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DAMASK_EICMD/dislocation_based_subroutine/constitutive.f90

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2007-10-15 17:33:52 +05:30
!************************************
!* Module: CONSTITUTIVE *
!************************************
!* contains: *
!* - parameters definition *
!* - constitutive equations *
!* - orientations *
!************************************
MODULE constitutive
!*** Include other modules ***
use prec, only: pReal,pInt
implicit none
! MISSING consistency check after reading 'mattex.mpie'
character(len=300), parameter :: mattexFile = 'mattex.mpie'
!*************************************
!* Definition of material properties *
!*************************************
!* Physical parameter, attack_frequency != Debye frequency
real(pReal), parameter :: attack_frequency = 1.0e10_pReal
!* Physical parameter, Boltzman constant in mJ/Kelvin
real(pReal), parameter :: Kb = 1.38e-20_pReal
!*************************************
!* Definition of material properties *
!*************************************
!* Number of materials
integer(pInt) material_maxN
!* Crystal structure and number of selected slip systems per material
integer(pInt), dimension(:) , allocatable :: material_CrystalStructure
integer(pInt), dimension(:) , allocatable :: material_Nslip
!* Maximum number of selected slip systems over materials
integer(pInt) material_maxNslip
!* Elastic constants and matrices
real(pReal), dimension(:) , allocatable :: material_C11
real(pReal), dimension(:) , allocatable :: material_C12
real(pReal), dimension(:) , allocatable :: material_C13
real(pReal), dimension(:) , allocatable :: material_C33
real(pReal), dimension(:) , allocatable :: material_C44
real(pReal), dimension(:) , allocatable :: material_Gmod
real(pReal), dimension(:,:,:), allocatable :: material_Cslip_66
!* Visco-plastic material parameters
real(pReal), dimension(:) , allocatable :: material_rho0
real(pReal), dimension(:) , allocatable :: material_bg
real(pReal), dimension(:) , allocatable :: material_Qedge
real(pReal), dimension(:) , allocatable :: material_tau0
real(pReal), dimension(:) , allocatable :: material_c1
real(pReal), dimension(:) , allocatable :: material_c2
real(pReal), dimension(:) , allocatable :: material_c3
real(pReal), dimension(:) , allocatable :: material_c4
real(pReal), dimension(:) , allocatable :: material_c5
real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff
!************************************
!* Definition of texture properties *
!************************************
!* Number of textures, maximum number of Gauss and Fiber components
integer(pInt) texture_maxN
integer(pInt) texture_maxNGauss
integer(pInt) texture_maxNFiber
!* Textures definition
character(len=80), dimension(:), allocatable :: texture_ODFfile
character(len=80), dimension(:), allocatable :: texture_symmetry
integer(pInt), dimension(:) , allocatable :: texture_Ngrains
integer(pInt), dimension(:) , allocatable :: texture_NGauss
integer(pInt),dimension(:) , allocatable :: texture_NFiber
integer(pInt),dimension(:) , allocatable :: texture_NRandom
integer(pInt),dimension(:) , allocatable :: texture_totalNgrains
real(pReal), dimension(:,:,:) , allocatable :: texture_Gauss
real(pReal), dimension(:,:,:) , allocatable :: texture_Fiber
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_EulerAngles
!************************************
!* Grains *
!************************************
integer(pInt) constitutive_maxNgrains
integer(pInt), dimension(:,:) , allocatable :: constitutive_Ngrains
integer(pInt), dimension(:,:,:) , allocatable :: constitutive_matID
real(pReal), dimension(:,:,:) , allocatable :: constitutive_matVolFrac
integer(pInt), dimension(:,:,:) , allocatable :: constitutive_texID
real(pReal), dimension(:,:,:) , allocatable :: constitutive_texVolFrac
!************************************
!* State variables *
!************************************
integer(pInt) constitutive_maxNstatevars
integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nstatevars
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_old
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_new
real(pReal), dimension(:) , allocatable :: constitutive_passing_stress
real(pReal), dimension(:) , allocatable :: constitutive_jump_width
real(pReal), dimension(:) , allocatable :: constitutive_activation_volume
real(pReal), dimension(:) , allocatable :: constitutive_rho_m
real(pReal), dimension(:) , allocatable :: constitutive_rho_f
real(pReal), dimension(:) , allocatable :: constitutive_rho_p
real(pReal), dimension(:) , allocatable :: constitutive_g0_slip
!************************************
!* Interaction matrices *
!************************************
