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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine for isotropic (ISOTROPIC) plasticity
!> @details Isotropic (ISOTROPIC) Plasticity which resembles the phenopowerlaw plasticity without
!! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an
!! untextured polycrystal
!--------------------------------------------------------------------------------------------------
module plastic_isotropic
use prec , only : &
pReal , &
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pInt , &
DAMASK_NaN
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implicit none
private
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integer ( pInt ) , dimension ( : ) , allocatable , public , protected :: &
plastic_isotropic_sizePostResults !< cumulative size of post results
integer ( pInt ) , dimension ( : , : ) , allocatable , target , public :: &
plastic_isotropic_sizePostResult !< size of each post result output
character ( len = 64 ) , dimension ( : , : ) , allocatable , target , public :: &
plastic_isotropic_output !< name of each post result output
integer ( pInt ) , dimension ( : ) , allocatable , target , public :: &
plastic_isotropic_Noutput !< number of outputs per instance
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enum , bind ( c )
enumerator :: undefined_ID , &
flowstress_ID , &
strainrate_ID
end enum
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type , private :: tParameters !< container type for internal constitutive parameters
integer ( kind ( undefined_ID ) ) , allocatable , dimension ( : ) :: &
outputID
real ( pReal ) :: &
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fTaylor = DAMASK_NaN , &
tau0 = DAMASK_NaN , &
gdot0 = DAMASK_NaN , &
n = DAMASK_NaN , &
h0 = DAMASK_NaN , &
h0_slopeLnRate = 0.0_pReal , &
tausat = DAMASK_NaN , &
a = DAMASK_NaN , &
aTolFlowstress = 1.0_pReal , &
aTolShear = 1.0e-6_pReal , &
tausat_SinhFitA = 0.0_pReal , &
tausat_SinhFitB = 0.0_pReal , &
tausat_SinhFitC = 0.0_pReal , &
tausat_SinhFitD = 0.0_pReal
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logical :: &
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dilatation = . false .
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end type
type ( tParameters ) , dimension ( : ) , allocatable , private :: param !< containers of constitutive parameters (len Ninstance)
type , private :: tIsotropicState !< internal state aliases
real ( pReal ) , pointer , dimension ( : ) :: & ! scalars along NipcMyInstance
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flowstress , &
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accumulatedShear
end type
type , private :: tIsotropicAbsTol !< internal alias for abs tolerance in state
real ( pReal ) , pointer :: & ! scalars along NipcMyInstance
flowstress , &
accumulatedShear
end type
type ( tIsotropicState ) , allocatable , dimension ( : ) , private :: & !< state aliases per instance
state , &
state0 , &
dotState
type ( tIsotropicAbsTol ) , allocatable , dimension ( : ) , private :: & !< state aliases per instance
stateAbsTol
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public :: &
plastic_isotropic_init , &
plastic_isotropic_LpAndItsTangent , &
plastic_isotropic_LiAndItsTangent , &
plastic_isotropic_dotState , &
plastic_isotropic_postResults
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_isotropic_init ( fileUnit )
use , intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use debug , only : &
debug_level , &
debug_constitutive , &
debug_levelBasic
use numerics , only : &
analyticJaco , &
worldrank , &
numerics_integrator
use math , only : &
math_Mandel3333to66 , &
math_Voigt66to3333
use IO , only : &
IO_read , &
IO_lc , &
IO_getTag , &
IO_isBlank , &
IO_stringPos , &
IO_stringValue , &
IO_floatValue , &
IO_error , &
IO_timeStamp , &
IO_EOF
use material , only : &
phase_plasticity , &
phase_plasticityInstance , &
phase_Noutput , &
PLASTICITY_ISOTROPIC_label , &
PLASTICITY_ISOTROPIC_ID , &
material_phase , &
plasticState , &
MATERIAL_partPhase
use lattice
implicit none
integer ( pInt ) , intent ( in ) :: fileUnit
integer ( pInt ) , allocatable , dimension ( : ) :: chunkPos
