1326 lines
62 KiB
Fortran
1326 lines
62 KiB
Fortran
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!************************************
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!* Module: CONSTITUTIVE *
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!************************************
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!* contains: *
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!* - constitutive equations *
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!* - parameters definition *
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!* - orientations *
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!************************************
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MODULE constitutive
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!*** Include other modules ***
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use prec, only: pReal,pInt
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implicit none
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! MISSING consistency check after reading 'mattex.mpie'
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character(len=300), parameter :: mattexFile = 'mattex.mpie'
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!*************************************
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!* Definition of material properties *
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!*************************************
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!* Physical parameter, attack_frequency != Debye frequency
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real(pReal), parameter :: attack_frequency = 1.0e10_pReal
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!* Physical parameter, Boltzmann constant in J/Kelvin
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real(pReal), parameter :: kB = 1.38e-23_pReal
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!* Physical parameter, Avogadro number in 1/mol
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real(pReal), parameter :: avogadro = 6.022e23_pReal
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!* Physical parameter, Gaz constant in J.mol/Kelvin
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real(pReal), parameter :: Rgaz = 8.314_pReal
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!*************************************
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!* Definition of material properties *
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!*************************************
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!* Number of materials
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integer(pInt) material_maxN
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!* Lattice structure and number of selected slip or twin systems per material
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integer(pInt), dimension(:) , allocatable :: material_CrystalStructure
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integer(pInt), dimension(:) , allocatable :: material_Nslip
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integer(pInt), dimension(:) , allocatable :: material_Ntwin
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!* Maximum number of selected slip or twin systems over materials
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integer(pInt) material_maxNslip
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integer(pInt) material_maxNtwin
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!* Elastic constants and matrices
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real(pReal), dimension(:) , allocatable :: material_C11
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real(pReal), dimension(:) , allocatable :: material_C12
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real(pReal), dimension(:) , allocatable :: material_C13
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real(pReal), dimension(:) , allocatable :: material_C33
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real(pReal), dimension(:) , allocatable :: material_C44
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real(pReal), dimension(:) , allocatable :: material_Gmod
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real(pReal), dimension(:,:,:) , allocatable :: material_Cslip_66
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real(preal), dimension(:,:,:,:) , allocatable :: material_Ctwin_66
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!* Visco-plastic material parameters
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real(pReal) material_sfe
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real(pReal), dimension(:) , allocatable :: material_rho0
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real(pReal), dimension(:) , allocatable :: material_bg
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real(pReal), dimension(:) , allocatable :: material_Qedge
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real(pReal), dimension(:) , allocatable :: material_GrainSize
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real(pReal), dimension(:) , allocatable :: material_StackSize
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real(pReal), dimension(:) , allocatable :: material_ActivationLength
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real(pReal), dimension(:) , allocatable :: material_TwinSaturation
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real(pReal), dimension(:) , allocatable :: material_SiteScaling
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real(pReal), dimension(:) , allocatable :: material_c1
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real(pReal), dimension(:) , allocatable :: material_c2
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real(pReal), dimension(:) , allocatable :: material_c3
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real(pReal), dimension(:) , allocatable :: material_c4
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real(pReal), dimension(:) , allocatable :: material_c5
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real(pReal), dimension(:) , allocatable :: material_c6
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real(pReal), dimension(:) , allocatable :: material_c7
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real(pReal), dimension(:) , allocatable :: material_q1
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real(pReal), dimension(:) , allocatable :: material_q2
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real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff
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!************************************
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!* Definition of texture properties *
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!************************************
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!* Number of textures, maximum number of Gauss and Fiber components
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integer(pInt) texture_maxN
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integer(pInt) texture_maxNGauss
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integer(pInt) texture_maxNFiber
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!* Textures definition
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character(len=80), dimension(:), allocatable :: texture_ODFfile
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character(len=80), dimension(:), allocatable :: texture_symmetry
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integer(pInt), dimension(:) , allocatable :: texture_Ngrains
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integer(pInt), dimension(:) , allocatable :: texture_NGauss
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integer(pInt),dimension(:) , allocatable :: texture_NFiber
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integer(pInt),dimension(:) , allocatable :: texture_NRandom
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integer(pInt),dimension(:) , allocatable :: texture_totalNgrains
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real(pReal), dimension(:,:,:) , allocatable :: texture_Gauss
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real(pReal), dimension(:,:,:) , allocatable :: texture_Fiber
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_EulerAngles
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!************************************
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!* Grains *
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!************************************
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integer(pInt) constitutive_maxNgrains
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integer(pInt), dimension(:,:) , allocatable :: constitutive_Ngrains
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integer(pInt), dimension(:,:,:) , allocatable :: constitutive_matID
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real(pReal), dimension(:,:,:) , allocatable :: constitutive_matVolFrac
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integer(pInt), dimension(:,:,:) , allocatable :: constitutive_texID
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real(pReal), dimension(:,:,:) , allocatable :: constitutive_texVolFrac
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!************************************
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!* Kinetics variables *
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!************************************
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real(pReal), dimension(:) , allocatable :: constitutive_tau_slip
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real(pReal), dimension(:) , allocatable :: constitutive_tau_twin
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real(pReal), dimension(:) , allocatable :: constitutive_gdot_slip
