DAMASK_EICMD/code/constitutive_nonlocal.f90

1214 lines
66 KiB
Fortran

!************************************
!* 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=16), dimension(7), parameter :: constitutive_nonlocal_stateList = (/ 'rhoEdgePos ', &
'rhoEdgeNeg ', &
'rhoScrewPos ', &
'rhoScrewNeg ', &
'rhoForest ', &
'tauSlipThreshold', &
'backStress_v ' /) ! list of microstructural state variables
character(len=16), dimension(4), parameter :: constitutive_nonlocal_stateListBasic = constitutive_nonlocal_stateList(1:4) ! list of "basic" microstructural state variables that are independent from other state variables
character(len=16), dimension(3), parameter :: constitutive_nonlocal_stateListDependent = constitutive_nonlocal_stateList(5:7) ! 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
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_rhoEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance
constitutive_nonlocal_v0BySlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_nonlocal_v0BySlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_nonlocal_lambda0BySlipFamily, & ! mean free path prefactor for each family and instance
constitutive_nonlocal_lambda0BySlipSystem, & ! mean free path prefactor for each slip system and instance
constitutive_nonlocal_burgersBySlipFamily, & ! absolute length of burgers vector [m] for each family and instance
constitutive_nonlocal_burgersBySlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
real(pReal), dimension(:,:,:), allocatable :: 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 material, only: 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, &
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,*)
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)); constitutive_nonlocal_sizeDotState = 0_pInt
allocate(constitutive_nonlocal_sizeState(maxNinstance)); constitutive_nonlocal_sizeState = 0_pInt
allocate(constitutive_nonlocal_sizePostResults(maxNinstance)); constitutive_nonlocal_sizePostResults = 0_pInt
allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance));constitutive_nonlocal_sizePostResult = 0_pInt
allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance)); constitutive_nonlocal_output = ''
allocate(constitutive_nonlocal_structureName(maxNinstance)); constitutive_nonlocal_structureName = ''
allocate(constitutive_nonlocal_structure(maxNinstance)); constitutive_nonlocal_structure = 0_pInt
allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_Nslip = 0_pInt
allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance)); constitutive_nonlocal_slipFamily = 0_pInt
allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance)); constitutive_nonlocal_slipSystemLattice = 0_pInt
allocate(constitutive_nonlocal_totalNslip(maxNinstance)); constitutive_nonlocal_totalNslip = 0_pInt
allocate(constitutive_nonlocal_CoverA(maxNinstance)); constitutive_nonlocal_CoverA = 0.0_pReal
allocate(constitutive_nonlocal_C11(maxNinstance)); constitutive_nonlocal_C11 = 0.0_pReal
allocate(constitutive_nonlocal_C12(maxNinstance)); constitutive_nonlocal_C12 = 0.0_pReal
allocate(constitutive_nonlocal_C13(maxNinstance)); constitutive_nonlocal_C13 = 0.0_pReal
allocate(constitutive_nonlocal_C33(maxNinstance)); constitutive_nonlocal_C33 = 0.0_pReal
allocate(constitutive_nonlocal_C44(maxNinstance)); constitutive_nonlocal_C44 = 0.0_pReal
allocate(constitutive_nonlocal_Gmod(maxNinstance)); constitutive_nonlocal_Gmod = 0.0_pReal
allocate(constitutive_nonlocal_nu(maxNinstance)); constitutive_nonlocal_nu = 0.0_pReal
allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance)); constitutive_nonlocal_Cslip_66 = 0.0_pReal
allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance)); constitutive_nonlocal_Cslip_3333 = 0.0_pReal
allocate(constitutive_nonlocal_rhoEdgePos0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoEdgePos0 = 0.0_pReal
allocate(constitutive_nonlocal_rhoEdgeNeg0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoEdgeNeg0 = 0.0_pReal
allocate(constitutive_nonlocal_rhoScrewPos0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoScrewPos0 = 0.0_pReal
allocate(constitutive_nonlocal_rhoScrewNeg0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoScrewNeg0 = 0.0_pReal
allocate(constitutive_nonlocal_v0BySlipFamily(lattice_maxNslipFamily, maxNinstance));
constitutive_nonlocal_v0BySlipFamily = 0.0_pReal
allocate(constitutive_nonlocal_burgersBySlipFamily(lattice_maxNslipFamily, maxNinstance));
constitutive_nonlocal_burgersBySlipFamily = 0.0_pReal
allocate(constitutive_nonlocal_Lambda0BySlipFamily(lattice_maxNslipFamily, maxNinstance));
constitutive_nonlocal_lambda0BySlipFamily = 0.0_pReal
allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction, maxNinstance))
constitutive_nonlocal_interactionSlipSlip = 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
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 ('(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 ('rhoedgepos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgePos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoedgeneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoscrewpos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewPos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoscrewneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('v0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_v0BySlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('lambda0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_lambda0BySlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('burgers')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_burgersBySlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('interaction_slipslip')
forall (it = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1+it)
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)
!*** sanity checks
!*** !!! not yet complete !!!