real(pReal), dimension(:,:,:), allocatable :: constitutive_Pforest
real(pReal), dimension(:,:,:), allocatable :: constitutive_Pparallel
!************************************
!* Results *
!************************************
integer(pInt) constitutive_maxNresults
integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_results
CONTAINS
!****************************************
!* - constitutive_Init
!* - constitutive_CountSections
!* - constitutive_Parse_UnknownPart
!* - constitutive_Parse_MaterialPart
!* - constitutive_Parse_TexturePart
!* - constitutive_Parse_MatTexDat
!* - constitutive_Assignment
!* - constitutive_HomogenizedC
!* - constitutive_Microstructure
!* - constitutive_LpAndItsTangent
!* - consistutive_DotState
!****************************************
subroutine constitutive_Init()
!**************************************
!* Module initialization *
!**************************************
call constitutive_Parse_MatTexDat(mattexFile)
call constitutive_Assignment()
end subroutine
subroutine constitutive_CountSections(file,count,part)
!*********************************************************************
!* This subroutine reads a "part" from the input file until the next *
!* part is reached and counts the number of "sections" in the part *
!* INPUT: *
!* - file : file ID *
!* OUTPUT: *
!* - part : name of the next "part" *
!* - count : number of sections inside the current "part" *
!*********************************************************************
use prec, only: pInt
use IO, only: IO_stringPos,IO_stringValue,IO_lc
implicit none
!* Definition of variables
character(len=80) part,line,tag
integer(pInt) file,count
integer(pInt), dimension(3) :: positions
count=0
part=''
do
read(file,'(a80)',END=100) line
positions=IO_stringPos(line,1)
tag=IO_lc(IO_stringValue(line,positions,1))
if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
cycle
elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
part=tag(2:len_trim(tag)-1)
exit
elseif (tag(1:1)=='[') then
count=count+1
endif
enddo
100 return
end subroutine
character(len=80) function constitutive_assignNGaussAndFiber(file)
!*********************************************************************
!*********************************************************************
use prec, only: pInt
use IO, only: IO_stringPos,IO_stringValue,IO_lc
implicit none
!* Definition of variables
character(len=80) line,tag
integer(pInt) file,section
integer(pInt), dimension(3) :: positions
constitutive_assignNGaussAndFiber=''
section = 0_pInt
do
read(file,'(a80)',END=100) line
positions=IO_stringPos(line,1)
tag=IO_lc(IO_stringValue(line,positions,1))
if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
cycle
elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
constitutive_assignNGaussAndFiber=tag(2:len_trim(tag)-1)
exit
elseif (tag(1:1)=='[') then
section=section+1
texture_NGauss(section) = 0_pInt
texture_NFiber(section) = 0_pInt
elseif (tag=='(gauss)') then
texture_NGauss(section)=texture_NGauss(section)+1
elseif (tag=='(fiber)') then
texture_NFiber(section)=texture_NFiber(section)+1
endif
enddo
100 return
end function
character(len=80) function constitutive_Parse_UnknownPart(file)
!*********************************************************************
!* read an unknown "part" from the input file until *
!* the next part is reached *
!* INPUT: *
!* - file : file ID *
!*********************************************************************
use prec, only: pInt
use IO, only: IO_stringPos,IO_stringValue,IO_lc
implicit none
!* Definition of variables
character(len=80) line,tag
integer(pInt), parameter :: maxNchunks = 1
integer(pInt) file
integer(pInt), dimension(1+2*maxNchunks) :: positions
constitutive_parse_unknownPart=''
do
read(file,'(a80)',END=100) line
positions=IO_stringPos(line,maxNchunks)
tag=IO_lc(IO_stringValue(line,positions,1))
if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
cycle
elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
constitutive_Parse_UnknownPart=tag(2:len_trim(tag)-1)
exit
endif
enddo
100 return
end function
character(len=80) function constitutive_Parse_MaterialPart(file)
!*********************************************************************
!* This function reads a material "part" from the input file until *
!* the next part is reached *
!* INPUT: *
!* - file : file ID *
!*********************************************************************
use prec, only: pInt,pReal
use IO
use crystal, only: crystal_MaxMaxNslipOfStructure
implicit none
!* Definition of variables
character(len=80) line,tag
integer(pInt), parameter :: maxNchunks = 2
integer(pInt) i,file,section
integer(pInt), dimension(1+2*maxNchunks) :: positions
section = 0
constitutive_parse_materialPart = ''
do while(.true.)
