! Copyright 2011-13 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see .
!
!##############################################################
!* $Id$
!*****************************************************
!* Module: CONSTITUTIVE_J2 *
!*****************************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!*****************************************************
! [Alu]
! plasticity j2
! (output) flowstress
! (output) strainrate
! c11 110.9e9 # (3 C11 + 2 C12 + 2 C44) / 5 ... with C44 = C11-C12 !!
! c12 58.34e9 # (1 C11 + 4 C12 - 1 C44) / 5
! taylorfactor 3
! tau0 31e6
! gdot0 0.001
! n 20
! h0 75e6
! tausat 63e6
! a 2.25
module constitutive_j2
use prec, only: pReal,pInt
implicit none
private
character (len=*), parameter, public :: constitutive_j2_LABEL = 'j2'
integer(pInt), dimension(:), allocatable, public :: &
constitutive_j2_sizeDotState, &
constitutive_j2_sizeState, &
constitutive_j2_sizePostResults
integer(pInt), dimension(:,:), allocatable, target, public :: &
constitutive_j2_sizePostResult ! size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
constitutive_j2_output ! name of each post result output
integer(pInt), dimension(:), allocatable, private :: &
constitutive_j2_Noutput !< name of each post result output
character(len=32), dimension(:), allocatable, private :: &
constitutive_j2_structureName
real(pReal), dimension(:), allocatable, private :: &
!* Visco-plastic constitutive_j2 parameters
constitutive_j2_fTaylor, &
constitutive_j2_tau0, &
constitutive_j2_gdot0, &
constitutive_j2_n, &
!* h0 as function of h0 = A + B log (gammadot)
constitutive_j2_h0, &
constitutive_j2_h0_slopeLnRate, &
constitutive_j2_tausat, &
constitutive_j2_a, &
constitutive_j2_aTolResistance, &
!* Parameters of normalized strain rate vs. stress function:
!* tausat += (asinh((gammadot / SinhFitA)**(1 / SinhFitD)))**(1 / SinhFitC) / (SinhFitB * (gammadot / gammadot0)**(1/n))
constitutive_j2_tausat_SinhFitA, &
constitutive_j2_tausat_SinhFitB, &
constitutive_j2_tausat_SinhFitC, &
constitutive_j2_tausat_SinhFitD
real(pReal), dimension(:,:,:), allocatable, private :: &
constitutive_j2_Cslip_66
public :: constitutive_j2_init, &
constitutive_j2_stateInit, &
constitutive_j2_aTolState, &
constitutive_j2_homogenizedC, &
constitutive_j2_microstructure, &
constitutive_j2_LpAndItsTangent, &
constitutive_j2_dotState, &
constitutive_j2_deltaState, &
constitutive_j2_dotTemperature, &
constitutive_j2_postResults
contains
subroutine constitutive_j2_init(myFile)
!**************************************
!* Module initialization *
!**************************************
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333
use IO, only: &
IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_error, &
IO_timeStamp
use material
use debug, only: &
debug_level, &
debug_constitutive, &
debug_levelBasic
use lattice, only: lattice_symmetrizeC66
implicit none
integer(pInt), intent(in) :: myFile
integer(pInt), parameter :: maxNchunks = 7_pInt
integer(pInt), dimension(1_pInt+2_pInt*maxNchunks) :: positions
integer(pInt) :: section = 0_pInt, maxNinstance, i,o, mySize
character(len=64) :: tag
character(len=1024) :: line = '' ! to start initialized
write(6,'(/,a)') ' <<<+- constitutive_'//trim(constitutive_j2_LABEL)//' init -+>>>'
write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == constitutive_j2_label),pInt)
if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) then
write(6,'(a16,1x,i5)') '# instances:',maxNinstance
write(6,*)
endif
allocate(constitutive_j2_sizeDotState(maxNinstance))
constitutive_j2_sizeDotState = 0_pInt
allocate(constitutive_j2_sizeState(maxNinstance))
constitutive_j2_sizeState = 0_pInt
allocate(constitutive_j2_sizePostResults(maxNinstance))
constitutive_j2_sizePostResults = 0_pInt
allocate(constitutive_j2_sizePostResult(maxval(phase_Noutput), maxNinstance))
constitutive_j2_sizePostResult = 0_pInt
allocate(constitutive_j2_output(maxval(phase_Noutput), maxNinstance))
constitutive_j2_output = ''
allocate(constitutive_j2_Noutput(maxNinstance))
constitutive_j2_Noutput = 0_pInt
allocate(constitutive_j2_structureName(maxNinstance))
constitutive_j2_structureName = ''
allocate(constitutive_j2_Cslip_66(6,6,maxNinstance))
