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DAMASK_EICMD
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DAMASK_EICMD/src/constitutive.f90

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added doxygen comments, some polishing, added "protected" statements where applicable
2012-10-02 18:23:25 +05:30
!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
some doxygen corrections
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
added doxygen comments, some polishing, added "protected" statements where applicable
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!> @brief elasticity, plasticity, internal microstructure state
!--------------------------------------------------------------------------------------------------
module constitutive
white space adjustments
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use math
use debug
use numerics
use IO
use config
use material
use results
use HDF5_utilities
use lattice
use mesh
use discretization
use plastic_none
use plastic_isotropic
use plastic_phenopowerlaw
use plastic_kinehardening
use plastic_dislotwin
use plastic_disloucla
use plastic_nonlocal
use geometry_plastic_nonlocal
use source_thermal_dissipation
use source_thermal_externalheat
use source_damage_isoBrittle
use source_damage_isoDuctile
use source_damage_anisoBrittle
use source_damage_anisoDuctile
use kinematics_cleavage_opening
use kinematics_slipplane_opening
use kinematics_thermal_expansion
implicit none
private
integer, public, protected :: &
constitutive_plasticity_maxSizePostResults, &
constitutive_plasticity_maxSizeDotState, &
constitutive_source_maxSizePostResults, &
constitutive_source_maxSizeDotState
public :: &
constitutive_init, &
constitutive_homogenizedC, &
constitutive_microstructure, &
constitutive_LpAndItsTangents, &
constitutive_LiAndItsTangents, &
constitutive_initialFi, &
constitutive_SandItsTangents, &
constitutive_collectDotState, &
constitutive_collectDeltaState, &
constitutive_postResults, &
constitutive_results
added new, flexible debugging scheme. now all modules have their own debug specification. compiles and runs, I hope nothing is broken did a lot of polishing
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contains
added doxygen comments, some polishing, added "protected" statements where applicable
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!--------------------------------------------------------------------------------------------------
!> @brief allocates arrays pointing to array of the various constitutive modules
!--------------------------------------------------------------------------------------------------
no pInt
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subroutine constitutive_init
implemented possibly diffusive vacancy physics. to be coupled with micro void nucleation and ductile damage
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white space adjustments
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integer, parameter :: FILEUNIT = 204
integer :: &
o, & !< counter in output loop
ph, & !< counter in phase loop
s, & !< counter in source loop
ins !< instance of plasticity/source
integer, dimension(:,:), pointer :: thisSize
character(len=64), dimension(:,:), pointer :: thisOutput
character(len=32) :: outputName !< name of output, intermediate fix until HDF5 output is ready
logical :: knownPlasticity, knownSource, nonlocalConstitutionPresent
nonlocalConstitutionPresent = .false.