read(file,'(a80)',END=100) line
positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
tag=IO_lc(IO_stringValue(line,positions,1))
if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
cycle
elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
constitutive_parse_materialPart=tag(2:len_trim(tag)-1)
exit
elseif (tag(1:1)=='[') then
section=section+1
else
if (section>0) then
select case(tag)
case ('crystal_structure')
material_CrystalStructure(section)=IO_intValue(line,positions,2)
case ('nslip')
material_Nslip(section)=IO_intValue(line,positions,2)
case ('c11')
material_C11(section)=IO_floatValue(line,positions,2)
case ('c12')
material_C12(section)=IO_floatValue(line,positions,2)
case ('c13')
material_C13(section)=IO_floatValue(line,positions,2)
case ('c33')
material_C33(section)=IO_floatValue(line,positions,2)
case ('c44')
material_C44(section)=IO_floatValue(line,positions,2)
case ('rho0') !* conversion in 1/mm<6D>
material_rho0(section)=IO_floatValue(line,positions,2)/1.0e6_pReal
case ('interaction_coefficient')
do i=1,crystal_MaxMaxNslipOfStructure
material_SlipIntCoeff(i,section)=IO_floatValue(line,positions,i+1)
enddo
case ('bg') !* conversion in mm
material_bg(section)=IO_floatValue(line,positions,2)*1.0e3_pReal
case ('Qedge') !* conversion in mJ/Kelvin
material_Qedge(section)=IO_floatValue(line,positions,2)*1.0e3_pReal
case ('tau0')
material_tau0(section)=IO_floatValue(line,positions,2)
case ('c1')
material_c1(section)=IO_floatValue(line,positions,2)
case ('c2')
material_c2(section)=IO_floatValue(line,positions,2)
case ('c3')
material_c3(section)=IO_floatValue(line,positions,2)
case ('c4')
material_c4(section)=IO_floatValue(line,positions,2)
case ('c5')
material_c5(section)=IO_floatValue(line,positions,2)
end select
endif
endif
enddo
100 return
end function
character(len=80) function constitutive_Parse_TexturePart(file)
!*********************************************************************
!* This function reads a texture "part" from the input file until *
!* the next part is reached *
!* INPUT: *
!* - file : file ID *
!*********************************************************************
use prec, only: pInt
use IO
use math, only: inRad
implicit none
!* Definition of variables
character(len=80) line,tag
integer(pInt), parameter :: maxNchunks = 13 ! may be more than 10 chunks ..?
integer(pInt) file,section,gaussCount,fiberCount,i
integer(pInt), dimension(1+2*maxNchunks) :: positions
section = 0
gaussCount = 0
fiberCount = 0
constitutive_parse_texturePart = ''
do while(.true.)
read(file,'(a80)',END=100) line
positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
tag=IO_lc(IO_stringValue(line,positions,1))
if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
cycle
elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
constitutive_parse_texturePart=tag(2:len_trim(tag)-1)
exit
elseif (tag(1:1)=='[') then
section=section+1
gaussCount=0
fiberCount=0
else
if (section>0) then
select case(tag)
case ('hybridIA')
texture_ODFfile(section)=IO_stringValue(line,positions,2)
case ('(gauss)')
gaussCount=gaussCount+1
do i=2,10,2
tag=IO_lc(IO_stringValue(line,positions,i))
select case (tag)
case('phi1')
texture_Gauss(1,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('phi')
texture_Gauss(2,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('phi2')
texture_Gauss(3,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('scatter')
texture_Gauss(4,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('fraction')
texture_Gauss(5,gaussCount,section)=IO_floatValue(line,positions,i+1)
end select
enddo
case ('(fiber)')
fiberCount=fiberCount+1
do i=2,12,2
tag=IO_lc(IO_stringValue(line,positions,i))
select case (tag)
case('alpha1')
texture_fiber(1,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('alpha2')
texture_fiber(2,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('beta1')
texture_fiber(3,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('beta2')
texture_fiber(4,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('scatter')
texture_fiber(5,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
case('fraction')
texture_fiber(6,fiberCount,section)=IO_floatValue(line,positions,i+1)
end select
enddo
case ('ngrains')
texture_Ngrains(section)=IO_intValue(line,positions,2)
case ('symmetry')
texture_symmetry(section)=IO_stringValue(line,positions,2)
end select
endif
endif
enddo
100 return
end function
subroutine constitutive_Parse_MatTexDat(filename)
!*********************************************************************
!* This function reads the material and texture input file *
!* INPUT: *
!* - filename : name of input file *
