460 lines
20 KiB
Fortran
460 lines
20 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Philip Eisenlohr, Michigan State University
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!> @author Zhuowen Zhao, Michigan State University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Phenomenological crystal plasticity using a power law formulation for the shear rates
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!! and a Voce-type kinematic hardening rule
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!--------------------------------------------------------------------------------------------------
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submodule(phase:plastic) kinehardening
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type :: tParameters
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real(pReal) :: &
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n = 1.0_pReal, & !< stress exponent for slip
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dot_gamma_0 = 1.0_pReal !< reference shear strain rate for slip
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real(pReal), allocatable, dimension(:) :: &
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h_0_f, & !< initial hardening rate of forward stress for each slip
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h_inf_f, & !< asymptotic hardening rate of forward stress for each slip
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h_0_b, & !< initial hardening rate of back stress for each slip
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h_inf_b, & !< asymptotic hardening rate of back stress for each slip
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xi_inf_f, &
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xi_inf_b
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real(pReal), allocatable, dimension(:,:) :: &
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interaction_slipslip !< slip resistance from slip activity
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real(pReal), allocatable, dimension(:,:,:) :: &
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P, &
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nonSchmid_pos, &
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nonSchmid_neg
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integer :: &
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sum_N_sl
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logical :: &
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nonSchmidActive = .false.
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character(len=pStringLen), allocatable, dimension(:) :: &
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output
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end type tParameters
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type :: tKinehardeningState
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real(pReal), pointer, dimension(:,:) :: & !< vectors along NipcMyInstance
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crss, & !< critical resolved stress
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crss_back, & !< critical resolved back stress
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sense, & !< sense of acting shear stress (-1 or +1)
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chi0, & !< backstress at last switch of stress sense
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gamma0, & !< accumulated shear at last switch of stress sense
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accshear !< accumulated (absolute) shear
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end type tKinehardeningState
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!--------------------------------------------------------------------------------------------------
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! containers for parameters and state
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type(tParameters), allocatable, dimension(:) :: param
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type(tKinehardeningState), allocatable, dimension(:) :: &
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dotState, &
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deltaState, &
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state
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Perform module initialization.
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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module function plastic_kinehardening_init() result(myPlasticity)
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logical, dimension(:), allocatable :: myPlasticity
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integer :: &
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ph, o, &
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Nmembers, &
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sizeState, sizeDeltaState, sizeDotState, &
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startIndex, endIndex
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integer, dimension(:), allocatable :: &
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N_sl
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real(pReal), dimension(:), allocatable :: &
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xi_0, & !< initial resistance against plastic flow
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a !< non-Schmid coefficients
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character(len=pStringLen) :: &
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extmsg = ''
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class(tNode), pointer :: &
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phases, &
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phase, &
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mech, &
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pl
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myPlasticity = plastic_active('kinehardening')
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if(count(myPlasticity) == 0) return
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print'(/,a)', ' <<<+- phase:mechanical:plastic:kinehardening init -+>>>'
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print'(a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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phases => config_material%get('phase')
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allocate(param(phases%length))
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allocate(state(phases%length))
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allocate(dotState(phases%length))
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allocate(deltaState(phases%length))
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do ph = 1, phases%length
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if(.not. myPlasticity(ph)) cycle
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associate(prm => param(ph), dot => dotState(ph), dlt => deltaState(ph), stt => state(ph))
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phase => phases%get(ph)
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mech => phase%get('mechanical')
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pl => mech%get('plastic')
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#if defined (__GFORTRAN__)
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prm%output = output_as1dString(pl)
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#else
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prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
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#endif
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(abs(N_sl))
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slipActive: if (prm%sum_N_sl > 0) then
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prm%P = lattice_SchmidMatrix_slip(N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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if(trim(phase%get_asString('lattice')) == 'cI') then
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a = pl%get_as1dFloat('a_nonSchmid',defaultVal = emptyRealArray)
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if(size(a) > 0) prm%nonSchmidActive = .true.
