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

 implicit none
 private
 integer, dimension(:), allocatable, private :: kinematics_cleavage_opening_instance

 type, private :: 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 :: &
     critDisp, &
     critLoad
 end type

! Begin Deprecated
 integer,                       dimension(:),           allocatable,         private :: &
   kinematics_cleavage_opening_totalNcleavage                                                       !< total number of cleavage systems
   
 integer,                       dimension(:,:),         allocatable,         private :: &
   kinematics_cleavage_opening_Ncleavage                                                            !< number of cleavage systems per family
   
 real(pReal),                   dimension(:),           allocatable,         private :: &
   kinematics_cleavage_opening_sdot_0, &
   kinematics_cleavage_opening_N

 real(pReal),                   dimension(:,:),         allocatable,         private :: &
   kinematics_cleavage_opening_critDisp, &
   kinematics_cleavage_opening_critLoad
! End Deprecated

 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()
 use debug, only: &
   debug_level,&
   debug_constitutive,&
   debug_levelBasic
 use config, only: &
   config_phase
 use IO, only: &
   IO_error
 use material, only: &
   phase_kinematics, &
   KINEMATICS_cleavage_opening_label, &
   KINEMATICS_cleavage_opening_ID
 use lattice, only: &
   lattice_maxNcleavageFamily, &
   lattice_NcleavageSystem

 integer, allocatable, dimension(:) :: tempInt
 real(pReal), allocatable, dimension(:) :: tempFloat

 integer :: maxNinstance,p,instance,kinematics

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

 maxNinstance = int(count(phase_kinematics == KINEMATICS_cleavage_opening_ID))
 if (maxNinstance == 0) return
 
 if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
   write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
 
 allocate(kinematics_cleavage_opening_instance(size(config_phase)), source=0)
 do p = 1, size(config_phase)
   kinematics_cleavage_opening_instance(p) = count(phase_kinematics(:,1:p) == kinematics_cleavage_opening_ID) ! ToDo: count correct?
 enddo
   
 allocate(kinematics_cleavage_opening_critDisp(lattice_maxNcleavageFamily,maxNinstance),  source=0.0_pReal) 
 allocate(kinematics_cleavage_opening_critLoad(lattice_maxNcleavageFamily,maxNinstance),  source=0.0_pReal) 
 allocate(kinematics_cleavage_opening_Ncleavage(lattice_maxNcleavageFamily,maxNinstance), source=0)
 allocate(kinematics_cleavage_opening_totalNcleavage(maxNinstance),                       source=0)
 allocate(kinematics_cleavage_opening_sdot_0(maxNinstance),                               source=0.0_pReal) 
 allocate(kinematics_cleavage_opening_N(maxNinstance),                                    source=0.0_pReal) 

 do p = 1, size(config_phase)
   if (all(phase_kinematics(:,p) /= KINEMATICS_cleavage_opening_ID)) cycle
   instance = kinematics_cleavage_opening_instance(p)
   kinematics_cleavage_opening_sdot_0(instance) = config_phase(p)%getFloat('anisobrittle_sdot0')
   kinematics_cleavage_opening_N(instance)      = config_phase(p)%getFloat('anisobrittle_ratesensitivity')
   tempInt = config_phase(p)%getInts('ncleavage')     
   kinematics_cleavage_opening_Ncleavage(1:size(tempInt),instance) = tempInt

   tempFloat = config_phase(p)%getFloats('anisobrittle_criticaldisplacement',requiredSize=size(tempInt))
   kinematics_cleavage_opening_critDisp(1:size(tempInt),instance) = tempFloat

   tempFloat = config_phase(p)%getFloats('anisobrittle_criticalload',requiredSize=size(tempInt))
   kinematics_cleavage_opening_critLoad(1:size(tempInt),instance) = tempFloat

   kinematics_cleavage_opening_Ncleavage(1:lattice_maxNcleavageFamily,instance) = &
       min(lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,p),&                            ! limit active cleavage systems per family to min of available and requested
           kinematics_cleavage_opening_Ncleavage(1:lattice_maxNcleavageFamily,instance))
     kinematics_cleavage_opening_totalNcleavage(instance)  = sum(kinematics_cleavage_opening_Ncleavage(:,instance)) ! how many cleavage systems altogether
     if (kinematics_cleavage_opening_sdot_0(instance) <= 0.0_pReal) &
       call IO_error(211,el=instance,ext_msg='sdot_0 ('//KINEMATICS_cleavage_opening_LABEL//')')
     if (any(kinematics_cleavage_opening_critDisp(1:size(tempInt),instance) < 0.0_pReal)) &
       call IO_error(211,el=instance,ext_msg='critical_displacement ('//KINEMATICS_cleavage_opening_LABEL//')')
     if (any(kinematics_cleavage_opening_critLoad(1:size(tempInt),instance) < 0.0_pReal)) &
       call IO_error(211,el=instance,ext_msg='critical_load ('//KINEMATICS_cleavage_opening_LABEL//')')
     if (kinematics_cleavage_opening_N(instance) <= 0.0_pReal) &
       call IO_error(211,el=instance,ext_msg='rate_sensitivity ('//KINEMATICS_cleavage_opening_LABEL//')')
 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)
 use math, only: &
   math_mul33xx33
 use material, only: &
   material_phase, &
   material_homogenizationAt, &
   damage, &
   damageMapping
 use lattice, only: &
   lattice_Scleavage, &
   lattice_maxNcleavageFamily, &
   lattice_NcleavageSystem
 
