use "state0" to make sure that fluxes on both sides of the (potential) timestep are equal.
my_rhoSgl = rhoSgl
my_v = v
if(numerics_timeSyncing) then
if (subfrac(g,ip,el) == 0.0_pReal) then
my_rhoSgl = rhoSgl0
my_v = v0
elseif (neighbor_n > 0_pInt) then
if (subfrac(g,neighbor_ip,neighbor_el) == 0.0_pReal) then
my_rhoSgl = rhoSgl0
my_v = v0
endif
endif
endif
normal_me2neighbor_defConf = math_det33(Favg) &
* math_mul33x3(math_inv33(math_transpose33(Favg)), &
mesh_ipAreaNormal(1:3,n,ip,el)) ! calculate the normal of the interface in (average) deformed configuration (pointing from me to my neighbor!!!)
normal_me2neighbor = math_mul33x3(math_transpose33(my_Fe), normal_me2neighbor_defConf) &
/ math_det33(my_Fe) ! interface normal in my lattice configuration
area = mesh_ipArea(n,ip,el) * math_norm3(normal_me2neighbor)
normal_me2neighbor = normal_me2neighbor / math_norm3(normal_me2neighbor) ! normalize the surface normal to unit length
do s = 1_pInt,ns
do t = 1_pInt,4_pInt
c = (t + 1_pInt) / 2_pInt
if (my_v(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from me to my neighbor == leaving flux for me (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
if (my_v(s,t) * neighbor_v(s,t) > 0.0_pReal) then ! no sign change in flux density
transmissivity = sum(compatibility(c,1_pInt:ns,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor
else ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
transmissivity = 0.0_pReal
endif
lineLength = my_rhoSgl(s,t) * my_v(s,t) &
* math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of mobiles that wants to leave through this interface
rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract dislocation flux from current type
rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) &
+ lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) &
* sign(1.0_pReal, my_v(s,t)) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
lineLength = my_rhoSgl(s,t+4_pInt) * my_v(s,t) &
* math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of deads that wants to leave through this interface
rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) &
- lineLength / mesh_ipVolume(ip,el) * transmissivity ! dead dislocations leaving through this interface
endif
enddo
enddo
endif
enddo ! neighbor loop
endif
!****************************************************************************
!*** calculate dipole formation and annihilation
!*** formation by glide
do c = 1_pInt,2_pInt
rhoDotSingle2DipoleGlide(1:ns,2*c-1) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,myInstance) &
* (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(1:ns,2*c+4)) * abs(gdot(1:ns,2*c-1))) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(1:ns,2*c) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,myInstance) &
* (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile
+ rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile
+ abs(rhoSgl(1:ns,2*c+3)) * abs(gdot(1:ns,2*c))) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(1:ns,2*c+3) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,myInstance) &
* rhoSgl(1:ns,2*c+3) * abs(gdot(1:ns,2*c)) ! negative mobile --> positive immobile
rhoDotSingle2DipoleGlide(1:ns,2*c+4) = -2.0_pReal * dUpper(1:ns,c) / burgers(1:ns,myInstance) &
* rhoSgl(1:ns,2*c+4) * abs(gdot(1:ns,2*c-1)) ! positive mobile --> negative immobile
rhoDotSingle2DipoleGlide(1:ns,c+8) = - rhoDotSingle2DipoleGlide(1:ns,2*c-1) - rhoDotSingle2DipoleGlide(1:ns,2*c) &
+ abs(rhoDotSingle2DipoleGlide(1:ns,2*c+3)) + abs(rhoDotSingle2DipoleGlide(1:ns,2*c+4))
enddo
!*** athermal annihilation
rhoDotAthermalAnnihilation = 0.0_pReal
forall (c=1_pInt:2_pInt) &
rhoDotAthermalAnnihilation(1:ns,c+8_pInt) = -2.0_pReal * dLower(1:ns,c) / burgers(1:ns,myInstance) &
* ( 2.0_pReal * (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) + rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1))) & ! was single hitting single
+ 2.0_pReal * (abs(rhoSgl(1:ns,2*c+3)) * abs(gdot(1:ns,2*c)) + abs(rhoSgl(1:ns,2*c+4)) * abs(gdot(1:ns,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
+ rhoDip(1:ns,c) * (abs(gdot(1:ns,2*c-1)) + abs(gdot(1:ns,2*c)))) ! single knocks dipole constituent
! annihilated screw dipoles leave edge jogs behind on the colinear system
if (myStructure == 1_pInt) then ! only fcc
forall (s = 1:ns, colinearSystem(s,myInstance) > 0_pInt) &
rhoDotAthermalAnnihilation(colinearSystem(s,myInstance),1:2) = - rhoDotAthermalAnnihilation(s,10) &
* 0.25_pReal * sqrt(rhoForest(s)) * (dUpper(s,2) + dLower(s,2)) * edgeJogFactor(myInstance)
endif
!*** thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal
selfDiffusion = Dsd0(myInstance) * exp(-selfDiffusionEnergy(myInstance) / (KB * Temperature))
vClimb = atomicVolume(myInstance) * selfDiffusion / ( KB * Temperature ) &
* mu(myInstance) / ( 2.0_pReal * PI * (1.0_pReal-nu(myInstance)) ) &
* 2.0_pReal / ( dUpper(1:ns,1) + dLower(1:ns,1) )
forall (s = 1_pInt:ns, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) - rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
!****************************************************************************
!*** assign the rates of dislocation densities to my dotState
