! Copyright 2011 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 . ! !############################################################## !* $Id$ !************************************ !* Module: CONSTITUTIVE_NONLOCAL * !************************************ !* contains: * !* - constitutive equations * !* - parameters definition * !************************************ MODULE constitutive_nonlocal !* Include other modules use prec, only: pReal,pInt implicit none private !* Definition of parameters character (len=*), parameter, public :: & constitutive_nonlocal_label = 'nonlocal' character(len=22), dimension(10), parameter, private :: & constitutive_nonlocal_listBasicStates = (/'rhoSglEdgePosMobile ', & 'rhoSglEdgeNegMobile ', & 'rhoSglScrewPosMobile ', & 'rhoSglScrewNegMobile ', & 'rhoSglEdgePosImmobile ', & 'rhoSglEdgeNegImmobile ', & 'rhoSglScrewPosImmobile', & 'rhoSglScrewNegImmobile', & 'rhoDipEdge ', & 'rhoDipScrew ' /)! list of "basic" microstructural state variables that are independent from other state variables character(len=16), dimension(3), parameter, private :: & constitutive_nonlocal_listDependentStates = (/'rhoForest ', & 'tauThreshold ', & 'tauBack ' /) ! list of microstructural state variables that depend on other state variables character(len=20), dimension(6), parameter, private :: & constitutive_nonlocal_listOtherStates = (/'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 :: & constitutive_nonlocal_Noutput ! number of outputs per instance of this plasticity 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 :: & constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance integer(pInt), dimension(:,:), allocatable, private :: & constitutive_nonlocal_Nslip, & ! number of active slip systems for each family and instance constitutive_nonlocal_slipFamily, & ! lookup table relating active slip system to slip family for each instance constitutive_nonlocal_slipSystemLattice, & ! lookup table relating active slip system index to lattice slip system index for each instance constitutive_nonlocal_colinearSystem ! colinear system to the active slip system (only valid for fcc!) real(pReal), dimension(:), allocatable, private :: & constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice constitutive_nonlocal_Gmod, & ! shear modulus constitutive_nonlocal_nu, & ! poisson's ratio constitutive_nonlocal_atomicVolume, & ! atomic volume constitutive_nonlocal_Dsd0, & ! prefactor for self-diffusion coefficient constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion constitutive_nonlocal_aTolRho, & ! absolute tolerance for dislocation density in state integration constitutive_nonlocal_significantRho, & ! density considered significant constitutive_nonlocal_significantN, & ! number of dislocations considered significant constitutive_nonlocal_R, & ! cutoff radius for dislocation stress constitutive_nonlocal_doublekinkwidth, & ! width of a doubkle kink in multiples of the burgers vector length b constitutive_nonlocal_solidSolutionEnergy, & ! activation energy for solid solution in J constitutive_nonlocal_solidSolutionSize, & ! solid solution obstacle size in multiples of the burgers vector length constitutive_nonlocal_solidSolutionConcentration, & ! concentration of solid solution in atomic parts constitutive_nonlocal_p, & ! parameter for kinetic law (Kocks,Argon,Ashby) constitutive_nonlocal_q, & ! parameter for kinetic law (Kocks,Argon,Ashby) constitutive_nonlocal_viscosity, & ! viscosity for dislocation glide in Pa s constitutive_nonlocal_fattack, & ! attack frequency in Hz constitutive_nonlocal_rhoSglScatter, & ! standard deviation of scatter in initial dislocation density constitutive_nonlocal_surfaceTransmissivity, & ! transmissivity at free surface constitutive_nonlocal_grainboundaryTransmissivity, & ! transmissivity at grain boundary (identified by different texture) constitutive_nonlocal_CFLfactor, & ! safety factor for CFL flux condition constitutive_nonlocal_fEdgeMultiplication, & ! factor that determines how much edge dislocations contribute to multiplication (0...1) constitutive_nonlocal_rhoSglRandom, & constitutive_nonlocal_rhoSglRandomBinning, & constitutive_nonlocal_linetensionEffect, & constitutive_nonlocal_edgeJogFactor real(pReal), dimension(:,:), allocatable, private :: & constitutive_nonlocal_rhoSglEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoDipEdge0, & ! initial edge dipole dislocation density per slip system for each family and instance constitutive_nonlocal_rhoDipScrew0, & ! initial screw dipole dislocation density per slip system for each family and instance constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance constitutive_nonlocal_lambda0, & ! mean free path prefactor for each slip system and instance constitutive_nonlocal_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each family and instance constitutive_nonlocal_burgers, & ! absolute length of burgers vector [m] for each slip system and instance constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance real(pReal), dimension(:,:,:), allocatable, private :: & constitutive_nonlocal_Cslip_66, & ! elasticity matrix in Mandel notation for each instance constitutive_nonlocal_minimumDipoleHeightPerSlipFamily, & ! minimum stable edge/screw dipole height for each family and instance constitutive_nonlocal_minimumDipoleHeight, & ! minimum stable edge/screw dipole height for each slip system and instance constitutive_nonlocal_peierlsStressPerSlipFamily, & ! Peierls stress (edge and screw) constitutive_nonlocal_peierlsStress, & ! Peierls stress (edge and screw) constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each instance constitutive_nonlocal_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance real(pReal), dimension(:,:,:,:), allocatable, private :: & constitutive_nonlocal_lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!) constitutive_nonlocal_accumulatedShear, & ! accumulated shear per slip system up to the start of the FE increment constitutive_nonlocal_rhoDotEdgeJogs, & constitutive_nonlocal_sourceProbability real(pReal), dimension(:,:,:,:,:), allocatable, private :: & constitutive_nonlocal_Cslip_3333, & ! elasticity matrix for each instance constitutive_nonlocal_rhoDotFlux, & ! dislocation convection term constitutive_nonlocal_rhoDotMultiplication, & constitutive_nonlocal_rhoDotSingle2DipoleGlide, & constitutive_nonlocal_rhoDotAthermalAnnihilation, & constitutive_nonlocal_rhoDotThermalAnnihilation real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: & constitutive_nonlocal_compatibility ! slip system compatibility between me and my neighbors real(pReal), dimension(:,:), allocatable, private :: & constitutive_nonlocal_nonSchmidCoeff logical, dimension(:), allocatable, private :: & constitutive_nonlocal_shortRangeStressCorrection, & ! flag indicating the use of the short range stress correction by a excess density gradient term constitutive_nonlocal_deadZoneScaling, & constitutive_nonlocal_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 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 prec, only: pInt, pReal use math, only: math_Mandel3333to66, & math_Voigt66to3333, & math_mul3x3, & math_transpose33 use IO, only: 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, & FE_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, & 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 Nchunks_SlipSlip, & Nchunks_SlipFamilies, & mySize = 0_pInt ! to suppress warnings, safe as init is called only once character(len=64) tag character(len=1024) :: 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(constitutive_nonlocal_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 = '' constitutive_nonlocal_Noutput = 0_pInt allocate(constitutive_nonlocal_structureName(maxNinstance)) allocate(constitutive_nonlocal_structure(maxNinstance)) allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance)) allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance)) allocate(constitutive_nonlocal_totalNslip(maxNinstance)) constitutive_nonlocal_structureName = '' constitutive_nonlocal_structure = 0_pInt constitutive_nonlocal_Nslip = 0_pInt constitutive_nonlocal_slipFamily = 0_pInt constitutive_nonlocal_slipSystemLattice = 0_pInt constitutive_nonlocal_totalNslip = 0_pInt allocate(constitutive_nonlocal_CoverA(maxNinstance)) allocate(constitutive_nonlocal_Gmod(maxNinstance)) allocate(constitutive_nonlocal_nu(maxNinstance)) allocate(constitutive_nonlocal_atomicVolume(maxNinstance)) allocate(constitutive_nonlocal_Dsd0(maxNinstance)) allocate(constitutive_nonlocal_Qsd(maxNinstance)) allocate(constitutive_nonlocal_aTolRho(maxNinstance)) allocate(constitutive_nonlocal_significantRho(maxNinstance)) allocate(constitutive_nonlocal_significantN(maxNinstance)) allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance)) allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance)) allocate(constitutive_nonlocal_R(maxNinstance)) allocate(constitutive_nonlocal_doublekinkwidth(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionEnergy(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionSize(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionConcentration(maxNinstance)) allocate(constitutive_nonlocal_p(maxNinstance)) allocate(constitutive_nonlocal_q(maxNinstance)) allocate(constitutive_nonlocal_viscosity(maxNinstance)) allocate(constitutive_nonlocal_fattack(maxNinstance)) allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance)) allocate(constitutive_nonlocal_rhoSglRandom(maxNinstance)) allocate(constitutive_nonlocal_rhoSglRandomBinning(maxNinstance)) allocate(constitutive_nonlocal_surfaceTransmissivity(maxNinstance)) allocate(constitutive_nonlocal_grainboundaryTransmissivity(maxNinstance)) allocate(constitutive_nonlocal_shortRangeStressCorrection(maxNinstance)) allocate(constitutive_nonlocal_deadZoneScaling(maxNinstance)) allocate(constitutive_nonlocal_probabilisticMultiplication(maxNinstance)) allocate(constitutive_nonlocal_CFLfactor(maxNinstance)) allocate(constitutive_nonlocal_fEdgeMultiplication(maxNinstance)) allocate(constitutive_nonlocal_linetensionEffect(maxNinstance)) allocate(constitutive_nonlocal_edgeJogFactor(maxNinstance)) constitutive_nonlocal_CoverA = 0.0_pReal constitutive_nonlocal_Gmod = 0.0_pReal constitutive_nonlocal_atomicVolume = 0.0_pReal constitutive_nonlocal_Dsd0 = -1.0_pReal constitutive_nonlocal_Qsd = 0.0_pReal constitutive_nonlocal_aTolRho = 0.0_pReal constitutive_nonlocal_significantRho = 0.0_pReal constitutive_nonlocal_significantN = 0.0_pReal constitutive_nonlocal_nu = 0.0_pReal constitutive_nonlocal_Cslip_66 = 0.0_pReal constitutive_nonlocal_Cslip_3333 = 0.0_pReal constitutive_nonlocal_R = -1.0_pReal constitutive_nonlocal_doublekinkwidth = 0.0_pReal constitutive_nonlocal_solidSolutionEnergy = 0.0_pReal constitutive_nonlocal_solidSolutionSize = 0.0_pReal constitutive_nonlocal_solidSolutionConcentration = 0.0_pReal constitutive_nonlocal_p = 1.0_pReal constitutive_nonlocal_q = 1.0_pReal constitutive_nonlocal_viscosity = 0.0_pReal constitutive_nonlocal_fattack = 0.0_pReal constitutive_nonlocal_rhoSglScatter = 0.0_pReal constitutive_nonlocal_rhoSglRandom = 0.0_pReal constitutive_nonlocal_rhoSglRandomBinning = 1.0_pReal constitutive_nonlocal_surfaceTransmissivity = 1.0_pReal constitutive_nonlocal_grainboundaryTransmissivity = -1.0_pReal constitutive_nonlocal_CFLfactor = 2.0_pReal constitutive_nonlocal_fEdgeMultiplication = 0.0_pReal constitutive_nonlocal_linetensionEffect = 0.0_pReal constitutive_nonlocal_edgeJogFactor = 1.0_pReal constitutive_nonlocal_shortRangeStressCorrection = .false. constitutive_nonlocal_deadZoneScaling = .false. constitutive_nonlocal_probabilisticMultiplication = .false. allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglScrewPos0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglScrewNeg0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoDipEdge0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoDipScrew0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction,maxNinstance)) constitutive_nonlocal_rhoSglEdgePos0 = -1.0_pReal constitutive_nonlocal_rhoSglEdgeNeg0 = -1.0_pReal constitutive_nonlocal_rhoSglScrewPos0 = -1.0_pReal constitutive_nonlocal_rhoSglScrewNeg0 = -1.0_pReal constitutive_nonlocal_rhoDipEdge0 = -1.0_pReal constitutive_nonlocal_rhoDipScrew0 = -1.0_pReal constitutive_nonlocal_burgersPerSlipFamily = 0.0_pReal constitutive_nonlocal_lambda0PerSlipFamily = 0.0_pReal constitutive_nonlocal_interactionSlipSlip = 0.0_pReal allocate(constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance)) allocate(constitutive_nonlocal_peierlsStressPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance)) constitutive_nonlocal_minimumDipoleHeightPerSlipFamily = -1.0_pReal constitutive_nonlocal_peierlsStressPerSlipFamily = 0.0_pReal allocate(constitutive_nonlocal_nonSchmidCoeff(lattice_maxNonSchmid,maxNinstance)) constitutive_nonlocal_nonSchmidCoeff = 0.0_pReal !*** readout data from material.config file rewind(myFile) line = '' section = 0_pInt do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to read(myFile,'(a1024)',END=100) line enddo do ! read thru sections of phase part read(myFile,'(a1024)',END=100) line 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 .and. 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)') constitutive_nonlocal_Noutput(i) = constitutive_nonlocal_Noutput(i) + 1_pInt constitutive_nonlocal_output(constitutive_nonlocal_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') constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2_pInt) case ('c11') constitutive_nonlocal_Cslip_66(1,1,i) = IO_floatValue(line,positions,2_pInt) case ('c12') constitutive_nonlocal_Cslip_66(1,2,i) = IO_floatValue(line,positions,2_pInt) case ('c13') constitutive_nonlocal_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt) case ('c22') constitutive_nonlocal_Cslip_66(2,2,i) = IO_floatValue(line,positions,2_pInt) case ('c23') constitutive_nonlocal_Cslip_66(2,3,i) = IO_floatValue(line,positions,2_pInt) case ('c33') constitutive_nonlocal_Cslip_66(3,3,i) = IO_floatValue(line,positions,2_pInt) case ('c44') constitutive_nonlocal_Cslip_66(4,4,i) = IO_floatValue(line,positions,2_pInt) case ('c55') constitutive_nonlocal_Cslip_66(5,5,i) = IO_floatValue(line,positions,2_pInt) case ('c66') constitutive_nonlocal_Cslip_66(6,6,i) = IO_floatValue(line,positions,2_pInt) case ('nslip') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1_pInt+f) enddo case ('rhosgledgepos0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoSglEdgePos0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('rhosgledgeneg0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoSglEdgeNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('rhosglscrewpos0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoSglScrewPos0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('rhosglscrewneg0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoSglScrewNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('rhodipedge0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoDipEdge0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('rhodipscrew0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_rhoDipScrew0(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('lambda0') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case ('burgers') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('cutoffradius','r') constitutive_nonlocal_R(i) = IO_floatValue(line,positions,2_pInt) case('minimumdipoleheightedge','ddipminedge') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('minimumdipoleheightscrew','ddipminscrew') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('atomicvolume') constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2_pInt) case('selfdiffusionprefactor','dsd0') constitutive_nonlocal_Dsd0(i) = IO_floatValue(line,positions,2_pInt) case('selfdiffusionenergy','qsd') constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2_pInt) case('atol_rho','absolutetolerancerho','absolutetolerance_rho','absolutetolerancedensity','absolutetolerance_density') constitutive_nonlocal_aTolRho(i) = IO_floatValue(line,positions,2_pInt) case('significantrho','significant_rho','significantdensity','significant_density') constitutive_nonlocal_significantRho(i) = IO_floatValue(line,positions,2_pInt) case('significantn','significant_n','significantdislocations','significant_dislcations') constitutive_nonlocal_significantN(i) = IO_floatValue(line,positions,2_pInt) case ('interaction_slipslip') do it = 1_pInt, Nchunks_SlipSlip constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1_pInt+it) enddo case('linetension','linetensioneffect','linetension_effect') constitutive_nonlocal_linetensionEffect(i) = IO_floatValue(line,positions,2_pInt) case('edgejog','edgejogs','edgejogeffect','edgejog_effect') constitutive_nonlocal_edgeJogFactor(i) = IO_floatValue(line,positions,2_pInt) case('peierlsstressedge','peierlsstress_edge') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_peierlsStressPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('peierlsstressscrew','peierlsstress_screw') do f = 1_pInt, Nchunks_SlipFamilies constitutive_nonlocal_peierlsStressPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('doublekinkwidth') constitutive_nonlocal_doublekinkwidth(i) = IO_floatValue(line,positions,2_pInt) case('solidsolutionenergy') constitutive_nonlocal_solidSolutionEnergy(i) = IO_floatValue(line,positions,2_pInt) case('solidsolutionsize') constitutive_nonlocal_solidSolutionSize(i) = IO_floatValue(line,positions,2_pInt) case('solidsolutionconcentration') constitutive_nonlocal_solidSolutionConcentration(i) = IO_floatValue(line,positions,2_pInt) case('p') constitutive_nonlocal_p(i) = IO_floatValue(line,positions,2_pInt) case('q') constitutive_nonlocal_q(i) = IO_floatValue(line,positions,2_pInt) case('viscosity','glideviscosity') constitutive_nonlocal_viscosity(i) = IO_floatValue(line,positions,2_pInt) case('attackfrequency','fattack') constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2_pInt) case('rhosglscatter') constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2_pInt) case('rhosglrandom') constitutive_nonlocal_rhoSglRandom(i) = IO_floatValue(line,positions,2_pInt) case('rhosglrandombinning') constitutive_nonlocal_rhoSglRandomBinning(i) = IO_floatValue(line,positions,2_pInt) case('surfacetransmissivity') constitutive_nonlocal_surfaceTransmissivity(i) = IO_floatValue(line,positions,2_pInt) case('grainboundarytransmissivity') constitutive_nonlocal_grainboundaryTransmissivity(i) = IO_floatValue(line,positions,2_pInt) case('cflfactor') constitutive_nonlocal_CFLfactor(i) = IO_floatValue(line,positions,2_pInt) case('fedgemultiplication','edgemultiplicationfactor','edgemultiplication') constitutive_nonlocal_fEdgeMultiplication(i) = IO_floatValue(line,positions,2_pInt) case('shortrangestresscorrection') constitutive_nonlocal_shortRangeStressCorrection(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal case ('nonschmid_coefficients') do f = 1_pInt, lattice_maxNonSchmid constitutive_nonlocal_nonSchmidCoeff(f,i) = IO_floatValue(line,positions,1_pInt+f) enddo case('deadzonescaling','deadzone','deadscaling') constitutive_nonlocal_deadZoneScaling(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal case('probabilisticmultiplication','randomsources','randommultiplication','discretesources') constitutive_nonlocal_probabilisticMultiplication(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal case default call IO_error(210_pInt,ext_msg=tag//' ('//constitutive_nonlocal_label//')') end select endif enddo 100 do i = 1_pInt,maxNinstance constitutive_nonlocal_structure(i) = & lattice_initializeStructure(constitutive_nonlocal_structureName(i), constitutive_nonlocal_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(constitutive_nonlocal_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 (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then if (constitutive_nonlocal_rhoSglEdgePos0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglEdgePos0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglEdgeNeg0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScrewPos0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScrewNeg0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoDipEdge0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoDipScrew0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='Burgers (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='lambda0 (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1,i) < 0.0_pReal) & call IO_error(211_pInt,ext_msg='minimumDipoleHeightEdge (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,2,i) < 0.0_pReal) & call IO_error(211_pInt,ext_msg='minimumDipoleHeightScrew (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,1,i) <= 0.0_pReal) & call IO_error(211_pInt,ext_msg='peierlsStressEdge (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,2,i) <= 0.0_pReal) & call IO_error(211_pInt,ext_msg='peierlsStressScrew (' & //constitutive_nonlocal_label//')') endif enddo if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) & call IO_error(211_pInt,ext_msg='interaction_SlipSlip (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_linetensionEffect(i) < 0.0_pReal .or. constitutive_nonlocal_linetensionEffect(i) > 1.0_pReal) & call IO_error(211_pInt,ext_msg='linetension (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_edgeJogFactor(i) < 0.0_pReal .or. constitutive_nonlocal_edgeJogFactor(i) > 1.0_pReal) & call IO_error(211_pInt,ext_msg='edgejog (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_R(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='r (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='atomicVolume (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_Dsd0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='selfDiffusionPrefactor (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='selfDiffusionEnergy (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_aTolRho(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_rho (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_significantRho(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='significantRho (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_significantN(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='significantN (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_doublekinkwidth(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='doublekinkwidth (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_solidSolutionEnergy(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='solidSolutionEnergy (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_solidSolutionSize(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='solidSolutionSize (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_solidSolutionConcentration(i) <= 0.0_pReal) & call IO_error(211_pInt,ext_msg='solidSolutionConcentration (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_p(i) <= 0.0_pReal .or. constitutive_nonlocal_p(i) > 1.0_pReal) call IO_error(211_pInt,ext_msg='p (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_q(i) < 1.0_pReal .or. constitutive_nonlocal_q(i) > 2.0_pReal) call IO_error(211_pInt,ext_msg='q (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_viscosity(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='viscosity (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='attackFrequency (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScatter (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglRandom(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglRandom (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_rhoSglRandomBinning(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglRandomBinning (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_surfaceTransmissivity(i) < 0.0_pReal & .or. constitutive_nonlocal_surfaceTransmissivity(i) > 1.0_pReal) call IO_error(211_pInt,ext_msg='surfaceTransmissivity (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_grainboundaryTransmissivity(i) > 1.0_pReal) call IO_error(211_pInt,& ext_msg='grainboundaryTransmissivity ('//constitutive_nonlocal_label//')') if (constitutive_nonlocal_CFLfactor(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='CFLfactor (' & //constitutive_nonlocal_label//')') if (constitutive_nonlocal_fEdgeMultiplication(i) < 0.0_pReal .or. constitutive_nonlocal_fEdgeMultiplication(i) > 1.0_pReal) & call IO_error(211_pInt,ext_msg='edgemultiplicationfactor ('& //constitutive_nonlocal_label//')') !*** determine total number of active slip systems constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i) = min( lattice_NslipSystem(1:lattice_maxNslipFamily, myStructure), & constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i) ) ! we can't use more slip systems per family than specified in lattice constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i)) enddo !*** allocation of variables whose size depends on the total number of active slip systems maxTotalNslip = maxval(constitutive_nonlocal_totalNslip) allocate(constitutive_nonlocal_burgers(maxTotalNslip, maxNinstance)) constitutive_nonlocal_burgers = 0.0_pReal allocate(constitutive_nonlocal_lambda0(maxTotalNslip, maxNinstance)) constitutive_nonlocal_lambda0 = 0.0_pReal allocate(constitutive_nonlocal_minimumDipoleHeight(maxTotalNslip,2,maxNinstance)) constitutive_nonlocal_minimumDipoleHeight = -1.0_pReal allocate(constitutive_nonlocal_forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance)) constitutive_nonlocal_forestProjectionEdge = 0.0_pReal allocate(constitutive_nonlocal_forestProjectionScrew(maxTotalNslip, maxTotalNslip, maxNinstance)) constitutive_nonlocal_forestProjectionScrew = 0.0_pReal allocate(constitutive_nonlocal_interactionMatrixSlipSlip(maxTotalNslip, maxTotalNslip, maxNinstance)) constitutive_nonlocal_interactionMatrixSlipSlip = 0.0_pReal allocate(constitutive_nonlocal_lattice2slip(1:3, 1:3, maxTotalNslip, maxNinstance)) constitutive_nonlocal_lattice2slip = 0.0_pReal allocate(constitutive_nonlocal_accumulatedShear(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) constitutive_nonlocal_accumulatedShear = 0.0_pReal allocate(constitutive_nonlocal_sourceProbability(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) constitutive_nonlocal_sourceProbability = 2.0_pReal allocate(constitutive_nonlocal_rhoDotFlux(maxTotalNslip, 8, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotMultiplication(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotSingle2DipoleGlide(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotAthermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotThermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotEdgeJogs(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) constitutive_nonlocal_rhoDotFlux = 0.0_pReal constitutive_nonlocal_rhoDotMultiplication = 0.0_pReal constitutive_nonlocal_rhoDotSingle2DipoleGlide = 0.0_pReal constitutive_nonlocal_rhoDotAthermalAnnihilation = 0.0_pReal constitutive_nonlocal_rhoDotThermalAnnihilation = 0.0_pReal constitutive_nonlocal_rhoDotEdgeJogs = 0.0_pReal allocate(constitutive_nonlocal_compatibility(2,maxTotalNslip, maxTotalNslip, FE_maxNipNeighbors, mesh_maxNips, mesh_NcpElems)) constitutive_nonlocal_compatibility = 0.0_pReal allocate(constitutive_nonlocal_peierlsStress(maxTotalNslip,2,maxNinstance)) constitutive_nonlocal_peierlsStress = 0.0_pReal allocate(constitutive_nonlocal_colinearSystem(maxTotalNslip,maxNinstance)) constitutive_nonlocal_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,constitutive_nonlocal_Nslip(f,i) l = l + 1_pInt constitutive_nonlocal_slipFamily(l,i) = f constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1_pInt, myStructure)) + s enddo; enddo !*** determine size of state array ns = constitutive_nonlocal_totalNslip(i) constitutive_nonlocal_sizeDotState(i) = int(size(constitutive_nonlocal_listBasicStates),pInt) * ns constitutive_nonlocal_sizeDependentState(i) = int(size(constitutive_nonlocal_listDependentStates),pInt) * ns constitutive_nonlocal_sizeState(i) = constitutive_nonlocal_sizeDotState(i) & + constitutive_nonlocal_sizeDependentState(i) & + int(size(constitutive_nonlocal_listOtherStates),pInt) * ns !*** determine size of postResults array do o = 1_pInt,constitutive_nonlocal_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', & '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 = constitutive_nonlocal_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 constitutive_nonlocal_Cslip_66(:,:,i) = lattice_symmetrizeC66(constitutive_nonlocal_structureName(i),& constitutive_nonlocal_Cslip_66(:,:,i)) constitutive_nonlocal_Gmod(i) = 0.2_pReal * ( constitutive_nonlocal_Cslip_66(1,1,i) - constitutive_nonlocal_Cslip_66(1,2,i) & + 3.0_pReal*constitutive_nonlocal_Cslip_66(4,4,i) ) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 constitutive_nonlocal_nu(i) = ( constitutive_nonlocal_Cslip_66(1,1,i) + 4.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) & - 2.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) ) & / ( 4.0_pReal*constitutive_nonlocal_Cslip_66(1,1,i) + 6.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) & + 2.0_pReal*constitutive_nonlocal_Cslip_66(4,4,i) ) constitutive_nonlocal_Cslip_66(1:6,1:6,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(1:6,1:6,i))) constitutive_nonlocal_Cslip_3333(1:3,1:3,1:3,1:3,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(1:6,1:6,i)) ! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 do s1 = 1_pInt,ns f = constitutive_nonlocal_slipFamily(s1,i) !*** burgers vector, mean free path prefactor and minimum dipole distance for each slip system constitutive_nonlocal_burgers(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i) constitutive_nonlocal_lambda0(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i) constitutive_nonlocal_minimumDipoleHeight(s1,1:2,i) = constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1:2,i) constitutive_nonlocal_peierlsStress(s1,1:2,i) = constitutive_nonlocal_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 constitutive_nonlocal_forestProjectionEdge(s1,s2,i) & = abs(math_mul3x3(lattice_sn(1:3,constitutive_nonlocal_slipSystemLattice(s1,i),myStructure), & lattice_st(1:3,constitutive_nonlocal_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 constitutive_nonlocal_forestProjectionScrew(s1,s2,i) & = abs(math_mul3x3(lattice_sn(1:3,constitutive_nonlocal_slipSystemLattice(s1,i),myStructure), & lattice_sd(1:3,constitutive_nonlocal_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 constitutive_nonlocal_interactionMatrixSlipSlip(s1,s2,i) & = constitutive_nonlocal_interactionSlipSlip(lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), & constitutive_nonlocal_slipSystemLattice(s2,i), & myStructure), i) !