DAMASK_EICMD/code/constitutive_nonlocal.f90

2540 lines
147 KiB
Fortran

!* $Id$
!************************************
!* Module: CONSTITUTIVE_NONLOCAL *
!************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!************************************
MODULE constitutive_nonlocal
!* Include other modules
use prec, only: pReal,pInt
implicit none
!* Definition of parameters
character (len=*), parameter :: constitutive_nonlocal_label = 'nonlocal'
character(len=22), dimension(10), parameter :: 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=15), dimension(3), parameter :: constitutive_nonlocal_listDependentStates = (/'rhoForest ', &
'tauThreshold ', &
'Tdislocation_v ' /) ! list of microstructural state variables that depend on other state variables
real(pReal), parameter :: kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin
!* Definition of global variables
integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_sizeDotState, & ! number of dotStates
constitutive_nonlocal_sizeState, & ! total number of microstructural state variables
constitutive_nonlocal_sizePostResults ! cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target :: constitutive_nonlocal_sizePostResult ! size of each post result output
character(len=64), dimension(:,:), allocatable, target :: constitutive_nonlocal_output ! name of each post result output
character(len=32), dimension(:), allocatable :: constitutive_nonlocal_structureName ! name of the lattice structure
integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_structure, & ! number representing the kind of lattice structure
constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance
integer(pInt), dimension(:,:), allocatable :: 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
real(pReal), dimension(:), allocatable :: constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice
constitutive_nonlocal_C11, & ! C11 element in elasticity matrix
constitutive_nonlocal_C12, & ! C12 element in elasticity matrix
constitutive_nonlocal_C13, & ! C13 element in elasticity matrix
constitutive_nonlocal_C33, & ! C33 element in elasticity matrix
constitutive_nonlocal_C44, & ! C44 element in elasticity matrix
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_R, & ! cutoff radius for dislocation stress
constitutive_nonlocal_d0, & ! wall depth as multiple of b
constitutive_nonlocal_tauObs, & ! obstacle strength in Pa
constitutive_nonlocal_fattack, & ! attack frequency in Hz
constitutive_nonlocal_vs, & ! maximum dislocation velocity = velocity of sound
constitutive_nonlocal_rhoSglScatter, & ! standard deviation of scatter in initial dislocation density
constitutive_nonlocal_surfaceTransmissivity ! transmissivity at free surface
real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable :: 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_lambda0PerSlipSystem, & ! 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_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
constitutive_nonlocal_dLowerEdgePerSlipFamily, & ! minimum stable edge dipole height for each family and instance
constitutive_nonlocal_dLowerEdgePerSlipSystem, & ! minimum stable edge dipole height for each slip system and instance
constitutive_nonlocal_dLowerScrewPerSlipFamily, & ! minimum stable screw dipole height for each family and instance
constitutive_nonlocal_dLowerScrewPerSlipSystem, & ! minimum stable screw dipole height for each slip system and instance
constitutive_nonlocal_Qeff0, & ! prefactor for activation enthalpy for dislocation glide in J
constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_v, & ! dislocation velocity
constitutive_nonlocal_rhoDotFlux ! dislocation convection term
real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_nonlocal_compatibility ! slip system compatibility between me and my neighbors
real(pReal), dimension(:,:,:), allocatable :: 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
CONTAINS
!****************************************
!* - constitutive_init
!* - constitutive_stateInit
!* - constitutive_homogenizedC
!* - constitutive_microstructure
!* - constitutive_LpAndItsTangent
!* - constitutive_dotState
!* - constitutive_dotTemperature
!* - constitutive_postResults
!****************************************
!**************************************
!* Module initialization *
!**************************************
subroutine constitutive_nonlocal_init(file)
use prec, only: pInt, pReal
use math, only: math_Mandel3333to66, &
math_Voigt66to3333, &
math_mul3x3
use IO, only: IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_intValue, &
IO_error
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
FE_maxNipNeighbors
use material, only: homogenization_maxNgrains, &
phase_constitution, &
phase_constitutionInstance, &
phase_Noutput
use lattice, only: lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_maxNslip, &
lattice_maxNtwin, &
lattice_maxNinteraction, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_initializeStructure, &
lattice_Qtwin, &
lattice_sd, &
lattice_sn, &
lattice_st, &
lattice_interactionSlipSlip
!*** output variables
!*** input variables
integer(pInt), intent(in) :: file
!*** local variables
integer(pInt), parameter :: maxNchunks = 21
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section, &
maxNinstance, &
maxTotalNslip, &
myStructure, &
f, & ! index of my slip family
i, & ! index of my instance of this constitution
j, &
k, &
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
output, &
mySize
character(len=64) tag
character(len=1024) line
write(6,*)
write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_nonlocal_label,' init -+>>>'
write(6,*) '$Id$'
write(6,*)
maxNinstance = count(phase_constitution == constitutive_nonlocal_label)
if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law
!*** space allocation for global variables
allocate(constitutive_nonlocal_sizeDotState(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))
constitutive_nonlocal_sizeDotState = 0_pInt
constitutive_nonlocal_sizeState = 0_pInt
constitutive_nonlocal_sizePostResults = 0_pInt
constitutive_nonlocal_sizePostResult = 0_pInt
constitutive_nonlocal_output = ''
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_C11(maxNinstance))
allocate(constitutive_nonlocal_C12(maxNinstance))
allocate(constitutive_nonlocal_C13(maxNinstance))
allocate(constitutive_nonlocal_C33(maxNinstance))
allocate(constitutive_nonlocal_C44(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_Cslip_66(6,6,maxNinstance))
allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance))
allocate(constitutive_nonlocal_R(maxNinstance))
allocate(constitutive_nonlocal_d0(maxNinstance))
allocate(constitutive_nonlocal_tauObs(maxNinstance))
allocate(constitutive_nonlocal_vs(maxNinstance))
allocate(constitutive_nonlocal_fattack(maxNinstance))
allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance))
allocate(constitutive_nonlocal_surfaceTransmissivity(maxNinstance))
constitutive_nonlocal_CoverA = 0.0_pReal
constitutive_nonlocal_C11 = 0.0_pReal
constitutive_nonlocal_C12 = 0.0_pReal
constitutive_nonlocal_C13 = 0.0_pReal
constitutive_nonlocal_C33 = 0.0_pReal
constitutive_nonlocal_C44 = 0.0_pReal
constitutive_nonlocal_Gmod = 0.0_pReal
constitutive_nonlocal_atomicVolume = 0.0_pReal
constitutive_nonlocal_Dsd0 = 0.0_pReal
constitutive_nonlocal_Qsd = 0.0_pReal
constitutive_nonlocal_aTolRho = 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_d0 = 0.0_pReal
constitutive_nonlocal_tauObs = 0.0_pReal
constitutive_nonlocal_vs = 0.0_pReal
constitutive_nonlocal_fattack = 0.0_pReal
constitutive_nonlocal_rhoSglScatter = 0.0_pReal
constitutive_nonlocal_surfaceTransmissivity = 1.0_pReal
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))
allocate(constitutive_nonlocal_dLowerEdgePerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_dLowerScrewPerSlipFamily(lattice_maxNslipFamily, 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
constitutive_nonlocal_dLowerEdgePerSlipFamily = 0.0_pReal
constitutive_nonlocal_dLowerScrewPerSlipFamily = 0.0_pReal
!*** readout data from material.config file
rewind(file)
line = ''
section = 0
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
read(file,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(file,'(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
output = 0 ! reset output counter
cycle
endif
if (section > 0 .and. phase_constitution(section) == constitutive_nonlocal_label) then ! one of my sections
i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
select case(tag)
case('constitution','/nonlocal/')
cycle
case ('(output)')
output = output + 1
constitutive_nonlocal_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
case ('lattice_structure')
constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
case ('covera_ratio')
constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2)
case ('c11')
constitutive_nonlocal_C11(i) = IO_floatValue(line,positions,2)
case ('c12')
constitutive_nonlocal_C12(i) = IO_floatValue(line,positions,2)
case ('c13')
constitutive_nonlocal_C13(i) = IO_floatValue(line,positions,2)
case ('c33')
constitutive_nonlocal_C33(i) = IO_floatValue(line,positions,2)
case ('c44')
constitutive_nonlocal_C44(i) = IO_floatValue(line,positions,2)
