DAMASK_EICMD/src/plastic_isotropic.f90

561 lines
28 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
implicit none
private
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, &
tau0, &
gdot0, &
n, &
h0, &
h0_slopeLnRate, &
tausat, &
a, &
aTolFlowstress, &
aTolShear, &
tausat_SinhFitA, &
tausat_SinhFitB, &
tausat_SinhFitC, &
tausat_SinhFitD
logical :: &
dilatation
end type
type(tParameters), dimension(:), allocatable, target, 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(tIsotropicState), allocatable, dimension(:), private :: & !< state aliases per instance
state, &
dotState
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()
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
use IO
use debug, only: &
debug_level, &
debug_constitutive, &
debug_levelBasic
use numerics, only: &
numerics_integrator
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333
use material, only: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
PLASTICITY_ISOTROPIC_label, &
PLASTICITY_ISOTROPIC_ID, &
material_phase, &
plasticState
use config, only: &
MATERIAL_partPhase, &
config_phase
use lattice
implicit none
type(tParameters), pointer :: prm
integer(pInt) :: &
phase, &
instance, &
maxNinstance, &
sizeDotState, &
sizeState, &
sizeDeltaState
character(len=65536) :: &
extmsg = ''
integer(pInt) :: NipcMyPhase,i
character(len=65536), dimension(:), allocatable :: outputs
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_ISOTROPIC_label//' init -+>>>'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_ISOTROPIC_ID),pInt)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
! public variables
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
allocate(state(maxNinstance)) ! internal state aliases
allocate(dotState(maxNinstance))
do phase = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(phase) == PLASTICITY_ISOTROPIC_ID) then
instance = phase_plasticityInstance(phase)
prm => param(instance) ! shorthand pointer to parameter object of my constitutive law
prm%tau0 = config_phase(phase)%getFloat('tau0')
prm%tausat = config_phase(phase)%getFloat('tausat')
prm%gdot0 = config_phase(phase)%getFloat('gdot0')
prm%n = config_phase(phase)%getFloat('n')
prm%h0 = config_phase(phase)%getFloat('h0')
prm%fTaylor = config_phase(phase)%getFloat('m')
prm%h0_slopeLnRate = config_phase(phase)%getFloat('h0_slopelnrate', defaultVal=0.0_pReal)
prm%tausat_SinhFitA = config_phase(phase)%getFloat('tausat_sinhfita',defaultVal=0.0_pReal)
prm%tausat_SinhFitB = config_phase(phase)%getFloat('tausat_sinhfitb',defaultVal=0.0_pReal)
prm%tausat_SinhFitC = config_phase(phase)%getFloat('tausat_sinhfitc',defaultVal=0.0_pReal)
prm%tausat_SinhFitD = config_phase(phase)%getFloat('tausat_sinhfitd',defaultVal=0.0_pReal)
prm%a = config_phase(phase)%getFloat('a')
prm%aTolFlowStress = config_phase(phase)%getFloat('atol_flowstress',defaultVal=1.0_pReal)
prm%aTolShear = config_phase(phase)%getFloat('atol_shear',defaultVal=1.0e-6_pReal)
prm%dilatation = config_phase(phase)%keyExists('/dilatation/')
#if defined(__GFORTRAN__)
outputs = ['GfortranBug86277']
outputs = config_phase(phase)%getStrings('(output)',defaultVal=outputs)
if (outputs(1) == 'GfortranBug86277') outputs = [character(len=65536)::]
#else
outputs = config_phase(phase)%getStrings('(output)',defaultVal=[character(len=65536)::])
#endif
allocate(prm%outputID(0))
do i=1_pInt, size(outputs)
select case(outputs(i))
case ('flowstress')
plastic_isotropic_Noutput(instance) = plastic_isotropic_Noutput(instance) + 1_pInt
plastic_isotropic_output(plastic_isotropic_Noutput(instance),instance) = outputs(i)
plasticState(phase)%sizePostResults = plasticState(phase)%sizePostResults + 1_pInt
plastic_isotropic_sizePostResult(i,instance) = 1_pInt
prm%outputID = [prm%outputID,flowstress_ID]
case ('strainrate')
plastic_isotropic_Noutput(instance) = plastic_isotropic_Noutput(instance) + 1_pInt
plastic_isotropic_output(plastic_isotropic_Noutput(instance),instance) = outputs(i)
plasticState(phase)%sizePostResults = &
plasticState(phase)%sizePostResults + 1_pInt
plastic_isotropic_sizePostResult(i,instance) = 1_pInt
prm%outputID = [prm%outputID,strainrate_ID]
end select
enddo
!--------------------------------------------------------------------------------------------------
! sanity checks
extmsg = ''
if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//"'aTolShear' "
if (prm%tau0 < 0.0_pReal) extmsg = trim(extmsg)//"'tau0' "
if (prm%gdot0 <= 0.0_pReal) extmsg = trim(extmsg)//"'gdot0' "
if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//"'n' "
if (prm%tausat <= prm%tau0) extmsg = trim(extmsg)//"'tausat' "
if (prm%a <= 0.0_pReal) extmsg = trim(extmsg)//"'a' "
if (prm%fTaylor <= 0.0_pReal) extmsg = trim(extmsg)//"'m' "
if (prm%aTolFlowstress <= 0.0_pReal) extmsg = trim(extmsg)//"'atol_flowstress' "