add pheno+ module in
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added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
Merge branch 'development' into New-Thermal
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! initialized plasticity
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if (any(phase_plasticity == PLASTICITY_NONE_ID)) call plastic_none_init
if (any(phase_plasticity == PLASTICITY_ISOTROPIC_ID)) call plastic_isotropic_init
if (any(phase_plasticity == PLASTICITY_PHENOPOWERLAW_ID)) call plastic_phenopowerlaw_init
if (any(phase_plasticity == PLASTICITY_KINEHARDENING_ID)) call plastic_kinehardening_init
if (any(phase_plasticity == PLASTICITY_DISLOTWIN_ID)) call plastic_dislotwin_init
if (any(phase_plasticity == PLASTICITY_DISLOUCLA_ID)) call plastic_disloucla_init
if (any(phase_plasticity == PLASTICITY_NONLOCAL_ID)) then
call plastic_nonlocal_init
else
call geometry_plastic_nonlocal_disable
endif
subsumed constitutive_damage/thermal into constitutive
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!--------------------------------------------------------------------------------------------------
Merge branch 'development' into New-Thermal
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! initialize source mechanisms
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if (any(phase_source == SOURCE_thermal_dissipation_ID)) call source_thermal_dissipation_init
if (any(phase_source == SOURCE_thermal_externalheat_ID)) call source_thermal_externalheat_init
if (any(phase_source == SOURCE_damage_isoBrittle_ID)) call source_damage_isoBrittle_init
if (any(phase_source == SOURCE_damage_isoDuctile_ID)) call source_damage_isoDuctile_init
if (any(phase_source == SOURCE_damage_anisoBrittle_ID)) call source_damage_anisoBrittle_init
if (any(phase_source == SOURCE_damage_anisoDuctile_ID)) call source_damage_anisoDuctile_init
file reading not required anymore
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subsumed constitutive_damage/thermal into constitutive
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!--------------------------------------------------------------------------------------------------
Merge branch 'development' into New-Thermal
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! initialize kinematic mechanisms
white space adjustments
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if (any(phase_kinematics == KINEMATICS_cleavage_opening_ID)) call kinematics_cleavage_opening_init
if (any(phase_kinematics == KINEMATICS_slipplane_opening_ID)) call kinematics_slipplane_opening_init
if (any(phase_kinematics == KINEMATICS_thermal_expansion_ID)) call kinematics_thermal_expansion_init
write(6,'(/,a)') ' <<<+- constitutive init -+>>>'
mainProcess: if (worldrank == 0) then
added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
added documentation and changed some names
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! write description file for constitutive output
white space adjustments
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call IO_write_jobFile(FILEUNIT,'outputConstitutive')
PhaseLoop: do ph = 1,material_Nphase
activePhase: if (any(material_phaseAt == ph)) then
ins = phase_plasticityInstance(ph)
knownPlasticity = .true. ! assume valid
plasticityType: select case(phase_plasticity(ph))
case (PLASTICITY_NONE_ID) plasticityType
outputName = PLASTICITY_NONE_label
thisOutput => null()
thisSize => null()
case (PLASTICITY_ISOTROPIC_ID) plasticityType
outputName = PLASTICITY_ISOTROPIC_label
thisOutput => plastic_isotropic_output
thisSize => plastic_isotropic_sizePostResult
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
outputName = PLASTICITY_PHENOPOWERLAW_label
thisOutput => plastic_phenopowerlaw_output
thisSize => plastic_phenopowerlaw_sizePostResult
case (PLASTICITY_KINEHARDENING_ID) plasticityType
outputName = PLASTICITY_KINEHARDENING_label
thisOutput => plastic_kinehardening_output
thisSize => plastic_kinehardening_sizePostResult
case (PLASTICITY_DISLOTWIN_ID) plasticityType
outputName = PLASTICITY_DISLOTWIN_label
thisOutput => plastic_dislotwin_output
thisSize => plastic_dislotwin_sizePostResult
case (PLASTICITY_DISLOUCLA_ID) plasticityType
outputName = PLASTICITY_DISLOUCLA_label
thisOutput => plastic_disloucla_output
thisSize => plastic_disloucla_sizePostResult
case (PLASTICITY_NONLOCAL_ID) plasticityType
outputName = PLASTICITY_NONLOCAL_label
thisOutput => plastic_nonlocal_output
thisSize => plastic_nonlocal_sizePostResult
case default plasticityType
knownPlasticity = .false.