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real(pReal), dimension(:) , allocatable :: constitutive_fdot_twin
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real(pReal), dimension(:) , allocatable :: constitutive_dgdot_dtauslip
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real(pReal), dimension(:) , allocatable :: constitutive_dfdot_dtautwin
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real(pReal), dimension(:,:) , allocatable :: constitutive_dfdot_dtauslip
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real(pReal), dimension(:) , allocatable :: constitutive_locks
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real(pReal), dimension(:) , allocatable :: constitutive_grainboundaries
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real(pReal), dimension(:) , allocatable :: constitutive_twinboundaries
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real(pReal), dimension(:) , allocatable :: constitutive_recovery
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!************************************
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!* State variables *
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!************************************
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integer(pInt) constitutive_maxNstatevars
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integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nstatevars
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_old
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_new
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real(pReal), dimension(:) , allocatable :: constitutive_passing_stress
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real(pReal), dimension(:) , allocatable :: constitutive_jump_width
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real(pReal), dimension(:) , allocatable :: constitutive_activation_volume
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real(pReal), dimension(:) , allocatable :: constitutive_rho_m
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real(pReal), dimension(:) , allocatable :: constitutive_rho_f
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real(pReal), dimension(:) , allocatable :: constitutive_rho_p
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real(pReal), dimension(:) , allocatable :: constitutive_g0_slip
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real(pReal), dimension(:) , allocatable :: constitutive_twin_volume
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real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_s
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real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_t
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real(pReal), dimension(:) , allocatable :: constitutive_twin_mfp
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!************************************
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!* Interaction matrices *
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!************************************
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real(pReal), dimension(:,:,:), allocatable :: constitutive_Pforest
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real(pReal), dimension(:,:,:), allocatable :: constitutive_Pparallel
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!************************************
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!* Results *
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!************************************
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integer(pInt) constitutive_maxNresults
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integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults
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CONTAINS
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!****************************************
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!* - constitutive_Init
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!* - constitutive_CountSections
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!* - constitutive_Parse_UnknownPart
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!* - constitutive_Parse_MaterialPart
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!* - constitutive_Parse_TexturePart
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!* - constitutive_Parse_MatTexDat
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!* - constitutive_Assignment
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!* - constitutive_HomogenizedC
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!* - constitutive_Microstructure
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!* - constitutive_LpAndItsTangent
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!* - consistutive_DotState
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!****************************************
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subroutine constitutive_Init()
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!**************************************
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!* Module initialization *
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!**************************************
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call constitutive_Parse_MatTexDat(mattexFile)
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call constitutive_Assignment()
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end subroutine
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subroutine constitutive_CountSections(file,count,part)
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!*********************************************************************
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!* This subroutine reads a "part" from the input file until the next *
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!* part is reached and counts the number of "sections" in the part *
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!* INPUT: *
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!* - file : file ID *
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!* OUTPUT: *
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!* - part : name of the next "part" *
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!* - count : number of sections inside the current "part" *
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) part,line,tag
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integer(pInt) file,count
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integer(pInt), dimension(3) :: positions
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count=0
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part=''
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,1)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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part=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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count=count+1
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endif
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enddo
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100 return
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end subroutine
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character(len=80) function constitutive_assignNGaussAndFiber(file)
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!*********************************************************************
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt) file,section
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integer(pInt), dimension(3) :: positions
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constitutive_assignNGaussAndFiber=''
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section = 0_pInt
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,1)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_assignNGaussAndFiber=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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texture_NGauss(section) = 0_pInt
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texture_NFiber(section) = 0_pInt
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elseif (tag=='(gauss)') then
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texture_NGauss(section)=texture_NGauss(section)+1
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elseif (tag=='(fiber)') then
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texture_NFiber(section)=texture_NFiber(section)+1
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_UnknownPart(file)
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!*********************************************************************
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!* read an unknown "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 1
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integer(pInt) file
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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constitutive_parse_unknownPart=''
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_Parse_UnknownPart=tag(2:len_trim(tag)-1)
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exit
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_MaterialPart(file)
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!*********************************************************************
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!* This function reads a material "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt,pReal
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use IO
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 7
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integer(pInt) i,file,section
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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section = 0
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constitutive_parse_materialPart = ''
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do while(.true.)