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prm%nonSchmid_pos = lattice_nonSchmidMatrix(N_sl,a,+1)
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prm%nonSchmid_neg = lattice_nonSchmidMatrix(N_sl,a,-1)
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else
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prm%nonSchmid_pos = prm%P
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prm%nonSchmid_neg = prm%P
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endif
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prm%interaction_SlipSlip = lattice_interaction_SlipBySlip(N_sl, &
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pl%get_as1dFloat('h_sl_sl'), &
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phase%get_asString('lattice'))
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xi_0 = pl%get_as1dFloat('xi_0', requiredSize=size(N_sl))
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prm%xi_inf_f = pl%get_as1dFloat('xi_inf_f', requiredSize=size(N_sl))
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prm%xi_inf_b = pl%get_as1dFloat('xi_inf_b', requiredSize=size(N_sl))
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prm%h_0_f = pl%get_as1dFloat('h_0_f', requiredSize=size(N_sl))
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prm%h_inf_f = pl%get_as1dFloat('h_inf_f', requiredSize=size(N_sl))
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prm%h_0_b = pl%get_as1dFloat('h_0_b', requiredSize=size(N_sl))
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prm%h_inf_b = pl%get_as1dFloat('h_inf_b', requiredSize=size(N_sl))
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prm%dot_gamma_0 = pl%get_asFloat('dot_gamma_0')
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prm%n = pl%get_asFloat('n')
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! expand: family => system
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xi_0 = math_expand(xi_0, N_sl)
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prm%xi_inf_f = math_expand(prm%xi_inf_f, N_sl)
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prm%xi_inf_b = math_expand(prm%xi_inf_b, N_sl)
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prm%h_0_f = math_expand(prm%h_0_f, N_sl)
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prm%h_inf_f = math_expand(prm%h_inf_f, N_sl)
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prm%h_0_b = math_expand(prm%h_0_b, N_sl)
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prm%h_inf_b = math_expand(prm%h_inf_b, N_sl)
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!--------------------------------------------------------------------------------------------------
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! sanity checks
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if ( prm%dot_gamma_0 <= 0.0_pReal) extmsg = trim(extmsg)//' dot_gamma_0'
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if ( prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' n'
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if (any(xi_0 <= 0.0_pReal)) extmsg = trim(extmsg)//' xi_0'
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if (any(prm%xi_inf_f <= 0.0_pReal)) extmsg = trim(extmsg)//' xi_inf_f'
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if (any(prm%xi_inf_b <= 0.0_pReal)) extmsg = trim(extmsg)//' xi_inf_b'
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!ToDo: Any sensible checks for theta?
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else slipActive
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xi_0 = emptyRealArray
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allocate(prm%xi_inf_f,prm%xi_inf_b,prm%h_0_f,prm%h_inf_f,prm%h_0_b,prm%h_inf_b,source=emptyRealArray)
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allocate(prm%interaction_SlipSlip(0,0))
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endif slipActive
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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Nmembers = count(material_phaseID == ph)
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sizeDotState = size(['crss ','crss_back', 'accshear ']) * prm%sum_N_sl !ToDo: adjust names like in material.yaml
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sizeDeltaState = size(['sense ', 'chi0 ', 'gamma0' ]) * prm%sum_N_sl !ToDo: adjust names like in material.yaml
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sizeState = sizeDotState + sizeDeltaState
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call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,sizeDeltaState)
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!--------------------------------------------------------------------------------------------------
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! state aliases and initialization
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startIndex = 1
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endIndex = prm%sum_N_sl
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stt%crss => plasticState(ph)%state (startIndex:endIndex,:)
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stt%crss = spread(xi_0, 2, Nmembers)
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dot%crss => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal)
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if(any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_xi'
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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stt%crss_back => plasticState(ph)%state (startIndex:endIndex,:)
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dot%crss_back => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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stt%accshear => plasticState(ph)%state (startIndex:endIndex,:)
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dot%accshear => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('atol_gamma',defaultVal=1.0e-6_pReal)
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if(any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_gamma'
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! global alias
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plasticState(ph)%slipRate => plasticState(ph)%dotState(startIndex:endIndex,:)
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o = plasticState(ph)%offsetDeltaState
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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stt%sense => plasticState(ph)%state (startIndex :endIndex ,:)
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dlt%sense => plasticState(ph)%deltaState(startIndex-o:endIndex-o,:)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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stt%chi0 => plasticState(ph)%state (startIndex :endIndex ,:)
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dlt%chi0 => plasticState(ph)%deltaState(startIndex-o:endIndex-o,:)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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stt%gamma0 => plasticState(ph)%state (startIndex :endIndex ,:)
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dlt%gamma0 => plasticState(ph)%deltaState(startIndex-o:endIndex-o,:)
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end associate
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!--------------------------------------------------------------------------------------------------
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! exit if any parameter is out of range
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if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(kinehardening)')
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enddo
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end function plastic_kinehardening_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate plastic velocity gradient and its tangent.
