!--------------------------------------------------------------------------------------------------
!> @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
!--------------------------------------------------------------------------------------------------
submodule(constitutive:constitutive_damage) kinematics_cleavage_opening
integer, dimension(:), allocatable :: kinematics_cleavage_opening_instance
type :: tParameters !< container type for internal constitutive parameters
integer :: &
sum_N_cl !< total number of cleavage planes
real(pReal) :: &
sdot0, & !< opening rate of cleavage planes
n !< damage rate sensitivity
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)
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
module function kinematics_cleavage_opening_init(kinematics_length) result(myKinematics)
integer, intent(in) :: kinematics_length
logical, dimension(:,:), allocatable :: myKinematics
integer :: Ninstance,p,k
integer, dimension(:), allocatable :: N_cl !< active number of cleavage systems per family
character(len=pStringLen) :: extmsg = ''
class(tNode), pointer :: &
phases, &
phase, &
pl, &
kinematics, &
kinematic_type
write(6,'(/,a)') ' <<<+- kinematics_cleavage_opening init -+>>>'
myKinematics = kinematics_active('cleavage_opening',kinematics_length)
Ninstance = count(myKinematics)
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance; flush(6)
if(Ninstance == 0) return
phases => material_root%get('phase')
allocate(param(Ninstance))
allocate(kinematics_cleavage_opening_instance(phases%length), source=0)
do p = 1, phases%length
if(any(myKinematics(:,p))) kinematics_cleavage_opening_instance(p) = count(myKinematics(:,1:p))
phase => phases%get(p)
pl => phase%get('plasticity')
if(count(myKinematics(:,p)) == 0) cycle
kinematics => phase%get('kinematics')
do k = 1, kinematics%length
if(myKinematics(k,p)) then
associate(prm => param(kinematics_cleavage_opening_instance(p)))
kinematic_type => kinematics%get(k)
N_cl = kinematic_type%get_asInts('N_cl')
prm%sum_N_cl = sum(abs(N_cl))
prm%n = kinematic_type%get_asFloat('q')
prm%sdot0 = kinematic_type%get_asFloat('dot_o')
prm%critLoad = kinematic_type%get_asFloats('g_crit',requiredSize=size(N_cl))
prm%cleavage_systems = lattice_SchmidMatrix_cleavage(N_cl,phase%get_asString('lattice'),&
phase%get_asFloat('c/a',defaultVal=0.0_pReal))
! expand: family => system
prm%critLoad = math_expand(prm%critLoad,N_cl)
! sanity checks
if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' q'
if (prm%sdot0 <= 0.0_pReal) extmsg = trim(extmsg)//' dot_o'
if (any(prm%critLoad < 0.0_pReal)) extmsg = trim(extmsg)//' g_crit'
!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(cleavage_opening)')
end associate
endif
enddo
enddo
end function kinematics_cleavage_opening_init
!--------------------------------------------------------------------------------------------------
!> @brief contains the constitutive equation for calculating the velocity gradient
!--------------------------------------------------------------------------------------------------
module 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%sum_N_cl
traction_crit = prm%critLoad(i)* damage(homog)%p(damageOffset)**2.0_pReal
traction_d = math_tensordot(S,prm%cleavage_systems(1:3,1:3,1,i))
if (abs(traction_d) > traction_crit + tol_math_check) 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_tensordot(S,prm%cleavage_systems(1:3,1:3,2,i))
if (abs(traction_t) > traction_crit + tol_math_check) 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_tensordot(S,prm%cleavage_systems(1:3,1:3,3,i))
if (abs(traction_n) > traction_crit + tol_math_check) 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 submodule kinematics_cleavage_opening