!*** if evolution rates lead to negative densities, a cutback is enforced
rhoDot = 0.0_pReal
rhoDot = rhoDotFlux &
+ rhoDotMultiplication &
+ rhoDotSingle2DipoleGlide &
+ rhoDotAthermalAnnihilation &
+ rhoDotThermalAnnihilation
if (numerics_integrationMode == 1_pInt) then ! save rates for output if in central integration mode
rhoDotFluxOutput(1:ns,1:8,g,ip,el) = rhoDotFlux(1:ns,1:8)
rhoDotMultiplicationOutput(1:ns,1:2,g,ip,el) = rhoDotMultiplication(1:ns,[1,3])
rhoDotSingle2DipoleGlideOutput(1:ns,1:2,g,ip,el) = rhoDotSingle2DipoleGlide(1:ns,9:10)
rhoDotAthermalAnnihilationOutput(1:ns,1:2,g,ip,el) = rhoDotAthermalAnnihilation(1:ns,9:10)
rhoDotThermalAnnihilationOutput(1:ns,1:2,g,ip,el) = rhoDotThermalAnnihilation(1:ns,9:10)
rhoDotEdgeJogsOutput(1:ns,g,ip,el) = 2.0_pReal * rhoDotThermalAnnihilation(1:ns,1)
endif
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', rhoDotFlux(1:ns,1:8) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
rhoDotAthermalAnnihilation * timestep
write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
rhoDotThermalAnnihilation(1:ns,9:10) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', rhoDot * timestep
write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', &
rhoDot(1:ns,1:8) * timestep / (abs(rhoSglOriginal)+1.0e-10), &
rhoDot(1:ns,9:10) * timestep / (rhoDipOriginal+1.0e-10)
write(6,*)
endif
#endif
if ( any(rhoSglOriginal(1:ns,1:4) + rhoDot(1:ns,1:4) * timestep < -aTolRho(myInstance)) &
.or. any(rhoDipOriginal(1:ns,1:2) + rhoDot(1:ns,9:10) * timestep < -aTolRho(myInstance))) then
#ifndef _OPENMP
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt) then
write(6,'(a,i5,a,i2)') '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
endif
#endif
constitutive_nonlocal_dotState = DAMASK_NaN
return
else
forall (s = 1:ns, t = 1_pInt:4_pInt)
constitutive_nonlocal_dotState(iRhoU(s,t,myInstance)) = rhoDot(s,t)
constitutive_nonlocal_dotState(iRhoB(s,t,myInstance)) = rhoDot(s,t+4_pInt)
endforall
forall (s = 1:ns, c = 1_pInt:2_pInt) &
constitutive_nonlocal_dotState(iRhoD(s,c,myInstance)) = rhoDot(s,c+8_pInt)
forall (s = 1:ns) &
constitutive_nonlocal_dotState(iGamma(s,myInstance)) = sum(gdot(s,1:4))
endif
endfunction
!*********************************************************************
!* COMPATIBILITY UPDATE *
!* Compatibility is defined as normalized product of signed cosine *
!* of the angle between the slip plane normals and signed cosine of *
!* the angle between the slip directions. Only the largest values *
!* that sum up to a total of 1 are considered, all others are set to *
!* zero. *
!*********************************************************************
subroutine constitutive_nonlocal_updateCompatibility(orientation,i,e)
use math, only: math_qDisorientation, &
math_mul3x3, &
math_qRot
use material, only: material_phase, &
material_texture, &
phase_localPlasticity, &
phase_plasticityInstance, &
homogenization_maxNgrains
use mesh, only: mesh_element, &
mesh_ipNeighborhood, &
mesh_maxNips, &
mesh_NcpElems, &
FE_NipNeighbors, &
FE_geomtype, &
FE_celltype
use lattice, only: lattice_sn, &
lattice_sd
implicit none
!* input variables
integer(pInt), intent(in) :: i, & ! ip index
e ! element index
real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
orientation ! crystal orientation in quaternions
!* output variables
!* local variables
integer(pInt) Nneighbors, & ! number of neighbors
n, & ! neighbor index
neighbor_e, & ! element index of my neighbor
neighbor_i, & ! integration point index of my neighbor
my_phase, &
neighbor_phase, &
my_texture, &
neighbor_texture, &
my_structure, & ! lattice structure
my_instance, & ! instance of plasticity
ns, & ! number of active slip systems
s1, & ! slip system index (me)
s2 ! slip system index (my neighbor)
real(pReal), dimension(4) :: absoluteMisorientation ! absolute misorientation (without symmetry) between me and my neighbor
real(pReal), dimension(2,totalNslip(phase_plasticityInstance(material_phase(1,i,e))),&
totalNslip(phase_plasticityInstance(material_phase(1,i,e))),&
FE_NipNeighbors(FE_celltype(FE_geomtype(mesh_element(2,e))))) :: &
my_compatibility ! my_compatibility for current element and ip
real(pReal), dimension(3,totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: &
slipNormal, &
slipDirection
real(pReal) my_compatibilitySum, &
thresholdValue, &
nThresholdValues
logical, dimension(totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: &
belowThreshold
Nneighbors = FE_NipNeighbors(FE_celltype(FE_geomtype(mesh_element(2,e))))
my_phase = material_phase(1,i,e)
my_texture = material_texture(1,i,e)
my_instance = phase_plasticityInstance(my_phase)
my_structure = constitutive_nonlocal_structure(my_instance)
ns = totalNslip(my_instance)
slipNormal(1:3,1:ns) = lattice_sn(1:3, slipSystemLattice(1:ns,my_instance), my_structure)
slipDirection(1:3,1:ns) = lattice_sd(1:3, slipSystemLattice(1:ns,my_instance), my_structure)
!*** start out fully compatible
my_compatibility = 0.0_pReal
forall(s1 = 1_pInt:ns) &
my_compatibility(1:2,s1,s1,1:Nneighbors) = 1.0_pReal
!*** Loop thrugh neighbors and check whether there is any my_compatibility.