case ('nslip')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1+f)
case ('rhosgledgepos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoSglEdgePos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhosgledgeneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoSglEdgeNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhosglscrewpos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoSglScrewPos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhosglscrewneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoSglScrewNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhodipedge0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoDipEdge0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhodipscrew0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoDipScrew0(f,i) = IO_floatValue(line,positions,1+f)
case ('lambda0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('burgers')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('r')
constitutive_nonlocal_R(i) = IO_floatValue(line,positions,2)
case('ddipminedge')
forall (f = 1:lattice_maxNslipFamily) &
constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('ddipminscrew')
forall (f = 1:lattice_maxNslipFamily) &
constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('atomicvolume')
constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2)
case('dsd0')
constitutive_nonlocal_Dsd0(i) = IO_floatValue(line,positions,2)
case('qsd')
constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2)
case('atol_rho')
constitutive_nonlocal_aTolRho(i) = IO_floatValue(line,positions,2)
case ('interaction_slipslip')
forall (it = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1+it)
case('d0')
constitutive_nonlocal_d0(i) = IO_floatValue(line,positions,2)
case('tauobs')
constitutive_nonlocal_tauObs(i) = IO_floatValue(line,positions,2)
case('vs')
constitutive_nonlocal_vs(i) = IO_floatValue(line,positions,2)
case('fattack')
constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2)
case('rhosglscatter')
constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2)
case('surfacetransmissivity')
constitutive_nonlocal_surfaceTransmissivity(i) = IO_floatValue(line,positions,2)
case default
call IO_error(236,ext_msg=tag)
end select
endif
enddo
100 do i = 1,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 .or. myStructure > 3) call IO_error(205)
if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0_pInt) call IO_error(235,ext_msg='Nslip')
do o = 1,maxval(phase_Noutput)
if(len(constitutive_nonlocal_output(o,i)) > 64) call IO_error(666)
enddo
do f = 1,lattice_maxNslipFamily
if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then
if (constitutive_nonlocal_rhoSglEdgePos0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoSglEdgePos0')
if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoSglEdgeNeg0')
if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoSglScrewPos0')
if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoSglScrewNeg0')
if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoDipEdge0')
if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(235,ext_msg='rhoDipScrew0')
if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(235,ext_msg='burgers')
if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(235,ext_msg='lambda0')
if (constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) <= 0.0_pReal) call IO_error(235,ext_msg='dDipMinEdge')
if (constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(235,ext_msg='dDipMinScrew')
endif
enddo
if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) &
call IO_error(235,ext_msg='interaction_SlipSlip')
if (constitutive_nonlocal_R(i) < 0.0_pReal) call IO_error(235,ext_msg='r')
if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(235,ext_msg='atomicVolume')
if (constitutive_nonlocal_Dsd0(i) <= 0.0_pReal) call IO_error(235,ext_msg='Dsd0')
if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(235,ext_msg='Qsd')
if (constitutive_nonlocal_aTolRho(i) <= 0.0_pReal) call IO_error(235,ext_msg='aTol_rho')
if (constitutive_nonlocal_d0(i) <= 0.0_pReal) call IO_error(235,ext_msg='d0')
if (constitutive_nonlocal_tauObs(i) <= 0.0_pReal) call IO_error(235,ext_msg='tauObs')
if (constitutive_nonlocal_vs(i) <= 0.0_pReal) call IO_error(235,ext_msg='vs')
if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(235,ext_msg='fAttack')
if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal) call IO_error(235,ext_msg='rhoSglScatter')
if (constitutive_nonlocal_surfaceTransmissivity(i) < 0.0_pReal &
.or. constitutive_nonlocal_surfaceTransmissivity(i) > 1.0_pReal) call IO_error(235,ext_msg='surfaceTransmissivity')
!*** 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_burgersPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_burgersPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_lambda0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_lambda0PerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_dLowerEdgePerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_dLowerEdgePerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_dLowerScrewPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_dLowerScrewPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_Qeff0(maxTotalNslip, maxNinstance))
constitutive_nonlocal_Qeff0 = 0.0_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_v(maxTotalNslip, 4, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
constitutive_nonlocal_v = 0.0_pReal
allocate(constitutive_nonlocal_rhoDotFlux(maxTotalNslip, 10, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
constitutive_nonlocal_rhoDotFlux = 0.0_pReal
allocate(constitutive_nonlocal_compatibility(2,maxTotalNslip, maxTotalNslip, FE_maxNipNeighbors, mesh_maxNips, mesh_NcpElems))
constitutive_nonlocal_compatibility = 0.0_pReal
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,lattice_maxNslipFamily
do s = 1,constitutive_nonlocal_Nslip(f,i)
l = l + 1
constitutive_nonlocal_slipFamily(l,i) = f
constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1, myStructure)) + s
enddo; enddo
!*** determine size of state array
ns = constitutive_nonlocal_totalNslip(i)
constitutive_nonlocal_sizeState(i) = size(constitutive_nonlocal_listBasicStates) * ns &
+ (size(constitutive_nonlocal_listDependentStates) - 1_pInt) * ns + 6_pInt
constitutive_nonlocal_sizeDotState(i) = size(constitutive_nonlocal_listBasicStates) * ns
!*** determine size of postResults array
do o = 1,maxval(phase_Noutput)
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_internal', &
'resolvedstress_external', &
'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_dip2sgl', &
'rho_dot_ann_ath', &
'rho_dot_ann_the', &
'rho_dot_flux', &
'rho_dot_flux_edge', &
'rho_dot_flux_screw', &
'dislocationvelocity', &
'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', &
'd_upper_edge', &
'd_upper_screw', &
'd_upper_dot_edge', &
'd_upper_dot_screw' )
mySize = constitutive_nonlocal_totalNslip(i)
case default
mySize = 0_pInt
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
select case (myStructure)
case(1:2) ! cubic(s)
forall(k=1:3)
forall(j=1:3) constitutive_nonlocal_Cslip_66(k,j,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(k,k,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(k+3,k+3,i) = constitutive_nonlocal_C44(i)
end forall
case(3:) ! all hex
constitutive_nonlocal_Cslip_66(1,1,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(2,2,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(3,3,i) = constitutive_nonlocal_C33(i)
constitutive_nonlocal_Cslip_66(1,2,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(2,1,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(1,3,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(3,1,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(2,3,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(3,2,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(4,4,i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_Cslip_66(5,5,i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_nonlocal_C11(i)- constitutive_nonlocal_C12(i))
end select
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))
constitutive_nonlocal_Gmod(i) = 0.2_pReal * ( constitutive_nonlocal_C11(i) - constitutive_nonlocal_C12(i) &
+ 3.0_pReal*constitutive_nonlocal_C44(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_C11(i) + 4.0_pReal*constitutive_nonlocal_C12(i) &
- 2.0_pReal*constitutive_nonlocal_C44(i) ) &
/ ( 4.0_pReal*constitutive_nonlocal_C11(i) + 6.0_pReal*constitutive_nonlocal_C12(i) &
+ 2.0_pReal*constitutive_nonlocal_C44(i) ) ! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
do s1 = 1,ns
f = constitutive_nonlocal_slipFamily(s1,i)
!*** burgers vector, mean free path prefactor and minimum dipole distance for each slip system
constitutive_nonlocal_burgersPerSlipSystem(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i)
constitutive_nonlocal_lambda0PerSlipSystem(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i)
constitutive_nonlocal_dLowerEdgePerSlipSystem(s1,i) = constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i)
constitutive_nonlocal_dLowerScrewPerSlipSystem(s1,i) = constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i)
do s2 = 1,ns
!*** calculation of forest projections for edge and screw dislocations. s2 acts as forest to 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 )