constitutive_j2_Cslip_66 = 0.0_pReal
allocate(constitutive_j2_fTaylor(maxNinstance))
constitutive_j2_fTaylor = 0.0_pReal
allocate(constitutive_j2_tau0(maxNinstance))
constitutive_j2_tau0 = 0.0_pReal
allocate(constitutive_j2_gdot0(maxNinstance))
constitutive_j2_gdot0 = 0.0_pReal
allocate(constitutive_j2_n(maxNinstance))
constitutive_j2_n = 0.0_pReal
allocate(constitutive_j2_h0(maxNinstance))
constitutive_j2_h0 = 0.0_pReal
allocate(constitutive_j2_h0_slopeLnRate(maxNinstance))
constitutive_j2_h0_slopeLnRate = 0.0_pReal
allocate(constitutive_j2_tausat(maxNinstance))
constitutive_j2_tausat = 0.0_pReal
allocate(constitutive_j2_a(maxNinstance))
constitutive_j2_a = 0.0_pReal
allocate(constitutive_j2_aTolResistance(maxNinstance))
constitutive_j2_aTolResistance = 0.0_pReal
allocate(constitutive_j2_tausat_SinhFitA(maxNinstance))
constitutive_j2_tausat_SinhFitA = 0.0_pReal
allocate(constitutive_j2_tausat_SinhFitB(maxNinstance))
constitutive_j2_tausat_SinhFitB = 0.0_pReal
allocate(constitutive_j2_tausat_SinhFitC(maxNinstance))
constitutive_j2_tausat_SinhFitC = 0.0_pReal
allocate(constitutive_j2_tausat_SinhFitD(maxNinstance))
constitutive_j2_tausat_SinhFitD = 0.0_pReal
rewind(myFile)
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to
read(myFile,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(myFile,'(a1024)',END=100) line
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1_pInt ! advance section counter
cycle
endif
if (section > 0_pInt .and. phase_plasticity(section) == constitutive_j2_label) then ! one of my sections
i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('plasticity','elasticity')
cycle
case ('(output)')
constitutive_j2_Noutput(i) = constitutive_j2_Noutput(i) + 1_pInt
constitutive_j2_output(constitutive_j2_Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('lattice_structure')
constitutive_j2_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('c11')
constitutive_j2_Cslip_66(1,1,i) = IO_floatValue(line,positions,2_pInt)
case ('c12')
constitutive_j2_Cslip_66(1,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c13')
constitutive_j2_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c22')
constitutive_j2_Cslip_66(2,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c23')
constitutive_j2_Cslip_66(2,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c33')
constitutive_j2_Cslip_66(3,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c44')
constitutive_j2_Cslip_66(4,4,i) = IO_floatValue(line,positions,2_pInt)
case ('c55')
constitutive_j2_Cslip_66(5,5,i) = IO_floatValue(line,positions,2_pInt)
case ('c66')
constitutive_j2_Cslip_66(6,6,i) = IO_floatValue(line,positions,2_pInt)
case ('tau0')
constitutive_j2_tau0(i) = IO_floatValue(line,positions,2_pInt)
case ('gdot0')
constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2_pInt)
case ('n')
constitutive_j2_n(i) = IO_floatValue(line,positions,2_pInt)
case ('h0')
constitutive_j2_h0(i) = IO_floatValue(line,positions,2_pInt)
case ('h0_slope','slopelnrate')
constitutive_j2_h0_slopeLnRate(i) = IO_floatValue(line,positions,2_pInt)
case ('tausat')
constitutive_j2_tausat(i) = IO_floatValue(line,positions,2_pInt)
case ('tausat_sinhfita')
constitutive_j2_tausat_SinhFitA(i) = IO_floatValue(line,positions,2_pInt)
case ('tausat_sinhfitb')
constitutive_j2_tausat_SinhFitB(i) = IO_floatValue(line,positions,2_pInt)
case ('tausat_sinhfitc')
constitutive_j2_tausat_SinhFitC(i) = IO_floatValue(line,positions,2_pInt)
case ('tausat_sinhfitd')
constitutive_j2_tausat_SinhFitD(i) = IO_floatValue(line,positions,2_pInt)
case ('a', 'w0')
constitutive_j2_a(i) = IO_floatValue(line,positions,2_pInt)
case ('taylorfactor')
constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2_pInt)
case ('atol_resistance')
constitutive_j2_aTolResistance(i) = IO_floatValue(line,positions,2_pInt)
case default
call IO_error(210_pInt,ext_msg=tag//' ('//constitutive_j2_label//')')
end select
endif
enddo
100 do i = 1_pInt,maxNinstance ! sanity checks
if (constitutive_j2_structureName(i) == '') call IO_error(205_pInt,e=i)
if (constitutive_j2_tau0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='tau0 (' &
//constitutive_j2_label//')')
if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='gdot0 (' &
