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doxygen documentation for J2

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Martin Diehl 2013-06-28 18:58:10 +00:00
parent e34a3dcb32
commit ef2c2af471
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code/constitutive_j2.f90
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@ -16,100 +16,90 @@
! You should have received a copy of the GNU General Public License ! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>. ! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
! !
!############################################################## !--------------------------------------------------------------------------------------------------
!* $Id$ ! $Id$
!***************************************************** !--------------------------------------------------------------------------------------------------
!* Module: CONSTITUTIVE_J2 * !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!***************************************************** !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!* contains: * !> @brief Isotropic (J2) Plasticity
!* - constitutive equations * !> @details Isotropic (J2) Plasticity which resembles the phenopowerlaw plasticity without
!* - parameters definition * !! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an
!***************************************************** !! untextured polycrystal
!--------------------------------------------------------------------------------------------------
! [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 module constitutive_j2
use prec, only: &
use prec, only: pReal,pInt pReal,&
pInt
implicit none implicit none
private private
character (len=*), parameter, public :: constitutive_j2_LABEL = 'j2' character (len=*), parameter, public :: &
CONSTITUTIVE_J2_label = 'j2' !< label for this constitutive model
integer(pInt), dimension(:), allocatable, public :: & integer(pInt), dimension(:), allocatable, public :: &
constitutive_j2_sizeDotState, & constitutive_j2_sizeDotState, &
constitutive_j2_sizeState, & constitutive_j2_sizeState, &
constitutive_j2_sizePostResults constitutive_j2_sizePostResults
integer(pInt), dimension(:,:), allocatable, target, public :: & integer(pInt), dimension(:,:), allocatable, target, public :: &
constitutive_j2_sizePostResult ! size of each post result output constitutive_j2_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: & character(len=64), dimension(:,:), allocatable, target, public :: &
constitutive_j2_output ! name of each post result output constitutive_j2_output !< name of each post result output
integer(pInt), dimension(:), allocatable, private :: & integer(pInt), dimension(:), allocatable, private :: &
constitutive_j2_Noutput !< name of each post result output constitutive_j2_Noutput !< ??
character(len=32), dimension(:), allocatable, private :: & character(len=32), dimension(:), allocatable, private :: &
constitutive_j2_structureName constitutive_j2_structureName
real(pReal), dimension(:), allocatable, private :: & real(pReal), dimension(:), allocatable, private :: &
!* Visco-plastic constitutive_j2 parameters constitutive_j2_fTaylor, & !< Taylor factor
constitutive_j2_fTaylor, & constitutive_j2_tau0, & !< initial plastic stress
constitutive_j2_tau0, & constitutive_j2_gdot0, & !< reference velocity
constitutive_j2_gdot0, & constitutive_j2_n, & !< Visco-plastic parameter
constitutive_j2_n, & !--------------------------------------------------------------------------------------------------
!* h0 as function of h0 = A + B log (gammadot) ! h0 as function of h0 = A + B log (gammadot)
constitutive_j2_h0, & constitutive_j2_h0, &
constitutive_j2_h0_slopeLnRate, & constitutive_j2_h0_slopeLnRate, &
constitutive_j2_tausat, & constitutive_j2_tausat, & !< final plastic stress
constitutive_j2_a, & constitutive_j2_a, &
constitutive_j2_aTolResistance, & constitutive_j2_aTolResistance, &
!* Parameters of normalized strain rate vs. stress function: !--------------------------------------------------------------------------------------------------
!* tausat += (asinh((gammadot / SinhFitA)**(1 / SinhFitD)))**(1 / SinhFitC) / (SinhFitB * (gammadot / gammadot0)**(1/n)) ! tausat += (asinh((gammadot / SinhFitA)**(1 / SinhFitD)))**(1 / SinhFitC) / (SinhFitB * (gammadot / gammadot0)**(1/n))
constitutive_j2_tausat_SinhFitA, & constitutive_j2_tausat_SinhFitA, & !< fitting parameter for normalized strain rate vs. stress function
