520 lines
25 KiB
Fortran
520 lines
25 KiB
Fortran
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!*****************************************************
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!* Module: CONSTITUTIVE_PHENOMENOLOGICAL *
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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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!*****************************************************
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! [Alu]
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! constitution phenomenological
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! (output) slipresistance
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! (output) rateofshear
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! lattice_structure 1
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! Nslip 12
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!
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! c11 106.75e9
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! c12 60.41e9
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! c44 28.34e9
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!
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! s0_slip 31e6
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! gdot0_slip 0.001
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! n_slip 20
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! h0 75e6
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! s_sat 63e6
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! w0 2.25
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! latent_ratio 1.4
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MODULE constitutive_phenomenological
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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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character (len=*), parameter :: constitutive_phenomenological_label = 'phenomenological'
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integer(pInt), dimension(:), allocatable :: constitutive_phenomenological_sizeDotState, &
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constitutive_phenomenological_sizeState, &
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constitutive_phenomenological_sizePostResults
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character(len=64), dimension(:,:), allocatable :: constitutive_phenomenological_output
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character(len=32), dimension(:), allocatable :: constitutive_phenomenological_structureName
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integer(pInt), dimension(:), allocatable :: constitutive_phenomenological_structure
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integer(pInt), dimension(:), allocatable :: constitutive_phenomenological_Nslip
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_CoverA
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_C11
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_C12
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_C13
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_C33
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_C44
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real(pReal), dimension(:,:,:), allocatable :: constitutive_phenomenological_Cslip_66
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!* Visco-plastic constitutive_phenomenological parameters
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_s0_slip
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_gdot0_slip
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_n_slip
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_h0
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_s_sat
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_w0
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real(pReal), dimension(:), allocatable :: constitutive_phenomenological_latent
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real(pReal), dimension(:,:,:), allocatable :: constitutive_phenomenological_HardeningMatrix
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CONTAINS
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!****************************************
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!* - constitutive_init
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!* - constitutive_stateInit
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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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!* - consistutive_postResults
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!****************************************
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subroutine constitutive_phenomenological_init(file)
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!**************************************
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!* Module initialization *
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!**************************************
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use prec, only: pInt, pReal
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use math, only: math_Mandel3333to66, math_Voigt66to3333
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use IO
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use material
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use lattice, only: lattice_initializeStructure
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integer(pInt), intent(in) :: file
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integer(pInt), parameter :: maxNchunks = 7
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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integer(pInt) section, maxNinstance, i,j,k, output
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character(len=64) tag
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character(len=1024) line
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maxNinstance = count(phase_constitution == constitutive_phenomenological_label)
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if (maxNinstance == 0) return
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allocate(constitutive_phenomenological_sizeDotState(maxNinstance)) ; constitutive_phenomenological_sizeDotState = 0_pInt
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allocate(constitutive_phenomenological_sizeState(maxNinstance)) ; constitutive_phenomenological_sizeState = 0_pInt
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allocate(constitutive_phenomenological_sizePostResults(maxNinstance)); constitutive_phenomenological_sizePostResults = 0_pInt
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allocate(constitutive_phenomenological_output(maxval(phase_Noutput), &
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maxNinstance)) ; constitutive_phenomenological_output = ''
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allocate(constitutive_phenomenological_structureName(maxNinstance)) ; constitutive_phenomenological_structureName = ''
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allocate(constitutive_phenomenological_structure(maxNinstance)) ; constitutive_phenomenological_structure = 0_pInt
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allocate(constitutive_phenomenological_Nslip(maxNinstance)) ; constitutive_phenomenological_Nslip = 0_pInt
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allocate(constitutive_phenomenological_CoverA(maxNinstance)) ; constitutive_phenomenological_CoverA = 0.0_pReal
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allocate(constitutive_phenomenological_C11(maxNinstance)) ; constitutive_phenomenological_C11 = 0.0_pReal
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allocate(constitutive_phenomenological_C12(maxNinstance)) ; constitutive_phenomenological_C12 = 0.0_pReal