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_parse_materialPart=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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else
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if (section>0) then
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!$OMP CRITICAL (write2out)
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select case(tag)
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case ('lattice_structure')
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material_CrystalStructure(section)=IO_intValue(line,positions,2)
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write(6,*) 'lattice_structure', material_CrystalStructure(section)
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case ('nslip')
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material_Nslip(section)=IO_intValue(line,positions,2)
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write(6,*) 'nslip', material_Nslip(section)
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case ('ntwin')
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material_Ntwin(section)=IO_intValue(line,positions,2)
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write(6,*) 'ntwin', material_Ntwin(section)
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case ('c11')
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material_C11(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c11', material_C11(section)
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case ('c12')
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material_C12(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c12', material_C12(section)
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case ('c13')
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material_C13(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c13', material_C13(section)
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case ('c33')
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material_C33(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c33', material_C33(section)
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case ('c44')
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material_C44(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c44', material_C44(section)
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case ('rho0')
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material_rho0(section)=IO_floatValue(line,positions,2)
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write(6,*) 'rho0', material_rho0(section)
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case ('interaction_coefficients')
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do i=1,6
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material_SlipIntCoeff(i,section)=IO_floatValue(line,positions,i+1)
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write(6,*) 'interaction_coefficients', material_SlipIntCoeff(i,section)
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enddo
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case ('burgers')
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material_bg(section)=IO_floatValue(line,positions,2)
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write(6,*) 'burgers', material_bg(section)
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case ('qedge')
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material_Qedge(section)=IO_floatValue(line,positions,2)
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write(6,*) 'Qedge', material_Qedge(section)
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case ('grain_size')
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material_GrainSize(section)=IO_floatValue(line,positions,2)
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write(6,*) 'grain_size', material_GrainSize(section)
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case ('stack_size')
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material_StackSize(section)=IO_floatValue(line,positions,2)
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write(6,*) 'stack_size', material_StackSize(section)
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case ('f_sat')
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material_TwinSaturation(section)=IO_floatValue(line,positions,2)
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write(6,*) 'twin saturation', material_TwinSaturation(section)
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case ('site_scaling')
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material_SiteScaling(section)=IO_floatValue(line,positions,2)
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write(6,*) 'site_scaling', material_SiteScaling(section)
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case ('c1')
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material_c1(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c1', material_c1(section)
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case ('c2')
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material_c2(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c2', material_c2(section)
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case ('c3')
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material_c3(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c3', material_c3(section)
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case ('c4')
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material_c4(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c4', material_c4(section)
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case ('c5')
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material_c5(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c5', material_c5(section)
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case ('c6')
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material_c6(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c6', material_c6(section)
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case ('c7')
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material_c7(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c7', material_c7(section)
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case ('q1')
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material_q1(section)=IO_floatValue(line,positions,2)
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write(6,*) 'q1', material_q1(section)
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case ('q2')
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material_q2(section)=IO_floatValue(line,positions,2)
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write(6,*) 'q2', material_q2(section)
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end select
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!$OMP END CRITICAL (write2out)
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endif
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_TexturePart(file)
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!*********************************************************************
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!* This function reads a texture "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt
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use IO
|
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use math, only: inRad
|
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implicit none
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!* Definition of variables
|
||
character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 13 ! may be more than 10 chunks ..?
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integer(pInt) file,section,gaussCount,fiberCount,i
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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section = 0
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gaussCount = 0
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fiberCount = 0
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constitutive_parse_texturePart = ''
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do while(.true.)
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
|
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
|
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constitutive_parse_texturePart=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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gaussCount=0
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fiberCount=0
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else
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if (section>0) then
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select case(tag)
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||
case ('hybridIA')
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texture_ODFfile(section)=IO_stringValue(line,positions,2)
|
||
case ('(gauss)')
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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 lattice, only: lattice_MaxMaxNslipOfStructure,lattice_MaxMaxNtwinOfStructure
|
||
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_Ntwin(material_maxN)) ; material_Ntwin=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_Ctwin_66(6,6,lattice_MaxMaxNtwinOfStructure,material_maxN)) ; material_Ctwin_66=0.0_pReal
|
||
allocate(material_rho0(material_maxN)) ; material_rho0=0.0_pReal
|
||
allocate(material_SlipIntCoeff(lattice_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_GrainSize(material_maxN)) ; material_GrainSize=0.0_pReal
|
||
allocate(material_StackSize(material_maxN)) ; material_StackSize=0.0_pReal
|
||
allocate(material_ActivationLength(material_maxN)) ; material_ActivationLength=0.0_pReal
|
||
allocate(material_TwinSaturation(material_maxN)) ; material_TwinSaturation=0.0_pReal
|
||
allocate(material_SiteScaling(material_maxN)) ; material_SiteScaling=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(material_c6(material_maxN)) ; material_c6=0.0_pReal
|
||
allocate(material_c7(material_maxN)) ; material_c7=0.0_pReal
|
||
allocate(material_q1(material_maxN)) ; material_q1=0.0_pReal
|
||
allocate(material_q2(material_maxN)) ; material_q2=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
|
||
select case (material_CrystalStructure(i))
|
||
case(1:2) ! cubic(s)
|
||
material_Gmod(i)=material_C44(i)
|
||
forall(k=1:3)
|
||
forall(j=1:3)
|
||
material_Cslip_66(k,j,i)=material_C12(i)
|
||
endforall
|
||
material_Cslip_66(k,k,i)=material_C11(i)
|
||
material_Cslip_66(k+3,k+3,i)=material_C44(i)
|
||
endforall
|
||
case(3) ! hcp
|
||
material_Gmod(i)=material_C44(i)
|
||
!* MISSING: Warning message: C44 in hexagonal structures?