constitutive_j2_tausat_SinhFitB, & constitutive_j2_tausat_SinhFitB, & !< fitting parameter for normalized strain rate vs. stress function
constitutive_j2_tausat_SinhFitC, & constitutive_j2_tausat_SinhFitC, & !< fitting parameter for normalized strain rate vs. stress function
constitutive_j2_tausat_SinhFitD constitutive_j2_tausat_SinhFitD !< fitting parameter for normalized strain rate vs. stress function
real(pReal), dimension(:,:,:), allocatable, private :: &
real(pReal), dimension(:,:,:), allocatable, private :: &
constitutive_j2_Cslip_66 constitutive_j2_Cslip_66
public :: constitutive_j2_init, & public :: &
constitutive_j2_stateInit, & constitutive_j2_init, &
constitutive_j2_aTolState, & constitutive_j2_stateInit, &
constitutive_j2_homogenizedC, & constitutive_j2_aTolState, &
constitutive_j2_microstructure, & constitutive_j2_homogenizedC, &
constitutive_j2_LpAndItsTangent, & constitutive_j2_microstructure, &
constitutive_j2_dotState, & constitutive_j2_LpAndItsTangent, &
constitutive_j2_deltaState, & constitutive_j2_dotState, &
constitutive_j2_dotTemperature, & constitutive_j2_deltaState, &
constitutive_j2_postResults constitutive_j2_dotTemperature, &
constitutive_j2_postResults
contains contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!--------------------------------------------------------------------------------------------------
subroutine constitutive_j2_init(myFile) subroutine constitutive_j2_init(myFile)
!************************************** use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
!* 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: & use math, only: &
math_Mandel3333to66, & math_Mandel3333to66, &
math_Voigt66to3333 math_Voigt66to3333
use IO, only: & use IO, only: &
IO_read, &
IO_lc, & IO_lc, &
IO_getTag, & IO_getTag, &
IO_isBlank, & IO_isBlank, &
@ -117,25 +107,28 @@ subroutine constitutive_j2_init(myFile)
IO_stringValue, & IO_stringValue, &
IO_floatValue, & IO_floatValue, &
IO_error, & IO_error, &
IO_timeStamp IO_timeStamp, &
IO_read
use material use material
use debug, only: & use debug, only: &
debug_level, & debug_level, &
debug_constitutive, & debug_constitutive, &
debug_levelBasic debug_levelBasic
use lattice, only: lattice_symmetrizeC66 use lattice, only: &
lattice_symmetrizeC66
implicit none implicit none
integer(pInt), intent(in) :: myFile integer(pInt), intent(in) :: myFile
integer(pInt), parameter :: maxNchunks = 7_pInt integer(pInt), parameter :: MAXNCHUNKS = 7_pInt
integer(pInt), dimension(1_pInt+2_pInt*maxNchunks) :: positions integer(pInt), dimension(1_pInt+2_pInt*MAXNCHUNKS) :: positions
integer(pInt) :: section = 0_pInt, maxNinstance, i,o, mySize integer(pInt) :: section = 0_pInt, maxNinstance, i,o, mySize
character(len=65536) :: tag character(len=65536) :: &
character(len=65536) :: line = '' ! to start initialized tag = '', &
line = '' ! to start initialized
write(6,'(/,a)') ' <<<+- constitutive_'//trim(constitutive_j2_LABEL)//' init -+>>>' write(6,'(/,a)') ' <<<+- constitutive_'//trim(CONSTITUTIVE_J2_label)//' init -+>>>'
write(6,'(a)') ' $Id$' write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp() write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90" #include "compilation_info.f90"
@ -144,8 +137,7 @@ subroutine constitutive_j2_init(myFile)
if (maxNinstance == 0_pInt) return if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) then if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) then
write(6,'(a16,1x,i5)') '# instances:',maxNinstance write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
write(6,*)
endif endif
allocate(constitutive_j2_sizeDotState(maxNinstance)) allocate(constitutive_j2_sizeDotState(maxNinstance))
@ -193,29 +185,30 @@ subroutine constitutive_j2_init(myFile)
rewind(myFile) rewind(myFile)
do while (trim(line) /= '#EOF#' .and. IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase> do while (trim(line) /= '#EOF#' .and. IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
line = IO_read(myFile) line = IO_read(myFile)
enddo enddo
do while (trim(line) /= '#EOF#') ! read thru sections of phase part do while (trim(line) /= '#EOF#') ! read through sections of phase part
line = IO_read(myFile) line = IO_read(myFile)
if (IO_isBlank(line)) cycle ! skip empty lines if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