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!--------------------------------------------------------------------------------------------------
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pure module subroutine kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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real(pReal), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pReal), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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integer :: &
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i,k,l,m,n
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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gdot_pos,gdot_neg, &
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dgdot_dtau_pos,dgdot_dtau_neg
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
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associate(prm => param(ph))
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call kinetics(Mp,ph,en,gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg)
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do i = 1, prm%sum_N_sl
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Lp = Lp + (gdot_pos(i)+gdot_neg(i))*prm%P(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ dgdot_dtau_pos(i) * prm%P(k,l,i) * prm%nonSchmid_pos(m,n,i) &
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+ dgdot_dtau_neg(i) * prm%P(k,l,i) * prm%nonSchmid_neg(m,n,i)
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enddo
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end associate
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end subroutine kinehardening_LpAndItsTangent
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate the rate of change of microstructure.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_kinehardening_dotState(Mp,ph,en)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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real(pReal) :: &
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sumGamma
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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gdot_pos,gdot_neg
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associate(prm => param(ph), stt => state(ph),&
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dot => dotState(ph))
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call kinetics(Mp,ph,en,gdot_pos,gdot_neg)
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dot%accshear(:,en) = abs(gdot_pos+gdot_neg)
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sumGamma = sum(stt%accshear(:,en))
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dot%crss(:,en) = matmul(prm%interaction_SlipSlip,dot%accshear(:,en)) &
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* ( prm%h_inf_f &
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+ (prm%h_0_f - prm%h_inf_f + prm%h_0_f*prm%h_inf_f*sumGamma/prm%xi_inf_f) &
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* exp(-sumGamma*prm%h_0_f/prm%xi_inf_f) &
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)
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dot%crss_back(:,en) = stt%sense(:,en)*dot%accshear(:,en) * &
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( prm%h_inf_b + &
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(prm%h_0_b - prm%h_inf_b &
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+ prm%h_0_b*prm%h_inf_b/(prm%xi_inf_b+stt%chi0(:,en))*(stt%accshear(:,en)-stt%gamma0(:,en))&
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) *exp(-(stt%accshear(:,en)-stt%gamma0(:,en)) *prm%h_0_b/(prm%xi_inf_b+stt%chi0(:,en))) &
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)
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end associate
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end subroutine plastic_kinehardening_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate (instantaneous) incremental change of microstructure.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_kinehardening_deltaState(Mp,ph,en)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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gdot_pos,gdot_neg, &
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sense
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associate(prm => param(ph), stt => state(ph), dlt => deltaState(ph))
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call kinetics(Mp,ph,en,gdot_pos,gdot_neg)
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sense = merge(state(ph)%sense(:,en), & ! keep existing...
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sign(1.0_pReal,gdot_pos+gdot_neg), & ! ...or have a defined
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dEq0(gdot_pos+gdot_neg,1e-10_pReal)) ! current sense of shear direction
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!--------------------------------------------------------------------------------------------------
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! switch in sense of shear?
