DAMASK_EICMD/src/plastic_phenopowerlaw.f90

!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine for phenomenological crystal plasticity formulation using a powerlaw
!! fitting
!--------------------------------------------------------------------------------------------------
module plastic_phenopowerlaw
 use prec, only: &
   pReal,&
   pInt

 implicit none
 private
 integer(pInt),                       dimension(:),     allocatable,         public, protected :: &
   plastic_phenopowerlaw_sizePostResults                                                       !< cumulative size of post results

 integer(pInt),                       dimension(:,:),   allocatable, target, public :: &
   plastic_phenopowerlaw_sizePostResult                                                        !< size of each post result output

 character(len=64),                   dimension(:,:),   allocatable, target, public :: &
   plastic_phenopowerlaw_output                                                                !< name of each post result output

 integer(pInt),                       dimension(:),     allocatable, target, public :: &
   plastic_phenopowerlaw_Noutput                                                               !< number of outputs per instance of this constitution

 integer(pInt),                       dimension(:),     allocatable,         private :: &
   totalNslip, &                                                         !< no. of slip system used in simulation
   totalNtwin                                                            !< no. of twin system used in simulation



 real(pReal),                         dimension(:,:,:),   allocatable,          private :: &
  
 interaction_SlipSlip, &                                               !< interaction factors slip - slip (input parameter)
   interaction_SlipTwin, &                                               !< interaction factors slip - twin (input parameter)
   interaction_TwinSlip, &                                               !< interaction factors twin - slip (input parameter)
  interaction_TwinTwin                                                  !< interaction factors twin - twin (input parameter)


 enum, bind(c)
   enumerator :: undefined_ID, &
                 resistance_slip_ID, &
                 accumulatedshear_slip_ID, &
                 shearrate_slip_ID, &
                 resolvedstress_slip_ID, &
                 totalshear_ID, &
                 resistance_twin_ID, &
                 accumulatedshear_twin_ID, &
                 shearrate_twin_ID, &
                 resolvedstress_twin_ID, &
                 totalvolfrac_twin_ID
 end enum
 integer(kind(undefined_ID)),         dimension(:,:),   allocatable,          private :: &
   plastic_phenopowerlaw_outputID                                                              !< ID of each post result output

 type, private :: tParameters                                                                       !< container type for internal constitutive parameters
   real(pReal) :: &
     gdot0_slip, &                                                                                  !< reference shear strain rate for slip
     gdot0_twin, &                                                                                  !< reference shear strain rate for twin
     n_slip, &                                                                                      !< stress exponent for slip
     n_twin, &                                                                                      !< stress exponent for twin
     spr, &                                                                                         !< push-up factor for slip saturation due to twinning
     twinB, &
     twinC, &
     twinD, &
     twinE, &
     h0_SlipSlip, &                                                                                 !< reference hardening slip - slip
     h0_TwinSlip, &                                                                                 !< reference hardening twin - slip
     h0_TwinTwin, &                                                                                 !< reference hardening twin - twin
     a_slip, &
     aTolResistance = 1.0_pReal, &                                                                  ! default absolute tolerance 1 Pa
     aTolShear      = 1.0e-6_pReal, &                                                               ! default absolute tolerance 1e-6
     aTolTwinfrac   = 1.0e-6_pReal                                                                  ! default absolute tolerance 1e-6
   integer(pInt), dimension(:),   allocatable :: &
     Nslip, &                                                                                       !< active number of slip systems per family
     Ntwin                                                                                          !< active number of twin systems per family
   real(pReal),   dimension(:),   allocatable :: &
     tau0_slip, &                                                                                   !< initial critical shear stress for slip
     tau0_twin, &                                                                                   !< initial critical shear stress for twin
     tausat_slip, &                                                                                 !< maximum critical shear stress for slip
     nonSchmidCoeff, &
     H_int, &                                                                                       !< per family hardening activity (optional)
     
     interaction_SlipSlip, &                                                                        !< slip resistance from slip activity
     interaction_SlipTwin, &                                                                        !< slip resistance from twin activity
     interaction_TwinSlip, &                                                                        !< twin resistance from slip activity
     interaction_TwinTwin                                                                           !< twin resistance from twin activity
 end type
 type(tParameters), dimension(:), allocatable, private :: param                                     !< containers of constitutive parameters (len Ninstance)

 type, private :: tPhenopowerlawState
   real(pReal), pointer,     dimension(:,:) :: &
     s_slip, &
     s_twin, &
     accshear_slip, &
     accshear_twin
   real(pReal), pointer,     dimension(:) :: &
     sumGamma, &
     sumF
 end type

 type(tPhenopowerlawState), allocatable, dimension(:), private :: &
   dotState, &
   state

 public :: &
   plastic_phenopowerlaw_init, &
   plastic_phenopowerlaw_LpAndItsTangent, &
   plastic_phenopowerlaw_dotState, &
   plastic_phenopowerlaw_postResults

contains


!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_init(fileUnit)
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
 use, intrinsic :: iso_fortran_env, only: &
   compiler_version, &
   compiler_options
#endif
 use prec, only: &
   dEq0
 use debug, only: &
   debug_level, &
   debug_constitutive,&
   debug_levelBasic
 use math, only: &
   math_Mandel3333to66, &
   math_Voigt66to3333, &
   math_expand
 use IO, only: &
   IO_read, &
   IO_lc, &
   IO_getTag, &
   IO_isBlank, &
   IO_stringPos, &
   IO_stringValue, &
   IO_floatValue, &
   IO_intValue, &
   IO_warning, &
   IO_error, &
   IO_timeStamp, &
   IO_EOF
 use material, only: &
   phase_plasticity, &
   phase_plasticityInstance, &
   phase_Noutput, &
   PLASTICITY_PHENOPOWERLAW_label, &
   PLASTICITY_PHENOPOWERLAW_ID, &
   material_phase, &
   plasticState, &
   MATERIAL_partPhase
 use lattice
 use numerics,only: &
   numerics_integrator

 implicit none
 integer(pInt), intent(in) :: fileUnit

 integer(pInt), allocatable, dimension(:) :: chunkPos
 integer(pInt) :: &
   maxNinstance, &
   instance,phase,j,k, f,o, &
   Nchunks_SlipSlip = 0_pInt, Nchunks_SlipTwin = 0_pInt, &
   Nchunks_TwinSlip = 0_pInt, Nchunks_TwinTwin = 0_pInt, &
   Nchunks_SlipFamilies = 0_pInt, Nchunks_TwinFamilies = 0_pInt, &
   Nchunks_TransFamilies = 0_pInt, Nchunks_nonSchmid = 0_pInt, &
   NipcMyPhase, &
   offset_slip, index_myFamily, index_otherFamily, &
   mySize=0_pInt,sizeState,sizeDotState, sizeDeltaState, &
   startIndex, endIndex
 character(len=65536) :: &
   tag       = '', &
   line      = '', &
   extmsg    = ''
 character(len=64) :: &
   outputtag = ''
 real(pReal), dimension(:), allocatable :: tempPerSlip