if (constitutive_nonlocal_structure(i) < 1 .or. constitutive_nonlocal_structure(i) > 3) call IO_error(205)
if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0) call IO_error(225)
do f = 1,lattice_maxNslipFamily
if (constitutive_nonlocal_Nslip(f,i) > 0) then
if (constitutive_nonlocal_rhoEdgePos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoEdgeNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoScrewPos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoScrewNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_burgersBySlipFamily(f,i) <= 0.0_pReal) call IO_error(221)
if (constitutive_nonlocal_v0BySlipFamily(f,i) <= 0.0_pReal) call IO_error(-1)
if (constitutive_nonlocal_lambda0BySlipFamily(f,i) <= 0.0_pReal) call IO_error(-1)
endif
enddo
if (sum(constitutive_nonlocal_interactionSlipSlip(:,i)) <= 0) call IO_error(-1)
!*** determine total number of active slip systems
constitutive_nonlocal_Nslip(:,i) &
= min( lattice_NslipSystem(:, constitutive_nonlocal_structure(i)), constitutive_nonlocal_Nslip(:,i) ) ! we can't use more slip systems per family than specified in lattice
constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(:,i))
enddo
!*** allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(constitutive_nonlocal_totalNslip)
allocate(constitutive_nonlocal_burgersBySlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_burgersBySlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_v0BySlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_v0BySlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_lambda0BySlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_lambda0BySlipSystem = 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
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
constitutive_nonlocal_sizeState(i) = (size(constitutive_nonlocal_stateList)-1) * constitutive_nonlocal_totalNslip(i) + 6_pInt ! the size of the list of states times the number of active slip systems gives the required size for the state array
constitutive_nonlocal_sizeDotState(i) = size(constitutive_nonlocal_stateListBasic) * constitutive_nonlocal_totalNslip(i) ! the size of the list of basic states times the number of active slip systems gives the required size for the dotState array
!*** determine size of postResults array
do o = 1,maxval(phase_Noutput)
select case(constitutive_nonlocal_output(o,i))
case( 'rho', &
'rho_edge', &
'rho_screw', &
'excess_rho_edge', &
'excess_rho_screw', &
'rho_forest', &
'shearrate', &
'resolvedstress', &
'resistance')
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(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i)))
constitutive_nonlocal_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i))
constitutive_nonlocal_Gmod(i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_nu(i) = constitutive_nonlocal_C12(i) / constitutive_nonlocal_C11(i)
!*** burgers vector, dislocation velocity prefactor and mean free path prefactor for each slip system
do s = 1,constitutive_nonlocal_totalNslip(i)
constitutive_nonlocal_burgersBySlipSystem(s,i) &
= constitutive_nonlocal_burgersBySlipFamily( constitutive_nonlocal_slipFamily(s,i), i )
constitutive_nonlocal_v0BySlipSystem(s,i) = constitutive_nonlocal_v0BySlipFamily(constitutive_nonlocal_slipFamily(s,i),i)
constitutive_nonlocal_lambda0BySlipSystem(s,i) &
= constitutive_nonlocal_lambda0BySlipFamily( constitutive_nonlocal_slipFamily(s,i), i )
enddo
!*** calculation of forest projections for edge and screw dislocations
do s1 = 1,constitutive_nonlocal_totalNslip(i)
do s2 = 1,constitutive_nonlocal_totalNslip(i)
constitutive_nonlocal_forestProjectionEdge(s1, s2, i) &
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
lattice_st(:, constitutive_nonlocal_slipSystemLattice(s2,i), myStructure))) ! forest projection of edge dislocations is the projection of (b x n) onto the slip normal of the respective splip plane
constitutive_nonlocal_forestProjectionScrew(s1, s2, i) &
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
lattice_sd(:, 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
