DAMASK_EICMD/src/kinematics_cleavage_opening.f90

!--------------------------------------------------------------------------------------------------
!> @author Luv Sharma, Max-Planck-Institut für Eisenforschung GmbH
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine incorporating kinematics resulting from opening of cleavage planes
!> @details to be done
!--------------------------------------------------------------------------------------------------
module kinematics_cleavage_opening
  use prec
  use IO
  use config
  use debug
  use math
  use lattice
  use material

  implicit none
  private

  integer, dimension(:), allocatable :: kinematics_cleavage_opening_instance

  type :: tParameters                                                                               !< container type for internal constitutive parameters
    integer :: &
      totalNcleavage
    integer, dimension(:),   allocatable :: &
      Ncleavage                                                                                     !< active number of cleavage systems per family
    real(pReal) :: &
      sdot0, &
      n
    real(pReal),   dimension(:),   allocatable :: &
      critLoad
    real(pReal), dimension(:,:,:,:), allocatable :: &
      cleavage_systems
  end type tParameters

  type(tParameters), dimension(:), allocatable :: param                                             !< containers of constitutive parameters (len Ninstance)

  public :: &
    kinematics_cleavage_opening_init, &
    kinematics_cleavage_opening_LiAndItsTangent

contains


!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine kinematics_cleavage_opening_init

  integer :: Ninstance,p
  character(len=pStringLen) :: extmsg = ''

  write(6,'(/,a)') ' <<<+-  kinematics_'//KINEMATICS_cleavage_opening_LABEL//' init  -+>>>'; flush(6)

  Ninstance = count(phase_kinematics == KINEMATICS_cleavage_opening_ID)
  if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
    write(6,'(a16,1x,i5,/)') '# instances:',Ninstance

  allocate(kinematics_cleavage_opening_instance(size(config_phase)), source=0)
  allocate(param(Ninstance))

  do p = 1, size(config_phase)
    kinematics_cleavage_opening_instance(p) = count(phase_kinematics(:,1:p) == kinematics_cleavage_opening_ID)
    if (all(phase_kinematics(:,p) /= KINEMATICS_cleavage_opening_ID)) cycle

    associate(prm => param(kinematics_cleavage_opening_instance(p)), &
              config => config_phase(p))

    prm%Ncleavage = config%getInts('ncleavage')
    prm%totalNcleavage = sum(prm%Ncleavage)

    prm%n         = config%getFloat('anisobrittle_ratesensitivity')
    prm%sdot0     = config%getFloat('anisobrittle_sdot0')

    prm%critLoad  = config%getFloats('anisobrittle_criticalload',requiredSize=size(prm%Ncleavage))

    prm%cleavage_systems  = lattice_SchmidMatrix_cleavage(prm%Ncleavage,config%getString('lattice_structure'),&
                                                          config%getFloat('c/a',defaultVal=0.0_pReal))

    ! expand: family => system
    prm%critLoad = math_expand(prm%critLoad, prm%Ncleavage)

    ! sanity checks
    if (prm%n            <= 0.0_pReal)  extmsg = trim(extmsg)//' anisobrittle_n'
    if (prm%sdot0        <= 0.0_pReal)  extmsg = trim(extmsg)//' anisobrittle_sdot0'
    if (any(prm%critLoad <  0.0_pReal)) extmsg = trim(extmsg)//' anisobrittle_critLoad'

!--------------------------------------------------------------------------------------------------
!  exit if any parameter is out of range
    if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'('//SOURCE_DAMAGE_ANISOBRITTLE_LABEL//')')

    end associate
  enddo

end subroutine kinematics_cleavage_opening_init


!--------------------------------------------------------------------------------------------------
!> @brief  contains the constitutive equation for calculating the velocity gradient
!--------------------------------------------------------------------------------------------------
subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, ip, el)

  integer, intent(in) :: &
    ipc, &                                                                                          !< grain number
    ip, &                                                                                           !< integration point number
    el                                                                                              !< element number
  real(pReal),   intent(in),  dimension(3,3) :: &
    S
  real(pReal),   intent(out), dimension(3,3) :: &
    Ld                                                                                              !< damage velocity gradient
  real(pReal),   intent(out), dimension(3,3,3,3) :: &
    dLd_dTstar                                                                                      !< derivative of Ld with respect to Tstar (4th-order tensor)
  integer :: &
    homog, damageOffset, &
    i, k, l, m, n
  real(pReal) :: &
    traction_d, traction_t, traction_n, traction_crit, &
    udotd, dudotd_dt, udott, dudott_dt, udotn, dudotn_dt

  homog = material_homogenizationAt(el)
  damageOffset = damageMapping(homog)%p(ip,el)

  Ld = 0.0_pReal
  dLd_dTstar = 0.0_pReal
  associate(prm => param(kinematics_cleavage_opening_instance(material_phaseAt(ipc,el))))
  do i = 1,prm%totalNcleavage
    traction_crit = prm%critLoad(i)* damage(homog)%p(damageOffset)**2.0_pReal

    traction_d = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,1,i))
    if (abs(traction_d) > tol_math_check + traction_crit) then
      udotd = sign(1.0_pReal,traction_d)* prm%sdot0 * ((abs(traction_d) - traction_crit)/traction_crit)**prm%n
      Ld = Ld + udotd*prm%cleavage_systems(1:3,1:3,1,i)
      dudotd_dt = sign(1.0_pReal,traction_d)*udotd*prm%n / (abs(traction_d) - traction_crit)
      forall (k=1:3,l=1:3,m=1:3,n=1:3) &
        dLd_dTstar(k,l,m,n) = dLd_dTstar(k,l,m,n) &
                            + dudotd_dt*prm%cleavage_systems(k,l,1,i) * prm%cleavage_systems(m,n,1,i)
    endif

    traction_t = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,2,i))
    if (abs(traction_t) > tol_math_check + traction_crit) then
      udott = sign(1.0_pReal,traction_t)* prm%sdot0 * ((abs(traction_t) - traction_crit)/traction_crit)**prm%n
      Ld = Ld + udott*prm%cleavage_systems(1:3,1:3,2,i)
      dudott_dt = sign(1.0_pReal,traction_t)*udott*prm%n / (abs(traction_t) - traction_crit)
      forall (k=1:3,l=1:3,m=1:3,n=1:3) &
        dLd_dTstar(k,l,m,n) = dLd_dTstar(k,l,m,n) &
                            + dudott_dt*prm%cleavage_systems(k,l,2,i) * prm%cleavage_systems(m,n,2,i)
    endif

    traction_n = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,3,i))
    if (abs(traction_n) > tol_math_check + traction_crit) then
      udotn = sign(1.0_pReal,traction_n)* prm%sdot0 * ((abs(traction_n) - traction_crit)/traction_crit)**prm%n
      Ld = Ld + udotn*prm%cleavage_systems(1:3,1:3,3,i)
      dudotn_dt = sign(1.0_pReal,traction_n)*udotn*prm%n / (abs(traction_n) - traction_crit)
      forall (k=1:3,l=1:3,m=1:3,n=1:3) &
        dLd_dTstar(k,l,m,n) = dLd_dTstar(k,l,m,n) &
                            + dudotn_dt*prm%cleavage_systems(k,l,3,i) * prm%cleavage_systems(m,n,3,i)
    endif
  enddo
  end associate

end subroutine kinematics_cleavage_opening_LiAndItsTangent

end module kinematics_cleavage_opening