 write(6,'(/,a)')   ' <<<+-  constitutive_'//PLASTICITY_PHENOPOWERLAW_label//' init  -+>>>'
 write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"

 maxNinstance = int(count(phase_plasticity == PLASTICITY_PHENOPOWERLAW_ID),pInt)
 if (maxNinstance == 0_pInt) return

 if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
   write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance


 allocate(plastic_phenopowerlaw_sizePostResults(maxNinstance),                   source=0_pInt)
 allocate(plastic_phenopowerlaw_sizePostResult(maxval(phase_Noutput),maxNinstance), &
                                                                                 source=0_pInt)
 allocate(plastic_phenopowerlaw_output(maxval(phase_Noutput),maxNinstance))
          plastic_phenopowerlaw_output               = ''
 allocate(plastic_phenopowerlaw_outputID(maxval(phase_Noutput),maxNinstance),source=undefined_ID)
 
 allocate(plastic_phenopowerlaw_Noutput(maxNinstance),                       source=0_pInt)

 allocate(totalNslip(maxNinstance),                    source=0_pInt)
 allocate(totalNtwin(maxNinstance),                    source=0_pInt)
  allocate(param(maxNinstance))                                                                      ! one container of parameters per instance

 rewind(fileUnit)
 phase = 0_pInt
 do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= material_partPhase)         ! wind forward to <phase>
   line = IO_read(fileUnit)
 enddo

 parsingFile: do while (trim(line) /= IO_EOF)                                                       ! read through sections of phase part
   line = IO_read(fileUnit)
   if (IO_isBlank(line)) cycle                                                                      ! skip empty lines
   if (IO_getTag(line,'<','>') /= '') then                                                          ! stop at next part
     line = IO_read(fileUnit, .true.)                                                               ! reset IO_read
     exit
   endif
   if (IO_getTag(line,'[',']') /= '') then                                                          ! next phase
     phase = phase + 1_pInt                                                                         ! advance phase section counter
     if (phase_plasticity(phase) == PLASTICITY_PHENOPOWERLAW_ID) then
          instance = phase_plasticityInstance(phase)                                                     ! which instance of my plasticity is present phase
       Nchunks_SlipFamilies  = count(lattice_NslipSystem(:,phase) > 0_pInt)                         ! maximum number of slip families according to lattice type of current phase
       Nchunks_TwinFamilies  = count(lattice_NtwinSystem(:,phase) > 0_pInt)                         ! maximum number of twin families according to lattice type of current phase
       Nchunks_SlipSlip =     maxval(lattice_interactionSlipSlip(:,:,phase))
       Nchunks_SlipTwin =     maxval(lattice_interactionSlipTwin(:,:,phase))
       Nchunks_TwinSlip =     maxval(lattice_interactionTwinSlip(:,:,phase))
       Nchunks_TwinTwin =     maxval(lattice_interactionTwinTwin(:,:,phase))
       Nchunks_nonSchmid =    lattice_NnonSchmid(phase)
       if(allocated(tempPerSlip)) deallocate(tempPerSlip)
       !allocate(param(instance)%H_int,source=tempPerSlip) gfortran 5 does not support this
              allocate(param(instance)%H_int(Nchunks_SlipFamilies),source=0.0_pReal)
       allocate(param(instance)%interaction_SlipSlip(Nchunks_SlipSlip),source=0.0_pReal)
       allocate(param(instance)%interaction_SlipTwin(Nchunks_SlipTwin),source=0.0_pReal)
       allocate(param(instance)%interaction_TwinSlip(Nchunks_TwinSlip),source=0.0_pReal)
       allocate(param(instance)%interaction_TwinTwin(Nchunks_TwinTwin),source=0.0_pReal)
       allocate(param(instance)%nonSchmidCoeff(Nchunks_nonSchmid),source=0.0_pReal)

       allocate(tempPerSlip(Nchunks_SlipFamilies))
     endif
     cycle                                                                                          ! skip to next line
   endif
   if (phase > 0_pInt ) then; if (phase_plasticity(phase) == PLASTICITY_PHENOPOWERLAW_ID) then      ! one of my phases. Do not short-circuit here (.and. between if-statements), it's not safe in Fortran

     chunkPos = IO_stringPos(line)
     tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt))                                             ! extract key
   select case(tag)
     
       case ('(output)')
         outputtag = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
         plastic_phenopowerlaw_Noutput(instance) = plastic_phenopowerlaw_Noutput(instance) + 1_pInt ! assume valid output
         plastic_phenopowerlaw_output(plastic_phenopowerlaw_Noutput(instance),instance) = outputtag ! assume valid output
         select case(IO_lc(IO_stringValue(line,chunkPos,2_pInt)))
           case ('resistance_slip')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = resistance_slip_ID

           case ('accumulatedshear_slip','accumulated_shear_slip')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = accumulatedshear_slip_ID

           case ('shearrate_slip')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = shearrate_slip_ID

           case ('resolvedstress_slip')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = resolvedstress_slip_ID

           case ('totalshear')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = totalshear_ID

           case ('resistance_twin')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = resistance_twin_ID

           case ('accumulatedshear_twin','accumulated_shear_twin')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = accumulatedshear_twin_ID
             
           case ('shearrate_twin')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = shearrate_twin_ID

           case ('resolvedstress_twin')