if (IO_getTag(line,'[',']') /= '') then ! next section if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1_pInt ! advance section counter section = section + 1_pInt ! advance section counter
cycle cycle
endif endif
if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if statemen). It's not safe in Fortran if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if-statement). It's not safe in Fortran
if (phase_plasticity(section) == constitutive_j2_LABEL) then ! one of my sections if (phase_plasticity(section) == CONSTITUTIVE_J2_label) then ! one of my sections
i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
positions = IO_stringPos(line,maxNchunks) positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag) select case(tag)
case ('plasticity','elasticity') case ('plasticity','elasticity')
cycle cycle
case ('(output)') case ('(output)')
constitutive_j2_Noutput(i) = constitutive_j2_Noutput(i) + 1_pInt 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)) constitutive_j2_output(constitutive_j2_Noutput(i),i) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('lattice_structure') case ('lattice_structure')
constitutive_j2_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt)) constitutive_j2_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('c11') case ('c11')
@ -269,23 +262,23 @@ subroutine constitutive_j2_init(myFile)
endif endif
enddo enddo
do i = 1_pInt,maxNinstance ! sanity checks sanityChecks: do i = 1_pInt,maxNinstance
if (constitutive_j2_structureName(i) == '') call IO_error(205_pInt,e=i) 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 (' & if (constitutive_j2_tau0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='tau0 (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='gdot0 (' & if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='gdot0 (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='n (' & if (constitutive_j2_n(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='n (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_tausat(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='tausat (' & if (constitutive_j2_tausat(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='tausat (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_a(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='a (' & if (constitutive_j2_a(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='a (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='taylorfactor (' & if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='taylorfactor (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
if (constitutive_j2_aTolResistance(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_resistance (' & if (constitutive_j2_aTolResistance(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_resistance (' &
//constitutive_j2_label//')') //CONSTITUTIVE_J2_label//')')
enddo enddo sanityChecks
do i = 1_pInt,maxNinstance do i = 1_pInt,maxNinstance
do o = 1_pInt,constitutive_j2_Noutput(i) do o = 1_pInt,constitutive_j2_Noutput(i)
@ -295,10 +288,10 @@ subroutine constitutive_j2_init(myFile)
case('strainrate') case('strainrate')
mySize = 1_pInt mySize = 1_pInt
case default case default
call IO_error(212_pInt,ext_msg=constitutive_j2_output(o,i)//' ('//constitutive_j2_label//')') call IO_error(212_pInt,ext_msg=constitutive_j2_output(o,i)//' ('//CONSTITUTIVE_J2_label//')')
end select end select
if (mySize > 0_pInt) then ! any meaningful output found if (mySize > 0_pInt) then ! any meaningful output found
constitutive_j2_sizePostResult(o,i) = mySize constitutive_j2_sizePostResult(o,i) = mySize
constitutive_j2_sizePostResults(i) = & constitutive_j2_sizePostResults(i) = &
constitutive_j2_sizePostResults(i) + mySize constitutive_j2_sizePostResults(i) + mySize
@ -308,387 +301,395 @@ subroutine constitutive_j2_init(myFile)
constitutive_j2_sizeDotState(i) = 1_pInt constitutive_j2_sizeDotState(i) = 1_pInt
constitutive_j2_sizeState(i) = 1_pInt constitutive_j2_sizeState(i) = 1_pInt
constitutive_j2_Cslip_66(:,:,i) = lattice_symmetrizeC66(constitutive_j2_structureName(i),& constitutive_j2_Cslip_66(1:6,1:6,i) = lattice_symmetrizeC66(constitutive_j2_structureName(i),&
constitutive_j2_Cslip_66(:,:,i)) constitutive_j2_Cslip_66(1:6,1:6,i))
constitutive_j2_Cslip_66(1:6,1:6,i) = & constitutive_j2_Cslip_66(1:6,1:6,i) = &
math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(1:6,1:6,i))) math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(1:6,1:6,i))) ! todo what is going on here?