do n = 1_pInt,Nneighbors
neighbor_e = mesh_ipNeighborhood(1,n,i,e)
neighbor_i = mesh_ipNeighborhood(2,n,i,e)
!* FREE SURFACE
!* Set surface transmissivity to the value specified in the material.config
if (neighbor_e <= 0_pInt .or. neighbor_i <= 0_pInt) then
forall(s1 = 1_pInt:ns) &
my_compatibility(1:2,s1,s1,n) = sqrt(surfaceTransmissivity(my_instance))
cycle
endif
!* PHASE BOUNDARY
!* If we encounter a different nonlocal "cpfem" phase at the neighbor,
!* we consider this to be a real "physical" phase boundary, so completely incompatible.
!* If one of the two "CPFEM" phases has a local plasticity law,
!* we do not consider this to be a phase boundary, so completely compatible.
neighbor_phase = material_phase(1,neighbor_i,neighbor_e)
if (neighbor_phase /= my_phase) then
if (.not. phase_localPlasticity(neighbor_phase) .and. .not. phase_localPlasticity(my_phase)) then
forall(s1 = 1_pInt:ns) &
my_compatibility(1:2,s1,s1,n) = 0.0_pReal ! = sqrt(0.0)
endif
cycle
endif
!* GRAIN BOUNDARY !
!* fixed transmissivity for adjacent ips with different texture (only if explicitly given in material.config)
if (grainboundaryTransmissivity(my_instance) >= 0.0_pReal) then
neighbor_texture = material_texture(1,neighbor_i,neighbor_e)
if (neighbor_texture /= my_texture) then
if (.not. phase_localPlasticity(neighbor_phase)) then
forall(s1 = 1_pInt:ns) &
my_compatibility(1:2,s1,s1,n) = sqrt(grainboundaryTransmissivity(my_instance))
endif
cycle
endif
!* GRAIN BOUNDARY ?
!* Compatibility defined by relative orientation of slip systems:
!* The my_compatibility value is defined as the product of the slip normal projection and the slip direction projection.
!* Its sign is always positive for screws, for edges it has the same sign as the slip normal projection.
!* Since the sum for each slip system can easily exceed one (which would result in a transmissivity larger than one),
!* only values above or equal to a certain threshold value are considered. This threshold value is chosen, such that
!* the number of compatible slip systems is minimized with the sum of the original my_compatibility values exceeding one.
!* Finally the smallest my_compatibility value is decreased until the sum is exactly equal to one.
!* All values below the threshold are set to zero.
else
absoluteMisorientation = math_qDisorientation(orientation(1:4,1,i,e), &
orientation(1:4,1,neighbor_i,neighbor_e), &
0_pInt) ! no symmetry
do s1 = 1_pInt,ns ! my slip systems
do s2 = 1_pInt,ns ! my neighbor's slip systems
my_compatibility(1,s2,s1,n) = math_mul3x3(slipNormal(1:3,s1), math_qRot(absoluteMisorientation, slipNormal(1:3,s2))) &
* abs(math_mul3x3(slipDirection(1:3,s1), math_qRot(absoluteMisorientation, slipDirection(1:3,s2))))
my_compatibility(2,s2,s1,n) = abs(math_mul3x3(slipNormal(1:3,s1), math_qRot(absoluteMisorientation, slipNormal(1:3,s2)))) &
* abs(math_mul3x3(slipDirection(1:3,s1), math_qRot(absoluteMisorientation, slipDirection(1:3,s2))))
enddo
my_compatibilitySum = 0.0_pReal
belowThreshold = .true.
do while (my_compatibilitySum < 1.0_pReal .and. any(belowThreshold(1:ns)))
thresholdValue = maxval(my_compatibility(2,1:ns,s1,n), belowThreshold(1:ns)) ! screws always positive
nThresholdValues = real(count(my_compatibility(2,1:ns,s1,n) == thresholdValue),pReal)
where (my_compatibility(2,1:ns,s1,n) >= thresholdValue) &
belowThreshold(1:ns) = .false.