             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = resolvedstress_twin_ID

           case ('totalvolfrac_twin')
             plastic_phenopowerlaw_outputID(plastic_phenopowerlaw_Noutput(instance),instance) = totalvolfrac_twin_ID

           case default
             plastic_phenopowerlaw_Noutput(instance) = plastic_phenopowerlaw_Noutput(instance) - 1_pInt ! correct for invalid

         end select
         
!--------------------------------------------------------------------------------------------------
! parameters depending on number of slip families
       case ('nslip')
         if (chunkPos(1) < Nchunks_SlipFamilies + 1_pInt) call IO_warning(50_pInt,ext_msg=extmsg)
         if (chunkPos(1) > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
         Nchunks_SlipFamilies = chunkPos(1) - 1_pInt                                                ! user specified number of (possibly) active slip families (e.g. 6 0 6 --> 3)
         allocate(param(instance)%Nslip(Nchunks_SlipFamilies),source=-1_pInt)
         do j = 1_pInt, Nchunks_SlipFamilies
           param(instance)%Nslip(j) = min(IO_intValue(line,chunkPos,1_pInt+j), &
                                          lattice_NslipSystem(j,phase))                             ! limit active slip systems per family to min of available and requested
         enddo
         totalNslip(instance) = sum(param(instance)%Nslip)                                          ! how many slip systems altogether
       
       case ('tausat_slip','tau0_slip','h_int')
         tempPerSlip = 0.0_pReal
         do j = 1_pInt, Nchunks_SlipFamilies
           if (param(instance)%Nslip(j) > 0_pInt) &
             tempPerSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo
         select case(tag)                                                                            ! here, all arrays are allocated automatically
           case ('tausat_slip')
             param(instance)%tausat_slip = tempPerSlip
           case ('tau0_slip')
             param(instance)%tau0_slip   = tempPerSlip
           case ('h_int')
             param(instance)%H_int       = tempPerSlip
         end select

!--------------------------------------------------------------------------------------------------
! parameters depending on number of twin families
       case ('ntwin')
         if (chunkPos(1) < Nchunks_TwinFamilies + 1_pInt) call IO_warning(51_pInt,ext_msg=extmsg)
         if (chunkPos(1) > Nchunks_TwinFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
         Nchunks_TwinFamilies = chunkPos(1) - 1_pInt
         allocate(param(instance)%Ntwin(Nchunks_TwinFamilies),source=-1_pInt)
         do j = 1_pInt, Nchunks_TwinFamilies
           param(instance)%Ntwin(j) = min(IO_intValue(line,chunkPos,1_pInt+j), &
                                          lattice_NtwinSystem(j,phase))                             ! limit active twin systems per family to min of available and requested
         enddo
         totalNtwin(instance) = sum(param(instance)%Ntwin)                                          ! how many twin systems altogether

       case ('tau0_twin')
         allocate(param(instance)%tau0_twin(Nchunks_TwinFamilies),source=0.0_pReal)
         do j = 1_pInt, Nchunks_TwinFamilies
           if (param(instance)%Ntwin(j) > 0_pInt) &
             param(instance)%tau0_twin(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

!--------------------------------------------------------------------------------------------------
! parameters depending on number of interactions
       case ('interaction_slipslip')
         if (chunkPos(1) < 1_pInt + Nchunks_SlipSlip) call IO_warning(52_pInt,ext_msg=extmsg)
         do j = 1_pInt, Nchunks_SlipSlip
           param(instance)%interaction_SlipSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

       case ('interaction_sliptwin')
         if (chunkPos(1) < 1_pInt + Nchunks_SlipTwin) call IO_warning(52_pInt,ext_msg=extmsg)
         do j = 1_pInt, Nchunks_SlipTwin
           param(instance)%interaction_SlipTwin(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

       case ('interaction_twinslip')
         if (chunkPos(1) < 1_pInt + Nchunks_TwinSlip) call IO_warning(52_pInt,ext_msg=extmsg)
         do j = 1_pInt, Nchunks_TwinSlip
           param(instance)%interaction_TwinSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

       case ('interaction_twintwin')
         if (chunkPos(1) < 1_pInt + Nchunks_TwinTwin) call IO_warning(52_pInt,ext_msg=extmsg)
         do j = 1_pInt, Nchunks_TwinTwin
           param(instance)%interaction_TwinTwin(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

       case ('nonschmid_coefficients')
         if (chunkPos(1) < 1_pInt + Nchunks_nonSchmid) call IO_warning(52_pInt,ext_msg=extmsg)
         do j = 1_pInt,Nchunks_nonSchmid
           param(instance)%nonSchmidCoeff(j) = IO_floatValue(line,chunkPos,1_pInt+j)
         enddo

!--------------------------------------------------------------------------------------------------
! parameters independent of number of slip/twin systems
       case ('gdot0_slip')
         param(instance)%gdot0_slip = IO_floatValue(line,chunkPos,2_pInt)
       case ('n_slip')
         param(instance)%n_slip = IO_floatValue(line,chunkPos,2_pInt)
       case ('a_slip', 'w0_slip')
         param(instance)%a_slip = IO_floatValue(line,chunkPos,2_pInt)
       case ('gdot0_twin')
         param(instance)%gdot0_twin = IO_floatValue(line,chunkPos,2_pInt)
       case ('n_twin')
         param(instance)%n_twin = IO_floatValue(line,chunkPos,2_pInt)
       case ('s_pr')
         param(instance)%spr = IO_floatValue(line,chunkPos,2_pInt)
       case ('twin_b')
         param(instance)%twinB = IO_floatValue(line,chunkPos,2_pInt)
       case ('twin_c')
         param(instance)%twinC = IO_floatValue(line,chunkPos,2_pInt)
       case ('twin_d')
         param(instance)%twinD = IO_floatValue(line,chunkPos,2_pInt)
       case ('twin_e')
         param(instance)%twinE = IO_floatValue(line,chunkPos,2_pInt)
       case ('h0_slipslip')
         param(instance)%h0_SlipSlip = IO_floatValue(line,chunkPos,2_pInt)
       case ('h0_twinslip')
         param(instance)%h0_TwinSlip = IO_floatValue(line,chunkPos,2_pInt)
       case ('h0_twintwin')
         param(instance)%h0_TwinTwin = IO_floatValue(line,chunkPos,2_pInt)
       case ('atol_resistance')
         param(instance)%aTolResistance = IO_floatValue(line,chunkPos,2_pInt)
       case ('atol_shear')
         param(instance)%aTolShear      = IO_floatValue(line,chunkPos,2_pInt)
       case ('atol_twinfrac')
         param(instance)%aTolTwinfrac   = IO_floatValue(line,chunkPos,2_pInt)
       case default