if (extmsg /= '') call IO_error(211_pInt,ip=instance,&
ext_msg=trim(extmsg)//'('//PLASTICITY_ISOTROPIC_label//')')
!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phase == phase) ! number of own material points (including point components ipc)
sizeDotState = size(["flowstress ","accumulated_shear"])
sizeDeltaState = 0_pInt ! no sudden jumps in state
sizeState = sizeDotState + sizeDeltaState
plasticState(phase)%sizeState = sizeState
plasticState(phase)%sizeDotState = sizeDotState
plasticState(phase)%sizeDeltaState = sizeDeltaState
plasticState(phase)%nSlip = 1
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 (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)
!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
state(instance)%flowstress => plasticState(phase)%state (1,1:NipcMyPhase)
dotState(instance)%flowstress => plasticState(phase)%dotState (1,1:NipcMyPhase)
plasticState(phase)%state0(1,1:NipcMyPhase) = prm%tau0
plasticState(phase)%aTolState(1) = prm%aTolFlowstress
state(instance)%accumulatedShear => plasticState(phase)%state (2,1:NipcMyPhase)
dotState(instance)%accumulatedShear => plasticState(phase)%dotState (2,1:NipcMyPhase)
plasticState(phase)%state0 (2,1:NipcMyPhase) = 0.0_pReal
plasticState(phase)%aTolState(2) = prm%aTolShear
! global alias
plasticState(phase)%slipRate => plasticState(phase)%dotState(2:2,1:NipcMyPhase)
plasticState(phase)%accumulatedSlip => plasticState(phase)%state (2:2,1:NipcMyPhase)
endif
enddo
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
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
type(tParameters), pointer :: prm
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))
prm => param(instance)
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 = prm%gdot0 &
* ( sqrt(1.5_pReal) * norm_Tstar_dev / prm%fTaylor / state(instance)%flowstress(of) ) &
**prm%n
Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/prm%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', &
transpose(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) = (prm%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 / prm%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
type(tParameters), pointer :: prm
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))
prm => param(instance)
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 (prm%dilatation .and. norm_Tstar_sph > 0.0_pReal) then ! Tstar == 0 or J2 plascitiy --> both Li and dLi_dTstar are zero
gamma_dot = prm%gdot0 &
* (sqrt(1.5_pReal) * norm_Tstar_sph / prm%fTaylor / state(instance)%flowstress(of) ) &
**prm%n
Li = Tstar_sph_33/norm_Tstar_sph * gamma_dot/prm%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) = (prm%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 / prm%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 prec, only: &
dEq0
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
type(tParameters), pointer :: prm
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))
prm => param(instance)
!--------------------------------------------------------------------------------------------------
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
if (prm%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 = prm%gdot0 * ( sqrt(1.5_pReal) * norm_Tstar_v &
/ &!-----------------------------------------------------------------------------------
(prm%fTaylor*state(instance)%flowstress(of) ))**prm%n
!--------------------------------------------------------------------------------------------------
! hardening coefficient
if (abs(gamma_dot) > 1e-12_pReal) then
if (dEq0(prm%tausat_SinhFitA)) then
saturation = prm%tausat
else
saturation = prm%tausat &
+ asinh( (gamma_dot / prm%tausat_SinhFitA&
)**(1.0_pReal / prm%tausat_SinhFitD)&
)**(1.0_pReal / prm%tausat_SinhFitC) &
/ ( prm%tausat_SinhFitB &
* (gamma_dot / prm%gdot0)**(1.0_pReal / prm%n) &
)
endif
hardening = ( prm%h0 + prm%h0_slopeLnRate * log(gamma_dot) ) &
* abs( 1.0_pReal - state(instance)%flowstress(of)/saturation )**prm%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: &
plasticState, &
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
type(tParameters), pointer :: prm
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: &
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))
prm => param(instance)
!--------------------------------------------------------------------------------------------------
! norm of (deviatoric) 2nd Piola-Kirchhoff stress
if (prm%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(prm%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) = &
prm%gdot0 * ( sqrt(1.5_pReal) * norm_Tstar_v &
/ &!----------------------------------------------------------------------------------
(prm%fTaylor * state(instance)%flowstress(of)) ) ** prm%n
c = c + 1_pInt
end select
enddo outputsLoop
end function plastic_isotropic_postResults
end module plastic_isotropic