enddo enddo
end subroutine constitutive_j2_init end subroutine constitutive_j2_init
!********************************************************************* !--------------------------------------------------------------------------------------------------
!* initial microstructural state * !> @brief initial microstructural state
!********************************************************************* !> @detail initial microstructural state is set to the value specified by tau0
!--------------------------------------------------------------------------------------------------
pure function constitutive_j2_stateInit(myInstance) pure function constitutive_j2_stateInit(myInstance)
implicit none implicit none
integer(pInt), intent(in) :: myInstance real(pReal), dimension(1) :: constitutive_j2_stateInit
real(pReal), dimension(1) :: constitutive_j2_stateInit integer(pInt), intent(in) :: myInstance !< number specifying the instance of the plasticity
constitutive_j2_stateInit = constitutive_j2_tau0(myInstance) constitutive_j2_stateInit = constitutive_j2_tau0(myInstance)
end function constitutive_j2_stateInit end function constitutive_j2_stateInit
!********************************************************************* !--------------------------------------------------------------------------------------------------
!* relevant microstructural state * !> @brief relevant state values for the current instance of this plasticity
!********************************************************************* !--------------------------------------------------------------------------------------------------
pure function constitutive_j2_aTolState(myInstance) pure function constitutive_j2_aTolState(myInstance)
implicit none implicit none
!*** input variables integer(pInt), intent(in) :: myInstance !< number specifying the instance of the plasticity
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the plasticity
!*** output variables
real(pReal), dimension(constitutive_j2_sizeState(myInstance)) :: & 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_aTolState = constitutive_j2_aTolResistance(myInstance) constitutive_j2_aTolState = constitutive_j2_aTolResistance(myInstance)
end function constitutive_j2_aTolState end function constitutive_j2_aTolState
!--------------------------------------------------------------------------------------------------
!> @brief homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
pure function constitutive_j2_homogenizedC(state,ipc,ip,el) pure function constitutive_j2_homogenizedC(state,ipc,ip,el)
!********************************************************************* use prec, only: &
!* homogenized elacticity matrix * p_vec
!* INPUT: * use mesh, only: &
!* - state : state variables * mesh_NcpElems,mesh_maxNips
!* - ipc : component-ID of current integration point * use material, only: &
!* - ip : current integration point * homogenization_maxNgrains,&
!* - el : current element * material_phase, &
!********************************************************************* phase_plasticityInstance
use prec, only: p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_plasticityInstance
implicit none 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 real(pReal), dimension(6,6) :: constitutive_j2_homogenizedC
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
matID = phase_plasticityInstance(material_phase(ipc,ip,el)) constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(1:6,1:6,&
constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(1:6,1:6,matID) phase_plasticityInstance(material_phase(ipc,ip,el)))
end function constitutive_j2_homogenizedC end function constitutive_j2_homogenizedC
pure subroutine constitutive_j2_microstructure(Temperature,state,ipc,ip,el) !--------------------------------------------------------------------------------------------------
!********************************************************************* !> @brief calculate derived quantities from state (not used here)
!* calculate derived quantities from state (not used here) * !--------------------------------------------------------------------------------------------------
!* INPUT: * pure subroutine constitutive_j2_microstructure(temperature,state,ipc,ip,el)
!* - Tp : temperature * use prec, only: &
!* - ipc : component-ID of current integration point * p_vec
!* - ip : current integration point * use mesh, only: &