end select plasticityType
write(FILEUNIT,'(/,a,/)') '['//trim(config_name_phase(ph))//']'
if (knownPlasticity) then
write(FILEUNIT,'(a)') '(plasticity)'//char(9)//trim(outputName)
if (phase_plasticity(ph) /= PLASTICITY_NONE_ID) then
OutputPlasticityLoop: do o = 1,size(thisOutput(:,ins))
if(len(trim(thisOutput(o,ins))) > 0) &
write(FILEUNIT,'(a,i4)') trim(thisOutput(o,ins))//char(9),thisSize(o,ins)
enddo OutputPlasticityLoop
endif
endif
SourceLoop: do s = 1, phase_Nsources(ph)
knownSource = .true. ! assume valid
sourceType: select case (phase_source(s,ph))
case (SOURCE_thermal_dissipation_ID) sourceType
ins = source_thermal_dissipation_instance(ph)
outputName = SOURCE_thermal_dissipation_label
thisOutput => source_thermal_dissipation_output
thisSize => source_thermal_dissipation_sizePostResult
case (SOURCE_thermal_externalheat_ID) sourceType
ins = source_thermal_externalheat_instance(ph)
outputName = SOURCE_thermal_externalheat_label
thisOutput => source_thermal_externalheat_output
thisSize => source_thermal_externalheat_sizePostResult
case (SOURCE_damage_isoBrittle_ID) sourceType
ins = source_damage_isoBrittle_instance(ph)
outputName = SOURCE_damage_isoBrittle_label
thisOutput => source_damage_isoBrittle_output
thisSize => source_damage_isoBrittle_sizePostResult
case (SOURCE_damage_isoDuctile_ID) sourceType
ins = source_damage_isoDuctile_instance(ph)
outputName = SOURCE_damage_isoDuctile_label
thisOutput => source_damage_isoDuctile_output
thisSize => source_damage_isoDuctile_sizePostResult
case (SOURCE_damage_anisoBrittle_ID) sourceType
ins = source_damage_anisoBrittle_instance(ph)
outputName = SOURCE_damage_anisoBrittle_label
thisOutput => source_damage_anisoBrittle_output
thisSize => source_damage_anisoBrittle_sizePostResult
case (SOURCE_damage_anisoDuctile_ID) sourceType
ins = source_damage_anisoDuctile_instance(ph)
outputName = SOURCE_damage_anisoDuctile_label
thisOutput => source_damage_anisoDuctile_output
thisSize => source_damage_anisoDuctile_sizePostResult
case default sourceType
knownSource = .false.
end select sourceType
if (knownSource) then
write(FILEUNIT,'(a)') '(source)'//char(9)//trim(outputName)
OutputSourceLoop: do o = 1,size(thisOutput(:,ins))
if(len(trim(thisOutput(o,ins))) > 0) &
write(FILEUNIT,'(a,i4)') trim(thisOutput(o,ins))//char(9),thisSize(o,ins)
enddo OutputSourceLoop
endif
enddo SourceLoop
endif activePhase
enddo PhaseLoop
close(FILEUNIT)
endif mainProcess
constitutive_plasticity_maxSizeDotState = 0
constitutive_plasticity_maxSizePostResults = 0
constitutive_source_maxSizeDotState = 0
constitutive_source_maxSizePostResults = 0
PhaseLoop2:do ph = 1,material_Nphase
added documentation and changed some names
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!--------------------------------------------------------------------------------------------------
! partition and inititalize state
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plasticState(ph)%partionedState0 = plasticState(ph)%state0
plasticState(ph)%state = plasticState(ph)%partionedState0
forall(s = 1:phase_Nsources(ph))
sourceState(ph)%p(s)%partionedState0 = sourceState(ph)%p(s)%state0
sourceState(ph)%p(s)%state = sourceState(ph)%p(s)%partionedState0
end forall
added documentation and changed some names
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!--------------------------------------------------------------------------------------------------
! determine max size of state and output
white space adjustments
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constitutive_plasticity_maxSizeDotState = max(constitutive_plasticity_maxSizeDotState, &
plasticState(ph)%sizeDotState)
constitutive_plasticity_maxSizePostResults = max(constitutive_plasticity_maxSizePostResults, &
plasticState(ph)%sizePostResults)
constitutive_source_maxSizeDotState = max(constitutive_source_maxSizeDotState, &
maxval(sourceState(ph)%p(:)%sizeDotState))
constitutive_source_maxSizePostResults = max(constitutive_source_maxSizePostResults, &
maxval(sourceState(ph)%p(:)%sizePostResults))
enddo PhaseLoop2
removed few bugs from nonlocal (newstate)
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some changes related to new state fixed assigning of wrong output in J2 model
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added doxygen comments, some polishing, added "protected" statements where applicable
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end subroutine constitutive_init
changed line endings to unix style