|
||
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,&
|
||
math_Mandel3333to66,math_Mandel66to3333
|
||
use mesh, only: mesh_NcpElems,FE_Nips,mesh_maxNips,mesh_element
|
||
use IO, only: IO_hybridIA
|
||
use lattice, only: lattice_SlipIntType,lattice_sn,lattice_st,lattice_Qtwin,lattice_Sslip_v,lattice_Sslip
|
||
implicit none
|
||
|
||
!* Definition of variables
|
||
integer(pInt) e,g,i,j,k,l,m,n,o,p,q,r,s
|
||
integer(pInt) matID,texID
|
||
real(pReal) x,y
|
||
integer(pInt), dimension(:,:,:), allocatable :: hybridIA_population
|
||
integer(pInt), dimension(texture_maxN) :: Ncomponents,Nsym,multiplicity,ODFmap,sampleCount
|
||
real(pReal), dimension(3,4*(1+texture_maxNGauss+texture_maxNfiber)) :: Euler
|
||
real(pReal), dimension(4*(1+texture_maxNGauss+texture_maxNfiber)) :: texVolfrac
|
||
real(pReal), dimension(texture_maxN) :: sumVolfrac
|
||
real(pReal), dimension(3,3,3,3) :: C_3333,Ctwin_3333
|
||
real(pReal), dimension(3,3) :: Qtwin
|
||
|
||
! 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
|
||
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
|
||
if (texture_ODFfile(texID)=='') then ! texture components
|
||
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
|
||
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"
|
||
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)
|
||
!$OMP CRITICAL (write2out)
|
||
write (6,*) 'changed Ngrains to',texture_Ngrains(texID),' for texture',texID
|
||
!$OMP END CRITICAL (write2out)
|
||
endif
|
||
enddo
|
||
|
||
!* publish globals
|
||
constitutive_maxNgrains = maxval(texture_Ngrains)
|
||
material_maxNslip = maxval(material_Nslip) ! max of slip systems among materials present
|
||
material_maxNtwin = maxval(material_Ntwin) ! max of twin systems among materials present
|
||
constitutive_maxNstatevars = maxval(material_Nslip) + maxval(material_Ntwin)
|
||
! -----------------------------------------------------------------------------------------------------------------------
|
||
constitutive_maxNresults = 2_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(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/Nsym,ODFmap /= 0),o))
|
||
do texID = 1,texture_maxN
|
||
if (ODFmap(texID) > 0) &
|
||
hybridIA_population(:,:,ODFmap(texID)) = IO_hybridIA(texture_totalNgrains(texID)/Nsym(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_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(material_maxNslip,material_maxNslip,material_maxN))
|
||
constitutive_Pforest=0.0_pReal
|
||
allocate(constitutive_Pparallel(material_maxNslip,material_maxNslip,material_maxN))
|
||
constitutive_Pparallel=0.0_pReal
|
||
allocate(constitutive_rho_p(material_maxNslip)) ; constitutive_rho_p=0.0_pReal
|
||
allocate(constitutive_rho_f(material_maxNslip)) ; constitutive_rho_f=0.0_pReal
|
||
allocate(constitutive_rho_m(material_maxNslip)) ; constitutive_rho_m=0.0_pReal
|
||
allocate(constitutive_passing_stress(material_maxNslip)) ; constitutive_passing_stress=0.0_pReal
|
||
allocate(constitutive_jump_width(material_maxNslip)) ; constitutive_jump_width=0.0_pReal
|
||
allocate(constitutive_activation_volume(material_maxNslip)) ; constitutive_activation_volume=0.0_pReal
|
||
allocate(constitutive_g0_slip(material_maxNslip)) ; constitutive_g0_slip=0.0_pReal
|
||
allocate(constitutive_twin_volume(material_maxNtwin)) ; constitutive_twin_volume=0.0_pReal
|
||
allocate(constitutive_inv_intertwin_len_s(material_maxNslip)) ; constitutive_inv_intertwin_len_s=0.0_pReal
|
||
allocate(constitutive_inv_intertwin_len_t(material_maxNtwin)) ; constitutive_inv_intertwin_len_t=0.0_pReal
|
||
allocate(constitutive_twin_mfp(material_maxNtwin)) ; constitutive_twin_mfp=0.0_pReal
|
||
allocate(constitutive_tau_slip(material_maxNslip)) ; constitutive_tau_slip=0.0_pReal
|
||
allocate(constitutive_tau_twin(material_maxNtwin)) ; constitutive_tau_twin=0.0_pReal
|
||
allocate(constitutive_gdot_slip(material_maxNslip)) ; constitutive_gdot_slip=0.0_pReal
|
||
allocate(constitutive_fdot_twin(material_maxNtwin)) ; constitutive_fdot_twin=0.0_pReal
|
||
allocate(constitutive_dgdot_dtauslip(material_maxNslip)) ; constitutive_dgdot_dtauslip=0.0_pReal
|
||
allocate(constitutive_dfdot_dtautwin(material_maxNtwin)) ; constitutive_dfdot_dtautwin=0.0_pReal
|
||
allocate(constitutive_dfdot_dtauslip(material_maxNtwin,material_maxNslip)) ; constitutive_dfdot_dtauslip=0.0_pReal
|
||
allocate(constitutive_locks(material_maxNslip)) ; constitutive_locks=0.0_pReal
|
||
allocate(constitutive_grainboundaries(material_maxNslip)) ; constitutive_grainboundaries=0.0_pReal
|
||
allocate(constitutive_twinboundaries(material_maxNslip)) ; constitutive_twinboundaries=0.0_pReal
|
||
allocate(constitutive_recovery(material_maxNslip)) ; constitutive_locks=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(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"
|