*** colinear slip system (only makes sense for fcc like it is defined here) if (lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), & constitutive_nonlocal_slipSystemLattice(s2,i), & myStructure) == 3_pInt) then constitutive_nonlocal_colinearSystem(s1,i) = s2 endif enddo !*** rotation matrix from lattice configuration to slip system constitutive_nonlocal_lattice2slip(1:3,1:3,s1,i) & = math_transpose33( reshape([ lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), & -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), & lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure)], [3,3])) enddo enddo endsubroutine !********************************************************************* !* initial microstructural state (just the "basic" states) * !********************************************************************* subroutine constitutive_nonlocal_stateInit(state) use prec, only: pReal, & pInt, & p_vec 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 implicit none !*** input/output variables type(p_vec), dimension(1,mesh_maxNips,mesh_NcpElems), intent(inout) :: & state ! microstructural state !*** local variables real(pReal), dimension(:), allocatable :: & rhoSglEdgePos, & ! positive edge dislocation density rhoSglEdgeNeg, & ! negative edge dislocation density rhoSglScrewPos, & ! positive screw dislocation density rhoSglScrewNeg, & ! negative screw dislocation density rhoDipEdge, & ! edge dipole dislocation density rhoDipScrew ! screw dipole dislocation density integer(pInt) el, & ip, & ns, & ! short notation for total number of active slip systems f, & ! index of lattice family from, & upto, & s, & ! index of slip system t, & i, & 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) if (maxNinstance > 0_pInt) then allocate(rhoSglEdgePos(maxval(constitutive_nonlocal_totalNslip))) allocate(rhoSglEdgeNeg(maxval(constitutive_nonlocal_totalNslip))) allocate(rhoSglScrewPos(maxval(constitutive_nonlocal_totalNslip))) allocate(rhoSglScrewNeg(maxval(constitutive_nonlocal_totalNslip))) allocate(rhoDipEdge(maxval(constitutive_nonlocal_totalNslip))) allocate(rhoDipScrew(maxval(constitutive_nonlocal_totalNslip))) endif do myInstance = 1_pInt,maxNinstance ns = constitutive_nonlocal_totalNslip(myInstance) ! randomly distribute dislocation segments on random slip system and of random type in the volume if (constitutive_nonlocal_rhoSglRandom(myInstance) > 0.0_pReal) then ! ititalize all states to zero and get the total volume of the instance minimumIpVolume = 1e99_pReal do el = 1_pInt,mesh_NcpElems do ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,el))) if (constitutive_nonlocal_label == phase_plasticity(material_phase(1,ip,el)) & .and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then totalVolume = totalVolume + mesh_ipVolume(ip,el) minimumIpVolume = min(minimumIpVolume, mesh_ipVolume(ip,el)) state(1,ip,el)%p = 0.0_pReal endif enddo enddo densityBinning = constitutive_nonlocal_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 < constitutive_nonlocal_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((t-1)*ns+s) = state(1,ip,el)%p((t-1)*ns+s) + densityBinning endif enddo ! homogeneous distribution of density with some noise else do el = 1_pInt,mesh_NcpElems do ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,el))) if (constitutive_nonlocal_label == phase_plasticity(material_phase(1,ip,el)) & .and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then do f = 1_pInt,lattice_maxNslipFamily from = 1_pInt + sum(constitutive_nonlocal_Nslip(1:f-1_pInt,myInstance)) upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance)) do s = from,upto do i = 1_pInt,2_pInt noise(i) = math_sampleGaussVar(0.0_pReal, constitutive_nonlocal_rhoSglScatter(myInstance)) enddo rhoSglEdgePos(s) = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance) + noise(1) rhoSglEdgeNeg(s) = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance) + noise(1) rhoSglScrewPos(s) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance) + noise(2) rhoSglScrewNeg(s) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance) + noise(2) enddo rhoDipEdge(from:upto) = constitutive_nonlocal_rhoDipEdge0(f, myInstance) rhoDipScrew(from:upto) = constitutive_nonlocal_rhoDipScrew0(f, myInstance) enddo state(1,ip,el)%p( 1: ns) = rhoSglEdgePos(1:ns) state(1,ip,el)%p( ns+1: 2*ns) = rhoSglEdgeNeg(1:ns) state(1,ip,el)%p( 2*ns+1: 3*ns) = rhoSglScrewPos(1:ns) state(1,ip,el)%p( 3*ns+1: 4*ns) = rhoSglScrewNeg(1:ns) state(1,ip,el)%p( 4*ns+1: 5*ns) = 0.0_pReal state(1,ip,el)%p( 5*ns+1: 6*ns) = 0.0_pReal state(1,ip,el)%p( 6*ns+1: 7*ns) = 0.0_pReal state(1,ip,el)%p( 7*ns+1: 8*ns) = 0.0_pReal state(1,ip,el)%p( 8*ns+1: 9*ns) = rhoDipEdge(1:ns) state(1,ip,el)%p( 9*ns+1:10*ns) = rhoDipScrew(1:ns) endif enddo enddo endif enddo if (maxNinstance > 0_pInt) then deallocate(rhoSglEdgePos) deallocate(rhoSglEdgeNeg) deallocate(rhoSglScrewPos) deallocate(rhoSglScrewNeg) deallocate(rhoDipEdge) deallocate(rhoDipScrew) endif endsubroutine !********************************************************************* !* absolute state tolerance * !********************************************************************* pure function constitutive_nonlocal_aTolState(myInstance) use prec, only: pReal, & pInt 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 constitutive_nonlocal_aTolState = constitutive_nonlocal_aTolRho(myInstance) endfunction !********************************************************************* !* calculates homogenized elacticity matrix * !********************************************************************* pure function constitutive_nonlocal_homogenizedC(state,g,ip,el) use prec, only: pReal, & pInt, & p_vec 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 = constitutive_nonlocal_Cslip_66(1:6,1:6,myInstance) endfunction !********************************************************************* !* calculates quantities characterizing the microstructure * !********************************************************************* subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, Fp, g, ip, el) use prec, only: pReal, & pInt, & p_vec use IO, only: IO_error use math, only: math_Mandel33to6, & math_mul33x33, & math_mul33x3, & math_mul3x3, & math_norm3, & math_inv33, & math_invert33, & math_transpose33, & pi 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, & FE_NipNeighbors, & FE_maxNipNeighbors, & FE_geomtype 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) :: g, & ! 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, & interactionCoefficient integer(pInt), dimension(2) :: neighbor real(pReal) nu, & ! poisson's ratio mu, & b, & detFe, & detFp, & FVsize, & temp, & correction, & myRhoForest real(pReal), dimension(2) :: rhoExcessGradient, & rhoExcessGradient_over_rho, & rhoTotal real(pReal), dimension(3) :: ipCoords, & neighboring_ipCoords, & rhoExcessDifferences real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,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,FE_maxNipNeighbors) :: & connection_latticeConf real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: & rhoExcess real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: & rhoDip ! dipole dislocation density (edge, screw) real(pReal), dimension(constitutive_nonlocal_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-) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))), & constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: & myInteractionMatrix ! corrected slip interaction matrix real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip),FE_maxNipNeighbors) :: & neighboring_rhoExcess ! excess density at neighboring material point real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: & m ! direction of dislocation motion logical inversionError phase = material_phase(g,ip,el) instance = phase_plasticityInstance(phase) latticeStruct = constitutive_nonlocal_structure(instance) ns = constitutive_nonlocal_totalNslip(instance) !*** get basic states forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) & rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal) ! ensure positive single mobile densities forall (t = 5_pInt:8_pInt) & rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns) forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) & rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal) ! ensure positive dipole densities where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(instance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(instance)) & rhoSgl = 0.0_pReal where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(instance) & .or. abs(rhoSgl) < constitutive_nonlocal_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)), & constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) & + dot_product((sum(abs(rhoSgl(1:ns,[3,4,7,8])),2) + rhoDip(1:ns,2)), & constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance)) !*** calculate the threshold shear stress for dislocation slip myInteractionMatrix = 0.0_pReal myInteractionMatrix(1:ns,1:ns) = constitutive_nonlocal_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),constitutive_nonlocal_significantRho(instance)) correction = ( 1.0_pReal - constitutive_nonlocal_linetensionEffect(instance) & + constitutive_nonlocal_linetensionEffect(instance) & * log(0.35_pReal * constitutive_nonlocal_burgers(s,instance) * sqrt(myRhoForest)) & / log(0.35_pReal * constitutive_nonlocal_burgers(s,instance) * 1e6_pReal)) ** 2.0_pReal do s2 = 1_pInt,ns interactionCoefficient = lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s,instance), & constitutive_nonlocal_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) = constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_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. constitutive_nonlocal_shortRangeStressCorrection(instance)) then call math_invert33(Fe, invFe, detFe, inversionError) call math_invert33(Fp, invFp, detFp, inversionError) ipCoords = mesh_ipCoordinates(1:3,ip,el) 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) nu = constitutive_nonlocal_nu(instance) mu = constitutive_nonlocal_Gmod(instance) !* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities do n = 1_pInt,FE_NipNeighbors(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(g,neighboring_ip,neighboring_el) neighboring_instance = phase_plasticityInstance(neighboring_phase) neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance) neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance) neighboring_ipCoords = mesh_ipCoordinates(1:3,neighboring_ip,neighboring_el) if (.not. phase_localPlasticity(neighboring_phase) & .and. neighboring_latticeStruct == latticeStruct & .and. neighboring_instance == instance) then if (neighboring_ns == ns) then if (neighboring_el /= el .or. neighboring_ip /= ip) then connection_latticeConf(1:3,n) = math_mul33x3(invFe, neighboring_ipCoords - ipCoords) forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) & neighboring_rhoExcess(c,s,n) = state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-2_pInt)*ns+s) & ! positive mobiles - state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*ns+s) ! negative mobiles else ! thats myself! probably using periodic images -> assume constant excess density connection_latticeConf(1:3,n) = math_mul33x3(math_transpose33(invFp), mesh_ipAreaNormal(1:3,n,ip,el)) ! direction of area normal neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess 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, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct) m(1:3,1:ns,2) = -lattice_st(1:3, constitutive_nonlocal_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(math_mul33x3(invConnections, rhoExcessDifferences), m(1:3,s,c)) 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 rhoTotal(1_pInt) = sum(abs(rhoSgl(s,[1_pInt,2_pInt,5_pInt,6_pInt]))) + rhoDip(s,1_pInt) rhoTotal(2_pInt) = sum(abs(rhoSgl(s,[3_pInt,4_pInt,7_pInt,8_pInt]))) + rhoDip(s,2_pInt) 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 b = constitutive_nonlocal_burgers(s,instance) tauBack(s) = - mu * b / (2.0_pReal * pi) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu) + rhoExcessGradient_over_rho(2)) enddo endif !*** set dependent states state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns) = rhoForest state(g,ip,el)%p(11_pInt*ns+1:12_pInt*ns) = tauThreshold state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) = tauBack #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_microstructure at el ip g',el,ip,g 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 prec, only: pReal, & pInt, & p_vec 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(constitutive_nonlocal_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(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), & intent(out) :: v ! velocity real(pReal), dimension(constitutive_nonlocal_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(constitutive_nonlocal_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 p, & ! shortcut to Kocks,Argon,Ashby parameter p q, & ! shortcut to Kocks,Argon,Ashby parameter q 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 = constitutive_nonlocal_totalNslip(instance) tauThreshold = state%p(11_pInt*ns+1:12_pInt*ns) tauEff = abs(tau) - tauThreshold p = constitutive_nonlocal_p(instance) q = constitutive_nonlocal_q(instance) 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 = constitutive_nonlocal_burgers(s,instance) jumpWidth_P = constitutive_nonlocal_burgers(s,instance) activationLength_P = constitutive_nonlocal_doublekinkwidth(instance) * constitutive_nonlocal_burgers(s,instance) activationVolume_P = activationLength_P * jumpWidth_P * constitutive_nonlocal_burgers(s,instance) criticalStress_P = constitutive_nonlocal_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 / constitutive_nonlocal_fattack(instance) & * exp(activationEnergy_P / (kB * Temperature) * (1.0_pReal - tauRel_P**p)**q) if (present(dv_dtau)) then if (tauEff(s) < criticalStress_P) then dtPeierls_dtau = tPeierls * p * q * activationVolume_P / (kB * Temperature) & * (1.0_pReal - tauRel_P**p)**(q-1.0_pReal) * tauRel_P**(p-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 = constitutive_nonlocal_burgers(s,instance) / sqrt(constitutive_nonlocal_solidSolutionConcentration(instance)) jumpWidth_S = constitutive_nonlocal_solidSolutionSize(instance) * constitutive_nonlocal_burgers(s,instance) activationLength_S = constitutive_nonlocal_burgers(s,instance) & / sqrt(constitutive_nonlocal_solidSolutionConcentration(instance)) activationVolume_S = activationLength_S * jumpWidth_S * constitutive_nonlocal_burgers(s,instance) activationEnergy_S = constitutive_nonlocal_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 / constitutive_nonlocal_fattack(instance) & * exp(activationEnergy_S / (kB * Temperature) * (1.0_pReal - tauRel_S**p)**q) if (present(dv_dtau)) then if (tauEff(s) < criticalStress_S) then dtSolidSolution_dtau = tSolidSolution * p * q * activationVolume_S / (kB * Temperature) & * (1.0_pReal - tauRel_S**p)**(q-1.0_pReal) * tauRel_S**(p-1.0_pReal) else dtSolidSolution_dtau = 0.0_pReal endif endif !* viscous glide velocity mobility = constitutive_nonlocal_burgers(s,instance) / constitutive_nonlocal_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 prec, only: pReal, & pInt, & p_vec 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) :: nonSchmid_tensor real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: & rhoSgl ! single dislocation densities (including used) real(pReal), dimension(constitutive_nonlocal_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(constitutive_nonlocal_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 myInstance = phase_plasticityInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance) !*** shortcut to state variables forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) & rhoSgl(s,t) = max(state%p((t-1_pInt)*ns+s), 0.0_pReal) forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) & rhoSgl(s,t) = state%p((t-1_pInt)*ns+s) tauBack = state%p(12_pInt*ns+1:13_pInt*ns) where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoSgl = 0.0_pReal !*** get effective resolved shear stress do s = 1_pInt,ns tau(s,1:4) = math_mul6x6(Tstar_v, lattice_Sslip_v(:,1,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) & + tauBack(s) !*** adding non schmid contributions to ONLY screw components if present (i.e. if NnonSchmid(myStructure) > 0) nonSchmid_tensor(1:3,1:3,1) = & math_Mandel6to33(lattice_Sslip_v(:,1,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,1) do k = 1_pInt, NnonSchmid(myStructure) tau(s,3) = tau(s,3) + constitutive_nonlocal_nonSchmidCoeff(k,myInstance)* & math_mul6x6(Tstar_v, lattice_Sslip_v(:,2*k,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) tau(s,4) = tau(s,4) + constitutive_nonlocal_nonSchmidCoeff(k,myInstance)* & math_mul6x6(Tstar_v, lattice_Sslip_v(:,2*k+1,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) nonSchmid_tensor(1:3,1:3,1) = nonSchmid_tensor(1:3,1:3,1) + constitutive_nonlocal_nonSchmidCoeff(k,myInstance)*& math_Mandel6to33(lattice_Sslip_v(:,2*k,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,2) + constitutive_nonlocal_nonSchmidCoeff(k,myInstance)*& math_Mandel6to33(lattice_Sslip_v(:,2*k+1,constitutive_nonlocal_slipSystemLattice(s,myInstance),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((12_pInt+t)*ns+1:(13_pInt+t)*ns) = v(1:ns,1) enddo else ! for all other lattice structures the velcities 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((12+t)*ns+1:(13+t)*ns) = 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 (constitutive_nonlocal_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) * constitutive_nonlocal_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) * constitutive_nonlocal_burgers(1:ns,myInstance) * (1.0_pReal - deadZoneSize) enddo !*** Calculation of Lp and its tangent do s = 1_pInt,ns sLattice = constitutive_nonlocal_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)*nonSchmid_tensor(k,l,1) +& dgdot_dtau(s,4)*lattice_Sslip(i,j,sLattice,myStructure)*nonSchmid_tensor(k,l,2) 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',Lp endif #endif endsubroutine !********************************************************************* !* incremental change of microstructure * !********************************************************************* subroutine constitutive_nonlocal_deltaState(deltaState, state, Tstar_v, Temperature, g,ip,el) use prec, only: pReal, & pInt, & p_vec 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(constitutive_nonlocal_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(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: & rhoSgl ! current single dislocation densities (positive/negative screw and edge without dipoles) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: & v ! dislocation glide velocity real(pReal), dimension(constitutive_nonlocal_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(constitutive_nonlocal_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 = constitutive_nonlocal_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((t-1_pInt)*ns+s), 0.0_pReal) forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) & rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s) forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) & rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal) tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) forall (t = 1_pInt:4_pInt) & v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) forall (c = 1_pInt:2_pInt) & dUpperOld(1_pInt:ns,c) = state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns) where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoSgl = 0.0_pReal where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_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 = constitutive_nonlocal_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 = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance) dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) & / (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau)) dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_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 (c = 1_pInt:2_pInt) & state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns) = dUpper(1_pInt:ns,c) !