integer ( pInt ) :: &
o , &
phase , &
instance , &
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maxNinstance , &
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mySize , &
sizeDotState , &
sizeState , &
sizeDeltaState
character ( len = 65536 ) :: &
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tag = '' , &
line = '' , &
extmsg = ''
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character ( len = 64 ) :: &
outputtag = ''
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integer ( pInt ) :: NipcMyPhase
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mainProcess : if ( worldrank == 0 ) then
write ( 6 , '(/,a)' ) ' <<<+- constitutive_' / / PLASTICITY_ISOTROPIC_label / / ' init -+>>>'
write ( 6 , '(a15,a)' ) ' Current time: ' , IO_timeStamp ( )
#include "compilation_info.f90"
endif mainProcess
maxNinstance = int ( count ( phase_plasticity == PLASTICITY_ISOTROPIC_ID ) , pInt )
if ( maxNinstance == 0_pInt ) return
if ( iand ( debug_level ( debug_constitutive ) , debug_levelBasic ) / = 0_pInt ) &
write ( 6 , '(a16,1x,i5,/)' ) '# instances:' , maxNinstance
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allocate ( plastic_isotropic_sizePostResults ( maxNinstance ) , source = 0_pInt )
allocate ( plastic_isotropic_sizePostResult ( maxval ( phase_Noutput ) , maxNinstance ) , source = 0_pInt )
allocate ( plastic_isotropic_output ( maxval ( phase_Noutput ) , maxNinstance ) )
plastic_isotropic_output = ''
allocate ( plastic_isotropic_Noutput ( maxNinstance ) , source = 0_pInt )
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allocate ( param ( maxNinstance ) ) ! one container of parameters per instance
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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 section
phase = phase + 1_pInt ! advance section counter
if ( phase_plasticity ( phase ) == PLASTICITY_ISOTROPIC_ID ) then
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instance = phase_plasticityInstance ( phase ) ! count instances of my constitutive law
allocate ( param ( instance ) % outputID ( phase_Noutput ( phase ) ) ) ! allocate space for IDs of every requested output
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endif
cycle ! skip to next line
endif
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if ( phase > 0_pInt ) then ; if ( phase_plasticity ( phase ) == PLASTICITY_ISOTROPIC_ID ) then ! one of my phases. Do not short-circuit here (.and. between if-statements), it's not safe in Fortran
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instance = phase_plasticityInstance ( phase ) ! which instance of my plasticity is present phase
chunkPos = IO_stringPos ( line )
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tag = IO_lc ( IO_stringValue ( line , chunkPos , 1_pInt ) ) ! extract key
extmsg = trim ( tag ) / / ' (' / / PLASTICITY_ISOTROPIC_label / / ')' ! prepare error message identifier
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select case ( tag )
case ( '(output)' )
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outputtag = IO_lc ( IO_stringValue ( line , chunkPos , 2_pInt ) )
select case ( outputtag )
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case ( 'flowstress' )
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plastic_isotropic_Noutput ( instance ) = plastic_isotropic_Noutput ( instance ) + 1_pInt
param ( instance ) % outputID ( plastic_isotropic_Noutput ( instance ) ) = flowstress_ID
plastic_isotropic_output ( plastic_isotropic_Noutput ( instance ) , instance ) = outputtag
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case ( 'strainrate' )
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plastic_isotropic_Noutput ( instance ) = plastic_isotropic_Noutput ( instance ) + 1_pInt
param ( instance ) % outputID ( plastic_isotropic_Noutput ( instance ) ) = strainrate_ID
plastic_isotropic_output ( plastic_isotropic_Noutput ( instance ) , instance ) = outputtag
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end select
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case ( '/dilatation/' )
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param ( instance ) % dilatation = . true .