enddo; enddo
!*** calculation of interaction matrices
do s1 = 1,constitutive_nonlocal_totalNslip(i)
do s2 = 1,constitutive_nonlocal_totalNslip(i)
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
enddo
endsubroutine
!*********************************************************************
!* initial microstructural state (just the "basic" states) *
!*********************************************************************
pure function constitutive_nonlocal_stateInit(myInstance)
use prec, only: pReal, &
pInt
use lattice, only: lattice_maxNslipFamily
use IO, only: IO_error
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)) :: &
rhoEdgePos, & ! positive edge dislocation density
rhoEdgeNeg, & ! negative edge dislocation density
rhoScrewPos, & ! positive screw dislocation density
rhoScrewNeg, & ! negative screw 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
s0, &
s1, &
s ! index of slip system
constitutive_nonlocal_stateInit = 0.0_pReal
ns = constitutive_nonlocal_totalNslip(myInstance)
!*** set the basic state variables
s1 = 0_pInt
do f = 1,lattice_maxNslipFamily
s0 = s1 + 1_pInt
s1 = s0 + constitutive_nonlocal_Nslip(f,myInstance) - 1_pInt
do s = s0,s1
rhoEdgePos(s) = constitutive_nonlocal_rhoEdgePos0(f, myInstance)
rhoEdgeNeg(s) = constitutive_nonlocal_rhoEdgeNeg0(f, myInstance)
rhoScrewPos(s) = constitutive_nonlocal_rhoScrewPos0(f, myInstance)
rhoScrewNeg(s) = constitutive_nonlocal_rhoScrewNeg0(f, myInstance)
enddo; enddo
!*** calculate the dependent state variables
! forest dislocation density
forall (s = 1:ns) &
rhoForest(s) = dot_product( (rhoEdgePos + rhoEdgeNeg), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) &
+ dot_product( (rhoScrewPos + rhoScrewNeg), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
! threshold shear stress for dislocation slip
forall (s = 1:ns) &
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
* constitutive_nonlocal_burgersBySlipSystem(s, myInstance) &
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg), &
constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) )
!*** put everything together and in right order
constitutive_nonlocal_stateInit( 1: ns) = rhoEdgePos
constitutive_nonlocal_stateInit( ns+1:2*ns) = rhoEdgeNeg
constitutive_nonlocal_stateInit(2*ns+1:3*ns) = rhoScrewPos
constitutive_nonlocal_stateInit(3*ns+1:4*ns) = rhoScrewNeg
constitutive_nonlocal_stateInit(4*ns+1:5*ns) = rhoForest
constitutive_nonlocal_stateInit(5*ns+1:6*ns) = tauSlipThreshold
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(:,:,myInstance)
endfunction
!*********************************************************************
!* calculates quantities characterizing the microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_microstructure(Temperature, Fp, state, 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, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipCenterOfGravity
use material, only: homogenization_maxNgrains, &
material_phase, &
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) :: &
Fp ! plastic deformation gradient
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! microstructural state
!*** output variables
!*** local variables
integer(pInt) 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
n, & ! index of my current neighbor
s, & ! index of my current slip system
sLattice ! index of my current slip system as specified by lattice
real(pReal) gb, & ! short notation for G*b/2/pi
x, & ! coordinate in direction of lvec
y, & ! coordinate in direction of bvec
z ! coordinate in direction of nvec
real(pReal), dimension(3) :: connectingVector ! vector connecting the centers of gravity of me and my neigbor
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(3,3) :: transform, & ! orthogonal transformation matrix from slip coordinate system with e1=bxn, e2=b, e3=n to lattice coordinate system
sigma ! backstress resulting from the excess dislocation density of a single slip system and a single neighbor calculated in the coordinate system of the slip system
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoEdgePos, & ! positive edge dislocation density