||
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) + material_Ntwin(matID)! number of state variables (i.e. tau_c of each slip system)
|
||
! -----------------------------------------------------------------------------------------------------------------------
|
||
constitutive_Nresults(g,i,e) = 2 ! number of constitutive results output by constitutive_post_results
|
||
! -----------------------------------------------------------------------------------------------------------------------
|
||
constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation
|
||
forall (l=1:material_Nslip(matID)) ! 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
|
||
sampleCount(texID) = sampleCount(texID)+1 ! next member of hybrid IA population
|
||
enddo ! multiplicity
|
||
enddo ! ip
|
||
enddo ! cp_element
|
||
|
||
!* Construction of the rotated elasticity matrices for twinning
|
||
do i=1,material_maxN
|
||
C_3333=math_Mandel66to3333(material_Cslip_66(:,:,i))
|
||
do j=1,material_Ntwin(i)
|
||
Qtwin=lattice_Qtwin(:,:,j,material_CrystalStructure(i))
|
||
do k=1,3
|
||
do l=1,3
|
||
do m=1,3
|
||
do n=1,3
|
||
Ctwin_3333(k,l,m,n)=0.0_pReal
|
||
do p=1,3
|
||
do q=1,3
|
||
do r=1,3
|
||
do s=1,3
|
||
Ctwin_3333(k,l,m,n)=Ctwin_3333(k,l,m,n)+C_3333(p,q,r,s)*Qtwin(k,p)*Qtwin(l,q)*Qtwin(m,r)*Qtwin(n,s)
|
||
enddo
|
||
enddo
|
||
enddo
|
||
enddo
|
||
enddo
|
||
enddo
|
||
enddo
|
||
enddo
|
||
!* Mapping back to 66-format of the matrices
|
||
material_Ctwin_66(:,:,j,i) = math_Mandel3333to66(Ctwin_3333)
|
||
enddo
|
||
enddo
|
||
|
||
!* Construction of the hardening matrices
|
||
do i=1,material_maxN
|
||
!* Iteration over the systems
|
||
do j=1,material_Nslip(i)
|
||
do k=1,material_Nslip(i)
|
||
!* Projection of the dislocation *
|
||
x=dot_product(lattice_sn(:,j,i),lattice_st(:,k,i))
|
||
y=1.0_pReal-x**(2.0_pReal)
|
||
!* Interaction matrix *
|
||
constitutive_Pforest(j,k,i)=abs(x)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
|
||
if (y>0.0_pReal) then
|
||
constitutive_Pparallel(j,k,i)=sqrt(y)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
|
||
else
|
||
constitutive_Pparallel(j,k,i)=0.0_pReal
|
||
endif
|
||
enddo
|
||
enddo
|
||
enddo
|
||
|
||
|
||
end subroutine
|
||
|
||
|
||
function constitutive_HomogenizedC(state,ipc,ip,el)
|
||
!*********************************************************************
|
||
!* This function returns the homogenized elacticity matrix *
|
||
!* INPUT: *
|
||
!* - state : state variables *
|
||
!* - 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,startIdxTwin
|
||
real(pReal), dimension(6,6) :: constitutive_homogenizedC
|
||
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)
|
||
startIdxTwin = material_Nslip(matID)
|
||
|
||
!* Homogenization scheme
|
||
constitutive_homogenizedC=(1-sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))))*&
|
||
material_Cslip_66(:,:,matID)
|
||
do i=1,material_Ntwin(matID)
|
||
constitutive_homogenizedC=constitutive_homogenizedC+state(startIdxTwin+i)*material_Ctwin_66(:,:,i,matID)
|
||
enddo
|
||
|
||
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
|
||
use math, only: pi
|
||
use lattice, only: lattice_TwinIntType,lattice_SlipTwinIntType
|
||
implicit none
|
||
|
||
!* Definition of variables
|
||
integer(pInt) ipc,ip,el
|
||
integer(pInt) matID,i,j,startIdxTwin
|
||
real(pReal) Tp,Ftwin
|
||
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
|
||
real(pReal) x_fe,x_Mn,x_C,beta_mart,Tp_mart,f_mart,beta_aust,Tp_aust,f_aust
|
||
real(pReal) deltaG1,deltaG2,deltaG3,deltaG4,deltaG5
|
||
|
||
!* Get the material-ID from the triplet(ipc,ip,el)
|
||
matID = constitutive_matID(ipc,ip,el)
|
||
startIdxTwin = material_Nslip(matID)
|
||
|
||
!* Quantities derived from state - slip
|
||
!$OMP CRITICAL (evilmatmul)
|
||
constitutive_rho_f=matmul(constitutive_Pforest (1:material_Nslip(matID),1:material_Nslip(matID),matID),state)
|
||
constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state)
|
||
!$OMP END CRITICAL (evilmatmul)
|
||
do i=1,material_Nslip(matID)
|
||
constitutive_passing_stress(i) = 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
|
||
|
||
!* Quantities derived from state - twin
|
||
Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
||
do i=1,material_Nslip(matID)
|
||
!* Inverse of the average distance between 2 twins of the same familly
|
||
constitutive_inv_intertwin_len_s(i)=0.0_pReal
|
||
do j=1,material_Ntwin(matID)
|
||
constitutive_inv_intertwin_len_s(i)=constitutive_inv_intertwin_len_s(i)+&
|
||
(lattice_SlipTwinIntType(i,j,material_CrystalStructure(matID))*state(startIdxTwin+j))/&
|
||
(2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin))
|
||
enddo
|
||
enddo
|
||
do i=1,material_Ntwin(matID)
|
||
!* Inverse of the average distance between 2 twins of the same familly
|
||
constitutive_inv_intertwin_len_t(i)=0.0_pReal