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case ( 'tau0' )
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param ( instance ) % tau0 = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % tau0 < 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'gdot0' )
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param ( instance ) % gdot0 = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % gdot0 < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'n' )
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param ( instance ) % n = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % n < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'h0' )
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param ( instance ) % h0 = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'h0_slope' , 'slopelnrate' )
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param ( instance ) % h0_slopeLnRate = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'tausat' )
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param ( instance ) % tausat = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % tausat < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'tausat_sinhfita' )
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param ( instance ) % tausat_SinhFitA = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'tausat_sinhfitb' )
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param ( instance ) % tausat_SinhFitB = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'tausat_sinhfitc' )
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param ( instance ) % tausat_SinhFitC = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'tausat_sinhfitd' )
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param ( instance ) % tausat_SinhFitD = IO_floatValue ( line , chunkPos , 2_pInt )
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case ( 'a' , 'w0' )
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param ( instance ) % a = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % a < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'taylorfactor' )
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param ( instance ) % fTaylor = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % fTaylor < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
case ( 'atol_flowstress' )
param ( instance ) % aTolFlowstress = IO_floatValue ( line , chunkPos , 2_pInt )
if ( param ( instance ) % aTolFlowstress < = 0.0_pReal ) call IO_error ( 211_pInt , ext_msg = extmsg )
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case ( 'atol_shear' )
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param ( instance ) % aTolShear = IO_floatValue ( line , chunkPos , 2_pInt )
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case default
end select
endif ; endif
enddo parsingFile
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allocate ( state ( maxNinstance ) ) ! internal state aliases
allocate ( state0 ( maxNinstance ) )
allocate ( dotState ( maxNinstance ) )
allocate ( stateAbsTol ( maxNinstance ) )
initializeInstances : do phase = 1_pInt , size ( phase_plasticity ) ! loop over every plasticity
myPhase : if ( phase_plasticity ( phase ) == PLASTICITY_isotropic_ID ) then ! isolate instances of own constitutive description
NipcMyPhase = count ( material_phase == phase ) ! number of own material points (including point components ipc)
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instance = phase_plasticityInstance ( phase )
!--------------------------------------------------------------------------------------------------
! sanity checks
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if ( param ( instance ) % aTolShear < = 0.0_pReal ) &
param ( instance ) % aTolShear = 1.0e-6_pReal ! default absolute tolerance 1e-6
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!--------------------------------------------------------------------------------------------------
! Determine size of postResults array
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outputsLoop : do o = 1_pInt , plastic_isotropic_Noutput ( instance )
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select case ( param ( instance ) % outputID ( o ) )
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case ( flowstress_ID , strainrate_ID )
mySize = 1_pInt
case default
end select
outputFound : if ( mySize > 0_pInt ) then
plastic_isotropic_sizePostResult ( o , instance ) = mySize
plastic_isotropic_sizePostResults ( instance ) = &
plastic_isotropic_sizePostResults ( instance ) + mySize
endif outputFound
enddo outputsLoop
!--------------------------------------------------------------------------------------------------