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allocate(constitutive_phenomenological_C13(maxNinstance)) ; constitutive_phenomenological_C13 = 0.0_pReal
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allocate(constitutive_phenomenological_C33(maxNinstance)) ; constitutive_phenomenological_C33 = 0.0_pReal
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allocate(constitutive_phenomenological_C44(maxNinstance)) ; constitutive_phenomenological_C44 = 0.0_pReal
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allocate(constitutive_phenomenological_Cslip_66(6,6,maxNinstance)) ; constitutive_phenomenological_Cslip_66 = 0.0_pReal
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allocate(constitutive_phenomenological_s0_slip(maxNinstance)) ; constitutive_phenomenological_s0_slip = 0.0_pReal
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allocate(constitutive_phenomenological_gdot0_slip(maxNinstance)) ; constitutive_phenomenological_gdot0_slip = 0.0_pReal
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allocate(constitutive_phenomenological_n_slip(maxNinstance)) ; constitutive_phenomenological_n_slip = 0.0_pReal
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allocate(constitutive_phenomenological_h0(maxNinstance)) ; constitutive_phenomenological_h0 = 0.0_pReal
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allocate(constitutive_phenomenological_s_sat(maxNinstance)) ; constitutive_phenomenological_s_sat = 0.0_pReal
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allocate(constitutive_phenomenological_w0(maxNinstance)) ; constitutive_phenomenological_w0 = 0.0_pReal
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allocate(constitutive_phenomenological_latent(maxNinstance)) ; constitutive_phenomenological_latent = 0.0_pReal
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rewind(file)
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line = ''
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section = 0
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do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
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read(file,'(a1024)',END=100) line
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enddo
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do ! read thru sections of phase part
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read(file,'(a1024)',END=100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
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if (IO_getTag(line,'[',']') /= '') then ! next section
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section = section + 1
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output = 0 ! reset output counter
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endif
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if (section > 0 .and. phase_constitution(section) == constitutive_phenomenological_label) then ! one of my sections
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i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
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positions = IO_stringPos(line,maxNchunks)
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tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
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select case(tag)
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case ('(output)')
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output = output + 1
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constitutive_phenomenological_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
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case ('lattice_structure')
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constitutive_phenomenological_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
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case ('nslip')
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constitutive_phenomenological_Nslip(i) = IO_intValue(line,positions,2)
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case ('covera_ratio')
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constitutive_phenomenological_CoverA(i) = IO_floatValue(line,positions,2)
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case ('c11')
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constitutive_phenomenological_C11(i) = IO_floatValue(line,positions,2)
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case ('c12')
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constitutive_phenomenological_C12(i) = IO_floatValue(line,positions,2)
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case ('c13')
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constitutive_phenomenological_C13(i) = IO_floatValue(line,positions,2)
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case ('c33')
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constitutive_phenomenological_C33(i) = IO_floatValue(line,positions,2)
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case ('c44')
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constitutive_phenomenological_C44(i) = IO_floatValue(line,positions,2)
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case ('s0_slip')
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constitutive_phenomenological_s0_slip(i) = IO_floatValue(line,positions,2)
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case ('gdot0_slip')
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constitutive_phenomenological_gdot0_slip(i) = IO_floatValue(line,positions,2)
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case ('n_slip')
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constitutive_phenomenological_n_slip(i) = IO_floatValue(line,positions,2)
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case ('h0')
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constitutive_phenomenological_h0(i) = IO_floatValue(line,positions,2)
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case ('s_sat')
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constitutive_phenomenological_s_sat(i) = IO_floatValue(line,positions,2)
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case ('w0')
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constitutive_phenomenological_w0(i) = IO_floatValue(line,positions,2)
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case ('latent_ratio')
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constitutive_phenomenological_latent(i) = IO_floatValue(line,positions,2)
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end select
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endif
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enddo
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100 do i = 1,maxNinstance
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constitutive_phenomenological_structure(i) = lattice_initializeStructure(constitutive_phenomenological_structureName(i), &
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constitutive_phenomenological_CoverA(i)) ! sanity checks
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if (constitutive_phenomenological_structure(i) < 1 .or. &
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constitutive_phenomenological_structure(i) > 3) call IO_error(201)
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if (constitutive_phenomenological_Nslip(i) < 1) call IO_error(202)
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if (constitutive_phenomenological_s0_slip(i) < 0.0_pReal) call IO_error(203)
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if (constitutive_phenomenological_gdot0_slip(i) <= 0.0_pReal) call IO_error(204)
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if (constitutive_phenomenological_n_slip(i) <= 0.0_pReal) call IO_error(205)
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if (constitutive_phenomenological_h0(i) <= 0.0_pReal) call IO_error(206)