     end select
   endif; endif
 enddo parsingFile

 sanityChecks: do phase = 1_pInt, size(phase_plasticity)
   myPhase: if (phase_plasticity(phase) == PLASTICITY_phenopowerlaw_ID) then
     instance = phase_plasticityInstance(phase)
     totalNslip(instance)  = sum(param(instance)%Nslip)           ! how many slip systems altogether. ToDo: ok for unallocated Nslip
     totalNtwin(instance)  = sum(param(instance)%Ntwin)           ! how many twin systems altogether. ToDo: ok for unallocated Ntwin
     slipActive: if (allocated(param(instance)%Nslip)) then
       if (any(param(instance)%tau0_slip < 0.0_pReal .and. &
               param(instance)%Nslip(:) > 0)) &
         call IO_error(211_pInt,el=instance,ext_msg='tau0_slip ('//PLASTICITY_PHENOPOWERLAW_label//')')
       if (param(instance)%gdot0_slip <= 0.0_pReal) &
         call IO_error(211_pInt,el=instance,ext_msg='gdot0_slip ('//PLASTICITY_PHENOPOWERLAW_label//')')
       if (param(instance)%n_slip <= 0.0_pReal) &
         call IO_error(211_pInt,el=instance,ext_msg='n_slip ('//PLASTICITY_PHENOPOWERLAW_label//')')
       if (any(param(instance)%tausat_slip <= 0.0_pReal .and. &
               param(instance)%Nslip(:) > 0)) &
         call IO_error(211_pInt,el=instance,ext_msg='tausat_slip ('//PLASTICITY_PHENOPOWERLAW_label//')')
       if (any(dEq0(param(instance)%a_slip) .and. param(instance)%Nslip(:) > 0)) &
         call IO_error(211_pInt,el=instance,ext_msg='a_slip ('//PLASTICITY_PHENOPOWERLAW_label//')')
      endif slipActive
      
     twinActive: if (allocated(param(instance)%Ntwin)) then
     !    if (any(param(instance)%tau0_twin < 0.0_pReal .and. &
    !           param(instance)%Ntwin(:) > 0)) &
    !     call IO_error(211_pInt,el=instance,ext_msg='tau0_twin ('//PLASTICITY_PHENOPOWERLAW_label//')')
    !   if (    param(instance)%gdot0_twin <= 0.0_pReal .and. &
    !       any(param(instance)%Ntwin(:) > 0)) &
    !     call IO_error(211_pInt,el=instance,ext_msg='gdot0_twin ('//PLASTICITY_PHENOPOWERLAW_label//')')
    !   if (    param(instance)%n_twin <= 0.0_pReal .and. &
    !      any(param(instance)%Ntwin(:) > 0)) &
    !     call IO_error(211_pInt,el=instance,ext_msg='n_twin ('//PLASTICITY_PHENOPOWERLAW_label//')')
     endif twinActive

     if (param(instance)%aTolResistance <= 0.0_pReal) &
       call IO_error(211_pInt,el=instance,ext_msg='aTolResistance ('//PLASTICITY_PHENOPOWERLAW_label//')')   
     if (param(instance)%aTolShear      <= 0.0_pReal) &
       call IO_error(211_pInt,el=instance,ext_msg='aTolShear ('//PLASTICITY_PHENOPOWERLAW_label//')')
     if (param(instance)%aTolTwinfrac   <= 0.0_pReal) &
       call IO_error(211_pInt,el=instance,ext_msg='aTolTwinfrac ('//PLASTICITY_PHENOPOWERLAW_label//')')
   endif myPhase
 enddo sanityChecks
 

 !--------------------------------------------------------------------------------------------------
! allocation of variables whose size depends on the total number of active slip systems
 allocate(interaction_SlipSlip(maxval(totalNslip),maxval(totalNslip),maxNinstance), source=0.0_pReal)
 allocate(interaction_SlipTwin(maxval(totalNslip),maxval(totalNtwin),maxNinstance), source=0.0_pReal)
 allocate(interaction_TwinSlip(maxval(totalNtwin),maxval(totalNslip),maxNinstance), source=0.0_pReal)
 allocate(interaction_TwinTwin(maxval(totalNtwin),maxval(totalNtwin),maxNinstance), source=0.0_pReal)


 allocate(state(maxNinstance))
 allocate(dotState(maxNinstance))

 initializeInstances: do phase = 1_pInt, size(phase_plasticity)                                     ! loop through all phases in material.config

   myPhase2: if (phase_plasticity(phase) == PLASTICITY_phenopowerlaw_ID) then                       ! only consider my phase
     NipcMyPhase = count(material_phase == phase)                                                   ! number of IPCs containing my phase
     instance = phase_plasticityInstance(phase)                                                     ! which instance of my phase

!--------------------------------------------------------------------------------------------------
!  Determine size of postResults array
     outputsLoop: do o = 1_pInt,plastic_phenopowerlaw_Noutput(instance)
       select case(plastic_phenopowerlaw_outputID(o,instance))
         case(resistance_slip_ID, &
              shearrate_slip_ID, &
              accumulatedshear_slip_ID, &
              resolvedstress_slip_ID &
              )
           mySize = totalNslip(instance)
         case(resistance_twin_ID, &
              shearrate_twin_ID, &
              accumulatedshear_twin_ID, &
              resolvedstress_twin_ID &
              )
           mySize = totalNtwin(instance)
         case(totalshear_ID, &
              totalvolfrac_twin_ID &
              )
           mySize = 1_pInt
         case default
       end select

       outputFound: if (mySize > 0_pInt) then
         plastic_phenopowerlaw_sizePostResult(o,instance) = mySize
         plastic_phenopowerlaw_sizePostResults(instance)  = plastic_phenopowerlaw_sizePostResults(instance) + mySize
       endif outputFound
     enddo outputsLoop
!--------------------------------------------------------------------------------------------------
! allocate state arrays
     sizeState = totalNslip(instance) &                         ! s_slip
               + totalNtwin(instance) &                         ! s_twin
               + 2_pInt &                                                             ! sum(gamma) + sum(f)
               + totalNslip(instance) &                         ! accshear_slip
               + totalNtwin(instance)                           ! accshear_twin