if (my_compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
where (abs(my_compatibility(1:2,1:ns,s1,n)) == thresholdValue) &
my_compatibility(1:2,1:ns,s1,n) = sign((1.0_pReal - my_compatibilitySum) &
/ nThresholdValues, my_compatibility(1:2,1:ns,s1,n))
my_compatibilitySum = my_compatibilitySum + nThresholdValues * thresholdValue
enddo
where (belowThreshold(1:ns)) my_compatibility(1,1:ns,s1,n) = 0.0_pReal
where (belowThreshold(1:ns)) my_compatibility(2,1:ns,s1,n) = 0.0_pReal
enddo ! my slip systems cycle
endif
enddo ! neighbor cycle
compatibility(1:2,1:ns,1:ns,1:Nneighbors,i,e) = my_compatibility
endsubroutine
!*********************************************************************
!* rate of change of temperature *
!*********************************************************************
pure function constitutive_nonlocal_dotTemperature(Tstar_v,Temperature,state,g,ip,el)
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains
implicit none
!* input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
!* output variables
real(pReal) constitutive_nonlocal_dotTemperature ! evolution of Temperature
!* local variables
constitutive_nonlocal_dotTemperature = 0.0_pReal
endfunction
!*********************************************************************
!* calculates quantities characterizing the microstructure *
!*********************************************************************
function constitutive_nonlocal_dislocationstress(state, Fe, g, ip, el)
use math, only: math_mul33x33, &
math_mul33x3, &
math_invert33, &
math_transpose33, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
mesh_node0, &
mesh_cellCenterCoordinates, &
mesh_ipVolume, &
mesh_periodicSurface, &
FE_Nips, &
FE_geomtype
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_localPlasticity, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe ! elastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
!*** input/output variables
!*** output variables
real(pReal), dimension(3,3) :: constitutive_nonlocal_dislocationstress
!*** local variables
integer(pInt) neighbor_el, & ! element number of neighbor material point
neighbor_ip, & ! integration point of neighbor material point
instance, & ! my instance of this plasticity
neighbor_instance, & ! instance of this plasticity of neighbor material point
latticeStruct, & ! my lattice structure
neighbor_latticeStruct, & ! lattice structure of neighbor material point
phase, &
neighbor_phase, &
ns, & ! total number of active slip systems at my material point
neighbor_ns, & ! total number of active slip systems at neighbor material point
c, & ! index of dilsocation character (edge, screw)
s, & ! slip system index
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
dir, &
deltaX, deltaY, deltaZ, &
side, &
j
integer(pInt), dimension(2,3) :: periodicImages
real(pReal) x, y, z, & ! coordinates of connection vector in neighbor lattice frame
xsquare, ysquare, zsquare, & ! squares of respective coordinates
distance, & ! length of connection vector
segmentLength, & ! segment length of dislocations
lambda, &
R, Rsquare, Rcube, &
denominator, &
flipSign, &
neighbor_ipVolumeSideLength, &
detFe
real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration
connection_neighborLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor
connection_neighborSlip, & ! connection vector between me and my neighbor in the slip system frame of my neighbor
maxCoord, minCoord, &
meshSize, &
coords, & ! x,y,z coordinates of cell center of ip volume
neighbor_coords ! x,y,z coordinates of cell center of neighbor ip volume
real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighbor material point's slip system frame
Tdislo_neighborLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighbor material point
invFe, & ! inverse of my elastic deformation gradient
neighbor_invFe, &
neighborLattice2myLattice ! mapping from neighbor MPs lattice configuration to my lattice configuration
real(pReal), dimension(2,2,maxval(totalNslip)) :: &
neighbor_rhoExcess ! excess density at neighbor material point (edge/screw,mobile/dead,slipsystem)
real(pReal), dimension(2,maxval(totalNslip)) :: &
rhoExcessDead
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
logical inversionError
phase = material_phase(g,ip,el)
instance = phase_plasticityInstance(phase)
latticeStruct = constitutive_nonlocal_structure(instance)
ns = totalNslip(instance)
!*** get basic states
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = max(state(g,ip,el)%p(iRhoU(s,t,instance)), 0.0_pReal) ! ensure positive single mobile densities
rhoSgl(s,t+4_pInt) = state(g,ip,el)%p(iRhoB(s,t,instance))
endforall
!*** calculate the dislocation stress of the neighboring excess dislocation densities
!*** zero for material points of local plasticity
constitutive_nonlocal_dislocationstress = 0.0_pReal
if (.not. phase_localPlasticity(phase)) then
call math_invert33(Fe(1:3,1:3,g,ip,el), invFe, detFe, inversionError)
!* in case of periodic surfaces we have to find out how many periodic images in each direction we need
do dir = 1_pInt,3_pInt
maxCoord(dir) = maxval(mesh_node0(dir,:))
minCoord(dir) = minval(mesh_node0(dir,:))
enddo
meshSize = maxCoord - minCoord
coords = mesh_cellCenterCoordinates(ip,el)
periodicImages = 0_pInt
do dir = 1_pInt,3_pInt
if (mesh_periodicSurface(dir)) then
periodicImages(1,dir) = floor((coords(dir) - cutoffRadius(instance) - minCoord(dir)) / meshSize(dir), pInt)
periodicImages(2,dir) = ceiling((coords(dir) + cutoffRadius(instance) - maxCoord(dir)) / meshSize(dir), pInt)
endif
enddo
!* loop through all material points (also through their periodic images if present),