//constitutive_j2_label//')')
if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='n (' &
//constitutive_j2_label//')')
if (constitutive_j2_tausat(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='tausat (' &
//constitutive_j2_label//')')
if (constitutive_j2_a(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='a (' &
//constitutive_j2_label//')')
if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='taylorfactor (' &
//constitutive_j2_label//')')
if (constitutive_j2_aTolResistance(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_resistance (' &
//constitutive_j2_label//')')
enddo
do i = 1_pInt,maxNinstance
do o = 1_pInt,constitutive_j2_Noutput(i)
select case(constitutive_j2_output(o,i))
case('flowstress')
mySize = 1_pInt
case('strainrate')
mySize = 1_pInt
case default
call IO_error(212_pInt,ext_msg=constitutive_j2_output(o,i)//' ('//constitutive_j2_label//')')
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_j2_sizePostResult(o,i) = mySize
constitutive_j2_sizePostResults(i) = &
constitutive_j2_sizePostResults(i) + mySize
endif
enddo
constitutive_j2_sizeDotState(i) = 1_pInt
constitutive_j2_sizeState(i) = 1_pInt
constitutive_j2_Cslip_66(:,:,i) = lattice_symmetrizeC66(constitutive_j2_structureName(i),&
constitutive_j2_Cslip_66(:,:,i))
constitutive_j2_Cslip_66(1:6,1:6,i) = &
math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(1:6,1:6,i)))
enddo
end subroutine constitutive_j2_init
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
pure function constitutive_j2_stateInit(myInstance)
implicit none
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(1) :: constitutive_j2_stateInit
constitutive_j2_stateInit = constitutive_j2_tau0(myInstance)
end function constitutive_j2_stateInit
!*********************************************************************
!* relevant microstructural state *
!*********************************************************************
pure function constitutive_j2_aTolState(myInstance)
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the plasticity
!*** output variables
real(pReal), dimension(constitutive_j2_sizeState(myInstance)) :: &
constitutive_j2_aTolState ! relevant state values for the current instance of this plasticity
constitutive_j2_aTolState = constitutive_j2_aTolResistance(myInstance)
end function constitutive_j2_aTolState
pure function constitutive_j2_homogenizedC(state,ipc,ip,el)
!*********************************************************************
!* homogenized elacticity matrix *
!* INPUT: *
!* - state : state variables *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_plasticityInstance
implicit none
integer(pInt), intent(in) :: ipc,ip,el
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
integer(pInt) :: matID
real(pReal), dimension(6,6) :: constitutive_j2_homogenizedC
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(1:6,1:6,matID)
end function constitutive_j2_homogenizedC
pure subroutine constitutive_j2_microstructure(Temperature,state,ipc,ip,el)
!*********************************************************************
!* calculate derived quantities from state (not used here) *
!* INPUT: *
!* - Tp : temperature *
!* - ipc : component-ID of current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_plasticityInstance
implicit none
!* Definition of variables
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: Temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
integer(pInt) :: matID
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
end subroutine constitutive_j2_microstructure
!****************************************************************
!* calculates plastic velocity gradient and its tangent *
!****************************************************************
pure subroutine constitutive_j2_LpAndItsTangent(Lp, dLp_dTstar_99, Tstar_v, Temperature, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: p_vec
use math, only: math_mul6x6, &
math_Mandel6to33, &
math_Plain3333to99, &
math_deviatoric33, &
math_mul33xx33
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in):: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar_99 ! derivative of Lp with respect to Tstar (9x9 matrix)
!*** local variables ***!