enddo; enddo
!*** calculation of prefactor for activation enthalpy for dislocation glide
constitutive_nonlocal_Qeff0(1:ns,i) = constitutive_nonlocal_burgersPerSlipSystem(1:ns,i) ** 3.0_pReal &
* dsqrt(0.5_pReal * constitutive_nonlocal_d0(i) ** 3.0_pReal &
* constitutive_nonlocal_Gmod(i) * constitutive_nonlocal_tauObs(i))
enddo
endsubroutine
!*********************************************************************
!* initial microstructural state (just the "basic" states) *
!*********************************************************************
function constitutive_nonlocal_stateInit(myInstance)
use prec, only: pReal, &
pInt
use lattice, only: lattice_maxNslipFamily
use math, only: math_sampleGaussVar
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
constitutive_nonlocal_stateInit
!*** local variables
real(pReal), dimension(constitutive_nonlocal_totalNslip(myInstance)) :: &
rhoSglEdgePos, & ! positive edge dislocation density
rhoSglEdgeNeg, & ! negative edge dislocation density
rhoSglScrewPos, & ! positive screw dislocation density
rhoSglScrewNeg, & ! negative screw dislocation density
rhoSglEdgePosUsed, & ! used positive edge dislocation density
rhoSglEdgeNegUsed, & ! used negative edge dislocation density
rhoSglScrewPosUsed, & ! used positive screw dislocation density
rhoSglScrewNegUsed, & ! used negative screw dislocation density
rhoDipEdge, & ! edge dipole dislocation density
rhoDipScrew, & ! screw dipole dislocation density
rhoForest, & ! forest dislocation density
tauSlipThreshold ! threshold shear stress for slip
integer(pInt) ns, & ! short notation for total number of active slip systems
f, & ! index of lattice family
from, &
upto, &
s, & ! index of slip system
i
real(pReal), dimension(2) :: noise
constitutive_nonlocal_stateInit = 0.0_pReal
ns = constitutive_nonlocal_totalNslip(myInstance)
!*** set the basic state variables
do f = 1,lattice_maxNslipFamily
from = 1 + sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance))
do s = from,upto
do i = 1,2
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
rhoSglEdgePosUsed(from:upto) = 0.0_pReal
rhoSglEdgeNegUsed(from:upto) = 0.0_pReal
rhoSglScrewPosUsed(from:upto) = 0.0_pReal
rhoSglScrewNegUsed(from:upto) = 0.0_pReal
rhoDipEdge(from:upto) = constitutive_nonlocal_rhoDipEdge0(f, myInstance)
rhoDipScrew(from:upto) = constitutive_nonlocal_rhoDipScrew0(f, myInstance)
enddo
!*** put everything together and in right order
constitutive_nonlocal_stateInit( 1: ns) = rhoSglEdgePos
constitutive_nonlocal_stateInit( ns+1: 2*ns) = rhoSglEdgeNeg
constitutive_nonlocal_stateInit( 2*ns+1: 3*ns) = rhoSglScrewPos
constitutive_nonlocal_stateInit( 3*ns+1: 4*ns) = rhoSglScrewNeg
constitutive_nonlocal_stateInit( 4*ns+1: 5*ns) = rhoSglEdgePosUsed
constitutive_nonlocal_stateInit( 5*ns+1: 6*ns) = rhoSglEdgeNegUsed
constitutive_nonlocal_stateInit( 6*ns+1: 7*ns) = rhoSglScrewPosUsed
constitutive_nonlocal_stateInit( 7*ns+1: 8*ns) = rhoSglScrewNegUsed
constitutive_nonlocal_stateInit( 8*ns+1: 9*ns) = rhoDipEdge
constitutive_nonlocal_stateInit( 9*ns+1:10*ns) = rhoDipScrew
endfunction
!*********************************************************************
!* 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 constitution
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
constitutive_nonlocal_aTolState ! absolute state tolerance for the current instance of this constitution
!*** 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_constitutionInstance
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 constitution
myInstance = phase_constitutionInstance(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, Tstar_v, Fe, Fp, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_Plain3333to99, &
math_Mandel33to6, &
math_Mandel6to33, &
math_mul33x33, &
math_mul3x3, &
math_mul33x3, &
math_inv3x3, &
math_det3x3, &
math_transpose3x3, &
pi
use debug, only: debugger, &
verboseDebugger
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_maxNipNeighbors, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipCenterOfGravity
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_localConstitution, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_maxNslip, &
lattice_sd, &
lattice_sn, &
lattice_st
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,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient
real(pReal), dimension(6), intent(in) :: &
Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! microstructural state
!*** output variables
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
myPhase, &
ns, & ! short notation for the total number of active slip systems
neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor
c, & ! index of dilsocation character (edge, screw)
n, & ! index of my current neighbor
s, & ! index of my current slip system
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
sLattice, & ! index of my current slip system according to lattice order
i, &
j
real(pReal) nu ! poisson's ratio
real(pReal), dimension(3,2) :: rhoExcessDifference, & ! finite differences of excess density (in 3 directions for edge and screw)
disloGradients ! spatial gradient in excess dislocation density (in 3 directions for edge and screw)
real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in its slip system frame
lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system with e1=bxn, e2=b, e3=n (passive rotation!!!)
F, & ! total deformation gradient
neighboring_F, & ! total deformation gradient of neighbor
invFe, & ! inverse elastic deformation gradient
Q ! inverse transpose of 3x3 matrix with finite differences of opposing position vectors
real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoExcess ! central excess density
real(pReal), dimension(6,2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
neighboring_rhoExcess ! excess density for each neighbor, dislo character and slip system
real(pReal), dimension(3,6) :: neighboring_position ! position vector of each neighbor when seen from the centreal material point's lattice frame
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip ! dipole dislocation density (edge, screw)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
transmissivity, & ! transmissivity
rhoForest, & ! forest dislocation density
tauThreshold, & ! threshold shear stress
tau ! resolved shear stress
myPhase = material_phase(g,ip,el)
myInstance = phase_constitutionInstance(myPhase)
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
!**********************************************************************
!*** get basic states
forall (t = 1:4) rhoSgl(1:ns,t) = max(state(g,ip,el)%p((t-1)*ns+1:t*ns), 0.0_pReal) ! ensure positive single mobile densities
forall (t = 5:8) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDip(1:ns,c) = max(state(g,ip,el)%p((c+7)*ns+1:(c+8)*ns), 0.0_pReal) ! ensure positive dipole densities
where(rhoSgl(1:ns,1:4) < min(0.1, 0.01*constitutive_nonlocal_aTolRho(myInstance))) &
rhoSgl(1:ns,1:4) = 0.0_pReal ! delete non-significant single density
!**********************************************************************
!*** calculate dependent states
!*** calculate the forest dislocation density
forall (s = 1: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, myInstance) ) &
+ dot_product( ( sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2) ), &
constitutive_nonlocal_forestProjectionScrew(s, 1:ns, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
! if (debugger) write(6,'(a30,3(i3,x),/,12(e10.3,x),/)') 'forest dislocation density at ',g,ip,el, rhoForest
!*** calculate the threshold shear stress for dislocation slip
forall (s = 1:ns) &
tauThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
* constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) &
* sqrt( dot_product( ( sum(abs(rhoSgl),2) + sum(abs(rhoDip),2) ), &
constitutive_nonlocal_interactionMatrixSlipSlip(s, 1:ns, myInstance) ) )
! if (debugger) write(6,'(a22,3(i3,x),/,12(f10.5,x),/)') 'tauThreshold / MPa at ',g,ip,el, tauThreshold/1e6
!*** calculate the dislocation stress of the neighboring excess dislocation densities
Tdislocation_v = 0.0_pReal
if (.not. phase_localConstitution(myPhase)) then ! only calculate dislocation stress for nonlocal material
F = math_mul33x33(Fe(1:3,1:3,g,ip,el), Fp(1:3,1:3,g,ip,el))
invFe = math_inv3x3(Fe(1:3,1:3,g,ip,el))
nu = constitutive_nonlocal_nu(myInstance)
forall (s = 1:ns, c = 1:2) &
rhoExcess(c,s) = state(g,ip,el)%p((2*c-2)*ns+s) + abs(state(g,ip,el)%p((2*c+2)*ns+s)) &
- state(g,ip,el)%p((2*c-1)*ns+s) - abs(state(g,ip,el)%p((2*c+3)*ns+s))
do n = 1,6
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then ! at free surfaces ...
neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip
neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution
neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip
neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
elseif (myPhase /= material_phase(1,neighboring_ip,neighboring_el)) then ! for neighbors with different phase
neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip
neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
else
transmissivity = sum(constitutive_nonlocal_compatibility(2,1:ns,1:ns,n,ip,el)**2.0_pReal, 1)
if ( any(transmissivity < 0.9_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ...
neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip
neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
else
neighboring_F = math_mul33x33(Fe(1:3,1:3,g,neighboring_ip,neighboring_el), Fp(1:3,1:3,g,neighboring_ip,neighboring_el))
neighboring_position(1:3,n) = &
0.5_pReal * math_mul33x3(math_mul33x33(invFe,neighboring_F) + Fp(1:3,1:3,g,ip,el), &
mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(1:3,ip,el))
forall (s = 1:ns, c = 1:2) &
neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) &
+ abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) &
- state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) &
- abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s))
endif
endif
enddo
Q = math_inv3x3(math_transpose3x3(neighboring_position(1:3,(/1,3,5/)) - neighboring_position(1:3,(/2,4,6/))))
do s = 1,ns
lattice2slip = math_transpose3x3(reshape((/ &
lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
-lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/)))
rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),1:2,s) - neighboring_rhoExcess((/2,4,6/),1:2,s)
forall (c = 1:2) &
disloGradients(1:3,c) = math_mul33x3(lattice2slip, math_mul33x3(Q, rhoExcessDifference(1:3,c)))
sigma = 0.0_pReal
sigma(1,1) = + 0.375_pReal / (1.0_pReal-nu) * disloGradients(3,1)
sigma(2,2) = + 0.5_pReal * nu / (1.0_pReal-nu) * disloGradients(3,1)
sigma(3,3) = + 0.125_pReal / (1.0_pReal-nu) * disloGradients(3,1)
sigma(1,2) = + 0.25_pReal * disloGradients(3,2)
sigma(1,3) = - 0.125_pReal / (1.0_pReal-nu) * disloGradients(1,1) - 0.25_pReal * disloGradients(2,2)
sigma(2,1) = sigma(1,2)
sigma(3,1) = sigma(1,3)
forall (i=1:3, j=1:3) &
sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
* constitutive_nonlocal_R(myInstance)**2.0_pReal
Tdislocation_v = Tdislocation_v + math_Mandel33to6(math_mul33x33(math_transpose3x3(lattice2slip), &
math_mul33x33(sigma, lattice2slip)))
enddo
endif
!**********************************************************************
!*** set states
state(g,ip,el)%p(1:8*ns) = reshape(rhoSgl,(/8*ns/)) ! ensure positive single mobile densities
state(g,ip,el)%p(8*ns+1:10*ns) = reshape(rhoDip,(/2*ns/)) ! ensure positive dipole densities
state(g,ip,el)%p(10*ns+1:11*ns) = rhoForest
state(g,ip,el)%p(11*ns+1:12*ns) = tauThreshold
state(g,ip,el)%p(12*ns+1:12*ns+6) = Tdislocation_v
endsubroutine
!*********************************************************************
!* calculates kinetics *
!*********************************************************************
subroutine constitutive_nonlocal_kinetics(Tstar_v, Temperature, state, g, ip, el, dv_dtau)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6, &
math_Mandel6to33
use debug, only: debugger, &
verboseDebugger, &
debug_g, &
debug_i, &
debug_e
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v
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
type(p_vec), intent(in) :: state ! microstructural state
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
!*** output variables
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))), &
intent(out), optional :: dv_dtau ! velocity derivative with respect to resolved shear stress
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
t, & ! dislocation type
s ! index of my current slip system
real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
tauThreshold, & ! threshold shear stress
tau, & ! resolved shear stress
rhoForest ! forest dislocation density
real(pReal) boltzmannProbability, &
tauRel, & ! relative thermally active resolved shear stress
wallFunc, & ! functions reflecting the shape of the obstacle wall (see PhD thesis Mohles p.53)
timeRatio ! ratio of travel to dwell time
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
rhoForest = state%p(10*ns+1:11*ns)
tauThreshold = state%p(11*ns+1:12*ns)
Tdislocation_v = state%p(12*ns+1:12*ns+6)
tau = 0.0_pReal
constitutive_nonlocal_v(1:ns,1:4,g,ip,el) = 0.0_pReal
if (present(dv_dtau)) dv_dtau = 0.0_pReal
if (Temperature > 0.0_pReal) then
do s = 1,ns
tau(s) = math_mul6x6(Tstar_v + Tdislocation_v, &
lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure))
!*** Only if the resolved shear stress exceeds the threshold stress, dislocations are able to cut the dislocation forest.
!*** In contrast to small atomic obstacles the forest can't be overcome by thermal activation.
!***
!*** mean travel distance
!*** The mean dislocation velocity is calculated as: --------------------------
!*** dwell time + travel time
!***
!*** with : mean travel distance = inverse of the root of forest density
!*** dwell time = inverse of attack frequency times probability of success
!*** travel time = mean travel distance over velocity of sound
tauRel = (abs(tau(s)) - tauThreshold(s)) / constitutive_nonlocal_tauObs(myInstance)
if (tauRel > 0.0_pReal .and. tauRel < 1.0_pReal) then
wallFunc = 4.0_pReal * dsqrt(2.0_pReal) / 3.0_pReal * dsqrt(1.0_pReal - tauRel) / tauRel
boltzmannProbability = dexp(- constitutive_nonlocal_Qeff0(s,myInstance) * wallFunc / (kB * Temperature))
timeRatio = boltzmannProbability * constitutive_nonlocal_fattack(myInstance) &
/ (constitutive_nonlocal_vs(myInstance) * dsqrt(rhoForest(s)))
constitutive_nonlocal_v(s,:,g,ip,el) = sign(constitutive_nonlocal_vs(myInstance),tau(s)) * timeRatio / (1.0_pReal + timeRatio)
if (present(dv_dtau)) then
dv_dtau(s) = abs(constitutive_nonlocal_v(s,1,g,ip,el)) * constitutive_nonlocal_Qeff0(s,myInstance) &
/ (kB * Temperature * (1.0_pReal + timeRatio)) &
* 0.5_pReal * wallFunc * (2.0_pReal - tauRel) &
/ ((1.0_pReal - tauRel) * (abs(tau(s)) - tauThreshold(s)))
endif
!*** If resolved stress exceeds threshold plus obstacle stress, the probability for thermal activation is 1.
!*** The tangent is zero, since no dependency of tau.
elseif (tauRel >= 1.0_pReal) then
constitutive_nonlocal_v(s,1:4,g,ip,el) = sign(constitutive_nonlocal_vs(myInstance), tau(s)) &
* constitutive_nonlocal_fattack(myInstance) &
/ (constitutive_nonlocal_vs(myInstance) * dsqrt(rhoForest(s)) &
+ constitutive_nonlocal_fattack(myInstance))
endif
enddo
endif
!if (verboseDebugger .and. s) then
! !$OMP CRITICAL (write2out)
! write(6,*) '::: kinetics',g,ip,el
! write(6,*)
! write(6,'(a,/,3(3(f12.3,x)/))') 'Tdislocation / MPa', math_Mandel6to33(Tdislocation_v/1e6)
! write(6,'(a,/,3(3(f12.3,x)/))') 'Tstar / MPa', math_Mandel6to33(Tstar_v/1e6)
! write(6,'(a,/,12(f12.5,x),/)') 'tau / MPa', tau/1e6_pReal
! write(6,'(a,/,12(e12.5,x),/)') 'rhoForest / 1/m**2', rhoForest
! write(6,'(a,/,4(12(f12.5,x),/))') 'v / 1e-3m/s', constitutive_nonlocal_v(:,:,g,ip,el)*1e3
! !$OMP END CRITICAL (write2out)
!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: debugger, &
verboseDebugger, &
debug_g, &
debug_i, &
debug_e
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v
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
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
!*** 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 constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
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(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: &
rhoSgl ! single dislocation densities (including used)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
gdot ! shear rate per dislocation type
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
tauThreshold, & ! threshold shear stress
gdotTotal, & ! shear rate
dv_dtau, & ! velocity derivative with respect to the shear stress
dgdotTotal_dtau, & ! derivative of the shear rate with respect to the shear stress
rhoForest ! forest dislocation density
!*** initialize local variables
gdot = 0.0_pReal
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
!*** shortcut to state variables
forall (t = 1:8) &
rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (s = 1:ns, t = 5:8, rhoSgl(s,t) * constitutive_nonlocal_v(s,t-4,g,ip,el) < 0.0_pReal) & ! contribution of used rho for changing sign of v
rhoSgl(s,t-4) = rhoSgl(s,t-4) + abs(rhoSgl(s,t))
rhoForest = state(g,ip,el)%p(10*ns+1:11*ns)
tauThreshold = state(g,ip,el)%p(11*ns+1:12*ns)
call constitutive_nonlocal_kinetics(Tstar_v, Temperature, state(g,ip,el), g, ip, el, dv_dtau) ! update dislocation velocity
!*** Calculation of gdot and its tangent
forall (t = 1:4) &
gdot(1:ns,t) = rhoSgl(1:ns,t) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
* constitutive_nonlocal_v(1:ns,t,g,ip,el)
gdotTotal = sum(gdot,2)
dgdotTotal_dtau = sum(rhoSgl,2) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) * dv_dtau
!*** Calculation of Lp and its tangent
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
Lp = Lp + gdotTotal(s) * lattice_Sslip(1:3,1:3,sLattice,myStructure)
forall (i=1:3,j=1:3,k=1:3,l=1:3) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) + dgdotTotal_dtau(s) * lattice_Sslip(i,j, sLattice,myStructure) &
* lattice_Sslip(k,l, sLattice,myStructure)
enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
!if (verboseDebugger .and. (debug_g==g .and. debug_i==i .and. debug_e==e)) then
! !$OMP CRITICAL (write2out)
! write(6,*) '::: LpandItsTangent',g,ip,el
! write(6,*)
! write(6,'(a,/,12(f12.5,x),/)') 'v / 1e-3m/s', constitutive_nonlocal_v(:,:,g,ip,el)*1e3
! write(6,'(a,/,12(f12.5,x),/)') 'gdot / 1e-3',gdot*1e3_pReal
! write(6,'(a,/,12(f12.5,x),/)') 'gdot total / 1e-3',gdotTotal*1e3_pReal
! write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp
! ! call flush(6)
! !$OMP END CRITICAL (write2out)
!endif
endsubroutine
