666 lines
34 KiB
Fortran
666 lines
34 KiB
Fortran
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
!> @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,&
|
||
|
|
pInt, &
|
||
|
|
DAMASK_NaN
|
||
|
|
|
||
|
|
implicit none
|
||
|
|
private
|
||
|
|
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
|
||
|
|
|
||
|
|
enum, bind(c)
|
||
|
|
enumerator :: undefined_ID, &
|
||
|
|
flowstress_ID, &
|
||
|
|
strainrate_ID
|
||
|
|
end enum
|
||
|
|
|
||
|
|
type, private :: tParameters !< container type for internal constitutive parameters
|
||
|
|
integer(kind(undefined_ID)), allocatable, dimension(:) :: &
|
||
|
|
outputID
|
||
|
|
real(pReal) :: &
|
||
|
|
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
|
||
|
|
logical :: &
|
||
|
|
dilatation = .false.
|
||
|
|
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
|
||
|
|
flowstress, &
|
||
|
|
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
|
||
|
|
|
||
|
|
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, &
|
||
|
|
maxNinstance, &
|
||
|
|
mySize, &
|
||
|
|
sizeDotState, &
|
||
|
|
sizeState, &
|
||
|
|
sizeDeltaState
|
||
|
|
character(len=65536) :: &
|
||
|
|
tag = '', &
|
||
|
|
line = '', &
|
||
|
|
extmsg = ''
|
||
|
|
character(len=64) :: &
|
||
|
|
outputtag = ''
|
||
|
|
integer(pInt) :: NipcMyPhase
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
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)
|
||
|
|
|
||
|
|
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 section
|
||
|
|
phase = phase + 1_pInt ! advance section counter
|
||
|
|
if (phase_plasticity(phase) == PLASTICITY_ISOTROPIC_ID) then
|
||
|
|
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
|
||
|
|
endif
|
||
|
|
cycle ! skip to next line
|
||
|
|
endif
|
||
|
|
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
|
||
|
|
instance = phase_plasticityInstance(phase) ! which instance of my plasticity is present phase
|
||
|
|
chunkPos = IO_stringPos(line)
|
||
|
|
tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key
|
||
|
|
extmsg = trim(tag)//' ('//PLASTICITY_ISOTROPIC_label//')' ! prepare error message identifier
|
||
|
|
|
||
|
|
select case(tag)
|
||
|
|
case ('(output)')
|
||
|
|
outputtag = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
|
||
|
|
select case(outputtag)
|
||
|
|
case ('flowstress')
|
||
|
|
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
|
||
|
|
case ('strainrate')
|
||
|
|
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
|
||
|
|
|
||
|
|
end select
|
||
|
|
|
||
|
|
case ('/dilatation/')
|
||
|
|
param(instance)%dilatation = .true.
|
||
|
|
|
||
|
|
case ('tau0')
|
||
|
|
param(instance)%tau0 = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
if (param(instance)%tau0 < 0.0_pReal) call IO_error(211_pInt,ext_msg=extmsg)
|
||
|
|
|
||
|
|
case ('gdot0')
|
||
|
|
param(instance)%gdot0 = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
if (param(instance)%gdot0 <= 0.0_pReal) call IO_error(211_pInt,ext_msg=extmsg)
|
||
|
|
|
||
|
|
case ('n')
|
||
|
|
param(instance)%n = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
if (param(instance)%n <= 0.0_pReal) call IO_error(211_pInt,ext_msg=extmsg)
|
||
|
|
|
||
|
|
case ('h0')
|
||
|
|
param(instance)%h0 = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('h0_slope','slopelnrate')
|
||
|
|
param(instance)%h0_slopeLnRate = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('tausat')
|
||
|
|
param(instance)%tausat = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
if (param(instance)%tausat <= 0.0_pReal) call IO_error(211_pInt,ext_msg=extmsg)
|
||
|
|
|
||
|
|
case ('tausat_sinhfita')
|
||
|
|
param(instance)%tausat_SinhFitA = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('tausat_sinhfitb')