! allocate state arrays
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sizeState = 2_pInt ! flowstress, accumulated_shear
sizeDotState = sizeState ! both evolve
sizeDeltaState = 0_pInt ! no sudden jumps in state
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plasticState ( phase ) % sizeState = sizeState
plasticState ( phase ) % sizeDotState = sizeDotState
plasticState ( phase ) % sizeDeltaState = sizeDeltaState
plasticState ( phase ) % sizePostResults = plastic_isotropic_sizePostResults ( instance )
plasticState ( phase ) % nSlip = 1
plasticState ( phase ) % nTwin = 0
plasticState ( phase ) % nTrans = 0
allocate ( plasticState ( phase ) % aTolState ( sizeState ) )
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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 )
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if ( . not . analyticJaco ) then
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allocate ( plasticState ( phase ) % state_backup ( sizeState , NipcMyPhase ) , source = 0.0_pReal )
allocate ( plasticState ( phase ) % dotState_backup ( sizeDotState , NipcMyPhase ) , source = 0.0_pReal )
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endif
if ( any ( numerics_integrator == 1_pInt ) ) then
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allocate ( plasticState ( phase ) % previousDotState ( sizeDotState , NipcMyPhase ) , source = 0.0_pReal )
allocate ( plasticState ( phase ) % previousDotState2 ( sizeDotState , NipcMyPhase ) , source = 0.0_pReal )
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endif
if ( any ( numerics_integrator == 4_pInt ) ) &
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allocate ( plasticState ( phase ) % RK4dotState ( sizeDotState , NipcMyPhase ) , source = 0.0_pReal )
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if ( any ( numerics_integrator == 5_pInt ) ) &
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allocate ( plasticState ( phase ) % RKCK45dotState ( 6 , sizeDotState , NipcMyPhase ) , source = 0.0_pReal )
!--------------------------------------------------------------------------------------------------
! globally required state aliases
plasticState ( phase ) % slipRate = > plasticState ( phase ) % dotState ( 2 : 2 , 1 : NipcMyPhase )
plasticState ( phase ) % accumulatedSlip = > plasticState ( phase ) % state ( 2 : 2 , 1 : NipcMyPhase )
!--------------------------------------------------------------------------------------------------
! locally defined state aliases
state ( instance ) % flowstress = > plasticState ( phase ) % state ( 1 , 1 : NipcMyPhase )
state0 ( instance ) % flowstress = > plasticState ( phase ) % state0 ( 1 , 1 : NipcMyPhase )
dotState ( instance ) % flowstress = > plasticState ( phase ) % dotState ( 1 , 1 : NipcMyPhase )
stateAbsTol ( instance ) % flowstress = > plasticState ( phase ) % aTolState ( 1 )
state ( instance ) % accumulatedShear = > plasticState ( phase ) % state ( 2 , 1 : NipcMyPhase )
state0 ( instance ) % accumulatedShear = > plasticState ( phase ) % state0 ( 2 , 1 : NipcMyPhase )
dotState ( instance ) % accumulatedShear = > plasticState ( phase ) % dotState ( 2 , 1 : NipcMyPhase )
stateAbsTol ( instance ) % accumulatedShear = > plasticState ( phase ) % aTolState ( 2 )
!--------------------------------------------------------------------------------------------------
! init state
state0 ( instance ) % flowstress = param ( instance ) % tau0
state0 ( instance ) % accumulatedShear = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! init absolute state tolerances
stateAbsTol ( instance ) % flowstress = param ( instance ) % aTolFlowstress
stateAbsTol ( instance ) % accumulatedShear = param ( instance ) % aTolShear
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endif myPhase
enddo initializeInstances
end subroutine plastic_isotropic_init
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_isotropic_LpAndItsTangent ( Lp , dLp_dTstar99 , Tstar_v , ipc , ip , el )
use debug , only : &
debug_level , &
debug_constitutive , &
debug_levelBasic , &
debug_levelExtensive , &
debug_levelSelective , &
debug_e , &
debug_i , &
debug_g
use math , only : &
math_mul6x6 , &
math_Mandel6to33 , &
math_Plain3333to99 , &
math_deviatoric33 , &
math_mul33xx33 , &
math_transpose33
use material , only : &
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phasememberAt , &
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material_phase , &
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
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
real ( pReal ) , dimension ( 3 , 3 ) :: &