!*********************************************************************
use prec, only: pReal,pInt
use IO, only: IO_error, IO_open_file
use math, only: math_Mandel3333to66, math_Voigt66to3333
use crystal, only: crystal_MaxMaxNslipOfStructure
implicit none
!* Definition of variables
character(len=*) filename
character(len=80) part,formerPart
integer(pInt) sectionCount,i,j,k, fileunit
! set fileunit
fileunit=200
!-----------------------------
!* First reading: number of materials and textures
!-----------------------------
!* determine material_maxN and texture_maxN from last respective parts
if(IO_open_file(fileunit,filename)==.false.) goto 100
part = '_dummy_'
do while (part/='')
formerPart = part
call constitutive_CountSections(fileunit,sectionCount,part)
select case (formerPart)
case ('materials')
material_maxN = sectionCount
case ('textures')
texture_maxN = sectionCount
end select
enddo
!* Array allocation
allocate(material_CrystalStructure(material_maxN)) ; material_CrystalStructure=0_pInt
allocate(material_Nslip(material_maxN)) ; material_Nslip=0_pInt
allocate(material_C11(material_maxN)) ; material_C11=0.0_pReal
allocate(material_C12(material_maxN)) ; material_C12=0.0_pReal
allocate(material_C13(material_maxN)) ; material_C13=0.0_pReal
allocate(material_C33(material_maxN)) ; material_C33=0.0_pReal
allocate(material_C44(material_maxN)) ; material_C44=0.0_pReal
allocate(material_Gmod(material_maxN)) ; material_Gmod=0.0_pReal
allocate(material_Cslip_66(6,6,material_maxN)) ; material_Cslip_66=0.0_pReal
allocate(material_rho0(material_maxN)) ; material_rho0=0.0_pReal
allocate(material_SlipIntCoeff(crystal_MaxMaxNslipOfStructure,material_maxN)) ; material_SlipIntCoeff=0.0_pReal
allocate(material_bg(material_maxN)) ; material_bg=0.0_pReal
allocate(material_Qedge(material_maxN)) ; material_Qedge=0.0_pReal
allocate(material_tau0(material_maxN)) ; material_tau0=0.0_pReal
allocate(material_c1(material_maxN)) ; material_c1=0.0_pReal
allocate(material_c2(material_maxN)) ; material_c2=0.0_pReal
allocate(material_c3(material_maxN)) ; material_c3=0.0_pReal
allocate(material_c4(material_maxN)) ; material_c4=0.0_pReal
allocate(material_c5(material_maxN)) ; material_c5=0.0_pReal
allocate(texture_ODFfile(texture_maxN)) ; texture_ODFfile=''
allocate(texture_Ngrains(texture_maxN)) ; texture_Ngrains=0_pInt
allocate(texture_symmetry(texture_maxN)) ; texture_symmetry=''
allocate(texture_NGauss(texture_maxN)) ; texture_NGauss=0_pInt
allocate(texture_NFiber(texture_maxN)) ; texture_NFiber=0_pInt
allocate(texture_NRandom(texture_maxN)) ; texture_NRandom=0_pInt
!-----------------------------
!* Second reading: number of Gauss and Fiber
!-----------------------------
rewind(fileunit)
part = '_dummy_'
do while (part/='')
select case (part)
case ('textures')
part = constitutive_assignNGaussAndFiber(fileunit)
case default
part = constitutive_Parse_UnknownPart(fileunit)
end select
enddo
!* Array allocation
texture_maxNGauss=maxval(texture_NGauss)
texture_maxNFiber=maxval(texture_NFiber)
allocate(texture_Gauss(5,texture_maxNGauss,texture_maxN)) ; texture_Gauss=0.0_pReal
allocate(texture_Fiber(6,texture_maxNFiber,texture_maxN)) ; texture_Fiber=0.0_pReal
!-----------------------------
!* Third reading: materials and textures are stored
!-----------------------------
rewind(fileunit)
part='_dummy_'
do while (part/='')
select case (part)
case ('materials')
part=constitutive_Parse_MaterialPart(fileunit)
case ('textures')
part=constitutive_Parse_TexturePart(fileunit)
case default
part=constitutive_Parse_UnknownPart(fileunit)
end select
enddo
close(fileunit)
!* Construction of the elasticity matrices
do i=1,material_maxN
material_Gmod(i)=material_C44(i)
select case (material_CrystalStructure(i))
case(1:2) ! cubic(s)
do k=1,3
do j=1,3
material_Cslip_66(k,j,i)=material_C12(i)
enddo
material_Cslip_66(k,k,i)=material_C11(i)
material_Cslip_66(k+3,k+3,i)=material_C44(i)
enddo
case(3) ! hcp
material_Cslip_66(1,1,i)=material_C11(i)
material_Cslip_66(2,2,i)=material_C11(i)
material_Cslip_66(3,3,i)=material_C33(i)
material_Cslip_66(1,2,i)=material_C12(i)
material_Cslip_66(2,1,i)=material_C12(i)
material_Cslip_66(1,3,i)=material_C13(i)
material_Cslip_66(3,1,i)=material_C13(i)
material_Cslip_66(2,3,i)=material_C13(i)
material_Cslip_66(3,2,i)=material_C13(i)
material_Cslip_66(4,4,i)=material_C44(i)
material_Cslip_66(5,5,i)=material_C44(i)
material_Cslip_66(6,6,i)=0.5_pReal*(material_C11(i)-material_C12(i))
end select
material_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(material_Cslip_66(:,:,i)))
enddo
! MISSING some consistency checks may be..?