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if (constitutive_phenomenological_s_sat(i) <= 0.0_pReal) call IO_error(207)
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if (constitutive_phenomenological_w0(i) <= 0.0_pReal) call IO_error(208)
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if (constitutive_phenomenological_latent(i) <= 0.0_pReal) call IO_error(209)
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enddo
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allocate(constitutive_phenomenological_hardeningMatrix(maxval(constitutive_phenomenological_Nslip),&
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maxval(constitutive_phenomenological_Nslip),&
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maxNinstance))
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do i = 1,maxNinstance
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constitutive_phenomenological_sizeDotState(i) = constitutive_phenomenological_Nslip(i)
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constitutive_phenomenological_sizeState(i) = constitutive_phenomenological_Nslip(i)
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do j = 1,maxval(phase_Noutput)
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select case(constitutive_phenomenological_output(j,i))
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case('slipresistance')
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constitutive_phenomenological_sizePostResults(i) = &
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constitutive_phenomenological_sizePostResults(i) + constitutive_phenomenological_Nslip(i)
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case('rateofshear')
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constitutive_phenomenological_sizePostResults(i) = &
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constitutive_phenomenological_sizePostResults(i) + constitutive_phenomenological_Nslip(i)
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end select
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enddo
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select case (constitutive_phenomenological_structure(i))
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case(1:2) ! cubic(s)
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forall(k=1:3)
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forall(j=1:3) &
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constitutive_phenomenological_Cslip_66(k,j,i) = constitutive_phenomenological_C12(i)
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constitutive_phenomenological_Cslip_66(k,k,i) = constitutive_phenomenological_C11(i)
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constitutive_phenomenological_Cslip_66(k+3,k+3,i) = constitutive_phenomenological_C44(i)
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end forall
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case(3) ! hcp
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constitutive_phenomenological_Cslip_66(1,1,i) = constitutive_phenomenological_C11(i)
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constitutive_phenomenological_Cslip_66(2,2,i) = constitutive_phenomenological_C11(i)
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constitutive_phenomenological_Cslip_66(3,3,i) = constitutive_phenomenological_C33(i)
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constitutive_phenomenological_Cslip_66(1,2,i) = constitutive_phenomenological_C12(i)
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constitutive_phenomenological_Cslip_66(2,1,i) = constitutive_phenomenological_C12(i)
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constitutive_phenomenological_Cslip_66(1,3,i) = constitutive_phenomenological_C13(i)
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constitutive_phenomenological_Cslip_66(3,1,i) = constitutive_phenomenological_C13(i)
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constitutive_phenomenological_Cslip_66(2,3,i) = constitutive_phenomenological_C13(i)
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constitutive_phenomenological_Cslip_66(3,2,i) = constitutive_phenomenological_C13(i)
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constitutive_phenomenological_Cslip_66(4,4,i) = constitutive_phenomenological_C44(i)
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constitutive_phenomenological_Cslip_66(5,5,i) = constitutive_phenomenological_C44(i)
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constitutive_phenomenological_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_phenomenological_C11(i)- &
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constitutive_phenomenological_C12(i))
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end select
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constitutive_phenomenological_Cslip_66(:,:,i) = &
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math_Mandel3333to66(math_Voigt66to3333(constitutive_phenomenological_Cslip_66(:,:,i)))
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constitutive_phenomenological_hardeningMatrix(:,:,i) = constitutive_phenomenological_latent(i)
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forall (j = 1:constitutive_phenomenological_Nslip(i)) &
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constitutive_phenomenological_hardeningMatrix(j,j,i) = 1.0_pReal
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enddo
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return
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end subroutine
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function constitutive_phenomenological_stateInit(myInstance)
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!*********************************************************************
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!* initial microstructural state *
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!*********************************************************************
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use prec, only: pReal,pInt
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implicit none
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!* Definition of variables
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integer(pInt), intent(in) :: myInstance
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real(pReal), dimension(constitutive_phenomenological_Nslip(myInstance)) :: constitutive_phenomenological_stateInit
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constitutive_phenomenological_stateInit = constitutive_phenomenological_s0_slip(myInstance)
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return
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end function
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function constitutive_phenomenological_homogenizedC(state,ipc,ip,el)
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!*********************************************************************
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!* homogenized elacticity matrix *
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!* INPUT: *
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!* - state : state variables *
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!* - ipc : component-ID of current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!*********************************************************************
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use prec, only: pReal,pInt,p_vec
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
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implicit none
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!* Definition of variables
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integer(pInt), intent(in) :: ipc,ip,el
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integer(pInt) matID