rhoEdgeNeg, & ! negative edge dislocation density
rhoScrewPos, & ! positive screw dislocation density
rhoScrewNeg, & ! negative screw dislocation density
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
neighboring_rhoEdgePos, & ! positive edge dislocation density of my neighbor
neighboring_rhoEdgeNeg, & ! negative edge dislocation density of my neighbor
neighboring_rhoScrewPos, & ! positive screw dislocation density of my neighbor
neighboring_rhoScrewNeg, & ! negative screw dislocation density of my neighbor
neighboring_rhoEdgeExcess, &! edge excess dislocation density of my neighbor
neighboring_rhoScrewExcess,&! screw excess dislocation density of my neighbor
neighboring_Nedge, & ! total number of edge excess dislocations in my neighbor
neighboring_Nscrew
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
!**********************************************************************
!*** get basic states
rhoEdgePos = state(g,ip,el)%p( 1: ns)
rhoEdgeNeg = state(g,ip,el)%p( ns+1:2*ns)
rhoScrewPos = state(g,ip,el)%p(2*ns+1:3*ns)
rhoScrewNeg = state(g,ip,el)%p(3*ns+1:4*ns)
!**********************************************************************
!*** calculate dependent states
!*** calculate the forest dislocation density
forall (s = 1:ns) &
rhoForest(s) = dot_product( (rhoEdgePos + rhoEdgeNeg), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) &
+ dot_product( (rhoScrewPos + rhoScrewNeg), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
!*** calculate the threshold shear stress for dislocation slip
forall (s = 1:ns) &
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
* constitutive_nonlocal_burgersBySlipSystem(s, myInstance) &
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg), &
constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) )
!*** calculate the backstress of the neighboring excess dislocation densities
backStress_v = 0.0_pReal
! loop through my neighbors (if it exists!)
do n = 1,FE_NipNeighbors(mesh_element(2,el))
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
if ( neighboring_el == 0 .or. neighboring_ip == 0 ) cycle
! calculate the connecting vector between me and my neighbor and his excess dislocation density
connectingVector = math_mul33x3( Fp(:,:,g,neighboring_ip,neighboring_el), &
(mesh_ipCenterOfGravity(:,ip,el) - mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el)) )
neighboring_rhoEdgePos = state(1, neighboring_ip, neighboring_el)%p( 1: ns)
neighboring_rhoEdgeNeg = state(1, neighboring_ip, neighboring_el)%p( ns+1:2*ns)
neighboring_rhoScrewPos = state(1, neighboring_ip, neighboring_el)%p(2*ns+1:3*ns)
neighboring_rhoScrewNeg = state(1, neighboring_ip, neighboring_el)%p(3*ns+1:4*ns)
neighboring_rhoEdgeExcess = neighboring_rhoEdgePos - neighboring_rhoEdgeNeg
neighboring_rhoScrewExcess = neighboring_rhoScrewPos - neighboring_rhoScrewNeg
neighboring_Nedge = neighboring_rhoEdgeExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
neighboring_Nscrew = neighboring_rhoScrewExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
! loop over slip systems and get their slip directions, slip normals, and sd x sn
do s = 1,ns
transform = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) )
! coordinate transformation of p from the lattice coordinate system to the slip coordinate system
x = math_mul3x3(connectingVector, transform(:,1))
y = math_mul3x3(connectingVector, transform(:,2))
z = math_mul3x3(connectingVector, transform(:,3))
! calculate the back stress in the slip coordinate system for this slip system
gb = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) / (2.0_pReal*pi)
sigma(2,2) = - gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* z * (3.0_pReal*y**2.0_pReal + z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
sigma(3,3) = gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* z * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
sigma(1,1) = constitutive_nonlocal_nu(myInstance) * (sigma(2,2) + sigma(3,3))
sigma(1,2) = gb * neighboring_Nscrew(s) * z / (x**2.0_pReal + z**2.0_pReal)