!* but only consider nonlocal neighbors within a certain cutoff radius R
do neighbor_el = 1_pInt,mesh_NcpElems
ipLoop: do neighbor_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighbor_el)))
neighbor_phase = material_phase(g,neighbor_ip,neighbor_el)
if (phase_localPlasticity(neighbor_phase)) then
cycle
endif
neighbor_instance = phase_plasticityInstance(neighbor_phase)
neighbor_latticeStruct = constitutive_nonlocal_structure(neighbor_instance)
neighbor_ns = totalNslip(neighbor_instance)
call math_invert33(Fe(1:3,1:3,1,neighbor_ip,neighbor_el), neighbor_invFe, detFe, inversionError)
neighbor_ipVolumeSideLength = mesh_ipVolume(neighbor_ip,neighbor_el) ** (1.0_pReal/3.0_pReal) ! reference volume used here
forall (s = 1_pInt:neighbor_ns, c = 1_pInt:2_pInt)
neighbor_rhoExcess(c,1,s) = state(g,neighbor_ip,neighbor_el)%p(iRhoU(s,2*c-1,neighbor_instance)) & ! positive mobiles
- state(g,neighbor_ip,neighbor_el)%p(iRhoU(s,2*c,neighbor_instance)) ! negative mobiles
neighbor_rhoExcess(c,2,s) = abs(state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,2*c-1,neighbor_instance))) & ! positive deads
- abs(state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,2*c,neighbor_instance))) ! negative deads
endforall
Tdislo_neighborLattice = 0.0_pReal
do deltaX = periodicImages(1,1),periodicImages(2,1)
do deltaY = periodicImages(1,2),periodicImages(2,2)
do deltaZ = periodicImages(1,3),periodicImages(2,3)
!* regular case
if (neighbor_el /= el .or. neighbor_ip /= ip &
.or. deltaX /= 0_pInt .or. deltaY /= 0_pInt .or. deltaZ /= 0_pInt) then
neighbor_coords = mesh_cellCenterCoordinates(neighbor_ip,neighbor_el) &
+ (/real(deltaX,pReal), real(deltaY,pReal), real(deltaZ,pReal)/) * meshSize
connection = neighbor_coords - coords
distance = sqrt(sum(connection * connection))
if (distance > cutoffRadius(instance)) then
cycle
endif
!* the segment length is the minimum of the third root of the control volume and the ip distance
!* this ensures, that the central MP never sits on a neighbor dislocation segment
connection_neighborLattice = math_mul33x3(neighbor_invFe, connection)
segmentLength = min(neighbor_ipVolumeSideLength, distance)
!* loop through all slip systems of the neighbor material point
!* and add up the stress contributions from egde and screw excess on these slip systems (if significant)
do s = 1_pInt,neighbor_ns
if (all(abs(neighbor_rhoExcess(:,:,s)) < significantRho(instance))) then
cycle ! not significant
endif
!* map the connection vector from the lattice into the slip system frame
connection_neighborSlip = math_mul33x3(lattice2slip(1:3,1:3,s,neighbor_instance), &
connection_neighborLattice)
!* edge contribution to stress
sigma = 0.0_pReal
x = connection_neighborSlip(1)
y = connection_neighborSlip(2)
z = connection_neighborSlip(3)
xsquare = x * x
ysquare = y * y
zsquare = z * z
do j = 1_pInt,2_pInt
if (abs(neighbor_rhoExcess(1,j,s)) < significantRho(instance)) then
cycle
elseif (j > 1_pInt) then
x = connection_neighborSlip(1) + sign(0.5_pReal * segmentLength, &
state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,1,neighbor_instance)) &
- state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,2,neighbor_instance)))
xsquare = x * x
endif
flipSign = sign(1.0_pReal, -y)
do side = 1_pInt,-1_pInt,-2_pInt
lambda = real(side,pReal) * 0.5_pReal * segmentLength - y
R = sqrt(xsquare + zsquare + lambda * lambda)
Rsquare = R * R
Rcube = Rsquare * R
denominator = R * (R + flipSign * lambda)
if (denominator == 0.0_pReal) then
exit ipLoop
endif
sigma(1,1) = sigma(1,1) - real(side,pReal) &
* flipSign * z / denominator &
* (1.0_pReal + xsquare / Rsquare + xsquare / denominator) &
* neighbor_rhoExcess(1,j,s)
sigma(2,2) = sigma(2,2) - real(side,pReal) &
* (flipSign * 2.0_pReal * nu(instance) * z / denominator + z * lambda / Rcube) &
* neighbor_rhoExcess(1,j,s)
sigma(3,3) = sigma(3,3) + real(side,pReal) &
* flipSign * z / denominator &
* (1.0_pReal - zsquare / Rsquare - zsquare / denominator) &
* neighbor_rhoExcess(1,j,s)
sigma(1,2) = sigma(1,2) + real(side,pReal) &
* x * z / Rcube * neighbor_rhoExcess(1,j,s)
sigma(1,3) = sigma(1,3) + real(side,pReal) &
* flipSign * x / denominator &
* (1.0_pReal - zsquare / Rsquare - zsquare / denominator) &
* neighbor_rhoExcess(1,j,s)
sigma(2,3) = sigma(2,3) - real(side,pReal) &
* (nu(instance) / R - zsquare / Rcube) * neighbor_rhoExcess(1,j,s)
enddo
enddo
!* screw contribution to stress
x = connection_neighborSlip(1) ! have to restore this value, because position might have been adapted for edge deads before
do j = 1_pInt,2_pInt
if (abs(neighbor_rhoExcess(2,j,s)) < significantRho(instance)) then
cycle
elseif (j > 1_pInt) then
y = connection_neighborSlip(2) + sign(0.5_pReal * segmentLength, &
state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,3,neighbor_instance)) &
- state(g,neighbor_ip,neighbor_el)%p(iRhoB(s,4,neighbor_instance)))
ysquare = y * y
endif
flipSign = sign(1.0_pReal, x)
do side = 1_pInt,-1_pInt,-2_pInt
lambda = x + real(side,pReal) * 0.5_pReal * segmentLength
R = sqrt(ysquare + zsquare + lambda * lambda)
Rsquare = R * R
Rcube = Rsquare * R
denominator = R * (R + flipSign * lambda)
if (denominator == 0.0_pReal) then
exit ipLoop
endif
sigma(1,2) = sigma(1,2) - real(side,pReal) * flipSign * z * (1.0_pReal - nu(instance)) / denominator &
* neighbor_rhoExcess(2,j,s)
sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * y * (1.0_pReal - nu(instance)) / denominator &
* neighbor_rhoExcess(2,j,s)
enddo
enddo
if (all(abs(sigma) < 1.0e-10_pReal)) then ! SIGMA IS NOT A REAL STRESS, THATS WHY WE NEED A REALLY SMALL VALUE HERE
cycle
endif
!* copy symmetric parts
sigma(2,1) = sigma(1,2)
sigma(3,1) = sigma(1,3)
sigma(3,2) = sigma(2,3)