Tstar_dev_33 !< deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: &
dLp_dTstar_3333 !< derivative of Lp with respect to Tstar as 4th order tensor
real ( pReal ) :: &
gamma_dot , & !< strainrate
norm_Tstar_dev , & !< euclidean norm of Tstar_dev
squarenorm_Tstar_dev !< square of the euclidean norm of Tstar_dev
integer ( pInt ) :: &
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instance , of , &
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k , l , m , n
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of = phasememberAt ( ipc , ip , el ) ! phasememberAt should be tackled by material and be renamed to material_phasemember
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instance = phase_plasticityInstance ( material_phase ( ipc , ip , el ) )
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Tstar_dev_33 = math_deviatoric33 ( math_Mandel6to33 ( Tstar_v ) ) ! deviatoric part of 2nd Piola-Kirchhoff stress
squarenorm_Tstar_dev = math_mul33xx33 ( Tstar_dev_33 , Tstar_dev_33 )
norm_Tstar_dev = sqrt ( squarenorm_Tstar_dev )
if ( norm_Tstar_dev < = 0.0_pReal ) then ! Tstar == 0 --> both Lp and dLp_dTstar are zero
Lp = 0.0_pReal
dLp_dTstar99 = 0.0_pReal
else
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gamma_dot = param ( instance ) % gdot0 &
* ( sqrt ( 1.5_pReal ) * norm_Tstar_dev / param ( instance ) % fTaylor / state ( instance ) % flowstress ( of ) ) &
** param ( instance ) % n
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Lp = Tstar_dev_33 / norm_Tstar_dev * gamma_dot / param ( instance ) % fTaylor
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if ( iand ( debug_level ( debug_constitutive ) , debug_levelExtensive ) / = 0_pInt &
. and . ( ( el == debug_e . and . ip == debug_i . and . ipc == debug_g ) &
. or . . not . iand ( debug_level ( debug_constitutive ) , debug_levelSelective ) / = 0_pInt ) ) then
write ( 6 , '(a,i8,1x,i2,1x,i3)' ) '<< CONST isotropic >> at el ip g ' , el , ip , ipc
write ( 6 , '(/,a,/,3(12x,3(f12.4,1x)/))' ) '<< CONST isotropic >> Tstar (dev) / MPa' , &
math_transpose33 ( Tstar_dev_33 ( 1 : 3 , 1 : 3 ) ) * 1.0e-6_pReal
write ( 6 , '(/,a,/,f12.5)' ) '<< CONST isotropic >> norm Tstar / MPa' , norm_Tstar_dev * 1.0e-6_pReal
write ( 6 , '(/,a,/,f12.5)' ) '<< CONST isotropic >> gdot' , gamma_dot
end if
!--------------------------------------------------------------------------------------------------
! Calculation of the tangent of Lp
forall ( k = 1_pInt : 3_pInt , l = 1_pInt : 3_pInt , m = 1_pInt : 3_pInt , n = 1_pInt : 3_pInt ) &
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dLp_dTstar_3333 ( k , l , m , n ) = ( param ( instance ) % n - 1.0_pReal ) * &
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Tstar_dev_33 ( k , l ) * Tstar_dev_33 ( m , n ) / squarenorm_Tstar_dev
forall ( k = 1_pInt : 3_pInt , l = 1_pInt : 3_pInt ) &
dLp_dTstar_3333 ( k , l , k , l ) = dLp_dTstar_3333 ( k , l , k , l ) + 1.0_pReal
forall ( k = 1_pInt : 3_pInt , m = 1_pInt : 3_pInt ) &
dLp_dTstar_3333 ( k , k , m , m ) = dLp_dTstar_3333 ( k , k , m , m ) - 1.0_pReal / 3.0_pReal
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dLp_dTstar99 = math_Plain3333to99 ( gamma_dot / param ( instance ) % fTaylor * &
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dLp_dTstar_3333 / norm_Tstar_dev )
end if
end subroutine plastic_isotropic_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_isotropic_LiAndItsTangent ( Li , dLi_dTstar_3333 , Tstar_v , ipc , ip , el )
use math , only : &
math_mul6x6 , &
math_Mandel6to33 , &
math_Plain3333to99 , &
math_spherical33 , &
math_mul33xx33
use material , only : &
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phasememberAt , &
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material_phase , &
phase_plasticityInstance
implicit none
real ( pReal ) , dimension ( 3 , 3 ) , intent ( out ) :: &
Li !< plastic velocity gradient
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real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) , intent ( out ) :: &
dLi_dTstar_3333 !< derivative of Li with respect to Tstar as 4th order tensor
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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
real ( pReal ) , dimension ( 3 , 3 ) :: &
Tstar_sph_33 !< sphiatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
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real ( pReal ) :: &
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gamma_dot , & !< strainrate
norm_Tstar_sph , & !< euclidean norm of Tstar_sph
squarenorm_Tstar_sph !< square of the euclidean norm of Tstar_sph
integer ( pInt ) :: &
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instance , of , &