! if ODFfile present then set NGauss NFiber =0
return
100 call IO_error(200) ! corrupt materials_textures file
end subroutine
subroutine constitutive_Assignment()
!*********************************************************************
!* This subroutine assign material parameters according to ipc,ip,el *
!*********************************************************************
use prec, only: pReal,pInt
use math, only: math_sampleGaussOri,math_sampleFiberOri,math_sampleRandomOri,math_symmetricEulers,math_EulerToR
use mesh, only: mesh_NcpElems,FE_Nips,FE_mapElemtype,mesh_maxNips,mesh_element
use IO, only: IO_hybridIA
use crystal, only: crystal_MaxNslipOfStructure,crystal_SlipIntType,crystal_sn,crystal_st
implicit none
!* Definition of variables
integer(pInt) e,i,j,k,l,m,o,g,s
integer(pInt) matID,texID
real(pReal) K_inter,x,y
integer(pInt), dimension(:,:,:), allocatable :: hybridIA_population
integer(pInt), dimension(texture_maxN) :: Ncomponents,Nsym,multiplicity,sumVolfrac,ODFmap,sampleCount
real(pReal), dimension(3,4*(1+texture_maxNGauss+texture_maxNfiber)) :: Euler
real(pReal), dimension(4*(1+texture_maxNGauss+texture_maxNfiber)) :: texVolfrac
! process textures
o = 0_pInt ! ODF counter
ODFmap = 0_pInt ! blank mapping
sampleCount = 0_pInt ! count orientations assigned per texture
do texID=1,texture_maxN
if (texture_ODFfile(texID)=='') then
sumVolfrac(texID) = sum(texture_gauss(5,:,texID))+sum(texture_fiber(6,:,texID))
if (sumVolfrac(texID)<1.0_pReal) texture_NRandom(texID) = 1_pInt ! check whether random component missing
select case (texture_symmetry(texID)) ! set symmetry factor
case ('orthotropic')
Nsym(texID) = 4_pInt
case ('monoclinic')
Nsym(texID) = 2_pInt
case default
Nsym(texID) = 1_pInt
end select
Ncomponents(texID) = texture_NGauss(texID)+texture_NFiber(texID)+texture_NRandom(texID)
else ! hybrid IA
o = o+1
ODFmap(texID) = o ! remember mapping
Ncomponents(texID) = 1_pInt ! single "component"
Nsym(texID) = 1_pInt ! no symmetry (use full ODF instead)
endif
! adjust multiplicity and number of grains per IP of components
multiplicity(texID) = max(1_pInt,texture_Ngrains(texID)/Ncomponents(texID)/Nsym(texID))
if (mod(texture_Ngrains(texID),Ncomponents(texID)*Nsym(texID)) /= 0_pInt) then
texture_Ngrains(texID) = multiplicity(texID)*Ncomponents(texID)*Nsym(texID)
write (6,*) 'changed Ngrains to',texture_Ngrains(texID),' for texture',texID
endif
enddo
!* publish globals
constitutive_maxNgrains = maxval(texture_Ngrains)
constitutive_maxNstatevars = maxval(material_Nslip) + 0_pInt
constitutive_maxNresults = 1_pInt
!* calc texture_totalNgrains
allocate(texture_totalNgrains(texture_maxN)) ; texture_totalNgrains=0_pInt
do i=1,mesh_NcpElems
texID = mesh_element(4,i)
texture_totalNgrains(texID) = texture_totalNgrains(texID) + FE_Nips(FE_mapElemtype(mesh_element(2,i)))*texture_Ngrains(texID)
enddo
! generate hybridIA samplings for ODFfile textures to later draw from these populations
allocate(hybridIA_population(3,maxval(texture_totalNgrains,ODFmap /= 0),o))
do texID = 1,texture_maxN
if (ODFmap(texID) > 0) &
hybridIA_population(:,:,ODFmap(texID)) = IO_hybridIA(texture_totalNgrains(texID),texture_ODFfile(texID))
enddo
!* Array allocation
allocate(constitutive_Ngrains(mesh_maxNips,mesh_NcpElems)) ; constitutive_Ngrains=0_pInt
allocate(constitutive_matID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_matID=0_pInt
allocate(constitutive_texID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_texID=0_pInt
allocate(constitutive_MatVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_MatVolFrac=0.0_pReal
allocate(constitutive_TexVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_TexVolFrac=0.0_pReal