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real(pReal), dimension(6,6) :: constitutive_phenomenological_homogenizedC
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
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matID = phase_constitutionInstance(material_phase(ipc,ip,el))
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constitutive_phenomenological_homogenizedC = constitutive_phenomenological_Cslip_66(:,:,matID)
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return
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end function
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subroutine constitutive_phenomenological_microstructure(Temperature,state,ipc,ip,el)
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!*********************************************************************
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!* calculate derived quantities from state (not used here) *
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!* INPUT: *
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!* - Tp : temperature *
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!* - ipc : component-ID of current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!*********************************************************************
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use prec, only: pReal,pInt,p_vec
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
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implicit none
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!* Definition of variables
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integer(pInt) ipc,ip,el, matID
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real(pReal) Temperature
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
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matID = phase_constitutionInstance(material_phase(ipc,ip,el))
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end subroutine
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subroutine constitutive_phenomenological_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
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!*********************************************************************
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!* plastic velocity gradient and its tangent *
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!* INPUT: *
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!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
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!* - ipc : component-ID at current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!* OUTPUT: *
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!* - Lp : plastic velocity gradient *
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!* - dLp_dTstar : derivative of Lp (4th-rank tensor) *
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!*********************************************************************
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use prec, only: pReal,pInt,p_vec
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use math, only: math_Plain3333to99
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use lattice, only: lattice_Sslip,lattice_Sslip_v
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
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implicit none
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!* Definition of variables
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integer(pInt) ipc,ip,el
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integer(pInt) matID,i,k,l,m,n
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real(pReal) Temperature
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
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real(pReal), dimension(6) :: Tstar_v
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real(pReal), dimension(3,3) :: Lp
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real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
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real(pReal), dimension(9,9) :: dLp_dTstar
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real(pReal), dimension(constitutive_phenomenological_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip,dgdot_dtauslip,tau_slip
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matID = phase_constitutionInstance(material_phase(ipc,ip,el))
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!* Calculation of Lp
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Lp = 0.0_pReal
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do i = 1,constitutive_phenomenological_Nslip(matID)
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tau_slip(i) = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_phenomenological_structure(matID)))
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gdot_slip(i) = constitutive_phenomenological_gdot0_slip(matID)*(abs(tau_slip(i))/state(ipc,ip,el)%p(i))**&
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constitutive_phenomenological_n_slip(matID)*sign(1.0_pReal,tau_slip(i))
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Lp = Lp + gdot_slip(i)*lattice_Sslip(:,:,i,constitutive_phenomenological_structure(matID))
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enddo
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!* Calculation of the tangent of Lp
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dLp_dTstar3333 = 0.0_pReal
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dLp_dTstar = 0.0_pReal
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do i = 1,constitutive_phenomenological_Nslip(matID)
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dgdot_dtauslip(i) = constitutive_phenomenological_gdot0_slip(matID)*(abs(tau_slip(i))/state(ipc,ip,el)%p(i))**&
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(constitutive_phenomenological_n_slip(matID)-1.0_pReal)*&
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constitutive_phenomenological_n_slip(matID)/state(ipc,ip,el)%p(i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
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dgdot_dtauslip(i)*lattice_Sslip(k,l,i,constitutive_phenomenological_structure(matID))* &
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lattice_Sslip(m,n,i,constitutive_phenomenological_structure(matID))
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enddo
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dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
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return
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end subroutine
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function constitutive_phenomenological_dotState(Tstar_v,Temperature,state,ipc,ip,el)
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!*********************************************************************
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!* rate of change of microstructure *
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!* INPUT: *
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!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
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!* - ipc : component-ID at current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!* OUTPUT: *
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!* - constitutive_dotState : evolution of state variable *
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!*********************************************************************
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use prec, only: pReal,pInt,p_vec
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use lattice, only: lattice_Sslip_v
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
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implicit none
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!* Definition of variables
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integer(pInt) ipc,ip,el