|
||
do j=1,material_Ntwin(matID)
|
||
constitutive_inv_intertwin_len_t(i)=constitutive_inv_intertwin_len_t(i)+&
|
||
(lattice_TwinIntType(i,j,material_CrystalStructure(matID))*state(startIdxTwin+j))/&
|
||
(2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin))
|
||
enddo
|
||
constitutive_twin_mfp(i)=1.0_pReal/((1.0_pReal/material_GrainSize(matID))+constitutive_inv_intertwin_len_t(i))
|
||
constitutive_twin_volume(i)=((4.0_pReal*pi)/3.0_pReal)*material_StackSize(matID)*constitutive_twin_mfp(i)**2.0_pReal
|
||
enddo
|
||
|
||
!* Stacking fault energy as function of temperature (see Allain PhD Thesis p40-42) *
|
||
x_Fe=0.774_pReal ! atomic %
|
||
x_Mn=0.218_pReal ! atomic %
|
||
x_C =0.027_pReal ! atomic %
|
||
|
||
!* Chemical contribution *
|
||
deltaG1=x_Fe*(4.309_pReal*Tp-2243.38_pReal)
|
||
deltaG2=x_Mn*(1.123_preal*Tp-1000.0_pReal)
|
||
deltaG3=x_Fe*x_Mn*(2873.0_pReal+717.0_pReal*(x_Fe-x_Mn))
|
||
deltaG4=1246.0_pReal*(1.0_pReal-exp(-24.29_pReal*x_C))-17175.0_pReal*x_Mn*x_C
|
||
|
||
!* Magnetical contribution *
|
||
beta_mart=0.62_pReal*x_Mn-4.0_pReal*x_C ! Magnetic spin in <20>B
|
||
Tp_mart=580.0_pReal*x_Mn ! N<>el Temperature
|
||
beta_aust=0.7_pReal*x_Fe+0.62_pReal*x_Mn-0.64_pReal*x_Fe*x_Mn-4.0_pReal*x_C ! Magnetic spin in <20>B
|
||
Tp_aust=669.27_pReal*(1.0_pReal-exp(-5.46_pReal*x_Mn))-2408.0_pReal*x_C*x_Fe-109.0_pReal ! N<>el Temperature
|
||
if (Tp<=Tp_mart) then
|
||
f_mart=1.0_pReal-(1.0_pReal/2.34_pReal)*((79.0_pReal*Tp_mart)/(140.0_pReal*0.28_pReal*Tp)+&
|
||
(474.0_pReal/497.0_pReal)*((1.0_pReal/0.28_pReal)-1.0_pReal)*(((Tp/Tp_mart)**3.0_pReal)/6.0_pReal+&
|
||
((Tp/Tp_mart)**9.0_pReal)/135.0_pReal+((Tp/Tp_mart)**15.0_pReal)/600.0_pReal))
|
||
else
|
||
f_mart=-(1.0_pReal/2.34_pReal)*(((Tp/Tp_mart)**-5.0_pReal)/10.0_pReal+((Tp/Tp_mart)**-15.0_pReal)/315.0_pReal+&
|
||
((Tp/Tp_mart)**-25.0_pReal)/1500.0_pReal)
|
||
endif
|
||
if (Tp<=Tp_aust) then
|
||
f_aust=1.0_pReal-(1.0_pReal/2.34_pReal)*((79.0_pReal*Tp_aust)/(140.0_pReal*0.28_pReal*Tp)+&
|
||
(474.0_pReal/497.0_pReal)*((1.0_pReal/0.28_pReal)-1.0_pReal)*(((Tp/Tp_aust)**3.0_pReal)/6.0_pReal+&
|
||
((Tp/Tp_aust)**9.0_pReal)/135.0_pReal+((Tp/Tp_aust)**15.0_pReal)/600.0_pReal))
|
||
else
|
||
f_aust=-(1.0_pReal/2.34_pReal)*(((Tp/Tp_aust)**-5.0_pReal)/10.0_pReal+((Tp/Tp_aust)**-15.0_pReal)/315.0_pReal+&
|
||
((Tp/Tp_aust)**-25.0_pReal)/1500.0_pReal)
|
||
endif
|
||
deltaG5=Rgaz*Tp*(log(beta_mart+1.0_pReal)*f_mart-log(beta_aust+1.0_pReal)*f_aust)
|
||
|
||
!* Final expression *
|
||
material_sfe=(4.0_pReal/(sqrt(3.0_pReal)*avogadro*material_bg(matID)**2.0_pReal))*&
|
||
(deltaG1+deltaG2+deltaG3+deltaG4+deltaG5)+2.0_pReal*0.0035_pReal
|
||
|
||
return
|
||
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 lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_TwinShear
|
||
use math, only: pi,math_Plain3333to99
|
||
implicit none
|
||
|
||
!* Definition of variables
|
||
integer(pInt) ipc,ip,el
|
||
integer(pInt) matID,startIdxTwin,i,j,k,l,m,n
|
||
real(pReal) Tp,Ftwin
|
||
real(pReal), dimension(6) :: Tstar_v
|
||
real(pReal), dimension(3,3) :: Lp,Sslip,Stwin
|
||
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
||
real(pReal), dimension(9,9) :: dLp_dTstar
|
||
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
|
||
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,dgdot_dtauslip,tau_slip
|
||
real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el))) :: sfe_eff,fdot_twin,dfdot_dtautwin,tau_twin,tauc_twin
|
||
real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el)),material_Nslip(constitutive_matID(ipc,ip,el))) :: dfdot_dtauslip
|
||
|
||
!* Get the material-ID from the triplet(ipc,ip,el)
|
||
matID = constitutive_matID(ipc,ip,el)
|
||
startIdxTwin = material_Nslip(matID)
|
||
Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
||
|
||
!* Calculation of Lp - slip
|
||
gdot_slip = 0.0_pReal
|
||
dgdot_dtauslip = 0.0_pReal
|
||
Lp = 0.0_pReal
|
||
do i=1,material_Nslip(matID)
|
||
tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID)))
|
||
if (abs(tau_slip(i))>constitutive_passing_stress(i)) then
|
||
gdot_slip(i) = constitutive_g0_slip(i)*sinh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
||
dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(kB*Tp)*&
|
||
cosh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
||
endif
|
||
Lp=Lp+(1.0_pReal-Ftwin)*gdot_slip(i)*lattice_Sslip(:,:,i,material_CrystalStructure(matID))
|
||
enddo
|
||
|
||
!write(6,*) '##############'
|
||
!write(6,*) '##############'
|
||
|
||