|
||
|
|
param(instance)%tausat_SinhFitB = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('tausat_sinhfitc')
|
||
|
|
param(instance)%tausat_SinhFitC = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('tausat_sinhfitd')
|
||
|
|
param(instance)%tausat_SinhFitD = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case ('a', 'w0')
|
||
|
|
param(instance)%a = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
if (param(instance)%a <= 0.0_pReal) call IO_error(211_pInt,ext_msg=extmsg)
|
||
|
|
|
||
|
|
case ('taylorfactor')
|
||
|
|
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)
|
||
|
|
|
||
|
|
case ('atol_shear')
|
||
|
|
param(instance)%aTolShear = IO_floatValue(line,chunkPos,2_pInt)
|
||
|
|
|
||
|
|
case default
|
||
|
|
|
||
|
|
end select
|
||
|
|
endif; endif
|
||
|
|
enddo parsingFile
|
||
|
|
|
||
|
|
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)
|
||
|
|
instance = phase_plasticityInstance(phase)
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! sanity checks
|
||
|
|
if (param(instance)%aTolShear <= 0.0_pReal) &
|
||
|
|
param(instance)%aTolShear = 1.0e-6_pReal ! default absolute tolerance 1e-6
|
||
|
|
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! Determine size of postResults array
|
||
|
|
outputsLoop: do o = 1_pInt,plastic_isotropic_Noutput(instance)
|
||
|
|
select case(param(instance)%outputID(o))
|
||
|
|
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
|
||
|
|
sizeState = 2_pInt ! flowstress, accumulated_shear
|
||
|
|
sizeDotState = sizeState ! both evolve
|
||
|
|
sizeDeltaState = 0_pInt ! no sudden jumps in state
|
||
|
|
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))
|
||
|
|
|
||
|
|
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 (.not. analyticJaco) then
|
||
|
|
allocate(plasticState(phase)%state_backup ( sizeState,NipcMyPhase),source=0.0_pReal)
|
||
|
|
allocate(plasticState(phase)%dotState_backup (sizeDotState,NipcMyPhase),source=0.0_pReal)
|
||
|
|
endif
|
||
|
|
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)
|
||
|
|
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! 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
|
||
|
|
|
||
|
|
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: &
|
||
|
|
phasememberAt, &
|
||
|
|
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) :: &
|
||
|
|
instance, of, &
|
||
|
|
k, l, m, n
|
||
|
|
|
||
|
|
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
|
||
|
|
instance = phase_plasticityInstance(material_phase(ipc,ip,el))
|
||
|
|
|
||
|
|
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
|
||
|
|
gamma_dot = param(instance)%gdot0 &
|
||
|
|
* ( sqrt(1.5_pReal) * norm_Tstar_dev / param(instance)%fTaylor / state(instance)%flowstress(of) ) &
|
||
|
|
**param(instance)%n
|
||
|
|
|
||
|
|
Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/param(instance)%fTaylor
|
||
|
|
|
||
|
|
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) &
|
||
|
|
dLp_dTstar_3333(k,l,m,n) = (param(instance)%n-1.0_pReal) * &
|
||
|
|
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
|
||
|
|
dLp_dTstar99 = math_Plain3333to99(gamma_dot / param(instance)%fTaylor * &
|
||
|
|
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: &
|
||
|
|
phasememberAt, &
|
||
|
|
material_phase, &
|
||
|
|
phase_plasticityInstance
|
||
|
|
|
||
|
|
implicit none
|
||
|
|
real(pReal), dimension(3,3), intent(out) :: &
|
||
|
|
Li !< plastic velocity gradient
|
||
|
|
real(pReal), dimension(3,3,3,3), intent(out) :: &
|
||
|
|
dLi_dTstar_3333 !< derivative of Li with respect to Tstar as 4th order tensor
|
||
|
|
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
|
||
|
|
real(pReal) :: &
|
||
|
|
gamma_dot, & !< strainrate