!* scale stresses and map them into the neighbor material point's lattice configuration
sigma = sigma * mu(neighbor_instance) * burgers(s,neighbor_instance) &
/ (4.0_pReal * pi * (1.0_pReal - nu(neighbor_instance))) &
* mesh_ipVolume(neighbor_ip,neighbor_el) / segmentLength ! reference volume is used here (according to the segment length calculation)
Tdislo_neighborLattice = Tdislo_neighborLattice &
+ math_mul33x33(math_transpose33(lattice2slip(1:3,1:3,s,neighbor_instance)), &
math_mul33x33(sigma, lattice2slip(1:3,1:3,s,neighbor_instance)))
enddo ! slip system loop
!* special case of central ip volume
!* only consider dead dislocations
!* we assume that they all sit at a distance equal to half the third root of V
!* in direction of the according slip direction
else
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
rhoExcessDead(c,s) = state(g,ip,el)%p(iRhoB(s,2*c-1,instance)) & ! positive deads (here we use symmetry: if this has negative sign it is treated as negative density at positive position instead of positive density at negative position)
+ state(g,ip,el)%p(iRhoB(s,2*c,instance)) ! negative deads (here we use symmetry: if this has negative sign it is treated as positive density at positive position instead of negative density at negative position)
do s = 1_pInt,ns
if (all(abs(rhoExcessDead(:,s)) < significantRho(instance))) then
cycle ! not significant
endif
sigma = 0.0_pReal ! all components except for sigma13 are zero
sigma(1,3) = - (rhoExcessDead(1,s) + rhoExcessDead(2,s) * (1.0_pReal - nu(instance))) &
* neighbor_ipVolumeSideLength * mu(instance) * burgers(s,instance) &
/ (sqrt(2.0_pReal) * pi * (1.0_pReal - nu(instance)))
sigma(3,1) = sigma(1,3)
Tdislo_neighborLattice = Tdislo_neighborLattice &
+ math_mul33x33(math_transpose33(lattice2slip(1:3,1:3,s,instance)), &
math_mul33x33(sigma, lattice2slip(1:3,1:3,s,instance)))
enddo ! slip system loop
endif
enddo ! deltaZ loop
enddo ! deltaY loop
enddo ! deltaX loop
!* map the stress from the neighbor MP's lattice configuration into the deformed configuration
!* and back into my lattice configuration
neighborLattice2myLattice = math_mul33x33(invFe, Fe(1:3,1:3,1,neighbor_ip,neighbor_el))
constitutive_nonlocal_dislocationstress = constitutive_nonlocal_dislocationstress &
+ math_mul33x33(neighborLattice2myLattice, &
math_mul33x33(Tdislo_neighborLattice, &
math_transpose33(neighborLattice2myLattice)))
enddo ipLoop
enddo ! element loop
endif
endfunction
!*********************************************************************
!* return array of constitutive results *
!*********************************************************************
function constitutive_nonlocal_postResults(Tstar_v, Fe, Temperature, dt, state, dotState, g,ip,el)
use math, only: math_mul6x6, &
math_mul33x3, &
math_mul33x33, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_ipVolume
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
phase_Noutput
use lattice, only: lattice_Sslip_v, &
lattice_sd, &
lattice_st, &
lattice_sn
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature, & ! temperature
dt ! time increment
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe ! elastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! current microstructural state
type(p_vec), intent(in) :: dotState ! evolution rate of microstructural state
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizePostResults(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_nonlocal_postResults
!*** local variables
integer(pInt) myInstance, & ! current instance of this plasticity
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
c, & ! character of dislocation
cs, & ! constitutive result index
o, & ! index of current output
t, & ! type of dislocation
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
rhoDotSgl ! evolution rate of single dislocation densities (positive/negative screw and edge without dipoles)
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
gdot, & ! shear rates
v ! velocities
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauThreshold, & ! threshold shear stress
tau, & ! current resolved shear stress
tauBack ! back stress from pileups on same slip system
real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
rhoDotDip, & ! evolution rate of dipole dislocation densities (screw and edge dipoles)
dLower, & ! minimum stable dipole distance for edges and screws
dUpper ! current maximum stable dipole distance for edges and screws
real(pReal), dimension(3,totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
m, & ! direction of dislocation motion for edge and screw (unit vector)
m_currentconf ! direction of dislocation motion for edge and screw (unit vector) in current configuration
real(pReal), dimension(3,totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
n_currentconf ! slip system normal (unit vector) in current configuration
real(pReal), dimension(3,3) :: sigma
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = totalNslip(myInstance)
cs = 0_pInt
constitutive_nonlocal_postResults = 0.0_pReal
!* short hand notations for state variables
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt)
rhoSgl(s,t) = state(g,ip,el)%p(iRhoU(s,t,myInstance))
rhoSgl(s,t+4_pInt) = state(g,ip,el)%p(iRhoB(s,t,myInstance))
v(s,t) = state(g,ip,el)%p(iV(s,t,myInstance))
rhoDotSgl(s,t) = dotState%p(iRhoU(s,t,myInstance))
rhoDotSgl(s,t+4_pInt) = dotState%p(iRhoB(s,t,myInstance))
endforall
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt)
rhoDip(s,c) = state(g,ip,el)%p(iRhoD(s,c,myInstance))
rhoDotDip(s,c) = dotState%p(iRhoD(s,c,myInstance))
endforall
rhoForest = state(g,ip,el)%p(iRhoF(1:ns,myInstance))