     sizeDotState = sizeState
     sizeDeltaState = 0_pInt
     plasticState(phase)%sizeState = sizeState
     plasticState(phase)%sizeDotState = sizeDotState
     plasticState(phase)%sizeDeltaState = sizeDeltaState
     plasticState(phase)%sizePostResults = plastic_phenopowerlaw_sizePostResults(instance)
     plasticState(phase)%nSlip =totalNslip(instance)
     plasticState(phase)%nTwin =totalNtwin(instance)
     plasticState(phase)%nTrans=0_pInt
     allocate(plasticState(phase)%aTolState          (   sizeState),             source=0.0_pReal)
     allocate(plasticState(phase)%state0             (   sizeState,NipcMyPhase), source=0.0_pReal)
     allocate(plasticState(phase)%partionedState0    (   sizeState,NipcMyPhase), source=0.0_pReal)
     allocate(plasticState(phase)%subState0          (   sizeState,NipcMyPhase), source=0.0_pReal)
     allocate(plasticState(phase)%state              (   sizeState,NipcMyPhase), source=0.0_pReal)
     allocate(plasticState(phase)%dotState           (sizeDotState,NipcMyPhase), source=0.0_pReal)
     allocate(plasticState(phase)%deltaState       (sizeDeltaState,NipcMyPhase), source=0.0_pReal)
     if (any(numerics_integrator == 1_pInt)) then
       allocate(plasticState(phase)%previousDotState (sizeDotState,NipcMyPhase),source=0.0_pReal)
       allocate(plasticState(phase)%previousDotState2(sizeDotState,NipcMyPhase),source=0.0_pReal)
     endif
     if (any(numerics_integrator == 4_pInt)) &
       allocate(plasticState(phase)%RK4dotState      (sizeDotState,NipcMyPhase), source=0.0_pReal)
     if (any(numerics_integrator == 5_pInt)) &
       allocate(plasticState(phase)%RKCK45dotState (6,sizeDotState,NipcMyPhase), source=0.0_pReal)

     offset_slip = plasticState(phase)%nSlip+plasticState(phase)%nTwin+2_pInt
     plasticState(phase)%slipRate => &
       plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
     plasticState(phase)%accumulatedSlip => &
       plasticState(phase)%state(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)

!--------------------------------------------------------------------------------------------------
! calculate hardening matrices and extend intitial values (per family -> per system)
     mySlipFamilies: do f = 1_pInt,size(param(instance)%Nslip,1)                                    ! >>> interaction slip -- X
       index_myFamily = sum(param(instance)%Nslip(1:f-1_pInt))
       
       mySlipSystems: do j = 1_pInt,param(instance)%Nslip(f)
         otherSlipFamilies: do o = 1_pInt,size(param(instance)%Nslip,1)
           index_otherFamily = sum(param(instance)%Nslip(1:o-1_pInt))
           otherSlipSystems: do k = 1_pInt,param(instance)%Nslip(o)
             interaction_SlipSlip(index_myFamily+j,index_otherFamily+k,instance) = &
                 param(instance)%interaction_SlipSlip(lattice_interactionSlipSlip( &
                                                                   sum(lattice_NslipSystem(1:f-1,phase))+j, &
                                                                   sum(lattice_NslipSystem(1:o-1,phase))+k, &
                                                                   phase))
         enddo otherSlipSystems; enddo otherSlipFamilies

         twinFamilies: do o = 1_pInt,size(param(instance)%Ntwin,1)
           index_otherFamily = sum(param(instance)%Ntwin(1:o-1_pInt))
           twinSystems: do k = 1_pInt,param(instance)%Ntwin(o)
             interaction_SlipTwin(index_myFamily+j,index_otherFamily+k,instance) = &
                 param(instance)%interaction_SlipTwin(lattice_interactionSlipTwin( &
                                                                   sum(lattice_NslipSystem(1:f-1_pInt,phase))+j, &
                                                                   sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
                                                                   phase))
         enddo twinSystems; enddo twinFamilies
       enddo mySlipSystems
     enddo mySlipFamilies

     myTwinFamilies: do f = 1_pInt,size(param(instance)%Ntwin,1)                                    ! >>> interaction twin -- X
       index_myFamily = sum(param(instance)%Ntwin(1:f-1_pInt))
       myTwinSystems: do j = 1_pInt,param(instance)%Ntwin(f)
         slipFamilies: do o = 1_pInt,size(param(instance)%Nslip,1)
           index_otherFamily = sum(param(instance)%Nslip(1:o-1_pInt))
           slipSystems: do k = 1_pInt,param(instance)%Nslip(o)
             interaction_TwinSlip(index_myFamily+j,index_otherFamily+k,instance) = &
                 param(instance)%interaction_TwinSlip(lattice_interactionTwinSlip( &
                                                                   sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
                                                                   sum(lattice_NslipSystem(1:o-1_pInt,phase))+k, &
                                                                   phase))
         enddo slipSystems; enddo slipFamilies

         otherTwinFamilies: do o = 1_pInt,size(param(instance)%Ntwin,1)
           index_otherFamily = sum(param(instance)%Ntwin(1:o-1_pInt))
           otherTwinSystems: do k = 1_pInt,param(instance)%Ntwin(o)
             interaction_TwinTwin(index_myFamily+j,index_otherFamily+k,instance) = &
                 param(instance)%interaction_TwinTwin(lattice_interactionTwinTwin( &
                                                                   sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
                                                                   sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
                                                                   phase))
         enddo otherTwinSystems; enddo otherTwinFamilies
       enddo myTwinSystems
     enddo myTwinFamilies

!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
     startIndex = 1_pInt
     endIndex   = totalNslip(instance)
     state   (instance)%s_slip=>plasticState(phase)%state   (startIndex:endIndex,:)
     dotState(instance)%s_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
     plasticState(phase)%state0(startIndex:endIndex,:) = &
       spread(math_expand(param(instance)%tau0_slip, param(instance)%Nslip), 2, NipcMyPhase)

     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolResistance

     startIndex = endIndex + 1_pInt
     endIndex   = endIndex + totalNtwin(instance)
     state   (instance)%s_twin=>plasticState(phase)%state   (startIndex:endIndex,:)
     dotState(instance)%s_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
     plasticState(phase)%state0(startIndex:endIndex,:) = &
       spread(math_expand(param(instance)%tau0_twin, param(instance)%Ntwin), 2, NipcMyPhase)
     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolResistance

     startIndex = endIndex + 1_pInt
     endIndex   = endIndex + 1_pInt
     state   (instance)%sumGamma=>plasticState(phase)%state   (startIndex,:)
     dotState(instance)%sumGamma=>plasticState(phase)%dotState(startIndex,:)
     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolShear

     startIndex = endIndex + 1_pInt
     endIndex   = endIndex + 1_pInt
     state   (instance)%sumF=>plasticState(phase)%state   (startIndex,:)
     dotState(instance)%sumF=>plasticState(phase)%dotState(startIndex,:)
     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolTwinFrac

     startIndex = endIndex + 1_pInt
     endIndex   = endIndex + totalNslip(instance)
     state   (instance)%accshear_slip=>plasticState(phase)%state   (startIndex:endIndex,:)
     dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolShear
     ! global alias
     plasticState(phase)%slipRate =>plasticState(phase)%dotState(startIndex:endIndex,:)
     plasticState(phase)%accumulatedSlip =>plasticState(phase)%state(startIndex:endIndex,:)