allocate(constitutive_EulerAngles(3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_EulerAngles=0.0_pReal
allocate(constitutive_Nresults(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nresults=0_pInt
allocate(constitutive_results(constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
constitutive_results=0.0_pReal
allocate(constitutive_Nstatevars(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nstatevars=0_pInt
allocate(constitutive_state_old(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
constitutive_state_old=0.0_pReal
allocate(constitutive_state_new(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
constitutive_state_new=0.0_pReal
allocate(constitutive_Pforest(constitutive_maxNstatevars,constitutive_maxNstatevars,material_maxN))
constitutive_Pforest=0.0_pReal
allocate(constitutive_Pparallel(constitutive_maxNstatevars,constitutive_maxNstatevars,material_maxN))
constitutive_Pparallel=0.0_pReal
allocate(constitutive_rho_p(constitutive_maxNstatevars)) ; constitutive_rho_p=0.0_pReal
allocate(constitutive_rho_f(constitutive_maxNstatevars)) ; constitutive_rho_f=0.0_pReal
allocate(constitutive_rho_m(constitutive_maxNstatevars)) ; constitutive_rho_m=0.0_pReal
allocate(constitutive_passing_stress(constitutive_maxNstatevars)) ; constitutive_passing_stress=0.0_pReal
allocate(constitutive_jump_width(constitutive_maxNstatevars)) ; constitutive_jump_width=0.0_pReal
allocate(constitutive_activation_volume(constitutive_maxNstatevars)) ; constitutive_activation_volume=0.0_pReal
allocate(constitutive_g0_slip(constitutive_maxNstatevars)) ; constitutive_g0_slip=0.0_pReal
!* Assignment of all grains in all IPs of all cp-elements
do e=1,mesh_NcpElems
matID=mesh_element(3,e)
texID=mesh_element(4,e)
do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e)))
g = 0_pInt ! grain counter
do m = 1,multiplicity(texID)
o = 0_pInt ! component counter
if (texture_ODFfile(texID)=='') then
do k = 1,texture_nGauss(texID) ! *** gauss ***
o = o+1
Euler(:,o) = math_sampleGaussOri(texture_Gauss(1:3,k,texID),texture_Gauss(4,k,texID))
texVolFrac(o) = texture_Gauss(5,k,texID)
enddo
do k = 1,texture_nFiber(texID) ! *** fiber ***
o = o+1
Euler(:,o) = math_sampleFiberOri(texture_Fiber(1:2,k,texID),texture_Fiber(3:4,k,texID),texture_Fiber(5,k,texID))
texVolFrac(o) = texture_Fiber(6,k,texID)
enddo
do k = 1,texture_nRandom(texID) ! *** random ***
o = o+1
Euler(:,o) = math_sampleRandomOri()
texVolfrac(o) = 1.0_pReal-sumVolfrac(texID)
enddo
else ! *** hybrid IA ***
o = 1 ! only singular orientation, i.e. single "component"
Euler(:,o) = hybridIA_population(:,1+sampleCount(texID),ODFmap(texID))
texVolfrac(o) = 1.0_pReal
endif
if (Nsym(texID) > 1) then ! symmetry generates additional orientations
forall (k=1:o)
Euler(:,1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = &
math_symmetricEulers(texture_symmetry(texID),Euler(:,k))
texVolfrac(1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = texVolfrac(k)
end forall
endif
do s = 1,Nsym(texID)*o ! loop over orientations to be assigned to ip (ex multiplicity)
g = g+1 ! next "grain"
sampleCount(texID) = sampleCount(texID)+1 ! next member of population
constitutive_matID(g,i,e) = matID ! copy matID of element
constitutive_texID(g,i,e) = texID ! copy texID of element
constitutive_MatVolFrac(g,i,e) = 1.0_pReal ! singular material (so far)
constitutive_TexVolFrac(g,i,e) = texVolfrac(s)/multiplicity(texID)/Nsym(texID)
constitutive_Nstatevars(g,i,e) = material_Nslip(matID) ! number of state variables (i.e. tau_c of each slip system)
constitutive_Nresults(g,i,e) = 0 ! number of constitutive results
constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation
forall (l=1:constitutive_Nstatevars(g,i,e)) ! initialize state variables
constitutive_state_old(l,g,i,e) = material_rho0(matID)
constitutive_state_new(l,g,i,e) = material_rho0(matID)
end forall
enddo ! components
enddo ! multiplicity
enddo ! ip
enddo ! cp_element
!* Construction of the hardening matrices
do i=1,material_maxN
!* Iteration over the systems
do j=1,constitutive_maxNstatevars
do k=1,constitutive_maxNstatevars
!* Hardening type *
select case (crystal_SlipIntType(j,k,i))
case (0)
K_inter=0.0_pReal
case (1)
K_inter=material_SlipIntCoeff(1,i)
case (2)
K_inter=material_SlipIntCoeff(2,i)
case (3)
K_inter=material_SlipIntCoeff(3,i)
case (4)
K_inter=material_SlipIntCoeff(4,i)
case (5)
K_inter=material_SlipIntCoeff(5,i)
case (6)
K_inter=material_SlipIntCoeff(6,i)
end select
!* Projection of the dislocation *
x=dot_product(crystal_sn(:,j,i),crystal_st(:,k,i))
y=1.0_pReal-x**(2.0_pReal)
!* Interaction matrix *
constitutive_Pforest(j,k,i)=abs(x)*K_inter
if (y>0.0_pReal) then
constitutive_Pparallel(j,k,i)=sqrt(y)*K_inter
else
constitutive_Pparallel(j,k,i)=0.0_pReal
endif
enddo
enddo
enddo
end subroutine
function constitutive_HomogenizedC(ipc,ip,el)
!*********************************************************************
!* This function returns the homogenized elacticity matrix *
!* INPUT: *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
real(pReal), dimension(6,6) :: constitutive_homogenizedC
!* Homogenization scheme
constitutive_homogenizedC=constitutive_MatVolFrac(ipc,ip,el)*material_Cslip_66(:,:,constitutive_matID(ipc,ip,el))
return
end function
subroutine constitutive_Microstructure(state,Tp,ipc,ip,el)
!*********************************************************************
!* This function calculates from state needed variables *
!* INPUT: *
!* - state : state variables *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i
real(pReal) Tp
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
!* Quantities derivated from state
constitutive_rho_f=matmul(constitutive_Pforest(1:constitutive_Nstatevars(ipc,ip,el),&
1:constitutive_Nstatevars(ipc,ip,el),matID),state)
constitutive_rho_p=matmul(constitutive_Pparallel(1:constitutive_Nstatevars(ipc,ip,el),&
1:constitutive_Nstatevars(ipc,ip,el),matID),state)
do i=1,material_Nslip(matID)
constitutive_passing_stress(i)=material_tau0(matID)+material_c1(matID)*material_Gmod(matID)*material_bg(matID)*&
sqrt(constitutive_rho_p(i))
constitutive_jump_width(i)=material_c2(matID)/sqrt(constitutive_rho_f(i))
constitutive_activation_volume(i)=material_c3(matID)*constitutive_jump_width(i)*material_bg(matID)**2.0_pReal
constitutive_rho_m(i)=(2.0_pReal*Kb*Tp*sqrt(constitutive_rho_p(i)))/&
(material_c1(matID)*material_c3(matID)*material_Gmod(matID)*constitutive_jump_width(i)*material_bg(matID)**3.0_pReal)
constitutive_g0_slip(i)=constitutive_rho_m(i)*material_bg(matID)*attack_frequency*constitutive_jump_width(i)*&
exp(-(material_Qedge(matID)+constitutive_passing_stress(i)*constitutive_activation_volume(i))/&
(Kb*Tp))
enddo
end subroutine
subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el)
!*********************************************************************
!* This subroutine contains the constitutive equation for *
!* calculating the velocity gradient *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - state : current microstructure *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!* OUTPUT: *
!* - Lp : plastic velocity gradient *
!* - dLp_dTstar : derivative of Lp (4th-order tensor) *
!*********************************************************************
use prec, only: pReal,pInt
use crystal, only: crystal_Sslip,crystal_Sslip_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,k,l,m,n