 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 :: &
   instance, phase, &
   homog, damageOffset, &
   f, i, index_myFamily, k, l, m, n
 real(pReal) :: &
   traction_d, traction_t, traction_n, traction_crit, &
   udotd, dudotd_dt, udott, dudott_dt, udotn, dudotn_dt

 phase = material_phase(ipc,ip,el)
 instance = kinematics_cleavage_opening_instance(phase)
 homog = material_homogenizationAt(el)
 damageOffset = damageMapping(homog)%p(ip,el)
 
 Ld = 0.0_pReal
 dLd_dTstar = 0.0_pReal
 do f = 1,lattice_maxNcleavageFamily
   index_myFamily = sum(lattice_NcleavageSystem(1:f-1,phase))                                       ! at which index starts my family
   do i = 1,kinematics_cleavage_opening_Ncleavage(f,instance)                                       ! process each (active) cleavage system in family
     traction_d    = math_mul33xx33(S,lattice_Scleavage(1:3,1:3,1,index_myFamily+i,phase))
     traction_t    = math_mul33xx33(S,lattice_Scleavage(1:3,1:3,2,index_myFamily+i,phase))
     traction_n    = math_mul33xx33(S,lattice_Scleavage(1:3,1:3,3,index_myFamily+i,phase))
     traction_crit = kinematics_cleavage_opening_critLoad(f,instance)* &
                     damage(homog)%p(damageOffset)*damage(homog)%p(damageOffset)
     udotd = &
       sign(1.0_pReal,traction_d)* &
       kinematics_cleavage_opening_sdot_0(instance)* &
       (max(0.0_pReal, abs(traction_d) - traction_crit)/traction_crit)**kinematics_cleavage_opening_N(instance)
     if (abs(udotd) > tol_math_check) then
       Ld = Ld + udotd*lattice_Scleavage(1:3,1:3,1,index_myFamily+i,phase)
       dudotd_dt = sign(1.0_pReal,traction_d)*udotd*kinematics_cleavage_opening_N(instance)/ &
                   max(0.0_pReal, 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*lattice_Scleavage(k,l,1,index_myFamily+i,phase)* &
                     lattice_Scleavage(m,n,1,index_myFamily+i,phase)
     endif                

     udott = &
       sign(1.0_pReal,traction_t)* &
       kinematics_cleavage_opening_sdot_0(instance)* &
       (max(0.0_pReal, abs(traction_t) - traction_crit)/traction_crit)**kinematics_cleavage_opening_N(instance)
     if (abs(udott) > tol_math_check) then
       Ld = Ld + udott*lattice_Scleavage(1:3,1:3,2,index_myFamily+i,phase)
       dudott_dt = sign(1.0_pReal,traction_t)*udott*kinematics_cleavage_opening_N(instance)/ &
                   max(0.0_pReal, 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*lattice_Scleavage(k,l,2,index_myFamily+i,phase)* &
                     lattice_Scleavage(m,n,2,index_myFamily+i,phase)
     endif                

     udotn = &
       sign(1.0_pReal,traction_n)* &
       kinematics_cleavage_opening_sdot_0(instance)* &
       (max(0.0_pReal, abs(traction_n) - traction_crit)/traction_crit)**kinematics_cleavage_opening_N(instance)
     if (abs(udotn) > tol_math_check) then
       Ld = Ld + udotn*lattice_Scleavage(1:3,1:3,3,index_myFamily+i,phase)
       dudotn_dt = sign(1.0_pReal,traction_n)*udotn*kinematics_cleavage_opening_N(instance)/ &
                   max(0.0_pReal, 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*lattice_Scleavage(k,l,3,index_myFamily+i,phase)* &
                     lattice_Scleavage(m,n,3,index_myFamily+i,phase)
     endif                
   enddo
 enddo
 
end subroutine kinematics_cleavage_opening_LiAndItsTangent

end module kinematics_cleavage_opening