     startIndex = endIndex + 1_pInt
     endIndex   = endIndex + totalNtwin(instance)
     state   (instance)%accshear_twin=>plasticState(phase)%state   (startIndex:endIndex,:)
     dotState(instance)%accshear_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
     plasticState(phase)%aTolState(startIndex:endIndex) = param(instance)%aTolShear

   endif myPhase2
 enddo initializeInstances


end subroutine plastic_phenopowerlaw_init


!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,ipc,ip,el)
 use prec, only: &
   dNeq0
 use math, only: &
   math_Plain3333to99, &
   math_Mandel6to33
 use lattice, only: &
   lattice_Sslip, &
   lattice_Sslip_v, &
   lattice_Stwin, &
   lattice_Stwin_v, &
   lattice_maxNslipFamily, &
   lattice_maxNtwinFamily, &
   lattice_NslipSystem, &
   lattice_NtwinSystem, &
   lattice_NnonSchmid
 use material, only: &
   phaseAt, phasememberAt, &
   phase_plasticityInstance

 implicit none
 real(pReal), dimension(3,3), intent(out) :: &
   Lp                                                                                               !< plastic velocity gradient
 real(pReal), dimension(9,9), intent(out) :: &
   dLp_dTstar99                                                                                     !< derivative of Lp with respect to 2nd Piola Kirchhoff stress

 integer(pInt),               intent(in) :: &
   ipc, &                                                                                           !< component-ID of integration point
   ip, &                                                                                            !< integration point
   el                                                                                               !< element
 real(pReal), dimension(6),   intent(in) :: &
   Tstar_v                                                                                          !< 2nd Piola Kirchhoff stress tensor in Mandel notation

 integer(pInt) :: &
   instance, &
   index_myFamily, &
   f,i,j,k,l,m,n, &
   of, &
   ph
 real(pReal) :: &
   tau_slip_pos,tau_slip_neg, &
   gdot_slip_pos,gdot_slip_neg, &
   dgdot_dtauslip_pos,dgdot_dtauslip_neg, &
   gdot_twin,dgdot_dtautwin,tau_twin
 real(pReal), dimension(3,3,3,3) :: &
   dLp_dTstar3333                                                                                   !< derivative of Lp with respect to Tstar as 4th order tensor
 real(pReal), dimension(3,3,2) :: &
   nonSchmid_tensor

 of = phasememberAt(ipc,ip,el)
 ph = phaseAt(ipc,ip,el)
 instance = phase_plasticityInstance(ph)

 Lp = 0.0_pReal
 dLp_dTstar3333 = 0.0_pReal
 dLp_dTstar99 = 0.0_pReal

!--------------------------------------------------------------------------------------------------
! Slip part
 j = 0_pInt
 slipFamilies: do f = 1_pInt,size(param(instance)%Nslip,1)
   index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph))                                          ! at which index starts my family
   slipSystems: do i = 1_pInt,param(instance)%Nslip(f)
     j = j+1_pInt

     ! Calculation of Lp
     tau_slip_pos  = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
     tau_slip_neg  = tau_slip_pos
     nonSchmid_tensor(1:3,1:3,1) = lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
     nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,1)
     do k = 1,lattice_NnonSchmid(ph)
       tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
       tau_slip_neg = tau_slip_neg + param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
       nonSchmid_tensor(1:3,1:3,1) = nonSchmid_tensor(1:3,1:3,1) + param(instance)%nonSchmidCoeff(k)*&
                                           lattice_Sslip(1:3,1:3,2*k,index_myFamily+i,ph)
       nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,2) + param(instance)%nonSchmidCoeff(k)*&
                                           lattice_Sslip(1:3,1:3,2*k+1,index_myFamily+i,ph)
     enddo
     gdot_slip_pos = 0.5_pReal*param(instance)%gdot0_slip* &
                    ((abs(tau_slip_pos)/(state(instance)%s_slip(j,of))) &
                    **param(instance)%n_slip)*sign(1.0_pReal,tau_slip_pos)

     gdot_slip_neg = 0.5_pReal*param(instance)%gdot0_slip* &
                    ((abs(tau_slip_neg)/(state(instance)%s_slip(j,of))) &
                    **param(instance)%n_slip)*sign(1.0_pReal,tau_slip_neg)

     Lp = Lp + (1.0_pReal-state(instance)%sumF(of))*&                                             ! 1-F
               (gdot_slip_pos+gdot_slip_neg)*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)

     ! Calculation of the tangent of Lp
     if (dNeq0(gdot_slip_pos)) then
       dgdot_dtauslip_pos = gdot_slip_pos*param(instance)%n_slip/tau_slip_pos
       forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
         dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
                                   dgdot_dtauslip_pos*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
                                                     nonSchmid_tensor(m,n,1)
     endif

     if (dNeq0(gdot_slip_neg)) then
       dgdot_dtauslip_neg = gdot_slip_neg*param(instance)%n_slip/tau_slip_neg
       forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
         dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
                                   dgdot_dtauslip_neg*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
                                                     nonSchmid_tensor(m,n,2)
     endif
   enddo slipSystems
 enddo slipFamilies

!--------------------------------------------------------------------------------------------------
! Twinning part
 j = 0_pInt
 twinFamilies: do f = 1_pInt,size(param(instance)%Ntwin,1)
   index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph))                                      ! at which index starts my family
   twinSystems: do i = 1_pInt,param(instance)%Ntwin(f)
     j = j+1_pInt

     ! Calculation of Lp
     tau_twin  = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
     gdot_twin = (1.0_pReal-state(instance)%sumF(of))*&                                          ! 1-F
                    param(instance)%gdot0_twin*&
                    (abs(tau_twin)/state(instance)%s_twin(j,of))**&
                    param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
     Lp = Lp + gdot_twin*lattice_Stwin(1:3,1:3,index_myFamily+i,ph)