!write(6,*) 'Schmid_1', lattice_Sslip_v(:,1,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_2', lattice_Sslip_v(:,2,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_3', lattice_Sslip_v(:,3,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_4', lattice_Sslip_v(:,4,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_5', lattice_Sslip_v(:,5,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_6', lattice_Sslip_v(:,6,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_7', lattice_Sslip_v(:,7,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_8', lattice_Sslip_v(:,8,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_9', lattice_Sslip_v(:,9,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_10', lattice_Sslip_v(:,10,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_11', lattice_Sslip_v(:,11,material_CrystalStructure(matID))
|
||
!write(6,*) 'Schmid_12', lattice_Sslip_v(:,12,material_CrystalStructure(matID))
|
||
!write(6,*) 'Tstar_v',Tstar_v
|
||
!write(6,*) 'state',state
|
||
!write(6,*) 'Tp', Tp
|
||
!write(6,*) 'ssd_f', constitutive_rho_f
|
||
!write(6,*) 'ssd_p', constitutive_rho_p
|
||
!write(6,*) 'jump_width', constitutive_jump_width
|
||
!write(6,*) 'activation_volume', constitutive_activation_volume
|
||
!write(6,*) 'passing_stress', constitutive_passing_stress
|
||
!write(6,*) 'ssd_m', constitutive_rho_m
|
||
!write(6,*) 'g0_slip', constitutive_g0_slip
|
||
!write(6,*) 'tau_slip',tau_slip
|
||
!write(6,*) 'gdot_slip', gdot_slip
|
||
!write(6,*) 'dgdot_dtauslip', dgdot_dtauslip
|
||
|
||
|
||
!* Calculation of Lp - twin
|
||
sfe_eff = 0.0_pReal
|
||
fdot_twin = 0.0_pReal
|
||
dfdot_dtautwin = 0.0_pReal
|
||
dfdot_dtauslip = 0.0_pReal
|
||
do i=1,material_Ntwin(matID)
|
||
tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_CrystalStructure(matID)))
|
||
if ((tau_twin(i) > 0.0_pReal).AND.(material_TwinSaturation(matID)-Ftwin>=0)) then
|
||
sfe_eff(i)=material_sfe-(sqrt(3.0_pReal)/3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i)
|
||
if (sfe_eff(i)<0.0_pReal) sfe_eff(i) = 0.0_pReal
|
||
fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*&
|
||
constitutive_twin_volume(i)*&
|
||
((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*&
|
||
sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*&
|
||
exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
|
||
dfdot_dtautwin(i) = (material_TwinSaturation(matID)-Ftwin)*&
|
||
constitutive_twin_volume(i)*&
|
||
((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*&
|
||
sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*&
|
||
((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**2.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*material_q2(matID)**4.0_pReal*tau_twin(i)**5.0_pReal))*&
|
||
(-sqrt(3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i)-&
|
||
4.0_pReal*sfe_eff(i))*&
|
||
exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
|
||
do j=1,material_Nslip(matID)
|
||
if (gdot_slip(j)>0.0_pReal) then
|
||
dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*&
|
||
constitutive_twin_volume(i)*&
|
||
((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*dgdot_dtauslip(j)*&
|
||
sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*&
|
||
exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
else
|
||
dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*&
|
||
constitutive_twin_volume(i)*&
|
||
((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*(-dgdot_dtauslip(j))*&
|
||
sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*&
|
||
exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
endif
|
||
enddo
|
||
endif
|
||
Lp=Lp+state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*constitutive_fdot_twin(i)*&
|
||
lattice_Stwin(:,:,i,material_CrystalStructure(matID))
|
||
enddo
|
||
|
||
|
||
!write(6,*) 'twin_mfp', constitutive_twin_mfp
|
||
!write(6,*) 'twin_volume', constitutive_twin_volume
|
||
!write(6,*) 'tau_twin',tau_twin
|
||
!write(6,*) 'part1:',material_TwinSaturation(matID)-Ftwin
|
||
!write(6,*) 'part2:',constitutive_twin_volume
|
||
!write(6,*) 'part3:',((2.0_pReal*sqrt(6.0_pReal)*sum(abs(gdot_slip))*&
|
||
! sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)
|
||
!do i=1,12
|
||
!write(6,*) 'part4:',exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
! (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
!write(6,*) 'part5:',(-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
! (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)
|
||
!enddo
|
||
!write(6,*) 'sfe', material_sfe
|
||
!write(6,*) 'sfe_eff',sfe_eff
|
||
!write(6,*) 'fdot_twin', fdot_twin
|
||
!write(6,*) 'dfdot_dtautwin', dfdot_dtautwin
|
||
!write(6,*) 'dfdot_dtauslip', dfdot_dtauslip
|
||
|
||
|
||
!* Calculation of the tangent of Lp
|
||
dLp_dTstar3333=0.0_pReal
|
||
do i=1,material_Nslip(matID)
|
||
Sslip = lattice_Sslip(:,:,i,material_CrystalStructure(matID))
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3)
|
||
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ &
|
||
(1.0_pReal-Ftwin)*dgdot_dtauslip(i)*Sslip(k,l)*Sslip(m,n) !force m,n symmetry
|
||
endforall
|
||
enddo
|
||
do i=1,material_Ntwin(matID)
|
||