!*********************************************************************
!* rate of change of microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, previousTstar_v, Fe, Fp, Temperature, dt_previous, &
state, previousState, aTolState, timestep, orientation, g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use IO, only: IO_error
use debug, only: debugger, &
debug_g, &
debug_i, &
debug_e, &
verboseDebugger
use math, only: math_norm3, &
math_mul6x6, &
math_mul3x3, &
math_mul33x3, &
math_mul33x33, &
math_inv3x3, &
math_det3x3, &
math_Mandel6to33, &
math_QuaternionDisorientation, &
math_qRot, &
pi, &
NaN
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_maxNipNeighbors, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipArea, &
mesh_ipAreaNormal, &
mesh_ipCenterOfGravity
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance, &
phase_localConstitution
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
lattice_sd, &
lattice_sn, &
lattice_st, &
lattice_maxNslipFamily, &
lattice_NslipSystem
use FEsolving, only:theInc, &
FEsolving_execElem, &
FEsolving_execIP
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
dt_previous ! time increment between previous and current state
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation
previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient
real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
orientation ! crystal lattice orientation
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state, & ! current microstructural state
previousState, & ! previous microstructural state
aTolState ! absolute state tolerance
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
dotState ! evolution of state variables / microstructure
!*** output variables
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
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_n, & ! index of my opposite neighbor
opposite_ip, & ! ip of my opposite neighbor
opposite_el, & ! element index of 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
i
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),10) :: &
rhoDot, & ! density evolution
rhoDotRemobilization, & ! density evolution by remobilization
rhoDotMultiplication, & ! density evolution by multiplication
rhoDotFlux, & ! density evolution by flux
neighboring_rhoDotFlux, & ! density evolution by flux at neighbor
rhoDotSingle2DipoleGlide, & ! density evolution by dipole formation (by glide)
rhoDotAthermalAnnihilation, & ! density evolution by athermal annihilation
rhoDotThermalAnnihilation, & ! density evolution by thermal annihilation
rhoDotDipole2SingleStressChange, & ! density evolution by dipole dissociation (by stress increase)
rhoDotSingle2DipoleStressChange ! density evolution by dipole formation (by stress decrease)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: &
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
previousRhoSgl ! previous single dislocation densities (positive/negative screw and edge without dipoles)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
fluxdensity, & ! flux density at central material point
neighboring_fluxdensity, & ! flux density at neighboring material point
gdot ! shear rates
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauThreshold, & ! threshold shear stress
tau, & ! current resolved shear stress
previousTau, & ! previous resolved shear stress
invLambda, & ! inverse of mean free path for dislocations
vClimb ! climb velocity of edge dipoles
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
previousRhoDip, & ! previous 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
previousDUpper, & ! previous maximum stable dipole distance for edges and screws
dUpperDot ! rate of change of the maximum stable dipole distance for edges and screws
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(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(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
previousTdislocation_v ! previous dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
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
correction
logical considerEnteringFlux, &
considerLeavingFlux
if (verboseDebugger .and. (debug_g==g .and. debug_i==ip .and. debug_e==el)) then
!$OMP CRITICAL (write2out)
write(6,*) '::: constitutive_nonlocal_dotState at ',g,ip,el
write(6,*)
!$OMP END CRITICAL (write2out)
endif
select case(mesh_element(2,el))
case (1,6,7,8,9)
! all fine
case default
call IO_error(-1,el,ip,g,'element type not supported for nonlocal constitution')
end select
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
tau = 0.0_pReal
previousTau = 0.0_pReal
gdot = 0.0_pReal
dLower = 0.0_pReal
dUpper = 0.0_pReal
previousDUpper = 0.0_pReal
dUpperDot = 0.0_pReal
!*** shortcut to state variables
forall (t = 1:8) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (t = 1:8) previousRhoSgl(1:ns,t) = previousState(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDip(1:ns,c) = state(g,ip,el)%p((7+c)*ns+1:(8+c)*ns)
forall (c = 1:2) previousRhoDip(1:ns,c) = previousState(g,ip,el)%p((7+c)*ns+1:(8+c)*ns)
rhoForest = state(g,ip,el)%p(10*ns+1:11*ns)
tauThreshold = state(g,ip,el)%p(11*ns+1:12*ns)
Tdislocation_v = state(g,ip,el)%p(12*ns+1:12*ns+6)
previousTdislocation_v = previousState(g,ip,el)%p(12*ns+1:12*ns+6)
!*** sanity check for timestep
if (timestep <= 0.0_pReal) then ! if illegal timestep...
dotState(g,ip,el)%p = 0.0_pReal ! ...return without doing anything (-> zero dotState)
return
endif
!****************************************************************************
!*** Calculate shear rate
call constitutive_nonlocal_kinetics(Tstar_v, Temperature, state(g,ip,el), g, ip, el) ! get velocities
forall (t = 1:4) &
gdot(1:ns,t) = rhoSgl(1:ns,t) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
* constitutive_nonlocal_v(1:ns,t,g,ip,el)
forall (s = 1:ns, t = 1:4, rhoSgl(s,t+4) * constitutive_nonlocal_v(s,t,g,ip,el) < 0.0_pReal) & ! contribution of used rho for changing sign of v
gdot(s,t) = gdot(s,t) + abs(rhoSgl(s,t+4)) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
* constitutive_nonlocal_v(s,t,g,ip,el)
if (verboseDebugger .and. (debug_g==g .and. debug_i==ip .and. debug_e==el)) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,10(12(e12.5,x),/))') 'rho / 1/m^2', rhoSgl, rhoDip
write(6,'(a,/,4(12(e12.5,x),/))') 'v / m/s', constitutive_nonlocal_v(:,:,g,ip,el)
write(6,'(a,/,4(12(e12.5,x),/))') 'gdot / 1/s',gdot
!$OMP END CRITICAL (write2out)
endif
!****************************************************************************
!*** calculate limits for stable dipole height and its rate of change
do s = 1,ns ! loop over slip systems
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
tau(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure) )
previousTau(s) = math_mul6x6( previousTstar_v + previousTdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure) )
enddo
dLower(1:ns,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(1:ns,myInstance)
dLower(1:ns,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(1:ns,myInstance)
dUpper(1:ns,2) = min( 1.0_pReal / sqrt( sum(abs(rhoSgl),2)+sum(rhoDip,2) ), &
constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
/ ( 8.0_pReal * pi * abs(tau) ) )
dUpper(1:ns,1) = dUpper(1:ns,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
previousDUpper(1:ns,2) = min( 1.0_pReal / sqrt( sum(abs(previousRhoSgl),2) + sum(previousRhoDip,2) ), &
constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
/ ( 8.0_pReal * pi * abs(previousTau) ) )
previousDUpper(1:ns,1) = previousDUpper(1:ns,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
if (dt_previous > 0.0_pReal) dUpperDot = (dUpper - previousDUpper) / dt_previous
!****************************************************************************
!*** dislocation remobilization (bauschinger effect)
rhoDotRemobilization = 0.0_pReal
if (timestep > 0.0_pReal) then
do t = 1,4
do s = 1,ns
if (rhoSgl(s,t+4) * constitutive_nonlocal_v(s,t,g,ip,el) < 0.0_pReal) then
rhoDotRemobilization(s,t) = abs(rhoSgl(s,t+4)) / timestep
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4))
rhoDotRemobilization(s,t+4) = - rhoSgl(s,t+4) / timestep
rhoSgl(s,t+4) = 0.0_pReal
endif
enddo
enddo
endif
!****************************************************************************
!*** calculate dislocation multiplication
rhoDotMultiplication = 0.0_pReal
where (rhoSgl(1:ns,3:4) > 0.0_pReal) &
rhoDotMultiplication(1:ns,1:2) = spread(0.5_pReal * sum(abs(gdot(1:ns,3:4)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(1:ns,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance), 2, 2)
where (rhoSgl(1:ns,1:2) > 0.0_pReal) &
rhoDotMultiplication(1:ns,3:4) = spread(0.5_pReal * sum(abs(gdot(1:ns,1:2)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(1:ns,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance), 2, 2)
!****************************************************************************
!*** calculate dislocation fluxes (only for nonlocal constitution)
constitutive_nonlocal_rhoDotFlux(:,:,g,ip,el) = 0.0_pReal
rhoDotFlux = 0.0_pReal
if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only for nonlocal constitution
!*** take care 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))
fluxdensity = rhoSgl(1:ns,1:4) * constitutive_nonlocal_v(1:ns,1:4,g,ip,el)
do n = 1,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
if (neighboring_el > 0_pInt .and. neighboring_ip > 0_pInt) then ! if neighbor exists ...