     ! Calculation of the tangent of Lp
     if (dNeq0(gdot_twin)) then
       dgdot_dtautwin = gdot_twin*param(instance)%n_twin/tau_twin
       forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
         dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
                                   dgdot_dtautwin*lattice_Stwin(k,l,index_myFamily+i,ph)* &
                                                  lattice_Stwin(m,n,index_myFamily+i,ph)
     endif
   enddo twinSystems
 enddo twinFamilies

 dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)


end subroutine plastic_phenopowerlaw_LpAndItsTangent

!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_dotState(Tstar_v,ipc,ip,el)
 use lattice, only: &
   lattice_Sslip_v, &
   lattice_Stwin_v, &
   lattice_maxNslipFamily, &
   lattice_maxNtwinFamily, &
   lattice_NslipSystem, &
   lattice_NtwinSystem, &
   lattice_shearTwin, &
   lattice_NnonSchmid
 use material, only: &
   material_phase, &
   phaseAt, phasememberAt, &
   plasticState, &
   phase_plasticityInstance

 implicit none
 real(pReal), dimension(6),  intent(in) :: &
   Tstar_v                                                                                          !< 2nd Piola Kirchhoff stress tensor in Mandel notation
 integer(pInt),              intent(in) :: &
   ipc, &                                                                                           !< component-ID of integration point
   ip, &                                                                                            !< integration point
   el                                                                                               !< element                                                                                    !< microstructure state

 integer(pInt) :: &
   instance,ph, &
   nSlip,nTwin, &
   f,i,j,k, &
   index_Gamma,index_F,index_myFamily, &
   offset_accshear_slip,offset_accshear_twin, &
   of
 real(pReal) :: &
   c_SlipSlip,c_TwinSlip,c_TwinTwin, &
   ssat_offset, &
   tau_slip_pos,tau_slip_neg,tau_twin

 real(pReal), dimension(totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
   gdot_slip,left_SlipSlip,left_SlipTwin,right_SlipSlip,right_TwinSlip
 real(pReal), dimension(totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
   gdot_twin,left_TwinSlip,left_TwinTwin,right_SlipTwin,right_TwinTwin

 of = phasememberAt(ipc,ip,el)
 ph = phaseAt(ipc,ip,el)
 instance = phase_plasticityInstance(ph)

 nSlip = totalNslip(instance)
 nTwin = totalNtwin(instance)

 index_Gamma = nSlip + nTwin + 1_pInt
 index_F     = nSlip + nTwin + 2_pInt
 offset_accshear_slip = nSlip + nTwin + 2_pInt
 offset_accshear_twin = nSlip + nTwin + 2_pInt + nSlip
 plasticState(ph)%dotState(:,of) = 0.0_pReal

!--------------------------------------------------------------------------------------------------
! system-independent (nonlinear) prefactors to M_Xx (X influenced by x) matrices
 c_SlipSlip = param(instance)%h0_slipslip*&
              (1.0_pReal + param(instance)%twinC*plasticState(ph)%state(index_F,of)**&
                                                           param(instance)%twinB)
 c_TwinSlip = param(instance)%h0_TwinSlip*&
              plasticState(ph)%state(index_Gamma,of)**param(instance)%twinE
 c_TwinTwin = param(instance)%h0_TwinTwin*&
              plasticState(ph)%state(index_F,of)**param(instance)%twinD

!--------------------------------------------------------------------------------------------------
!  calculate left and right vectors and calculate dot gammas
 ssat_offset = param(instance)%spr*sqrt(plasticState(ph)%state(index_F,of))
 j = 0_pInt
 slipFamilies1: do f =1_pInt,size(param(instance)%Nslip,1)
   index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph))                                         ! at which index starts my family
   slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
     j = j+1_pInt
     left_SlipSlip(j) = 1.0_pReal + param(instance)%H_int(f)                         ! modified no system-dependent left part
     left_SlipTwin(j) = 1.0_pReal                                                                   ! no system-dependent left part
     right_SlipSlip(j) = abs(1.0_pReal-plasticState(ph)%state(j,of) / &
                                    (param(instance)%tausat_slip(f)+ssat_offset)) &
                         **param(instance)%a_slip&
                         *sign(1.0_pReal,1.0_pReal-plasticState(ph)%state(j,of) / &
                                    (param(instance)%tausat_slip(f)+ssat_offset))
     right_TwinSlip(j) = 1.0_pReal                                                                  ! no system-dependent part

!--------------------------------------------------------------------------------------------------
! Calculation of dot gamma
     tau_slip_pos  = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
     tau_slip_neg  = tau_slip_pos
     nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
       tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,  index_myFamily+i,ph))
       tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
     enddo nonSchmidSystems
     gdot_slip(j) = param(instance)%gdot0_slip*0.5_pReal* &
                  ((abs(tau_slip_pos)/(plasticState(ph)%state(j,of)))**param(instance)%n_slip &
                  *sign(1.0_pReal,tau_slip_pos) &
                  +(abs(tau_slip_neg)/(plasticState(ph)%state(j,of)))**param(instance)%n_slip &
                  *sign(1.0_pReal,tau_slip_neg))
   enddo slipSystems1
 enddo slipFamilies1



 j = 0_pInt
 twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
   index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph))                                         ! at which index starts my family
   twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
     j = j+1_pInt
     left_TwinSlip(j)  = 1.0_pReal                                                                  ! no system-dependent left part
     left_TwinTwin(j)  = 1.0_pReal                                                                  ! no system-dependent left part
     right_SlipTwin(j) = 1.0_pReal                                                                  ! no system-dependent right part
     right_TwinTwin(j) = 1.0_pReal                                                                  ! no system-dependent right part

!--------------------------------------------------------------------------------------------------
! Calculation of dot vol frac
     tau_twin  = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
     gdot_twin(j) = (1.0_pReal-plasticState(ph)%state(index_F,of))*&                                       ! 1-F
                    param(instance)%gdot0_twin*&
                    (abs(tau_twin)/plasticState(ph)%state(nslip+j,of))**&
                    param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
    enddo twinSystems1
  enddo twinFamilies1

!--------------------------------------------------------------------------------------------------
! calculate the overall hardening based on above
 j = 0_pInt
 slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
   slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
     j = j+1_pInt
     plasticState(ph)%dotState(j,of) = &                                                            ! evolution of slip resistance j
       c_SlipSlip * left_SlipSlip(j) * &
       dot_product(interaction_SlipSlip(j,1:totalNslip(instance),instance), &
                   right_SlipSlip*abs(gdot_slip)) + &                                               ! dot gamma_slip modulated by right-side slip factor
       dot_product(interaction_SlipTwin(j,1:totalNtwin(instance),instance), &
                   right_SlipTwin*gdot_twin)                                                        ! dot gamma_twin modulated by right-side twin factor
     plasticState(ph)%dotState(index_Gamma,of) = plasticState(ph)%dotState(index_Gamma,of) + &
                                                        abs(gdot_slip(j))
     plasticState(ph)%dotState(offset_accshear_slip+j,of) = abs(gdot_slip(j))
   enddo slipSystems2
 enddo slipFamilies2