sigma(2,3) = gb * ( neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal) &
- neighboring_Nscrew(s) * x / (x**2.0_pReal + z**2.0_pReal) )
sigma(2,1) = sigma(1,2)
sigma(3,2) = sigma(2,3)
sigma(1,3) = 0.0_pReal
sigma(3,1) = 0.0_pReal
! coordinate transformation from the slip coordinate system to the lattice coordinate system
backStress_v = backStress_v + math_Mandel33to6( math_mul33x33(transpose(transform), math_mul33x33(sigma, transform) ) )
enddo
enddo
!**********************************************************************
!*** set dependent states
state(g,ip,el)%p(4*ns+1:5*ns) = rhoForest
state(g,ip,el)%p(5*ns+1:6*ns) = tauSlipThreshold
state(g,ip,el)%p(6*ns+1:6*ns+6) = backstress_v
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
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 as specified by lattice
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix)
real(pReal), dimension(4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rho ! dislocation densities
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
tauSlip, & ! resolved shear stress
gdotSlip, & ! shear rate
dgdot_dtauSlip, & ! derivative of the shear rate with respect to the shear stress
v ! dislocation velocity
!*** initialize local variables
v = 0.0_pReal
tauSlip = 0.0_pReal
gdotSlip = 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 = 1:4) rho(t,:) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
rhoForest = state(g,ip,el)%p(4*ns+1:5*ns)
tauSlipThreshold = state(g,ip,el)%p(5*ns+1:6*ns)
backStress_v = state(g,ip,el)%p(6*ns+1:6*ns+6)
! if (debugger) write(6,'(a20,3(i3,x),/,3(3(f12.3,x)/))') 'backstress / MPa at ', g,ip,el, math_Mandel6to33(backStress_v/1e6)
! if (debugger) write(6,'(a15,3(i3,x),/,3(3(f12.3,x)/))') 'Tstar / MPa at ',g,ip,el, math_Mandel6to33(Tstar_v/1e6)
!*** loop over slip systems
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
!*** Calculation of Lp
tauSlip(s) = math_mul6x6( Tstar_v + backStress_v, lattice_Sslip_v(:,sLattice,myStructure) )
if (rhoForest(s) > 0.0_pReal) &
v(s) = constitutive_nonlocal_v0BySlipSystem(s,myInstance) &
* exp( - ( tauSlipThreshold(s) - abs(tauSlip(s)) ) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
/ ( kB * Temperature * sqrt(rhoForest(s)) ) ) &
* sign(1.0_pReal,tauSlip(s))
gdotSlip(s) = sum(rho(:,s)) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) * v(s)
Lp = Lp + gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure)
! if (debugger) write(6,'(a4,i2,a3,/,3(3(f15.7)/))') 'dLp(',s,'): ',gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure)
!*** Calculation of the tangent of Lp
dgdot_dtauSlip(s) = gdotSlip(s) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
/ ( kB * Temperature * sqrt(rhoForest(s)) )
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) + dgdot_dtauSlip(s) * lattice_Sslip(i,j, sLattice,myStructure) &
* lattice_Sslip(k,l, sLattice,myStructure)
enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
! if (debugger) write(6,'(a23,3(i3,x),/,12(e10.3,x),/)') 'dislocation density at ',g,ip,el, rho
! if (debugger) write(6,'(a26,3(i3,x),/,12(f10.5,x),/)') 'tauSlipThreshold / MPa at ',g,ip,el, tauSlipThreshold/1e6
! if (debugger) write(6,'(a15,3(i3,x),/,12(f10.5,x),/)') 'tauSlip / MPa at ',g,ip,el, tauSlip/1e6
! if (debugger) write(6,'(a5,3(i3,x),/,12(e10.3,x),/)') 'v at ',g,ip,el, v
! if (debugger) write(6,'(a15,3(i3,x),/,12(e10.3,x),/)') 'gdotSlip at ',g,ip,el, gdotSlip
! if (debugger) write(6,'(a6,3(i3,x),/,3(3(f15.7)/))') 'Lp at ',g,ip,el, Lp
endsubroutine
!*********************************************************************
!* rate of change of microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, Fp, invFp, Temperature, state, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use debug, only: debugger
use math, only: math_norm3, &
math_mul6x6, &
math_mul3x3, &
math_mul33x3, &
math_transpose3x3
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipArea, &
mesh_ipAreaNormal
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
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