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added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenize elasticity matrix
unified syntax _v for vector representation of tensor conflicts with 3333 suffix for 4-th order tensors. General idea: Mark symmetric second order tensors in vector notation with '6' and fourth order tensors in second order matrix notation with '99'. Append nothing for 'natural' representation, i.e. F and NOT F33, Lp_dTstar and NOT Lp_dTstar3333
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!> ToDo: homogenizedC66 would be more consistent
added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
changed to new state, please report bugs to Luv or Martin
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function constitutive_homogenizedC(ipc,ip,el)
moved reading in of lattice type and elastic constants to lattice module removed structure type for hex, fcc, bcc, now defining slip/twin systems for each phase found in material.config constitutive modules will only be initialized if needed homogenizedC function is only needed for models incorporating twinning in a physical way (titanmod and dislotwin)
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white space adjustments
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real(pReal), dimension(6,6) :: constitutive_homogenizedC
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_DISLOTWIN_ID) plasticityType
constitutive_homogenizedC = plastic_dislotwin_homogenizedC(ipc,ip,el)
case default plasticityType
constitutive_homogenizedC = lattice_C66(1:6,1:6,material_phaseAt(ipc,el))
end select plasticityType
changed line endings to unix style
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added doxygen comments, some polishing, added "protected" statements where applicable
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end function constitutive_homogenizedC
white space adjustments
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added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
!> @brief calls microstructure function of the different constitutive models
!--------------------------------------------------------------------------------------------------
using new rotation class
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subroutine constitutive_microstructure(Fe, Fp, ipc, ip, el)
prepared new state for dislotwin
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white space adjustments
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integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
Fe, & !< elastic deformation gradient
Fp !< plastic deformation gradient
integer :: &
ho, & !< homogenization
tme, & !< thermal member position
instance, of
ho = material_homogenizationAt(el)
tme = thermalMapping(ho)%p(ip,el)
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_DISLOTWIN_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_dislotwin_dependentState(temperature(ho)%p(tme),instance,of)
case (PLASTICITY_DISLOUCLA_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_disloUCLA_dependentState(instance,of)
case (PLASTICITY_NONLOCAL_ID) plasticityType
call plastic_nonlocal_dependentState (Fe,Fp,ip,el)
end select plasticityType
add pheno+ module in
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added doxygen comments and unified naming scheme for ip, element and grain
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end subroutine constitutive_microstructure
openmp parallelization working again (at least for j2 and nonlocal constitutive model). In order to keep it like that, please follow these simple rules: DON'T use implicit array subscripts: example: real, dimension(3,3) :: A,B A(:,2) = B(:,1) <--- DON'T USE A(1:3,2) = B(1:3,1) <--- BETTER USE In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks. Enclose all write statements with the following: !$OMP CRITICAL (write2out) <your write statement> !$OMP END CRITICAL (write2out) Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
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added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
add pheno+ module in
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!> @brief contains the constitutive equation for calculating the velocity gradient
use parameter structure and avoid conversion 33<->6
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! ToDo: Discuss wheter it makes sense if crystallite handles the configuration conversion, i.e.