!* - el : current element * mesh_NcpElems,&
!********************************************************************* mesh_maxNips
use prec, only: p_vec use material, only: &
use mesh, only: mesh_NcpElems,mesh_maxNips homogenization_maxNgrains, &
use material, only: homogenization_maxNgrains,material_phase, phase_plasticityInstance material_phase, &
phase_plasticityInstance
implicit none implicit none
!* Definition of variables integer(pInt), intent(in) :: &
integer(pInt), intent(in) :: ipc,ip,el ipc, & !< component-ID of integration point
real(pReal), intent(in) :: Temperature ip, & !< integration point
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state el !< element
integer(pInt) :: matID real(pReal), intent(in) :: &
temperature !< temperature at IP
matID = phase_plasticityInstance(material_phase(ipc,ip,el)) type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
end subroutine constitutive_j2_microstructure end subroutine constitutive_j2_microstructure
!**************************************************************** !--------------------------------------------------------------------------------------------------
!* calculates plastic velocity gradient and its tangent * !> @brief calculates plastic velocity gradient and its tangent
!**************************************************************** !--------------------------------------------------------------------------------------------------
pure subroutine constitutive_j2_LpAndItsTangent(Lp, dLp_dTstar_99, Tstar_v, Temperature, state, g, ip, el) pure subroutine constitutive_j2_LpAndItsTangent(Lp,dLp_dTstar_99,Tstar_v,&
temperature,state,ipc,ip,el)
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
!*** variables and functions from other modules ***! implicit none
use prec, only: p_vec real(pReal), dimension(6), intent(in) :: &
use math, only: math_mul6x6, & Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
math_Mandel6to33, & real(pReal), intent(in) :: &
math_Plain3333to99, & temperature !< temperature at IP
math_deviatoric33, & integer(pInt), intent(in) :: &
math_mul33xx33 ipc, & !< component-ID of integration point
use mesh, only: mesh_NcpElems, & ip, & !< integration point
mesh_maxNips el !< element
use material, only: homogenization_maxNgrains, & type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
material_phase, & state !< microstructure state
phase_plasticityInstance
implicit none real(pReal), dimension(3,3), intent(out) :: &
!*** input variables ***! Lp !< plastic velocity gradient
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation real(pReal), dimension(9,9), intent(out) :: &
real(pReal), intent(in):: Temperature dLp_dTstar_99 !< derivative of Lp with respect to 2nd Piola Kirchhoff stress
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) :: &
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient Tstar_dev_33 !< deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar_99 ! derivative of Lp with respect to Tstar (9x9 matrix) 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
!*** local variables ***! matID = phase_plasticityInstance(material_phase(ipc,ip,el))
real(pReal), dimension(3,3) :: Tstar_dev_33 ! deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor Tstar_dev_33 = math_deviatoric33(math_Mandel6to33(Tstar_v)) ! deviatoric part of 2nd Piola-Kirchhoff stress
real(pReal), dimension(3,3,3,3) :: dLp_dTstar_3333 ! derivative of Lp with respect to Tstar as 4th order tensor squarenorm_Tstar_dev = math_mul33xx33(Tstar_dev_33,Tstar_dev_33)
real(pReal) gamma_dot, & ! strainrate norm_Tstar_dev = sqrt(squarenorm_Tstar_dev)
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)) if (norm_Tstar_dev <= 0.0_pReal) then ! Tstar == 0 --> both Lp and dLp_dTstar are zero
Lp = 0.0_pReal
dLp_dTstar_99 = 0.0_pReal
else
gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
/ &!----------------------------------------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) **constitutive_j2_n(matID)
! deviatoric part of 2nd Piola-Kirchhoff stress Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID)
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) ! 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) &
! Initialization of Lp and dLp_dTstar dLp_dTstar_3333(k,l,m,n) = (constitutive_j2_n(matID)-1.0_pReal) * &
Lp = 0.0_pReal Tstar_dev_33(k,l)*Tstar_dev_33(m,n) / squarenorm_Tstar_dev
dLp_dTstar_99 = 0.0_pReal 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