**************************************************************************** !*** assign the changes in the dislocation densities to deltaState deltaRho = 0.0_pReal deltaRho = deltaRhoRemobilization & + deltaRhoDipole2SingleStress deltaState%p = reshape(deltaRho,(/10_pInt*ns/)) #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: pReal, & pInt, & p_vec, & 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_maxNipNeighbors, & mesh_ipNeighborhood, & mesh_ipVolume, & mesh_ipArea, & mesh_ipAreaNormal, & FE_NipNeighbors, & FE_geomtype 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 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 neighboring_el, & !< element number of my neighbor neighboring_ip, & !< integration point of my neighbor neighboring_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(constitutive_nonlocal_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(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: & rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles) rhoSglOriginal, & rhoSgl0, & !< single dislocation densities at start of cryst inc (positive/negative screw and edge without dipoles) rhoSglMe, & !< single dislocation densities of central ip (positive/negative screw and edge without dipoles) neighboring_rhoSgl !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: & v, & !< current dislocation glide velocity v0, & !< dislocation glide velocity at start of cryst inc vMe, & !< dislocation glide velocity of central ip neighboring_v, & !< dislocation glide velocity of enighboring ip gdot !< shear rates real(pReal), dimension(constitutive_nonlocal_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(constitutive_nonlocal_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,constitutive_nonlocal_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 neighboring_F, & !< total deformation gradient of my neighbor my_Fe, & !< my elastic deformation gradient neighboring_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 D, & !< 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 = constitutive_nonlocal_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((t-1_pInt)*ns+s), 0.0_pReal) forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) & rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s) forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) & rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal) rhoForest = state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns) tauThreshold = state(g,ip,el)%p(11_pInt*ns+1_pInt:12_pInt*ns) tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) forall (t = 1_pInt:4_pInt) & v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) rhoSglOriginal = rhoSgl rhoDipOriginal = rhoDip where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoSgl = 0.0_pReal where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoDip = 0.0_pReal !*** 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) * constitutive_nonlocal_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 = constitutive_nonlocal_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 = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance) dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) & / (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau)) dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_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 (constitutive_nonlocal_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) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(rhoSgl(1:ns,3:4),2)) & / sum(rhoSgl(1:ns,1:4),2) * meshlength / constitutive_nonlocal_lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns)) elsewhere nSources = meshlength / constitutive_nonlocal_lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns)) endwhere do s = 1_pInt,ns if (nSources(s) < 1.0_pReal) then if (constitutive_nonlocal_sourceProbability(s,g,ip,el) > 1.0_pReal) then call random_number(rnd) constitutive_nonlocal_sourceProbability(s,g,ip,el) = rnd !$OMP FLUSH(constitutive_nonlocal_sourceProbability) endif if (constitutive_nonlocal_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 constitutive_nonlocal_sourceProbability(s,g,ip,el) = 2.0_pReal rhoDotMultiplication(s,1:4) = & (sum(abs(gdot(s,1:2))) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(abs(gdot(s,3:4)))) & / constitutive_nonlocal_burgers(s,myInstance) * sqrt(rhoForest(s)) / constitutive_nonlocal_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) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(abs(gdot(1:ns,3:4)),2)) & * sqrt(rhoForest(1:ns)) / constitutive_nonlocal_lambda0(1:ns,myInstance) / constitutive_nonlocal_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. constitutive_nonlocal_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. constitutive_nonlocal_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 if (numerics_timeSyncing) then forall (t = 1_pInt:4_pInt) & v0(1_pInt:ns,t) = state0(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) forall (t = 1_pInt:8_pInt) & rhoSgl0(1_pInt:ns,t) = state0(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns) where (abs(rhoSgl0) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl0) < constitutive_nonlocal_significantRho(myInstance)) & rhoSgl0 = 0.0_pReal 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, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,2) = -lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,3) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,4) = lattice_st(1:3, constitutive_nonlocal_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_geomtype(mesh_element(2,el))) ! loop through my neighbors neighboring_el = mesh_ipNeighborhood(1,n,ip,el) neighboring_ip = mesh_ipNeighborhood(2,n,ip,el) neighboring_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 (neighboring_n > 0_pInt) then ! if neighbor exists, average deformation gradient neighboring_Fe = Fe(1:3,1:3,g,neighboring_ip,neighboring_el) neighboring_F = math_mul33x33(neighboring_Fe, Fp(1:3,1:3,g,neighboring_ip,neighboring_el)) Favg = 0.5_pReal * (my_F + neighboring_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. neighboring_v = 0.0_pReal ! needed for check of sign change in flux density below neighboring_rhoSgl = 0.0_pReal if (neighboring_n > 0_pInt) then if (phase_plasticity(material_phase(1,neighboring_ip,neighboring_el)) == constitutive_nonlocal_label & .and. any(constitutive_nonlocal_compatibility(:,:,:,n,ip,el) > 0.0_pReal)) & considerEnteringFlux = .true. endif if (considerEnteringFlux) then if(numerics_timeSyncing .and. (subfrac(g,neighboring_ip,neighboring_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 (t = 1_pInt:4_pInt) & neighboring_v(1_pInt:ns,t) = state0(g,neighboring_ip,neighboring_el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) forall (t = 1_pInt:8_pInt) & neighboring_rhoSgl(1_pInt:ns,t) = state0(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns) else forall (t = 1_pInt:4_pInt) & neighboring_v(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) forall (t = 1_pInt:8_pInt) & neighboring_rhoSgl(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns) endif where (abs(neighboring_rhoSgl) * mesh_ipVolume(neighboring_ip,neighboring_el) ** 0.667_pReal & < constitutive_nonlocal_significantN(myInstance) & .or. abs(neighboring_rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & neighboring_rhoSgl = 0.0_pReal normal_neighbor2me_defConf = math_det33(Favg) & * math_mul33x3(math_inv33(transpose(Favg)), mesh_ipAreaNormal(1:3,neighboring_n,neighboring_ip,neighboring_el)) ! calculate the normal of the interface in (average) deformed configuration (now pointing from my neighbor to me!!!) normal_neighbor2me = math_mul33x3(transpose(neighboring_Fe), normal_neighbor2me_defConf) / math_det33(neighboring_Fe) ! interface normal in the lattice configuration of my neighbor area = mesh_ipArea(neighboring_n,neighboring_ip,neighboring_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 (neighboring_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) * neighboring_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(neighboring_rhoSgl(s,t+deads)) * neighboring_v(s,t) & * math_mul3x3(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface where (constitutive_nonlocal_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 * constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal where (constitutive_nonlocal_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 * constitutive_nonlocal_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. rhoSglMe = rhoSgl vMe = v if(numerics_timeSyncing) then if (subfrac(g,ip,el) == 0.0_pReal) then rhoSglMe = rhoSgl0 vMe = v0 elseif (neighboring_n > 0_pInt) then if (subfrac(g,neighboring_ip,neighboring_el) == 0.0_pReal) then rhoSglMe = rhoSgl0 vMe = 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 (vMe(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 (vMe(s,t) * neighboring_v(s,t) >= 0.0_pReal) then ! no sign change in flux density transmissivity = sum(constitutive_nonlocal_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 = rhoSglMe(s,t) * vMe(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, vMe(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 = rhoSglMe(s,t+4_pInt) * vMe(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) / constitutive_nonlocal_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) / constitutive_nonlocal_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) / constitutive_nonlocal_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) / constitutive_nonlocal_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) / constitutive_nonlocal_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, constitutive_nonlocal_colinearSystem(s,myInstance) > 0_pInt) & rhoDotAthermalAnnihilation(constitutive_nonlocal_colinearSystem(s,myInstance),1:2) = -rhoDotAthermalAnnihilation(s,10) & * 0.25_pReal * sqrt(rhoForest(s)) * (dUpper(s,2) + dLower(s,2)) & * constitutive_nonlocal_edgeJogFactor(myInstance) endif !