do neighboring_n = 1,FE_NipNeighbors(mesh_element(2,neighboring_el)) ! find neighboring index that points from my neighbor to myself
if ( el == mesh_ipNeighborhood(1,neighboring_n,neighboring_ip,neighboring_el) &
.and. ip == mesh_ipNeighborhood(2,neighboring_n,neighboring_ip,neighboring_el) ) &
exit
enddo
endif
opposite_n = n + mod(n,2) - mod(n+1,2)
opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el)
opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el)
if (neighboring_el > 0_pInt .and. neighboring_ip > 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 ME TO MY NEIGHBOR
!* This is not considered, if my opposite neighbor has a local constitution.
!* 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_el > 0 .and. opposite_ip > 0) then
if (phase_localConstitution(material_phase(1,opposite_ip,opposite_el))) &
considerLeavingFlux = .false.
endif
if (considerLeavingFlux) then
normal_me2neighbor_defConf = math_det3x3(Favg) * math_mul33x3(math_inv3x3(transpose(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(transpose(my_Fe), normal_me2neighbor_defConf) / math_det3x3(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,ns
do t = 1,4
c = (t + 1) / 2
if (fluxdensity(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)
lineLength = fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length that wants to leave through this interface
transmissivity = sum(constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor
rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract dislocation flux from current mobile type
rhoDotFlux(s,t+4) = rhoDotFlux(s,t+4) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) &
* sign(1.0_pReal, fluxdensity(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
endif
enddo
enddo
endif
!* FLUX FROM MY NEIGHBOR TO ME
!* This is only considered, if I have a neighbor of nonlocal constitution 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.
if (neighboring_el > 0_pInt .or. neighboring_ip > 0_pInt) then
if (.not. phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el)) &
.and. any(constitutive_nonlocal_compatibility(:,:,:,n,ip,el) > 0.0_pReal)) &
considerEnteringFlux = .true.
endif
if (considerEnteringFlux) then
forall (t = 1:4) &
neighboring_fluxdensity(1:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1)*ns+1:t*ns) &
* constitutive_nonlocal_v(1:ns,t,g,neighboring_ip,neighboring_el)
normal_neighbor2me_defConf = math_det3x3(Favg) &
* math_mul33x3(math_inv3x3(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_det3x3(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,ns
do t = 1,4
c = (t + 1) / 2
topp = t + mod(t,2) - mod(t+1,2)
if (neighboring_fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal) then ! flux from my neighbor to me == entering flux for me
lineLength = neighboring_fluxdensity(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:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility...
rhoDotFlux(1:ns,t) = rhoDotFlux(1:ns,t) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed dislocation type
* constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal
where (constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility...
rhoDotFlux(1:ns,topp) = rhoDotFlux(1:ns,topp) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed dislocation type
* constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal
endif
enddo
enddo
endif
enddo ! neighbor loop
constitutive_nonlocal_rhoDotFlux(1:ns,1:10,g,ip,el) = constitutive_nonlocal_rhoDotFlux(1:ns,1:10,g,ip,el) + rhoDotFlux
endif
!****************************************************************************
!*** calculate dipole formation and annihilation
!*** formation by glide
do c = 1,2
rhoDotSingle2DipoleGlide(1:ns,2*c-1) = -2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgersPerSlipSystem(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_burgersPerSlipSystem(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_burgersPerSlipSystem(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_burgersPerSlipSystem(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=1:2) &
rhoDotAthermalAnnihilation(1:ns,c+8) = -2.0_pReal * dLower(1:ns,c) / constitutive_nonlocal_burgersPerSlipSystem(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
!*** thermally activated annihilation of dipoles
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) )
rhoDotThermalAnnihilation(1:ns,9) = - 4.0_pReal * rhoDip(1:ns,1) * vClimb / (dUpper(1:ns,1) - dLower(1:ns,1)) ! edge climb
rhoDotThermalAnnihilation(1:ns,10) = 0.0_pReal !!! cross slipping still has to be implemented !!!
!*** formation/dissociation by stress change = alteration in dUpper
rhoDotDipole2SingleStressChange = 0.0_pReal
forall (c=1:2, s=1:ns, dUpperDot(s,c) < 0.0_pReal) & ! increased stress => dipole dissociation
rhoDotDipole2SingleStressChange(s,8+c) = rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c))
forall (t=1:4) &
rhoDotDipole2SingleStressChange(1:ns,t) = -0.5_pReal * rhoDotDipole2SingleStressChange(1:ns,(t-1)/2+9)
rhoDotSingle2DipoleStressChange = 0.0_pReal
do c = 1,2
do s = 1,ns
if (dUpperDot(s,c) > 0.0_pReal) then ! stress decrease => dipole formation
rhoDotSingle2DipoleStressChange(s,2*(c-1)+1) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+1) &
* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+2) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+2) &
* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+5) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+5) &
* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+6) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+6) &
* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
endif
enddo
enddo
forall (c = 1:2) &
rhoDotSingle2DipoleStressChange(1:ns,8+c) = abs(rhoDotSingle2DipoleStressChange(1:ns,2*(c-1)+1)) &
+ abs(rhoDotSingle2DipoleStressChange(1:ns,2*(c-1)+2)) &
+ abs(rhoDotSingle2DipoleStressChange(1:ns,2*(c-1)+5)) &
+ abs(rhoDotSingle2DipoleStressChange(1:ns,2*(c-1)+6))
!****************************************************************************
!*** assign the rates of dislocation densities to my dotState
rhoDot = 0.0_pReal
forall (t = 1:10) &
rhoDot(1:ns,t) = rhoDotFlux(1:ns,t) &
+ rhoDotMultiplication(1:ns,t) &
+ rhoDotRemobilization(1:ns,t) &
+ rhoDotSingle2DipoleGlide(1:ns,t) &
+ rhoDotAthermalAnnihilation(1:ns,t) &
+ rhoDotThermalAnnihilation(1:ns,t)
! + rhoDotDipole2SingleStressChange(1:ns,t)
! + rhoDotSingle2DipoleStressChange(1:ns,t)
if (verboseDebugger .and. (debug_g==g .and. debug_i==ip .and. debug_e==el)) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation remobilization', rhoDotRemobilization(1:ns,1:8) * timestep
write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation flux', rhoDotFlux(1:ns,1:8) * timestep
write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', rhoDotAthermalAnnihilation(1:ns,1:2) * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', rhoDotThermalAnnihilation(1:ns,9:10) * timestep
! write(6,'(a,/,10(12(e12.5,x),/))') 'dipole dissociation by stress increase', rhoDotDipole2SingleStressChange * timestep
! write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by stress decrease', rhoDotSingle2DipoleStressChange * timestep
write(6,'(a,/,10(12(e12.5,x),/))') 'total density change', rhoDot * timestep
write(6,'(a,/,10(12(f12.7,x),/))') 'relative density change', rhoDot(1:ns,1:8) * timestep / (abs(rhoSgl)+1.0e-10), &
rhoDot(1:ns,9:10) * timestep / (rhoDip+1.0e-10)
write(6,*)
!$OMP END CRITICAL (write2out)
endif
!$OMP CRITICAL (copy2dotState)
dotState(g,ip,el)%p(1:10*ns) = dotState(g,ip,el)%p(1:10*ns) + reshape(rhoDot,(/10*ns/))
!$OMP END CRITICAL (copy2dotState)
endsubroutine
!*********************************************************************
!* 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_QuaternionDisorientation, &
math_mul3x3, &
math_qRot
use material, only: material_phase, &
phase_constitution, &
phase_localConstitution, &
phase_constitutionInstance, &
homogenization_maxNgrains
use mesh, only: mesh_element, &
mesh_ipNeighborhood, &
FE_NipNeighbors, &
FE_maxNipNeighbors, &
mesh_maxNips, &
mesh_NcpElems
use lattice, only: lattice_sn, &
lattice_sd, &
lattice_st
use debug, only: debugger, &
debug_e, debug_i, debug_g, &
verboseDebugger
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_structure, & ! lattice structure
my_instance, & ! instance of constitution
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_constitutionInstance(material_phase(1,i,e)))) :: &
compatibility ! compatibility of one specific slip system to all neighbors slip systems's for edges and screws
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(1,i,e)))) :: &
slipNormal, &
slipDirection
real(pReal) compatibilitySum, &
thresholdValue, &
nThresholdValues
logical, dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(1,i,e)))) :: &
belowThreshold
Nneighbors = FE_NipNeighbors(mesh_element(2,e))
my_phase = material_phase(1,i,e)
my_instance = phase_constitutionInstance(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
constitutive_nonlocal_compatibility(:,:,:,:,i,e) = 0.0_pReal
forall(s1 = 1:maxval(constitutive_nonlocal_totalNslip)) &
constitutive_nonlocal_compatibility(1:2,s1,s1,1:Nneighbors,i,e) = 1.0_pReal
!*** Loop thrugh neighbors and check whether there is any compatibility.