! Mp in, dLp_dMp out
added doxygen comments and unified naming scheme for ip, element and grain
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!--------------------------------------------------------------------------------------------------
use parameter structure and avoid conversion 33<->6
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subroutine constitutive_LpAndItsTangents(Lp, dLp_dS, dLp_dFi, &
S, Fi, ipc, ip, el)
add pheno+ module in
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white space adjustments
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integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
S, & !< 2nd Piola-Kirchhoff stress
Fi !< intermediate deformation gradient
real(pReal), intent(out), dimension(3,3) :: &
Lp !< plastic velocity gradient
real(pReal), intent(out), dimension(3,3,3,3) :: &
dLp_dS, &
dLp_dFi !< derivative of Lp with respect to Fi
real(pReal), dimension(3,3,3,3) :: &
dLp_dMp !< derivative of Lp with respect to Mandel stress
real(pReal), dimension(3,3) :: &
Mp !< Mandel stress work conjugate with Lp
integer :: &
ho, & !< homogenization
tme !< thermal member position
integer :: &
i, j, instance, of
ho = material_homogenizationAt(el)
tme = thermalMapping(ho)%p(ip,el)
Mp = matmul(matmul(transpose(Fi),Fi),S)
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_NONE_ID) plasticityType
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
case (PLASTICITY_ISOTROPIC_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_isotropic_LpAndItsTangent (Lp,dLp_dMp,Mp,instance,of)
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_phenopowerlaw_LpAndItsTangent (Lp,dLp_dMp,Mp,instance,of)
case (PLASTICITY_KINEHARDENING_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_kinehardening_LpAndItsTangent (Lp,dLp_dMp, Mp,instance,of)
case (PLASTICITY_NONLOCAL_ID) plasticityType
call plastic_nonlocal_LpAndItsTangent (Lp,dLp_dMp,Mp, &
temperature(ho)%p(tme),geometry_plastic_nonlocal_IPvolume0(ip,el),ip,el)
case (PLASTICITY_DISLOTWIN_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_dislotwin_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of)
case (PLASTICITY_DISLOUCLA_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_disloucla_LpAndItsTangent (Lp,dLp_dMp,Mp,temperature(ho)%p(tme),instance,of)
end select plasticityType
do i=1,3; do j=1,3
dLp_dFi(i,j,1:3,1:3) = matmul(matmul(Fi,S),transpose(dLp_dMp(i,j,1:3,1:3))) + &
matmul(matmul(Fi,dLp_dMp(i,j,1:3,1:3)),S)
dLp_dS(i,j,1:3,1:3) = matmul(matmul(transpose(Fi),Fi),dLp_dMp(i,j,1:3,1:3)) ! ToDo: @PS: why not: dLp_dMp:(FiT Fi)
enddo; enddo
add pheno+ module in
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return more than one tangent
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end subroutine constitutive_LpAndItsTangents
changed line endings to unix style
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overhaul of kinematics from FeFp to FeFiFp decomposition
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!--------------------------------------------------------------------------------------------------
add pheno+ module in
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!> @brief contains the constitutive equation for calculating the velocity gradient
avoid conversion 33<->6 3333<->9
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! ToDo: MD: S is Mi?
overhaul of kinematics from FeFp to FeFiFp decomposition
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!--------------------------------------------------------------------------------------------------
move stress conversion one level up should be totally avoided
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subroutine constitutive_LiAndItsTangents(Li, dLi_dS, dLi_dFi, &
S, Fi, ipc, ip, el)
add pheno+ module in
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white space adjustments
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integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
S !< 2nd Piola-Kirchhoff stress