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integer(pInt) matID,i,n
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real(pReal) Temperature,tau_slip,gdot_slip
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
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real(pReal), dimension(6) :: Tstar_v
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real(pReal), dimension(constitutive_phenomenological_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
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constitutive_phenomenological_dotState,self_hardening
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matID = phase_constitutionInstance(material_phase(ipc,ip,el))
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n = constitutive_phenomenological_Nslip(matID)
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!* Self-Hardening of each system
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do i = 1,n
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tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_phenomenological_structure(matID)))
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gdot_slip = constitutive_phenomenological_gdot0_slip(matID)*(abs(tau_slip)/state(ipc,ip,el)%p(i))**&
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constitutive_phenomenological_n_slip(matID)*sign(1.0_pReal,tau_slip)
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self_hardening(i) = constitutive_phenomenological_h0(matID)*(1.0_pReal-state(ipc,ip,el)%p(i)/&
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constitutive_phenomenological_s_sat(matID))**constitutive_phenomenological_w0(matID)*abs(gdot_slip)
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enddo
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!$OMP CRITICAL (evilmatmul)
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constitutive_phenomenological_dotState = matmul(constitutive_phenomenological_hardeningMatrix(1:n,1:n,matID),self_hardening)
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!$OMP END CRITICAL (evilmatmul)
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return
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end function
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function constitutive_phenomenological_dotTemperature(Tstar_v,Temperature,state,ipc,ip,el)
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!*********************************************************************
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!* rate of change of microstructure *
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!* INPUT: *
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!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
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!* - ipc : component-ID at current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!* OUTPUT: *
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!* - constitutive_dotTemperature : evolution of temperature *
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!*********************************************************************
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use prec, only: pReal,pInt,p_vec
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use lattice, only: lattice_Sslip_v
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
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implicit none
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!* Definition of variables
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integer(pInt) ipc,ip,el
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integer(pInt) matID,i,n
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real(pReal) Temperature
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
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real(pReal), dimension(6) :: Tstar_v
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real(pReal) constitutive_phenomenological_dotTemperature
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constitutive_phenomenological_dotTemperature = 0.0_pReal
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return
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end function
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pure function constitutive_phenomenological_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
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!*********************************************************************
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!* return array of constitutive results *
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|
!* INPUT: *
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|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
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|
!* - dt : current time increment *
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|
!* - ipc : component-ID at current integration point *
|
|
!* - ip : current integration point *
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|
!* - el : current element *
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|
!*********************************************************************
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|
use prec, only: pReal,pInt,p_vec
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use lattice, only: lattice_Sslip_v
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use mesh, only: mesh_NcpElems,mesh_maxNips
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use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
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implicit none
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|
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!* Definition of variables
|
|
integer(pInt), intent(in) :: ipc,ip,el
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|
real(pReal), intent(in) :: dt,Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
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|
integer(pInt) matID,o,i,c,n
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|
real(pReal) tau_slip
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real(pReal), dimension(constitutive_phenomenological_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
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|
constitutive_phenomenological_postResults
|
|
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
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|
n = constitutive_phenomenological_Nslip(matID)
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|
c = 0_pInt
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|
constitutive_phenomenological_postResults = 0.0_pReal
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|
|
|
do o = 1,phase_Noutput(material_phase(ipc,ip,el))
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select case(constitutive_phenomenological_output(o,matID))
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|
|
|
case ('slipresistance')
|
|
constitutive_phenomenological_postResults(c+1:c+n) = state(ipc,ip,el)%p(1:n)
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|
c = c + n
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|
|
|
case ('rateofshear')
|
|
do i = 1,n
|
|
tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_phenomenological_structure(matID)))
|
|
constitutive_phenomenological_postResults(c+i) = sign(1.0_pReal,tau_slip)*constitutive_phenomenological_gdot0_slip(matID)*&
|
|
(abs(tau_slip)/state(ipc,ip,el)%p(i))**&
|
|
constitutive_phenomenological_n_slip(matID)
|
|
enddo
|
|
c = c + n
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|
|
|
end select
|
|
enddo
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|
|
|
return
|
|
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|
end function
|
|
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END MODULE
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