*** thermally activated annihilation of edge dipoles by climb rhoDotThermalAnnihilation = 0.0_pReal D = constitutive_nonlocal_Dsd0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature)) vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) & * constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_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 constitutive_nonlocal_rhoDotFlux(1:ns,1:8,g,ip,el) = rhoDotFlux(1:ns,1:8) constitutive_nonlocal_rhoDotMultiplication(1:ns,1:2,g,ip,el) = rhoDotMultiplication(1:ns,[1,3]) constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1:2,g,ip,el) = rhoDotSingle2DipoleGlide(1:ns,9:10) constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotAthermalAnnihilation(1:ns,9:10) constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotThermalAnnihilation(1:ns,9:10) constitutive_nonlocal_rhoDotEdgeJogs(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 < -constitutive_nonlocal_aTolRho(myInstance)) & .or. any(rhoDipOriginal(1:ns,1:2) + rhoDot(1:ns,9:10) * timestep < -constitutive_nonlocal_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 constitutive_nonlocal_dotState(1:10_pInt*ns) = reshape(rhoDot,(/10_pInt*ns/)) 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 prec, only: pReal, & pInt 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 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 neighboring_e, & ! element index of my neighbor neighboring_i, & ! integration point index of my neighbor my_phase, & neighboring_phase, & my_texture, & neighboring_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,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e))),& constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e))),& FE_NipNeighbors(FE_geomtype(mesh_element(2,e)))) :: & compatibility ! compatibility for current element and ip real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: & slipNormal, & slipDirection real(pReal) compatibilitySum, & thresholdValue, & nThresholdValues logical, dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: & belowThreshold Nneighbors = FE_NipNeighbors(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 = constitutive_nonlocal_totalNslip(my_instance) slipNormal(1:3,1:ns) = lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,my_instance), my_structure) slipDirection(1:3,1:ns) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,my_instance), my_structure) !*** start out fully compatible compatibility = 0.0_pReal forall(s1 = 1_pInt:ns) & compatibility(1:2,s1,s1,1:Nneighbors) = 1.0_pReal !*** Loop thrugh neighbors and check whether there is any compatibility. do n = 1_pInt,Nneighbors neighboring_e = mesh_ipNeighborhood(1,n,i,e) neighboring_i = mesh_ipNeighborhood(2,n,i,e) !* FREE SURFACE !* Set surface transmissivity to the value specified in the material.config if (neighboring_e <= 0_pInt .or. neighboring_i <= 0_pInt) then forall(s1 = 1_pInt:ns) & compatibility(1:2,s1,s1,n) = sqrt(constitutive_nonlocal_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. neighboring_phase = material_phase(1,neighboring_i,neighboring_e) if (neighboring_phase /= my_phase) then if (.not. phase_localPlasticity(neighboring_phase) .and. .not. phase_localPlasticity(my_phase)) then forall(s1 = 1_pInt:ns) & 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 (constitutive_nonlocal_grainboundaryTransmissivity(my_instance) >= 0.0_pReal) then neighboring_texture = material_texture(1,neighboring_i,neighboring_e) if (neighboring_texture /= my_texture) then if (.not. phase_localPlasticity(neighboring_phase)) then forall(s1 = 1_pInt:ns) & compatibility(1:2,s1,s1,n) = sqrt(constitutive_nonlocal_grainboundaryTransmissivity(my_instance)) endif cycle endif !* GRAIN BOUNDARY ? !* Compatibility defined by relative orientation of slip systems: !* The 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 compatibility values exceeding one. !* Finally the smallest 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,neighboring_i,neighboring_e), & 0_pInt) ! no symmetry do s1 = 1_pInt,ns ! my slip systems do s2 = 1_pInt,ns ! my neighbor's slip systems 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)))) 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 compatibilitySum = 0.0_pReal belowThreshold = .true. do while (compatibilitySum < 1.0_pReal .and. any(belowThreshold(1:ns))) thresholdValue = maxval(compatibility(2,1:ns,s1,n), belowThreshold(1:ns)) ! screws always positive nThresholdValues = real(count(compatibility(2,1:ns,s1,n) == thresholdValue),pReal) where (compatibility(2,1:ns,s1,n) >= thresholdValue) & belowThreshold(1:ns) = .false. if (compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) & where (abs(compatibility(1:2,1:ns,s1,n)) == thresholdValue) & compatibility(1:2,1:ns,s1,n) = sign((1.0_pReal - compatibilitySum) / nThresholdValues, compatibility(1:2,1:ns,s1,n)) compatibilitySum = compatibilitySum + nThresholdValues * thresholdValue enddo where (belowThreshold(1:ns)) compatibility(1,1:ns,s1,n) = 0.0_pReal where (belowThreshold(1:ns)) compatibility(2,1:ns,s1,n) = 0.0_pReal enddo ! my slip systems cycle endif enddo ! neighbor cycle constitutive_nonlocal_compatibility(1:2,1:ns,1:ns,1:Nneighbors,i,e) = compatibility endsubroutine !********************************************************************* !* rate of change of temperature * !********************************************************************* pure function constitutive_nonlocal_dotTemperature(Tstar_v,Temperature,state,g,ip,el) use prec, only: pReal, & pInt, & p_vec 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 prec, only: pReal, & pInt, & p_vec 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) 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 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) nu, & ! poisson's ratio x, y, z, & ! coordinates of connection vector in neighboring 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, & neighboring_ipVolumeSideLength, & detFe real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration connection_neighboringLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor connection_neighboringSlip, & ! 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 neighboring_coords ! x,y,z coordinates of cell center of neighboring ip volume real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighboring material point's slip system frame Tdislo_neighboringLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighboring material point invFe, & ! inverse of my elastic deformation gradient neighboring_invFe, & neighboringLattice2myLattice ! mapping from neighboring MPs lattice configuration to my lattice configuration real(pReal), dimension(2,2,maxval(constitutive_nonlocal_totalNslip)) :: & neighboring_rhoExcess ! excess density at neighboring material point (edge/screw,mobile/dead,slipsystem) real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip)) :: & rhoExcessDead real(pReal), dimension(constitutive_nonlocal_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 = constitutive_nonlocal_totalNslip(instance) !*** get basic states forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) & rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal) ! ensure positive single mobile densities forall (t = 5_pInt:8_pInt) & rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns) !*** 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) ! if (inversionError) then ! return ! endif !* 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) - constitutive_nonlocal_R(instance) - minCoord(dir)) / meshSize(dir), pInt) periodicImages(2,dir) = ceiling((coords(dir) + constitutive_nonlocal_R(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 neighboring_el = 1_pInt,mesh_NcpElems ipLoop: do neighboring_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighboring_el))) neighboring_phase = material_phase(g,neighboring_ip,neighboring_el) if (phase_localPlasticity(neighboring_phase)) then cycle endif neighboring_instance = phase_plasticityInstance(neighboring_phase) neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance) neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance) call math_invert33(Fe(1:3,1:3,1,neighboring_ip,neighboring_el), neighboring_invFe, detFe, inversionError) ! if (inversionError) then ! return ! endif neighboring_ipVolumeSideLength = mesh_ipVolume(neighboring_ip,neighboring_el) ** (1.0_pReal/3.0_pReal) ! reference volume used here forall (s = 1_pInt:neighboring_ns, c = 1_pInt:2_pInt) & neighboring_rhoExcess(c,1,s) = state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-2_pInt)*neighboring_ns+s) & ! positive mobiles - state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*neighboring_ns+s) ! negative mobiles forall (s = 1_pInt:neighboring_ns, c = 1_pInt:2_pInt) & neighboring_rhoExcess(c,2,s) = abs(state(g,neighboring_ip,neighboring_el)%p((2_pInt*c+2_pInt)*neighboring_ns+s)) & ! positive deads - abs(state(g,neighboring_ip,neighboring_el)%p((2_pInt*c+3_pInt)*neighboring_ns+s)) ! negative deads nu = constitutive_nonlocal_nu(neighboring_instance) Tdislo_neighboringLattice = 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 (neighboring_el /= el .or. neighboring_ip /= ip & .or. deltaX /= 0_pInt .or. deltaY /= 0_pInt .or. deltaZ /= 0_pInt) then neighboring_coords = mesh_cellCenterCoordinates(neighboring_ip,neighboring_el) & + (/real(deltaX,pReal), real(deltaY,pReal), real(deltaZ,pReal)/) * meshSize connection = neighboring_coords - coords distance = sqrt(sum(connection * connection)) if (distance > constitutive_nonlocal_R(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 neighboring dislocation segment connection_neighboringLattice = math_mul33x3(neighboring_invFe, connection) segmentLength = min(neighboring_ipVolumeSideLength, distance) !* loop through all slip systems of the neighboring material point !* and add up the stress contributions from egde and screw excess on these slip systems (if significant) do s = 1_pInt,neighboring_ns if (all(abs(neighboring_rhoExcess(:,:,s)) < constitutive_nonlocal_significantRho(instance))) then cycle ! not significant endif !