tauThreshold = state(g,ip,el)%p(iTauF(1:ns,myInstance))
tauBack = state(g,ip,el)%p(iTauB(1:ns,myInstance))
!* Calculate shear rate
forall (t = 1_pInt:4_pInt) &
gdot(1:ns,t) = rhoSgl(1:ns,t) * burgers(1:ns,myInstance) * v(1:ns,t)
!* calculate limits for stable dipole height
do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance)
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure)) + tauBack(s)
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
enddo
dLower = minDipoleHeight(1:ns,1:2,myInstance)
dUpper(1:ns,1) = mu(myInstance) * burgers(1:ns,myInstance) &
/ (8.0_pReal * pi * (1.0_pReal - nu(myInstance)) * abs(tau))
dUpper(1:ns,2) = mu(myInstance) * burgers(1:ns,myInstance) &
/ (4.0_pReal * pi * abs(tau))
forall (c = 1_pInt:2_pInt) &
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
dUpper(1:ns,c))
dUpper = max(dUpper,dLower)
!*** dislocation motion
m(1:3,1:ns,1) = lattice_sd(1:3,slipSystemLattice(1:ns,myInstance),myStructure)
m(1:3,1:ns,2) = -lattice_st(1:3,slipSystemLattice(1:ns,myInstance),myStructure)
forall (c = 1_pInt:2_pInt, s = 1_pInt:ns) &
m_currentconf(1:3,s,c) = math_mul33x3(Fe(1:3,1:3,g,ip,el), m(1:3,s,c))
forall (s = 1_pInt:ns) &
n_currentconf(1:3,s) = math_mul33x3(Fe(1:3,1:3,g,ip,el), &
lattice_sn(1:3,slipSystemLattice(s,myInstance),myStructure))
do o = 1_pInt,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_nonlocal_output(o,myInstance))
case ('rho')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl),2) + sum(rhoDip,2)
cs = cs + ns
case ('rho_sgl')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl),2)
cs = cs + ns
case ('rho_sgl_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,1:4)),2)
cs = cs + ns
case ('rho_sgl_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,5:8),2)
cs = cs + ns
case ('rho_dip')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDip,2)
cs = cs + ns
case ('rho_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)
cs = cs + ns
case ('rho_sgl_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2)
cs = cs + ns
case ('rho_sgl_edge_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,1:2),2)
cs = cs + ns
case ('rho_sgl_edge_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,5:6),2)
cs = cs + ns
case ('rho_sgl_edge_pos')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))
cs = cs + ns
case ('rho_sgl_edge_pos_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1)
cs = cs + ns
case ('rho_sgl_edge_pos_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,5)
cs = cs + ns
case ('rho_sgl_edge_neg')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6))
cs = cs + ns
case ('rho_sgl_edge_neg_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,2)
cs = cs + ns
case ('rho_sgl_edge_neg_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,6)
cs = cs + ns
case ('rho_dip_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDip(1:ns,1)
cs = cs + ns
case ('rho_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)
cs = cs + ns
case ('rho_sgl_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2)
cs = cs + ns
case ('rho_sgl_screw_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,3:4),2)
cs = cs + ns
case ('rho_sgl_screw_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,7:8),2)
cs = cs + ns
case ('rho_sgl_screw_pos')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))
cs = cs + ns
case ('rho_sgl_screw_pos_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3)
cs = cs + ns
case ('rho_sgl_screw_pos_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,7)
cs = cs + ns
case ('rho_sgl_screw_neg')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8))
cs = cs + ns
case ('rho_sgl_screw_neg_mobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,4)
cs = cs + ns
case ('rho_sgl_screw_neg_immobile')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,8)
cs = cs + ns
case ('rho_dip_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDip(1:ns,2)
cs = cs + ns
case ('excess_rho')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))) &
- (rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6))) &
+ (rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))) &
- (rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8)))
cs = cs + ns
case ('excess_rho_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))) &
- (rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6)))
cs = cs + ns
case ('excess_rho_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))) &
- (rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8)))
cs = cs + ns
case ('rho_forest')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoForest
cs = cs + ns
case ('delta')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2) + sum(rhoDip,2))
cs = cs + ns
case ('delta_sgl')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2))
cs = cs + ns
case ('delta_dip')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(rhoDip,2))
cs = cs + ns
case ('shearrate')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(gdot,2)
cs = cs + ns
case ('resolvedstress')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tau
cs = cs + ns
case ('resolvedstress_back')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tauBack
cs = cs + ns
case ('resolvedstress_external')
do s = 1_pInt,ns
sLattice = slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(cs+s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,1,sLattice,myStructure))
enddo
cs = cs + ns
case ('resistance')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tauThreshold
cs = cs + ns
case ('rho_dot')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotSgl,2) + sum(rhoDotDip,2)
cs = cs + ns
case ('rho_dot_sgl')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotSgl,2)