! Tstar == 0 --> both Lp and dLp_dTstar are zero dLp_dTstar_99 = math_Plain3333to99(gamma_dot / constitutive_j2_fTaylor(matID) * &
if (norm_Tstar_dev > 0.0_pReal) then dLp_dTstar_3333 / norm_Tstar_dev)
end if
! 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 end subroutine constitutive_j2_LpAndItsTangent
!**************************************************************** !--------------------------------------------------------------------------------------------------
!* calculates the rate of change of microstructure * !> @brief calculates the rate of change of microstructure
!**************************************************************** !--------------------------------------------------------------------------------------------------
pure function constitutive_j2_dotState(Tstar_v, Temperature, state, g, ip, el) pure function constitutive_j2_dotState(Tstar_v,Temperature,state,ipc,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
use prec, only: & implicit none
p_vec real(pReal), dimension(1) :: &
use math, only: & constitutive_j2_dotState
math_mul6x6 real(pReal), dimension(6), intent(in):: &
use mesh, only: & Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
mesh_NcpElems, & real(pReal), intent(in) :: &
mesh_maxNips Temperature !< temperature at integration point
use material, only: & integer(pInt), intent(in) :: &
homogenization_maxNgrains, & ipc, & !< component-ID of integration point
material_phase, & ip, & !< integration point
phase_plasticityInstance el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
implicit none real(pReal), dimension(6) :: &
!*** input variables ***! Tstar_dev_v !< deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation real(pReal) :: &
real(pReal), intent(in) :: Temperature gamma_dot, & !< strainrate
integer(pInt), intent(in):: g, & ! grain number hardening, & !< hardening coefficient
ip, & ! integration point number saturation, & !< saturation resistance
el ! element number norm_Tstar_dev !< euclidean norm of Tstar_dev
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure integer(pInt) :: &
matID
!*** output variables ***! matID = phase_plasticityInstance(material_phase(ipc,ip,el))
real(pReal), dimension(1) :: constitutive_j2_dotState ! evolution of state variable !--------------------------------------------------------------------------------------------------
! norm of 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))
!*** local variables ***! !--------------------------------------------------------------------------------------------------
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation ! strain rate
real(pReal) gamma_dot, & ! strainrate gamma_dot = constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
hardening, & ! hardening coefficient / &!-----------------------------------------------------------------------------------
saturation, & ! saturation resistance (constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID
matID = phase_plasticityInstance(material_phase(g,ip,el)) !--------------------------------------------------------------------------------------------------
! 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(ipc,ip,el)%p(1)/saturation )**constitutive_j2_a(matID) &
* sign(1.0_pReal, 1.0_pReal - state(ipc,ip,el)%p(1)/saturation)
else
hardening = 0.0_pReal
endif
! deviatoric part of 2nd Piola-Kirchhoff stress constitutive_j2_dotState = hardening * gamma_dot
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 end function constitutive_j2_dotState
!--------------------------------------------------------------------------------------------------
!> @brief (instantaneous) incremental change of microstructure (dummy function)
!--------------------------------------------------------------------------------------------------
pure function constitutive_j2_deltaState(Tstar_v,temperature,state,ipc,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
!* (instantaneous) incremental change of microstructure * real(pReal), dimension(6), intent(in):: &
!********************************************************************* Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
function constitutive_j2_deltaState(Tstar_v, Temperature, state, g,ip,el) real(pReal), intent(in) :: &
Temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
use prec, only: pReal, & real(pReal), dimension(constitutive_j2_sizeDotState(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