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k , l , m , n
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of = phasememberAt ( ipc , ip , el ) ! phasememberAt should be tackled by material and be renamed to material_phasemember
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instance = phase_plasticityInstance ( material_phase ( ipc , ip , el ) )
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Tstar_sph_33 = math_spherical33 ( math_Mandel6to33 ( Tstar_v ) ) ! spherical part of 2nd Piola-Kirchhoff stress
squarenorm_Tstar_sph = math_mul33xx33 ( Tstar_sph_33 , Tstar_sph_33 )
norm_Tstar_sph = sqrt ( squarenorm_Tstar_sph )
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if ( param ( instance ) % dilatation . and . norm_Tstar_sph > 0.0_pReal ) then ! Tstar == 0 or J2 plascitiy --> both Li and dLi_dTstar are zero
gamma_dot = param ( instance ) % gdot0 &
* ( sqrt ( 1.5_pReal ) * norm_Tstar_sph / param ( instance ) % fTaylor / state ( instance ) % flowstress ( of ) ) &
** param ( instance ) % n
Li = Tstar_sph_33 / norm_Tstar_sph * gamma_dot / param ( instance ) % fTaylor
!--------------------------------------------------------------------------------------------------
! Calculation of the tangent of Li
forall ( k = 1_pInt : 3_pInt , l = 1_pInt : 3_pInt , m = 1_pInt : 3_pInt , n = 1_pInt : 3_pInt ) &
dLi_dTstar_3333 ( k , l , m , n ) = ( param ( instance ) % n - 1.0_pReal ) * &
Tstar_sph_33 ( k , l ) * Tstar_sph_33 ( m , n ) / squarenorm_Tstar_sph
forall ( k = 1_pInt : 3_pInt , l = 1_pInt : 3_pInt ) &
dLi_dTstar_3333 ( k , l , k , l ) = dLi_dTstar_3333 ( k , l , k , l ) + 1.0_pReal
dLi_dTstar_3333 = gamma_dot / param ( instance ) % fTaylor * &
dLi_dTstar_3333 / norm_Tstar_sph
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else
Li = 0.0_pReal
dLi_dTstar_3333 = 0.0_pReal
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endif
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end subroutine plastic_isotropic_LiAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_isotropic_dotState ( Tstar_v , ipc , ip , el )
use math , only : &
math_mul6x6
use material , only : &
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phasememberAt , &
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material_phase , &
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
real ( pReal ) , dimension ( 6 ) :: &
Tstar_dev_v !< deviatoric 2nd Piola Kirchhoff stress tensor in Mandel notation
real ( pReal ) :: &
gamma_dot , & !< strainrate
hardening , & !< hardening coefficient
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saturation , & !< saturation flowstress
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norm_Tstar_v !< euclidean norm of Tstar_dev
integer ( pInt ) :: &
instance , & !< instance of my instance (unique number of my constitutive model)
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of !< shortcut notation for offset position in state array
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of = phasememberAt ( ipc , ip , el ) ! phasememberAt should be tackled by material and be renamed to material_phasemember
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instance = phase_plasticityInstance ( material_phase ( ipc , ip , el ) )
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!--------------------------------------------------------------------------------------------------
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
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if ( param ( instance ) % dilatation ) then
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norm_Tstar_v = sqrt ( math_mul6x6 ( Tstar_v , Tstar_v ) )
else
Tstar_dev_v ( 1 : 3 ) = Tstar_v ( 1 : 3 ) - sum ( Tstar_v ( 1 : 3 ) ) / 3.0_pReal
Tstar_dev_v ( 4 : 6 ) = Tstar_v ( 4 : 6 )
norm_Tstar_v = sqrt ( math_mul6x6 ( Tstar_dev_v , Tstar_dev_v ) )
end if
!--------------------------------------------------------------------------------------------------
! strain rate
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gamma_dot = param ( instance ) % gdot0 * ( sqrt ( 1.5_pReal ) * norm_Tstar_v &
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/ & !-----------------------------------------------------------------------------------
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( param ( instance ) % fTaylor * state ( instance ) % flowstress ( of ) ) ) ** param ( instance ) % n
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!--------------------------------------------------------------------------------------------------
! hardening coefficient
if ( abs ( gamma_dot ) > 1e-12_pReal ) then