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) matID, &
k, &
l, &
m, &
n
matID = phase_plasticityInstance(material_phase(g,ip,el))
! deviatoric part of 2nd Piola-Kirchhoff stress
Tstar_dev_33 = math_deviatoric33(math_Mandel6to33(Tstar_v))
squarenorm_Tstar_dev = math_mul33xx33(Tstar_dev_33,Tstar_dev_33)
norm_Tstar_dev = sqrt(squarenorm_Tstar_dev)
! Initialization of Lp and dLp_dTstar
Lp = 0.0_pReal
dLp_dTstar_99 = 0.0_pReal
! Tstar == 0 --> both Lp and dLp_dTstar are zero
if (norm_Tstar_dev > 0.0_pReal) then
! Calculation of gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) **constitutive_j2_n(matID)
! Calculation of Lp
Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID)
!* 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) = (constitutive_j2_n(matID)-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
dLp_dTstar_99 = math_Plain3333to99(gamma_dot / constitutive_j2_fTaylor(matID) * dLp_dTstar_3333 / norm_Tstar_dev)
end if
end subroutine constitutive_j2_LpAndItsTangent
!****************************************************************
!* calculates the rate of change of microstructure *
!****************************************************************
pure function constitutive_j2_dotState(Tstar_v, Temperature, state, g, ip, el)
use prec, only: &
p_vec
use math, only: &
math_mul6x6
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(1) :: constitutive_j2_dotState ! evolution of state variable
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) gamma_dot, & ! strainrate
hardening, & ! hardening coefficient
saturation, & ! saturation resistance
norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID
matID = phase_plasticityInstance(material_phase(g,ip,el))
! deviatoric part of 2nd Piola-Kirchhoff stress
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_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
! gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
! hardening coefficient
if (abs(gamma_dot) > 1e-12_pReal) then
if (constitutive_j2_tausat_SinhFitA(matID) == 0.0_pReal) then
saturation = constitutive_j2_tausat(matID)
else
saturation = ( constitutive_j2_tausat(matID) &
+ ( log( ( gamma_dot / constitutive_j2_tausat_SinhFitA(matID)&
)**(1.0_pReal / constitutive_j2_tausat_SinhFitD(matID))&
+ sqrt( ( gamma_dot / constitutive_j2_tausat_SinhFitA(matID) &
)**(2.0_pReal / constitutive_j2_tausat_SinhFitD(matID)) &
+ 1.0_pReal ) &
) & ! asinh(K) = ln(K + sqrt(K^2 +1))
)**(1.0_pReal / constitutive_j2_tausat_SinhFitC(matID)) &
/ ( constitutive_j2_tausat_SinhFitB(matID) &
* (gamma_dot / constitutive_j2_gdot0(matID))**(1.0_pReal / constitutive_j2_n(matID)) &
) &
)
endif
hardening = ( constitutive_j2_h0(matID) + constitutive_j2_h0_slopeLnRate(matID) * log(gamma_dot) ) &
* abs( 1.0_pReal - state(g,ip,el)%p(1)/saturation )**constitutive_j2_a(matID) &
* sign(1.0_pReal, 1.0_pReal - state(g,ip,el)%p(1)/saturation)
else
hardening = 0.0_pReal
endif
! dotState
constitutive_j2_dotState = hardening * gamma_dot
end function constitutive_j2_dotState
!*********************************************************************
!* (instantaneous) incremental change of microstructure *
!*********************************************************************
function constitutive_j2_deltaState(Tstar_v, Temperature, state, g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! current microstructural state
!*** output variables
real(pReal), dimension(constitutive_j2_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_j2_deltaState ! change of state variables / microstructure
!*** local variables
constitutive_j2_deltaState = 0.0_pReal
endfunction
!****************************************************************
!* calculates the rate of change of temperature *
!****************************************************************
pure function constitutive_j2_dotTemperature(Tstar_v, Temperature, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal) constitutive_j2_dotTemperature ! rate of change of temperature
! calculate dotTemperature
constitutive_j2_dotTemperature = 0.0_pReal
end function constitutive_j2_dotTemperature
!*********************************************************************
!* return array of constitutive results *
!*********************************************************************
pure function constitutive_j2_postResults(Tstar_v, Temperature, dt, state, g, ip, el)
!*** variables and functions from other modules ***!
use prec, only: p_vec
use math, only: math_mul6x6
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
phase_Noutput
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature, &
dt ! current time increment
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(constitutive_j2_sizePostResults(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_j2_postResults
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID, &
o, &
c
!*** global variables ***!
! constitutive_j2_gdot0
! constitutive_j2_fTaylor
! constitutive_j2_n
matID = phase_plasticityInstance(material_phase(g,ip,el))
! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm
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_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
c = 0_pInt
constitutive_j2_postResults = 0.0_pReal
do o = 1_pInt,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_j2_output(o,matID))
case ('flowstress')
constitutive_j2_postResults(c+1_pInt) = state(g,ip,el)%p(1)
c = c + 1_pInt
case ('strainrate')
constitutive_j2_postResults(c+1_pInt) = &
constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
c = c + 1_pInt
end select
enddo
end function constitutive_j2_postResults
end module constitutive_j2