|
||
|
|
norm_Tstar_sph, & !< euclidean norm of Tstar_sph
|
||
|
|
squarenorm_Tstar_sph !< square of the euclidean norm of Tstar_sph
|
||
|
|
integer(pInt) :: &
|
||
|
|
instance, of, &
|
||
|
|
k, l, m, n
|
||
|
|
|
||
|
|
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
|
||
|
|
instance = phase_plasticityInstance(material_phase(ipc,ip,el))
|
||
|
|
|
||
|
|
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)
|
||
|
|
|
||
|
|
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
|
||
|
|
else
|
||
|
|
Li = 0.0_pReal
|
||
|
|
dLi_dTstar_3333 = 0.0_pReal
|
||
|
|
endif
|
||
|
|
|
||
|
|
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: &
|
||
|
|
phasememberAt, &
|
||
|
|
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
|
||
|
|
saturation, & !< saturation flowstress
|
||
|
|
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
|
||
|
|
|
||
|
|
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
|
||
|
|
instance = phase_plasticityInstance(material_phase(ipc,ip,el))
|
||
|
|
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
|
||
|
|
if (param(instance)%dilatation) then
|
||
|
|
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
|
||
|
|
gamma_dot = param(instance)%gdot0 * ( sqrt(1.5_pReal) * norm_Tstar_v &
|
||
|
|
/ &!-----------------------------------------------------------------------------------
|
||
|
|
(param(instance)%fTaylor*state(instance)%flowstress(of) ))**param(instance)%n
|
||
|
|
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! hardening coefficient
|
||
|
|
if (abs(gamma_dot) > 1e-12_pReal) then
|
||
|
|
if (abs(param(instance)%tausat_SinhFitA) <= tiny(0.0_pReal)) then
|
||
|
|
saturation = param(instance)%tausat
|
||
|
|
else
|
||
|
|
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) &
|
||
|
|
+ 1.0_pReal ) &
|
||
|
|
) & ! asinh(K) = ln(K + sqrt(K^2 +1))
|
||
|
|
)**(1.0_pReal / param(instance)%tausat_SinhFitC) &
|
||
|
|
/ ( param(instance)%tausat_SinhFitB &
|
||
|
|
* (gamma_dot / param(instance)%gdot0)**(1.0_pReal / param(instance)%n) &
|
||
|
|
) &
|
||
|
|
)
|
||
|
|
endif
|
||
|
|
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)
|
||
|
|
else
|
||
|
|
hardening = 0.0_pReal
|
||
|
|
endif
|
||
|
|
|
||
|
|
dotState(instance)%flowstress (of) = hardening * gamma_dot
|
||
|
|
dotState(instance)%accumulatedShear(of) = gamma_dot
|
||
|
|
|
||
|
|
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, &
|
||
|
|
phasememberAt, &
|
||
|
|
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
|
||
|
|
|
||
|
|
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
|
||
|
|
instance = phase_plasticityInstance(material_phase(ipc,ip,el))
|
||
|
|
|
||
|
|
!--------------------------------------------------------------------------------------------------
|
||
|
|
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
|
||
|
|
if (param(instance)%dilatation) then
|
||
|
|
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
|
||
|
|
|
||
|
|
outputsLoop: do o = 1_pInt,plastic_isotropic_Noutput(instance)
|
||
|
|
select case(param(instance)%outputID(o))
|
||
|
|
case (flowstress_ID)
|
||
|
|
plastic_isotropic_postResults(c+1_pInt) = state(instance)%flowstress(of)
|
||
|
|
c = c + 1_pInt
|
||
|
|
case (strainrate_ID)
|
||
|
|
plastic_isotropic_postResults(c+1_pInt) = &
|
||
|
|
param(instance)%gdot0 * ( sqrt(1.5_pReal) * norm_Tstar_v &
|
||
|
|
/ &!----------------------------------------------------------------------------------
|
||
|
|
(param(instance)%fTaylor * state(instance)%flowstress(of)) ) ** param(instance)%n
|
||
|
|
c = c + 1_pInt
|
||
|
|
end select
|
||
|
|
enddo outputsLoop
|
||
|
|
|
||
|
|
end function plastic_isotropic_postResults
|
||
|
|
|
||
|
|
|
||
|
|
end module plastic_isotropic
|