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(3,3), intent(in) :: Fp, & ! plastic deformation gradient
invFp ! inverse of plastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
!*** 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
neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor
n, & ! index of my current neighbor
t, & ! type of dislocation
s ! index of my current slip system
real(pReal), dimension(4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rho, & ! dislocation densities
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
tauSlipThreshold, & ! threshold shear stress
tauSlip, & ! resolved shear stress
v, & ! dislocation velocity
invLambda ! inverse of mean free path for dislocations
real(pReal), dimension(3,4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
m ! direction of dislocation motion
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress
real(pReal), dimension(3) :: surfaceNormal ! surface normal of the current interface
real(pReal) norm_surfaceNormal, & ! euclidic norm of the surface normal
area ! area of the current interface
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
tauSlip = 0.0_pReal
v = 0.0_pReal
gdot = 0.0_pReal
!*** shortcut to state variables
forall (t = 1:4) rho(t,:) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
rhoForest = state(g,ip,el)%p(4*ns+1:5*ns)
tauSlipThreshold = state(g,ip,el)%p(5*ns+1:6*ns)
backStress_v = state(g,ip,el)%p(6*ns+1:6*ns+6)
!****************************************************************************
!*** Calculate shear rate
do s = 1,ns
tauSlip(s) = math_mul6x6( Tstar_v + backStress_v, &
lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure) )
forall (s = 1:ns, rhoForest(s) > 0.0_pReal) &
v(s) = constitutive_nonlocal_v0BySlipSystem(s,myInstance) &
* exp( - ( tauSlipThreshold(s) - abs(tauSlip(s)) ) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
/ ( kB * Temperature * sqrt(rhoForest(s)) ) ) &
* sign(1.0_pReal,tauSlip(s))
forall (t = 1:4, s = 1:ns) &
gdot(t,s) = rho(t,s) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) * v(s)
enddo
!****************************************************************************
!*** calculate dislocation multiplication
invLambda = sqrt(rhoForest) / constitutive_nonlocal_lambda0BySlipSystem(:,myInstance)
forall (t = 1:4) &
dotState(1,ip,el)%p((t-1)*ns+1:t*ns) = dotState(1,ip,el)%p((t-1)*ns+1:t*ns) + 0.25_pReal * sum(abs(gdot),1) * invLambda &
/ constitutive_nonlocal_burgersBySlipSystem(:,myInstance)
! if (debugger) write(6,'(a30,3(i3,x),/,12(e10.3,x),/)') 'dislocation multiplication at ',g,ip,el, &
! 0.25_pReal * sum(abs(gdot),1) * invLambda / constitutive_nonlocal_burgersBySlipSystem(:,myInstance)
!****************************************************************************
!*** calculate dislocation fluxes
! Direction of dislocation motion
m(:,1,:) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,2,:) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,3,:) = lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,4,:) = -lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
! loop through my neighbors
do n = 1,FE_NipNeighbors(mesh_element(2,el))
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
! calculate the area and the surface normal of the interface
surfaceNormal = math_mul33x3(math_transpose3x3(invFp), mesh_ipAreaNormal(:,n,ip,el))
norm_surfaceNormal = math_norm3(surfaceNormal)
surfaceNormal = surfaceNormal / norm_surfaceNormal
area = mesh_ipArea(n,ip,el) / norm_surfaceNormal
! loop through my interfaces
do s = 1,ns
lineLength = 0.0_pReal
! loop through dislocation types
do t = 1,4
if ( sign(1.0_pReal,math_mul3x3(m(:,t,s),surfaceNormal)) == sign(1.0_pReal,gdot(t,s)) ) then
! dislocation line length that leaves this interface per second
lineLength(t,s) = gdot(t,s) / constitutive_nonlocal_burgersBySlipSystem(s,myInstance) &
* math_mul3x3(m(:,t,s),surfaceNormal) * area
! subtract dislocation density rate (= line length over volume) that leaves through an interface from my dotState ...