real(pReal) Tp
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(3,3) :: Lp
real(pReal), dimension(3,3,3,3) :: dLp_dTstar
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state,gdot_slip,dgdot_dtauslip,tau_slip
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
!* Calculation of Lp
Lp = 0.0_pReal
do i=1,material_Nslip(matID)
tau_slip(i)=dot_product(Tstar_v,crystal_Sslip_v(:,i,material_CrystalStructure(matID)))
gdot_slip(i)=constitutive_g0_slip(i)*sinh((abs(tau_slip(i))*constitutive_activation_volume(i))/(Kb*Tp))*&
sign(1.0_pReal,tau_slip(i))
Lp=Lp+gdot_slip(i)*crystal_Sslip(:,:,i,material_CrystalStructure(matID))
enddo
!* Calculation of the tangent of Lp
dLp_dTstar=0.0_pReal
do i=1,material_Nslip(matID)
dgdot_dtauslip(i)=((constitutive_g0_slip(i)*constitutive_activation_volume(i))/(Kb*Tp))*&
cosh((abs(tau_slip(i))*constitutive_activation_volume(i))/(Kb*Tp))
forall (k=1:3,l=1:3,m=1:3,n=1:3)
dLp_dTstar(k,l,m,n) = dLp_dTstar(k,l,m,n)+ &
dgdot_dtauslip(i)*crystal_Sslip(k,l,i,material_CrystalStructure(matID))* &
(crystal_Sslip(m,n,i,material_CrystalStructure(matID))+ &
crystal_Sslip(n,m,i,material_CrystalStructure(matID)))/2.0_pReal ! force m,n symmetry
endforall
enddo
return
end subroutine
function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el)
!*********************************************************************
!* This subroutine contains the constitutive equation for *
!* calculating the velocity gradient *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - state : current microstructure *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!* OUTPUT: *
!* - constitutive_DotState : evolution of state variable *
!*********************************************************************
use prec, only: pReal,pInt
use crystal, only: crystal_Sslip_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i
real(pReal) Tp,tau_slip,gdot_slip
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state,lock,recovery
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
!* Hardening of each system
do i=1,constitutive_Nstatevars(ipc,ip,el)
tau_slip = dot_product(Tstar_v,crystal_Sslip_v(:,i,material_CrystalStructure(matID)))
gdot_slip = constitutive_g0_slip(i)*sinh((abs(tau_slip)*constitutive_activation_volume(i))/(Kb*Tp))*&
sign(1.0_pReal,tau_slip)
if (abs(tau_slip)>1.0e-20_pReal) then
lock(i)=(material_c4(matID)*sqrt(constitutive_rho_f(i))*abs(gdot_slip))/material_bg(matID)
recovery(i)=material_c5(matID)*state(i)*abs(gdot_slip)
constitutive_dotState(i)=lock(i)-recovery(i)
else
constitutive_dotState(i)=0.0_pReal
endif
enddo
return
end function
function constitutive_post_results(Tstar_v,state,dt,Tp,ipc,ip,el)
!*********************************************************************
!* return array of constitutive results *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - state : current microstructure *
!* - dt : current time increment *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt
use crystal, only: crystal_Sslip_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i
real(pReal) dt,Tp,tau_slip
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
real(pReal), dimension(constitutive_Nresults(ipc,ip,el)) :: constitutive_post_results
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
if(constitutive_Nresults(ipc,ip,el)==0) return
do i=1,material_Nslip(matID)
constitutive_post_results(i) = state(i)
tau_slip=dot_product(Tstar_v,crystal_Sslip_v(:,i,material_CrystalStructure(matID)))
constitutive_post_results(i+material_Nslip(matID)) = &
dt*constitutive_g0_slip(i)*sinh((abs(tau_slip)*constitutive_activation_volume(i))/(Kb*Tp))*&
sign(1.0_pReal,tau_slip)
enddo
return
end function
END MODULE