 j = 0_pInt
 twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
   index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph))                                         ! at which index starts my family
   twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
     j = j+1_pInt
     plasticState(ph)%dotState(j+nSlip,of) = &                                                      ! evolution of twin resistance j
       c_TwinSlip * left_TwinSlip(j) * &
       dot_product(interaction_TwinSlip(j,1:totalNslip(instance),instance), &
                   right_TwinSlip*abs(gdot_slip)) + &                                               ! dot gamma_slip modulated by right-side slip factor
       c_TwinTwin * left_TwinTwin(j) * &
       dot_product(interaction_TwinTwin(j,1:totalNtwin(instance),instance), &
                   right_TwinTwin*gdot_twin)                                                        ! dot gamma_twin modulated by right-side twin factor
     if (plasticState(ph)%state(index_F,of) < 0.98_pReal) &                                         ! ensure twin volume fractions stays below 1.0
       plasticState(ph)%dotState(index_F,of) = plasticState(ph)%dotState(index_F,of) + &
                                                      gdot_twin(j)/lattice_shearTwin(index_myFamily+i,ph)
     plasticState(ph)%dotState(offset_accshear_twin+j,of) = abs(gdot_twin(j))
   enddo twinSystems2
 enddo twinFamilies2


end subroutine plastic_phenopowerlaw_dotState

!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_phenopowerlaw_postResults(Tstar_v,ipc,ip,el)
 use material, only: &
   material_phase, &
   plasticState, &
   phaseAt, phasememberAt, &
   phase_plasticityInstance
 use lattice, only: &
   lattice_Sslip_v, &
   lattice_Stwin_v, &
   lattice_maxNslipFamily, &
   lattice_maxNtwinFamily, &
   lattice_NslipSystem, &
   lattice_NtwinSystem, &
   lattice_NnonSchmid

 implicit none
 real(pReal), dimension(6), intent(in) :: &
   Tstar_v                                                                                          !< 2nd Piola Kirchhoff stress tensor in Mandel notation
 integer(pInt),             intent(in) :: &
   ipc, &                                                                                           !< component-ID of integration point
   ip, &                                                                                            !< integration point
   el                                                                                               !< element                                                                                        !< microstructure state

 real(pReal), dimension(plastic_phenopowerlaw_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
   plastic_phenopowerlaw_postResults

 integer(pInt) :: &
   instance,ph, of, &
   nSlip,nTwin, &
   o,f,i,c,j,k, &
   index_Gamma,index_F,index_accshear_slip,index_accshear_twin,index_myFamily
 real(pReal) :: &
   tau_slip_pos,tau_slip_neg,tau

 of = phasememberAt(ipc,ip,el)
 ph = phaseAt(ipc,ip,el)
 instance = phase_plasticityInstance(ph)

 nSlip = totalNslip(instance)
 nTwin = totalNtwin(instance)

 index_Gamma = nSlip + nTwin + 1_pInt
 index_F     = nSlip + nTwin + 2_pInt
 index_accshear_slip = nSlip + nTwin + 3_pInt
 index_accshear_twin = nSlip + nTwin + 3_pInt + nSlip

 plastic_phenopowerlaw_postResults = 0.0_pReal
 c = 0_pInt

 outputsLoop: do o = 1_pInt,plastic_phenopowerlaw_Noutput(instance)
   select case(plastic_phenopowerlaw_outputID(o,instance))
     case (resistance_slip_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = plasticState(ph)%state(1:nSlip,of)
       c = c + nSlip

     case (accumulatedshear_slip_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = plasticState(ph)%state(index_accshear_slip:&
                                                                        index_accshear_slip+nSlip-1_pInt,of)
       c = c + nSlip

     case (shearrate_slip_ID)
       j = 0_pInt
       slipFamilies1: do f = 1_pInt,size(param(instance)%Nslip,1)
         index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph))                                ! at which index starts my family
         slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
           j = j + 1_pInt
           tau_slip_pos  = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
           tau_slip_neg  = tau_slip_pos
           do k = 1,lattice_NnonSchmid(ph)
             tau_slip_pos = tau_slip_pos +param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
             tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
                                   dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
           enddo
           plastic_phenopowerlaw_postResults(c+j) = param(instance)%gdot0_slip*0.5_pReal* &
                    ((abs(tau_slip_pos)/plasticState(ph)%state(j,of))**param(instance)%n_slip &
                    *sign(1.0_pReal,tau_slip_pos) &
                    +(abs(tau_slip_neg)/(plasticState(ph)%state(j,of)))**param(instance)%n_slip &
                    *sign(1.0_pReal,tau_slip_neg))
         enddo slipSystems1
       enddo slipFamilies1
       c = c + nSlip

     case (resolvedstress_slip_ID)
       j = 0_pInt
       slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
         index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph))                                ! at which index starts my family
         slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
           j = j + 1_pInt
           plastic_phenopowerlaw_postResults(c+j) = &
                             dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
         enddo slipSystems2
       enddo slipFamilies2
       c = c + nSlip

     case (totalshear_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt) = &
                             plasticState(ph)%state(index_Gamma,of)
       c = c + 1_pInt

     case (resistance_twin_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
                             plasticState(ph)%state(1_pInt+nSlip:1_pInt+nSlip+nTwin-1_pInt,of)
       c = c + nTwin

     case (accumulatedshear_twin_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
                             plasticState(ph)%state(index_accshear_twin:index_accshear_twin+nTwin-1_pInt,of)
       c = c + nTwin
     case (shearrate_twin_ID)
       j = 0_pInt
       twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
         index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph))                                ! at which index starts my family
         twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
           j = j + 1_pInt
           tau = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
           plastic_phenopowerlaw_postResults(c+j) = (1.0_pReal-plasticState(ph)%state(index_F,of))*&  ! 1-F
                                                         param(instance)%gdot0_twin*&
                                                         (abs(tau)/plasticState(ph)%state(j+nSlip,of))**&
                                           param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau))
         enddo twinSystems1
       enddo twinFamilies1
       c = c + nTwin

     case (resolvedstress_twin_ID)
       j = 0_pInt
       twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
         index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph))                                ! at which index starts my family
         twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
           j = j + 1_pInt
           plastic_phenopowerlaw_postResults(c+j) = &
                             dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
         enddo twinSystems2
       enddo twinFamilies2
       c = c + nTwin

     case (totalvolfrac_twin_ID)
       plastic_phenopowerlaw_postResults(c+1_pInt) = plasticState(ph)%state(index_F,of)
       c = c + 1_pInt

   end select
 enddo outputsLoop

end function plastic_phenopowerlaw_postResults

end module plastic_phenopowerlaw