!*** This is only the case for
do n = 1,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 .or. neighboring_i <= 0) then
forall(s1 = 1:ns) &
constitutive_nonlocal_compatibility(1:2,s1,s1,n,i,e) = 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 fully incompatible.
!* If the neighboring "cpfem" phase has a local constitution,
!* we do not consider this to be a phase boundary, so fully compatible.
neighboring_phase = material_phase(1,neighboring_i,neighboring_e)
if (neighboring_phase /= my_phase) then
if (.not. phase_localConstitution(neighboring_phase)) then
constitutive_nonlocal_compatibility(:,:,:,n,i,e) = 0.0_pReal
endif
cycle
endif
!* GRAIN BOUNDARY ?
!* 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.
absoluteMisorientation = math_QuaternionDisorientation(orientation(1:4,1,i,e), &
orientation(1:4,1,neighboring_i,neighboring_e), &
0_pInt) ! no symmetry
do s1 = 1,ns ! my slip systems
do s2 = 1,ns ! my neighbor's slip systems
compatibility(1,s2) = 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) = 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), belowThreshold(1:ns)) ! screws always positive
nThresholdValues = dble(count(compatibility(2,1:ns) == thresholdValue))
where (compatibility(2,1:ns) >= thresholdValue) &
belowThreshold(1:ns) = .false.
if (compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
where (abs(compatibility(1:2,1:ns)) == thresholdValue) &
compatibility(1:2,1:ns) = sign((1.0_pReal - compatibilitySum) / nThresholdValues, compatibility(1:2,1:ns))
compatibilitySum = compatibilitySum + nThresholdValues * thresholdValue
enddo
where (belowThreshold(1:ns)) compatibility(1,1:ns) = 0.0_pReal
where (belowThreshold(1:ns)) compatibility(2,1:ns) = 0.0_pReal
constitutive_nonlocal_compatibility(1:2,1:ns,s1,n,i,e) = compatibility(1:2,1:ns)
enddo ! my slip systems cycle
enddo ! neighbor cycle
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
!*********************************************************************
!* return array of constitutive results *
!*********************************************************************
function constitutive_nonlocal_postResults(Tstar_v, previousTstar_v, Fe, Fp, Temperature, disorientation, dt, dt_previous, &
state, previousState, dotState, g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_norm3, &
math_mul6x6, &
math_mul3x3, &
math_mul33x3, &
math_mul33x33, &
math_inv3x3, &
math_det3x3, &
math_Mandel6to33, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_maxNipNeighbors, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipArea, &
mesh_ipAreaNormal
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance, &
phase_Noutput
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
lattice_sd, &
lattice_sn, &
lattice_st, &
lattice_maxNslipFamily, &
lattice_NslipSystem
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
dt_previous ! time increment between previous and current state
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation
previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: &
disorientation ! crystal disorientation between me and my neighbor (axis, angle pair)
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
previousState, & ! previous microstructural state
dotState ! evolution rate of microstructural state
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
constitutive_nonlocal_postResults
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor
c, & ! character of dislocation
cs, & ! constitutive result index
n, & ! index of my current neighbor
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_constitutionInstance(material_phase(g,ip,el))),6,4) :: &
fluxes ! outgoing fluxes per slipsystem, neighbor and dislocation type
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: &
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
previousRhoSgl, & ! previous 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_constitutionInstance(material_phase(g,ip,el))),4) :: &
gdot, & ! shear rates
lineLength ! dislocation line length leaving the current interface
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauThreshold, & ! threshold shear stress
tau, & ! current resolved shear stress
previousTau, & ! previous resolved shear stress
invLambda, & ! inverse of mean free path for dislocations
vClimb ! climb velocity of edge dipoles
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
previousRhoDip, & ! previous 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
previousDUpper, & ! previous maximum stable dipole distance for edges and screws
dUpperDot ! rate of change of the maximum stable dipole distance for edges and screws
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(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) :: F, & ! total deformation gradient
neighboring_F, & ! total deformation gradient of my neighbor
Favg ! average total deformation gradient of me and my neighbor
real(pReal), dimension(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
previousTdislocation_v ! previous dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
real(pReal), dimension(3) :: surfaceNormal, & ! surface normal in lattice configuration
surfaceNormal_currentconf ! surface normal in current configuration
real(pReal) area, & ! area of the current interface
detFe, & ! determinant of elastic defornmation gradient
D ! self diffusion
myInstance = phase_constitutionInstance(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 (t = 1:8) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (t = 1:8) previousRhoSgl(1:ns,t) = previousState(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDip(1:ns,c) = state(g,ip,el)%p((7+c)*ns+1:(8+c)*ns)
forall (c = 1:2) previousRhoDip(1:ns,c) = previousState(g,ip,el)%p((7+c)*ns+1:(8+c)*ns)
rhoForest = state(g,ip,el)%p(10*ns+1:11*ns)
tauThreshold = state(g,ip,el)%p(11*ns+1:12*ns)
Tdislocation_v = state(g,ip,el)%p(12*ns+1:12*ns+6)
previousTdislocation_v = previousState(g,ip,el)%p(12*ns+1:12*ns+6)
forall (t = 1:8) rhoDotSgl(1:ns,t) = dotState(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDotDip(1:ns,c) = dotState(g,ip,el)%p((7+c)*ns+1:(8+c)*ns)
!* Calculate shear rate
call constitutive_nonlocal_kinetics(Tstar_v, Temperature, state(g,ip,el), g, ip, el) ! need to calculate dislocation velocity again, because it was overwritten during stiffness calculation
do t = 1,4
do s = 1,ns
if (rhoSgl(s,t+4) * constitutive_nonlocal_v(s,t,g,ip,el) < 0.0_pReal) then
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4)) ! remobilization of immobile singles for changing sign of v (bauschinger effect)
rhoSgl(s,t+4) = 0.0_pReal ! remobilization of immobile singles for changing sign of v (bauschinger effect)
endif
enddo
enddo
forall (t = 1:4) &
gdot(1:ns,t) = rhoSgl(1:ns,t) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
* constitutive_nonlocal_v(1:ns,t,g,ip,el)
!* calculate limits for stable dipole height and its rate of change
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
tau(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure) )
previousTau(s) = math_mul6x6( previousTstar_v + previousTdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure) )
enddo
dLower(1:ns,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(1:ns,myInstance)
dLower(1:ns,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(1:ns,myInstance)
dUpper(1:ns,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
/ (8.0_pReal * pi * abs(tau)), &
1.0_pReal / sqrt(sum(abs(rhoSgl),2)+sum(rhoDip,2)) )
dUpper(1:ns,1) = dUpper(1:ns,2) / (1.0_pReal - constitutive_nonlocal_nu(myInstance))
previousDUpper(1:ns,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance) &
/ (8.0_pReal * pi * abs(previousTau)), &
1.0_pReal / sqrt(sum(abs(previousRhoSgl),2) + sum(previousRhoDip,2)) )
previousDUpper(1:ns,1) = previousDUpper(1:ns,2) / (1.0_pReal - constitutive_nonlocal_nu(myInstance))
if (dt_previous > 0.0_pReal) then
dUpperDot = (dUpper - previousDUpper) / dt_previous
else
dUpperDot = 0.0_pReal
endif
!*** 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 = 1:2, s = 1:ns) &
m_currentconf(1:3,s,c) = math_mul33x3(Fe(1:3,1:3,g,ip,el), m(1:3,s,c))
do o = 1,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_nonlocal_output(o,myInstance))
case ('rho')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl),2) + sum(rhoDip,2)
cs = cs + ns
case ('rho_sgl')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl),2)
cs = cs + ns
case ('rho_sgl_mobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl(1:ns,1:4)),2)
cs = cs + ns