Stwin = lattice_Stwin(:,:,i,material_CrystalStructure(matID))
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3)
|
||
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ &
|
||
state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*&
|
||
dfdot_dtautwin(i)*Stwin(k,l)*Stwin(m,n) !force m,n symmetry
|
||
endforall
|
||
do j=1,material_Nslip(matID)
|
||
Sslip = lattice_Sslip(:,:,j,material_CrystalStructure(matID))
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3)
|
||
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ &
|
||
state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*&
|
||
dfdot_dtauslip(i,j)*Stwin(k,l)*Sslip(m,n) !force m,n symmetry
|
||
endforall
|
||
enddo
|
||
enddo
|
||
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
|
||
|
||
return
|
||
end subroutine
|
||
|
||
|
||
function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el)
|
||
!*********************************************************************
|
||
!* This subroutine contains the constitutive equation for *
|
||
!* calculating rate of change of microstructure *
|
||
!* 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 math, only: pi
|
||
use lattice, only: lattice_Sslip_v,lattice_Stwin_v
|
||
implicit none
|
||
|
||
!* Definition of variables
|
||
integer(pInt) ipc,ip,el
|
||
integer(pInt) matID,i,j,startIdxTwin
|
||
real(pReal) Tp,Ftwin
|
||
real(pReal), dimension(6) :: Tstar_v
|
||
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state
|
||
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,tau_slip
|
||
real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el))) :: sfe_eff,fdot_twin,tau_twin,tauc_twin
|
||
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: locks,grainboundaries,recovery
|
||
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: twinboundaries
|
||
|
||
!* Get the material-ID from the triplet(ipc,ip,el)
|
||
matID = constitutive_matID(ipc,ip,el)
|
||
startIdxTwin = material_Nslip(matID)
|
||
Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
||
constitutive_dotState = 0.0_pReal
|
||
|
||
!* Dislocation density evolution
|
||
gdot_slip = 0.0_pReal
|
||
do i=1,material_Nslip(matID)
|
||
tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID)))
|
||
if (abs(tau_slip(i))>constitutive_passing_stress(i)) &
|
||
gdot_slip(i) = constitutive_g0_slip(i)*sinh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
||
|
||
locks(i) = (sqrt(constitutive_rho_f(i))*abs(gdot_slip(i)))/(material_c4(matID)*material_bg(matID))
|
||
grainboundaries(i) = abs(gdot_slip(i))/(material_c5(matID)*material_bg(matID)*material_GrainSize(matID))
|
||
twinboundaries(i) = (abs(gdot_slip(i))*constitutive_inv_intertwin_len_s(i))/(material_c6(matID)*material_bg(matID))
|
||
recovery(i) = material_c7(matID)*state(i)*abs(gdot_slip(i))
|
||
|
||
constitutive_dotState(i) = locks(i)+grainboundaries(i)+twinboundaries(i)-recovery(i)
|
||
enddo
|
||
|
||
!* Twin volume fraction evolution
|
||
fdot_twin = 0.0_pReal
|
||
do i=1,material_Ntwin(matID)
|
||
tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_CrystalStructure(matID)))
|
||
if (tau_twin(i)>0.0_pReal) then
|
||
sfe_eff(i)=material_sfe-(sqrt(3.0_pReal)/3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i)
|
||
if (sfe_eff(i)<0.0_pReal) sfe_eff(i) = 0.0_pReal
|
||
fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*&
|
||
constitutive_twin_volume(i)*&
|
||
((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*&
|
||
sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*&
|
||
exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/&
|
||
(3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal))
|
||
endif
|
||
constitutive_dotState(startIdxTwin+i) = fdot_twin(i)
|
||
enddo
|
||
|
||
return
|
||
end function
|
||
|
||
|
||
function constitutive_post_results(Tstar_v,state,Tp,dt,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 *
|
||
!* constitutive_Nresults has to be set accordingly in _Assignment *
|
||
!*********************************************************************
|
||
use prec, only: pReal,pInt
|
||
use lattice, only: lattice_Sslip_v
|
||
implicit none
|
||
|
||
!* Definition of variables
|
||
integer(pInt) ipc,ip,el
|
||
integer(pInt) matID,i,startIdxTwin
|
||
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)
|
||
startIdxTwin = material_Nslip(matID)
|
||
|
||
if(constitutive_Nresults(ipc,ip,el)==0) return
|
||
|
||
constitutive_post_results=0.0_pReal
|
||
!do i=1,material_Nslip(matID)
|
||
! constitutive_post_results(i) = state(i)
|
||
!enddo
|
||
!do i=1,material_Ntwin(matID)
|
||
! constitutive_post_results(startIdxTwin+i) = state(startIdxTwin+i)
|
||
!enddo
|
||
constitutive_post_results(1) = sum(state(1:material_Nslip(matID)))
|
||
constitutive_post_results(2) = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
||
|
||
return
|
||
end function
|
||
|
||
END MODULE |