pInt, & constitutive_j2_deltaState
p_vec
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none constitutive_j2_deltaState = 0.0_pReal
!*** input variables end function constitutive_j2_deltaState
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 !--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of temperature (dummy function)
!--------------------------------------------------------------------------------------------------
real(pReal) pure function constitutive_j2_dotTemperature(Tstar_v,temperature,state,ipc,ip,el)
use prec, only: &
p_vec
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains
endfunction implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
constitutive_j2_dotTemperature = 0.0_pReal
!****************************************************************
!* 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 end function constitutive_j2_dotTemperature
!********************************************************************* !--------------------------------------------------------------------------------------------------
!* return array of constitutive results * !> @brief return array of constitutive results
!********************************************************************* !--------------------------------------------------------------------------------------------------
pure function constitutive_j2_postResults(Tstar_v, Temperature, dt, state, g, ip, el) pure function constitutive_j2_postResults(Tstar_v,temperature,dt,state,ipc,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, &
phase_Noutput
!*** variables and functions from other modules ***! implicit none
use prec, only: p_vec real(pReal), dimension(6), intent(in) :: &
use math, only: math_mul6x6 Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
use mesh, only: mesh_NcpElems, & real(pReal), intent(in) :: &
mesh_maxNips temperature, & !< temperature at integration point
use material, only: homogenization_maxNgrains, & dt
material_phase, & integer(pInt), intent(in) :: &
phase_plasticityInstance, & ipc, & !< component-ID of integration point
phase_Noutput ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state
real(pReal), dimension(constitutive_j2_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
constitutive_j2_postResults
implicit none real(pReal), dimension(6) :: &
!*** input variables ***! Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation real(pReal) :: &
real(pReal), intent(in):: Temperature, & norm_Tstar_dev ! euclidean norm of Tstar_dev
dt ! current time increment integer(pInt) :: &
integer(pInt), intent(in):: g, & ! grain number matID, &
ip, & ! integration point number o, &
el ! element number c
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***! matID = phase_plasticityInstance(material_phase(ipc,ip,el))
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 ! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm
real(pReal) norm_Tstar_dev ! euclidean norm of Tstar_dev Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal
integer(pInt) matID, & Tstar_dev_v(4:6) = Tstar_v(4:6)
o, & norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
c
!*** global variables ***! c = 0_pInt
! constitutive_j2_gdot0 constitutive_j2_postResults = 0.0_pReal
! constitutive_j2_fTaylor
! constitutive_j2_n
outputsLoop: do o = 1_pInt,phase_Noutput(material_phase(ipc,ip,el))
matID = phase_plasticityInstance(material_phase(g,ip,el)) select case(constitutive_j2_output(o,matID))
case ('flowstress')
! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm constitutive_j2_postResults(c+1_pInt) = state(ipc,ip,el)%p(1)
Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3.0_pReal c = c + 1_pInt
Tstar_dev_v(4:6) = Tstar_v(4:6) case ('strainrate')
norm_Tstar_dev = sqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v)) constitutive_j2_postResults(c+1_pInt) = &
constitutive_j2_gdot0(matID) * ( sqrt(1.5_pReal) * norm_Tstar_dev &
c = 0_pInt / &!----------------------------------------------------------------------------------
constitutive_j2_postResults = 0.0_pReal (constitutive_j2_fTaylor(matID) * state(ipc,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
c = c + 1_pInt
do o = 1_pInt,phase_Noutput(material_phase(g,ip,el)) end select
select case(constitutive_j2_output(o,matID)) enddo outputsLoop
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 function constitutive_j2_postResults