case ('rho_sgl_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl(1:ns,5:8)),2)
cs = cs + ns
case ('rho_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDip,2)
cs = cs + ns
case ('rho_edge')
constitutive_nonlocal_postResults(cs+1: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: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:cs+ns) = sum(rhoSgl(1:ns,1:2),2)
cs = cs + ns
case ('rho_sgl_edge_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl(1:ns,5:6)),2)
cs = cs + ns
case ('rho_sgl_edge_pos')
constitutive_nonlocal_postResults(cs+1: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:cs+ns) = rhoSgl(1:ns,1)
cs = cs + ns
case ('rho_sgl_edge_pos_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = abs(rhoSgl(1:ns,5))
cs = cs + ns
case ('rho_sgl_edge_neg')
constitutive_nonlocal_postResults(cs+1: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:cs+ns) = rhoSgl(1:ns,2)
cs = cs + ns
case ('rho_sgl_edge_neg_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = abs(rhoSgl(1:ns,6))
cs = cs + ns
case ('rho_dip_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(1:ns,1)
cs = cs + ns
case ('rho_screw')
constitutive_nonlocal_postResults(cs+1: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: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:cs+ns) = sum(rhoSgl(1:ns,3:4),2)
cs = cs + ns
case ('rho_sgl_screw_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(rhoSgl(1:ns,7:8)),2)
cs = cs + ns
case ('rho_sgl_screw_pos')
constitutive_nonlocal_postResults(cs+1: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:cs+ns) = rhoSgl(1:ns,3)
cs = cs + ns
case ('rho_sgl_screw_pos_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = abs(rhoSgl(1:ns,7))
cs = cs + ns
case ('rho_sgl_screw_neg')
constitutive_nonlocal_postResults(cs+1: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:cs+ns) = rhoSgl(1:ns,4)
cs = cs + ns
case ('rho_sgl_screw_neg_immobile')
constitutive_nonlocal_postResults(cs+1:cs+ns) = abs(rhoSgl(1:ns,8))
cs = cs + ns
case ('rho_dip_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(1:ns,2)
cs = cs + ns
case ('excess_rho')
constitutive_nonlocal_postResults(cs+1: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: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: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:cs+ns) = rhoForest
cs = cs + ns
case ('delta')
constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2) + sum(rhoDip,2))
cs = cs + ns
case ('delta_sgl')
constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2))
cs = cs + ns
case ('delta_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt(sum(rhoDip,2))
cs = cs + ns
case ('shearrate')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(gdot,2)
cs = cs + ns
case ('resolvedstress')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(cs+s) = math_mul6x6(Tstar_v + Tdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure))
enddo
cs = cs + ns
case ('resolvedstress_internal')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(cs+s) = math_mul6x6(Tdislocation_v, lattice_Sslip_v(1:6,sLattice,myStructure))
enddo
cs = cs + ns
case ('resolvedstress_external')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(cs+s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure))
enddo
cs = cs + ns
case ('resistance')
constitutive_nonlocal_postResults(cs+1:cs+ns) = tauThreshold
cs = cs + ns
case ('rho_dot')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDotSgl,2) + sum(rhoDotDip,2)
cs = cs + ns
case ('rho_dot_sgl')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDotSgl,2)
cs = cs + ns
case ('rho_dot_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDotDip,2)
cs = cs + ns
case ('rho_dot_gen')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(gdot),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(1:ns,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance)
cs = cs + ns
case ('rho_dot_gen_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(gdot(1:ns,3:4)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(1:ns,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance)
cs = cs + ns
case ('rho_dot_gen_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(gdot(1:ns,1:2)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(1:ns,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(1:ns,myInstance)
cs = cs + ns
case ('rho_dot_sgl2dip')
do c=1,2 ! dipole formation by glide
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + &
2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgersPerSlipSystem(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/used single
enddo
! do c=1,2
! forall (s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! dipole formation by stress decrease
! constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) + &
! 8.0_pReal * rhoSgl(s,2*c-1) * rhoSgl(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c)
! enddo
cs = cs + ns
case ('rho_dot_dip2sgl')
do c=1,2
forall (s=1:ns, dUpperDot(s,c) < 0.0_pReal) &
constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) - &
rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c))
enddo
cs = cs + ns
case ('rho_dot_ann_ath')
do c=1,2
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + &
2.0_pReal * dLower(1:ns,c) / constitutive_nonlocal_burgersPerSlipSystem(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/used single
+ rhoDip(1:ns,c) * (abs(gdot(1:ns,2*c-1)) + abs(gdot(1:ns,2*c)))) ! single knocks dipole constituent
enddo
cs = cs + ns
case ('rho_dot_ann_the')
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))
constitutive_nonlocal_postResults(cs+1:cs+ns) = 4.0_pReal * rhoDip(1:ns,1) * vClimb / (dUpper(1:ns,1) - dLower(1:ns,1))
! !!! cross-slip of screws missing !!!
cs = cs + ns
case ('rho_dot_flux')
constitutive_nonlocal_postResults(cs+1: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: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: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 ('dislocationvelocity')
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_v(1:ns,1,g,ip,el)
cs = cs + ns
case ('fluxdensity_edge_pos_x')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,1) * constitutive_nonlocal_v(1:ns,1,g,ip,el) &
* m_currentconf(1,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_pos_y')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,1) * constitutive_nonlocal_v(1:ns,1,g,ip,el) &
* m_currentconf(2,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_pos_z')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,1) * constitutive_nonlocal_v(1:ns,1,g,ip,el) &
* m_currentconf(3,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg_x')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,2) * constitutive_nonlocal_v(1:ns,2,g,ip,el) &
* m_currentconf(1,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg_y')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,2) * constitutive_nonlocal_v(1:ns,2,g,ip,el) &
* m_currentconf(2,1:ns,1)
cs = cs + ns
case ('fluxdensity_edge_neg_z')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,2) * constitutive_nonlocal_v(1:ns,2,g,ip,el) &
* m_currentconf(3,1:ns,1)
cs = cs + ns
case ('fluxdensity_screw_pos_x')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,3) * constitutive_nonlocal_v(1:ns,3,g,ip,el) &
* m_currentconf(1,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_pos_y')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,3) * constitutive_nonlocal_v(1:ns,3,g,ip,el) &
* m_currentconf(2,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_pos_z')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoSgl(1:ns,3) * constitutive_nonlocal_v(1:ns,3,g,ip,el) &
* m_currentconf(3,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg_x')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,4) * constitutive_nonlocal_v(1:ns,4,g,ip,el) &
* m_currentconf(1,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg_y')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,4) * constitutive_nonlocal_v(1:ns,4,g,ip,el) &
* m_currentconf(2,1:ns,2)
cs = cs + ns
case ('fluxdensity_screw_neg_z')
constitutive_nonlocal_postResults(cs+1:cs+ns) = - rhoSgl(1:ns,4) * constitutive_nonlocal_v(1:ns,4,g,ip,el) &
* m_currentconf(3,1:ns,2)
cs = cs + ns
case ('d_upper_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(1:ns,1)
cs = cs + ns
case ('d_upper_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(1:ns,2)
cs = cs + ns
case ('d_upper_dot_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(1:ns,1)
cs = cs + ns
case ('d_upper_dot_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(1:ns,2)
cs = cs + ns
end select
enddo
endfunction
END MODULE