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where(dNeq(sense,stt%sense(:,en),0.1_pReal))
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dlt%sense (:,en) = sense - stt%sense(:,en) ! switch sense
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dlt%chi0 (:,en) = abs(stt%crss_back(:,en)) - stt%chi0(:,en) ! remember current backstress magnitude
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dlt%gamma0(:,en) = stt%accshear(:,en) - stt%gamma0(:,en) ! remember current accumulated shear
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else where
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dlt%sense (:,en) = 0.0_pReal
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dlt%chi0 (:,en) = 0.0_pReal
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dlt%gamma0(:,en) = 0.0_pReal
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end where
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end associate
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end subroutine plastic_kinehardening_deltaState
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!--------------------------------------------------------------------------------------------------
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!> @brief Write results to HDF5 output file.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_kinehardening_results(ph,group)
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integer, intent(in) :: ph
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character(len=*), intent(in) :: group
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integer :: o
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associate(prm => param(ph), stt => state(ph))
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outputsLoop: do o = 1,size(prm%output)
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select case(trim(prm%output(o)))
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case ('xi')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%crss,group,trim(prm%output(o)), &
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'resistance against plastic slip','Pa')
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case ('tau_b')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%crss_back,group,trim(prm%output(o)), &
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'back stress against plastic slip','Pa')
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case ('sgn(gamma)')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%sense,group,trim(prm%output(o)), & ! ToDo: could be int
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'sense of shear','1')
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case ('chi_0')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%chi0,group,trim(prm%output(o)), &
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'tbd','Pa')
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case ('gamma_0')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%gamma0,group,trim(prm%output(o)), &
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'tbd','1')
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case ('gamma')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%accshear,group,trim(prm%output(o)), &
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'plastic shear','1')
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end select
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enddo outputsLoop
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end associate
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end subroutine plastic_kinehardening_results
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on slip systems and their derivatives with respect to resolved
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! stress.
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!> @details: Derivatives are calculated only optionally.
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! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
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! have the optional arguments at the end.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics(Mp,ph,en, &
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gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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real(pReal), intent(out), dimension(param(ph)%sum_N_sl) :: &
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gdot_pos, &
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gdot_neg
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real(pReal), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
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dgdot_dtau_pos, &
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dgdot_dtau_neg
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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tau_pos, &
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tau_neg
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integer :: i
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associate(prm => param(ph), stt => state(ph))
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do i = 1, prm%sum_N_sl
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tau_pos(i) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,i)) - stt%crss_back(i,en)
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tau_neg(i) = merge(math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,i)) - stt%crss_back(i,en), &
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0.0_pReal, prm%nonSchmidActive)
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enddo
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where(dNeq0(tau_pos))
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gdot_pos = prm%dot_gamma_0 * merge(0.5_pReal,1.0_pReal, prm%nonSchmidActive) & ! 1/2 if non-Schmid active
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* sign(abs(tau_pos/stt%crss(:,en))**prm%n, tau_pos)
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else where
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gdot_pos = 0.0_pReal
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end where
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where(dNeq0(tau_neg))
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gdot_neg = prm%dot_gamma_0 * 0.5_pReal & ! only used if non-Schmid active, always 1/2
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* sign(abs(tau_neg/stt%crss(:,en))**prm%n, tau_neg)
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else where
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gdot_neg = 0.0_pReal
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end where
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if (present(dgdot_dtau_pos)) then
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where(dNeq0(gdot_pos))
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dgdot_dtau_pos = gdot_pos*prm%n/tau_pos
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else where
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dgdot_dtau_pos = 0.0_pReal
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end where
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endif
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if (present(dgdot_dtau_neg)) then
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where(dNeq0(gdot_neg))
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dgdot_dtau_neg = gdot_neg*prm%n/tau_neg
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else where
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dgdot_dtau_neg = 0.0_pReal
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end where
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endif
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end associate
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end subroutine kinetics
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end submodule kinehardening
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