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if ( abs ( param ( instance ) % tausat_SinhFitA ) < = tiny ( 0.0_pReal ) ) then
saturation = param ( instance ) % tausat
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else
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saturation = ( param ( instance ) % tausat &
+ ( log ( ( gamma_dot / param ( instance ) % tausat_SinhFitA &
) ** ( 1.0_pReal / param ( instance ) % tausat_SinhFitD ) &
+ sqrt ( ( gamma_dot / param ( instance ) % tausat_SinhFitA &
) ** ( 2.0_pReal / param ( instance ) % tausat_SinhFitD ) &
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+ 1.0_pReal ) &
) & ! asinh(K) = ln(K + sqrt(K^2 +1))
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) ** ( 1.0_pReal / param ( instance ) % tausat_SinhFitC ) &
/ ( param ( instance ) % tausat_SinhFitB &
* ( gamma_dot / param ( instance ) % gdot0 ) ** ( 1.0_pReal / param ( instance ) % n ) &
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) &
)
endif
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hardening = ( param ( instance ) % h0 + param ( instance ) % h0_slopeLnRate * log ( gamma_dot ) ) &
* abs ( 1.0_pReal - state ( instance ) % flowstress ( of ) / saturation ) ** param ( instance ) % a &
* sign ( 1.0_pReal , 1.0_pReal - state ( instance ) % flowstress ( of ) / saturation )
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else
hardening = 0.0_pReal
endif
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dotState ( instance ) % flowstress ( of ) = hardening * gamma_dot
dotState ( instance ) % accumulatedShear ( of ) = gamma_dot
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end subroutine plastic_isotropic_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_isotropic_postResults ( Tstar_v , ipc , ip , el )
use math , only : &
math_mul6x6
use material , only : &
material_phase , &
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phasememberAt , &
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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
real ( pReal ) , dimension ( plastic_isotropic_sizePostResults ( phase_plasticityInstance ( material_phase ( ipc , ip , el ) ) ) ) :: &
plastic_isotropic_postResults
real ( pReal ) , dimension ( 6 ) :: &
Tstar_dev_v !< deviatoric 2nd Piola Kirchhoff stress tensor in Mandel notation
real ( pReal ) :: &
norm_Tstar_v ! euclidean norm of Tstar_dev
integer ( pInt ) :: &
instance , & !< instance of my instance (unique number of my constitutive model)
of , & !< shortcut notation for offset position in state array
c , &
o
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of = phasememberAt ( ipc , ip , el ) ! phasememberAt should be tackled by material and be renamed to material_phasemember
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instance = phase_plasticityInstance ( material_phase ( ipc , ip , el ) )
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!--------------------------------------------------------------------------------------------------
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
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if ( param ( instance ) % dilatation ) then
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norm_Tstar_v = sqrt ( math_mul6x6 ( Tstar_v , Tstar_v ) )
else
Tstar_dev_v ( 1 : 3 ) = Tstar_v ( 1 : 3 ) - sum ( Tstar_v ( 1 : 3 ) ) / 3.0_pReal
Tstar_dev_v ( 4 : 6 ) = Tstar_v ( 4 : 6 )
norm_Tstar_v = sqrt ( math_mul6x6 ( Tstar_dev_v , Tstar_dev_v ) )
end if
c = 0_pInt
plastic_isotropic_postResults = 0.0_pReal
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outputsLoop : do o = 1_pInt , plastic_isotropic_Noutput ( instance )
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select case ( param ( instance ) % outputID ( o ) )
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case ( flowstress_ID )
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plastic_isotropic_postResults ( c + 1_pInt ) = state ( instance ) % flowstress ( of )
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c = c + 1_pInt
case ( strainrate_ID )
plastic_isotropic_postResults ( c + 1_pInt ) = &
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param ( instance ) % gdot0 * ( sqrt ( 1.5_pReal ) * norm_Tstar_v &
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/ & !----------------------------------------------------------------------------------
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( param ( instance ) % fTaylor * state ( instance ) % flowstress ( of ) ) ) ** param ( instance ) % n
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c = c + 1_pInt
end select
enddo outputsLoop
end function plastic_isotropic_postResults
end module plastic_isotropic