dotState(1,ip,el)%p((t-1)*ns+s) = dotState(1,ip,el)%p((t-1)*ns+s) - lineLength(t,s) / mesh_ipVolume(ip,el)
! ... and add them to the neighboring dotState (if neighbor exists)
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then
!*****************************************************************************************************
!*** OMP locking for this neighbor missing
!*****************************************************************************************************
dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) = dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) &
+ lineLength(t,s) / mesh_ipVolume(neighboring_ip,neighboring_el)
endif
endif
enddo
enddo
enddo
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 *
!*********************************************************************
pure function constitutive_nonlocal_postResults(Tstar_v, Temperature, dt, state, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance, &
phase_Noutput
use lattice, only: lattice_Sslip_v, &
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) :: dt, & ! time increment
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), 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
o, & ! index of current output
s, & ! index of current slip system
sLattice, & ! index of current slip system as specified by lattice
c
real(pReal) tau, & ! resolved shear stress on current slip system
v ! dislocation velocity on current slip system
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
c = 0_pInt
constitutive_nonlocal_postResults = 0.0_pReal
do o = 1,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_nonlocal_output(o,myInstance))
case ('rho')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) + state(g,ip,el)%p(ns+1:2*ns) &
+ state(g,ip,el)%p(2*ns+1:3*ns) + state(g,ip,el)%p(3*ns+1:4*ns)
c = c + ns
case ('rho_edge')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) + state(g,ip,el)%p(ns+1:2*ns)
c = c + ns
case ('rho_screw')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(2*ns+1:3*ns) + state(g,ip,el)%p(3*ns+1:4*ns)
c = c + ns
case ('excess_rho_edge')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) - state(g,ip,el)%p(ns+1:2*ns)
c = c + ns
case ('excess_rho_screw')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(2*ns+1:3*ns) - state(g,ip,el)%p(3*ns+1:4*ns)
c = c + ns
case ('rho_forest')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(4*ns+1:5*ns)
c = c + ns
case ('shearrate')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
tau = math_mul6x6( Tstar_v + state(g,ip,el)%p(6*ns+1:6*ns+6), lattice_Sslip_v(:,sLattice,myStructure) )
if (state(g,ip,el)%p(4*ns+s) > 0.0_pReal) then
v = constitutive_nonlocal_v0BySlipSystem(s,myInstance) &
* exp( - ( state(g,ip,el)%p(5*ns+s) - abs(tau) ) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
/ ( kB * Temperature * sqrt(state(g,ip,el)%p(4*ns+s)) ) ) &
* sign(1.0_pReal,tau)
else
v = 0.0_pReal
endif
constitutive_nonlocal_postResults(c+s) = ( state(g,ip,el)%p(s) + state(g,ip,el)%p(ns+s) &
+ state(g,ip,el)%p(2*ns+s) + state(g,ip,el)%p(3*ns+s) ) &
* constitutive_nonlocal_burgersBySlipSystem(s,myInstance) * v
enddo
c = c + ns
case ('resolvedstress')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(c+s) = math_mul6x6( Tstar_v + state(g,ip,el)%p(6*ns+1:6*ns+6), &
lattice_Sslip_v(:,sLattice,myStructure) )
enddo
c = c + ns
case ('resistance')
constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(5*ns+1:6*ns)
c = c + ns
end select
enddo
endfunction
END MODULE