cs = cs + ns
case ('rho_dot_dip')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotDip,2)
cs = cs + ns
case ('rho_dot_gen')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotMultiplicationOutput(1:ns,1,g,ip,el) &
+ rhoDotMultiplicationOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_gen_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotMultiplicationOutput(1:ns,1,g,ip,el)
cs = cs + ns
case ('rho_dot_gen_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotMultiplicationOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_sgl2dip')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotSingle2DipoleGlideOutput(1:ns,1,g,ip,el) &
+ rhoDotSingle2DipoleGlideOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_sgl2dip_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotSingle2DipoleGlideOutput(1:ns,1,g,ip,el)
cs = cs + ns
case ('rho_dot_sgl2dip_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotSingle2DipoleGlideOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_ann_ath')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotAthermalAnnihilationOutput(1:ns,1,g,ip,el) &
+ rhoDotAthermalAnnihilationOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_ann_the')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotThermalAnnihilationOutput(1:ns,1,g,ip,el) &
+ rhoDotThermalAnnihilationOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_ann_the_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotThermalAnnihilationOutput(1:ns,1,g,ip,el)
cs = cs + ns
case ('rho_dot_ann_the_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotThermalAnnihilationOutput(1:ns,2,g,ip,el)
cs = cs + ns
case ('rho_dot_edgejogs')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDotEdgeJogsOutput(1:ns,g,ip,el)
cs = cs + ns
case ('rho_dot_flux')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotFluxOutput(1:ns,1:4,g,ip,el),2) &
+ sum(abs(rhoDotFluxOutput(1:ns,5:8,g,ip,el)),2)
cs = cs + ns
case ('rho_dot_flux_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotFluxOutput(1:ns,1:2,g,ip,el),2) &
+ sum(abs(rhoDotFluxOutput(1:ns,5:6,g,ip,el)),2)
cs = cs + ns
case ('rho_dot_flux_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotFluxOutput(1:ns,3:4,g,ip,el),2) &
+ sum(abs(rhoDotFluxOutput(1:ns,7:8,g,ip,el)),2)
cs = cs + ns
case ('velocity_edge_pos')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,1)
cs = cs + ns
case ('velocity_edge_neg')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,2)
cs = cs + ns
case ('velocity_screw_pos')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,3)
cs = cs + ns
case ('velocity_screw_neg')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,4)
cs = cs + ns
case ('slipdirection.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = m_currentconf(1,1:ns,1)
cs = cs + ns
case ('slipdirection.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = m_currentconf(2,1:ns,1)
cs = cs + ns
case ('slipdirection.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = m_currentconf(3,1:ns,1)
cs = cs + ns
case ('slipnormal.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = n_currentconf(1,1:ns)
cs = cs + ns
case ('slipnormal.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = n_currentconf(2,1:ns)
cs = cs + ns
case ('slipnormal.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = n_currentconf(3,1:ns)
cs = cs + ns
case ('fluxdensity_edge_pos.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(1,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_pos.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(2,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_pos.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(3,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(1,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(2,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(3,1:ns,1)
cs = cs + ns
case ('fluxdensity_screw_pos.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(1,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_pos.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(2,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_pos.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(3,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg.x')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(1,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg.y')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(2,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg.z')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(3,1:ns,2)
cs = cs + ns
case ('maximumdipoleheight_edge')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = dUpper(1:ns,1)
cs = cs + ns
case ('maximumdipoleheight_screw')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = dUpper(1:ns,2)
cs = cs + ns
case('dislocationstress')
sigma = constitutive_nonlocal_dislocationstress(state, Fe, g, ip, el)
constitutive_nonlocal_postResults(cs+1_pInt) = sigma(1,1)
constitutive_nonlocal_postResults(cs+2_pInt) = sigma(2,2)
constitutive_nonlocal_postResults(cs+3_pInt) = sigma(3,3)
constitutive_nonlocal_postResults(cs+4_pInt) = sigma(1,2)
constitutive_nonlocal_postResults(cs+5_pInt) = sigma(2,3)
constitutive_nonlocal_postResults(cs+6_pInt) = sigma(3,1)
cs = cs + 6_pInt
case('accumulatedshear')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(iGamma(1:ns,myInstance))
cs = cs + ns
case('boundarylayer')
do s = 1_pInt,ns
if (sum(abs(rhoSgl(s,1:8))) > 0.0_pReal) then
constitutive_nonlocal_postResults(cs+s) = maxval(abs(rhoSgl(s,5:8))/(rhoSgl(s,1:4)+abs(rhoSgl(s,5:8))))
else
constitutive_nonlocal_postResults(cs+s) = 0.0_pReal
endif
enddo
cs = cs + ns
end select
enddo
endfunction
END MODULE