* map the connection vector from the lattice into the slip system frame connection_neighboringSlip = math_mul33x3(constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_instance), & connection_neighboringLattice) !* edge contribution to stress sigma = 0.0_pReal x = connection_neighboringSlip(1) y = connection_neighboringSlip(2) z = connection_neighboringSlip(3) xsquare = x * x ysquare = y * y zsquare = z * z do j = 1_pInt,2_pInt if (abs(neighboring_rhoExcess(1,j,s)) < constitutive_nonlocal_significantRho(instance)) then cycle elseif (j > 1_pInt) then x = connection_neighboringSlip(1) + sign(0.5_pReal * segmentLength, & state(g,neighboring_ip,neighboring_el)%p(4*neighboring_ns+s) & - state(g,neighboring_ip,neighboring_el)%p(5*neighboring_ns+s)) 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) & * neighboring_rhoExcess(1,j,s) sigma(2,2) = sigma(2,2) - real(side,pReal) * (flipSign * 2.0_pReal * nu * z / denominator + z * lambda / Rcube)& * neighboring_rhoExcess(1,j,s) sigma(3,3) = sigma(3,3) + real(side,pReal) * flipSign * z / denominator & * (1.0_pReal - zsquare / Rsquare - zsquare / denominator) & * neighboring_rhoExcess(1,j,s) sigma(1,2) = sigma(1,2) + real(side,pReal) * x * z / Rcube * neighboring_rhoExcess(1,j,s) sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * x / denominator & * (1.0_pReal - zsquare / Rsquare - zsquare / denominator) & * neighboring_rhoExcess(1,j,s) sigma(2,3) = sigma(2,3) - real(side,pReal) * (nu / R - zsquare / Rcube) * neighboring_rhoExcess(1,j,s) enddo enddo !* screw contribution to stress x = connection_neighboringSlip(1) ! have to restore this value, because position might have been adapted for edge deads before do j = 1_pInt,2_pInt if (abs(neighboring_rhoExcess(2,j,s)) < constitutive_nonlocal_significantRho(instance)) then cycle elseif (j > 1_pInt) then y = connection_neighboringSlip(2) + sign(0.5_pReal * segmentLength, & state(g,neighboring_ip,neighboring_el)%p(6_pInt*neighboring_ns+s) & - state(g,neighboring_ip,neighboring_el)%p(7_pInt*neighboring_ns+s)) 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) / denominator & * neighboring_rhoExcess(2,j,s) sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * y * (1.0_pReal - nu) / denominator & * neighboring_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 neighboring material point's lattice configuration sigma = sigma * constitutive_nonlocal_Gmod(neighboring_instance) & * constitutive_nonlocal_burgers(s,neighboring_instance) & / (4.0_pReal * pi * (1.0_pReal - nu)) & * mesh_ipVolume(neighboring_ip,neighboring_el) / segmentLength ! reference volume is used here (according to the segment length calculation) Tdislo_neighboringLattice = Tdislo_neighboringLattice & + math_mul33x33(math_transpose33(constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_instance)), & math_mul33x33(sigma, constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_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((2_pInt*c+2_pInt)*ns+s) & ! 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((2_pInt*c+3_pInt)*ns+s) ! 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)) < constitutive_nonlocal_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)) * neighboring_ipVolumeSideLength & * constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) & / (sqrt(2.0_pReal) * pi * (1.0_pReal - nu)) sigma(3,1) = sigma(1,3) Tdislo_neighboringLattice = Tdislo_neighboringLattice & + math_mul33x33(math_transpose33(constitutive_nonlocal_lattice2slip(1:3,1:3,s,instance)), & math_mul33x33(sigma, constitutive_nonlocal_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 neighboring MP's lattice configuration into the deformed configuration !* and back into my lattice configuration neighboringLattice2myLattice = math_mul33x33(invFe, Fe(1:3,1:3,1,neighboring_ip,neighboring_el)) constitutive_nonlocal_dislocationstress = constitutive_nonlocal_dislocationstress & + math_mul33x33(neighboringLattice2myLattice, & math_mul33x33(Tdislo_neighboringLattice, & math_transpose33(neighboringLattice2myLattice))) 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 prec, only: pReal, & pInt, & p_vec 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 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(constitutive_nonlocal_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(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: & gdot, & ! shear rates v ! velocities real(pReal), dimension(constitutive_nonlocal_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(constitutive_nonlocal_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,constitutive_nonlocal_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(3,3) :: sigma myInstance = phase_plasticityInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_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) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal) forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) & rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s) forall (c = 1_pInt:2_pInt) & rhoDip(1:ns,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+1_pInt:(8_pInt+c)*ns), 0.0_pReal) rhoForest = state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns) tauThreshold = state(g,ip,el)%p(11_pInt*ns+1:12_pInt*ns) tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) forall (t = 1_pInt:8_pInt) rhoDotSgl(1:ns,t) = dotState%p((t-1_pInt)*ns+1_pInt:t*ns) forall (c = 1_pInt:2_pInt) rhoDotDip(1:ns,c) = dotState%p((7_pInt+c)*ns+1_pInt:(8_pInt+c)*ns) forall (t = 1_pInt:4_pInt) v(1:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoSgl = 0.0_pReal where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) & .or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) & rhoDip = 0.0_pReal !* Calculate shear rate do t = 1_pInt,4_pInt do s = 1_pInt,ns if (rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) then rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4_pInt)) ! remobilization of immobile singles for changing sign of v (bauschinger effect) rhoSgl(s,t+4_pInt) = 0.0_pReal ! remobilization of immobile singles for changing sign of v (bauschinger effect) endif enddo enddo forall (t = 1_pInt:4_pInt) & gdot(1:ns,t) = rhoSgl(1:ns,t) * constitutive_nonlocal_burgers(1:ns,myInstance) * v(1:ns,t) !* calculate limits for stable dipole height do s = 1_pInt,ns sLattice = constitutive_nonlocal_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 = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance) dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) & / (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau)) dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_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,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure) m(1:3,1:ns,2) = -lattice_st(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure) forall (c = 1_pInt:2_pInt, s = 1_pInt:ns) & m_currentconf(1:3,s,c) = math_mul33x3(Fe, m(1:3,s,c)) 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) = state(g,ip,el)%p(1:ns) cs = cs + ns case ('rho_sgl_edge_pos_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(4*ns+1:5*ns) 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) = state(g,ip,el)%p(ns+1:2*ns) cs = cs + ns case ('rho_sgl_edge_neg_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(5*ns+1:6*ns) cs = cs + ns case ('rho_dip_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(8*ns+1:9*ns) 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) = state(g,ip,el)%p(2*ns+1:3*ns) cs = cs + ns case ('rho_sgl_screw_pos_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(6*ns+1:7*ns) 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) = state(g,ip,el)%p(3*ns+1:4*ns) cs = cs + ns case ('rho_sgl_screw_neg_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(7*ns+1:8*ns) cs = cs + ns case ('rho_dip_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(9*ns+1:10*ns) 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 = constitutive_nonlocal_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) = constitutive_nonlocal_rhoDotMultiplication(1:ns,1,g,ip,el) & + constitutive_nonlocal_rhoDotMultiplication(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_gen_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotMultiplication(1:ns,1,g,ip,el) cs = cs + ns case ('rho_dot_gen_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotMultiplication(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_sgl2dip') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1,g,ip,el) & + constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_sgl2dip_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1,g,ip,el) cs = cs + ns case ('rho_dot_sgl2dip_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_ann_ath') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1,g,ip,el) & + constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_ann_the') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1,g,ip,el) & + constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_ann_the_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1,g,ip,el) cs = cs + ns case ('rho_dot_ann_the_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el) cs = cs + ns case ('rho_dot_edgejogs') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotEdgeJogs(1:ns,g,ip,el) cs = cs + ns case ('rho_dot_flux') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,1:4,g,ip,el),2) & + sum(abs(constitutive_nonlocal_rhoDotFlux(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(constitutive_nonlocal_rhoDotFlux(1:ns,1:2,g,ip,el),2) & + sum(abs(constitutive_nonlocal_rhoDotFlux(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(constitutive_nonlocal_rhoDotFlux(1:ns,3:4,g,ip,el),2) & + sum(abs(constitutive_nonlocal_rhoDotFlux(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 ('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_accumulatedShear(1:ns,g,ip,el) = constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el) + sum(gdot,2)*dt !$OMP FLUSH(constitutive_nonlocal_accumulatedShear) constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el) 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