real(pReal), intent(in), dimension(3,3) :: &
Fi !< intermediate deformation gradient
real(pReal), intent(out), dimension(3,3) :: &
Li !< intermediate velocity gradient
real(pReal), intent(out), dimension(3,3,3,3) :: &
dLi_dS, & !< derivative of Li with respect to S
dLi_dFi
real(pReal), dimension(3,3) :: &
my_Li, & !< intermediate velocity gradient
FiInv, &
temp_33
real(pReal), dimension(3,3,3,3) :: &
my_dLi_dS
real(pReal) :: &
detFi
integer :: &
k, i, j, &
instance, of
Li = 0.0_pReal
dLi_dS = 0.0_pReal
dLi_dFi = 0.0_pReal
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_isotropic_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_isotropic_LiAndItsTangent(my_Li, my_dLi_dS, S ,instance,of)
case default plasticityType
my_Li = 0.0_pReal
my_dLi_dS = 0.0_pReal
end select plasticityType
Li = Li + my_Li
dLi_dS = dLi_dS + my_dLi_dS
KinematicsLoop: do k = 1, phase_Nkinematics(material_phaseAt(ipc,el))
kinematicsType: select case (phase_kinematics(k,material_phaseAt(ipc,el)))
case (KINEMATICS_cleavage_opening_ID) kinematicsType
call kinematics_cleavage_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
case (KINEMATICS_slipplane_opening_ID) kinematicsType
call kinematics_slipplane_opening_LiAndItsTangent(my_Li, my_dLi_dS, S, ipc, ip, el)
case (KINEMATICS_thermal_expansion_ID) kinematicsType
call kinematics_thermal_expansion_LiAndItsTangent(my_Li, my_dLi_dS, ipc, ip, el)
case default kinematicsType
my_Li = 0.0_pReal
my_dLi_dS = 0.0_pReal
end select kinematicsType
Li = Li + my_Li
dLi_dS = dLi_dS + my_dLi_dS
enddo KinematicsLoop
FiInv = math_inv33(Fi)
detFi = math_det33(Fi)
Li = matmul(matmul(Fi,Li),FiInv)*detFi !< push forward to intermediate configuration
temp_33 = matmul(FiInv,Li)
do i = 1,3; do j = 1,3
dLi_dS(1:3,1:3,i,j) = matmul(matmul(Fi,dLi_dS(1:3,1:3,i,j)),FiInv)*detFi
dLi_dFi(1:3,1:3,i,j) = dLi_dFi(1:3,1:3,i,j) + Li*FiInv(j,i)
dLi_dFi(1:3,i,1:3,j) = dLi_dFi(1:3,i,1:3,j) + math_I3*temp_33(j,i) + Li*FiInv(j,i)
polishing
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enddo; enddo
add pheno+ module in
2015-10-14 00:22:01 +05:30
return more than one tangent
2018-08-28 18:37:39 +05:30
end subroutine constitutive_LiAndItsTangents
overhaul of kinematics from FeFp to FeFiFp decomposition
2014-11-01 00:33:08 +05:30
openmp parallelization working again (at least for j2 and nonlocal constitutive model). In order to keep it like that, please follow these simple rules: DON'T use implicit array subscripts: example: real, dimension(3,3) :: A,B A(:,2) = B(:,1) <--- DON'T USE A(1:3,2) = B(1:3,1) <--- BETTER USE In many cases the use of explicit array subscripts is inevitable for parallelization. Additionally, it is an easy means to prevent memory leaks. Enclose all write statements with the following: !$OMP CRITICAL (write2out) <your write statement> !$OMP END CRITICAL (write2out) Whenever you change something in the code and are not sure if it affects parallelization and leads to nonconforming behavior, please ask me and/or Franz to check this.
2011-03-17 16:16:17 +05:30
initialise Fi correctly for initial field values away from equilibrium
2015-07-24 20:17:18 +05:30
!--------------------------------------------------------------------------------------------------
add pheno+ module in
2015-10-14 00:22:01 +05:30
!> @brief collects initial intermediate deformation gradient
initialise Fi correctly for initial field values away from equilibrium
2015-07-24 20:17:18 +05:30
!--------------------------------------------------------------------------------------------------
pure function constitutive_initialFi(ipc, ip, el)
add pheno+ module in
2015-10-14 00:22:01 +05:30
white space adjustments
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integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), dimension(3,3) :: &
constitutive_initialFi !< composite initial intermediate deformation gradient
integer :: &
k !< counter in kinematics loop
integer :: &
phase, &
homog, offset
constitutive_initialFi = math_I3
phase = material_phaseAt(ipc,el)
KinematicsLoop: do k = 1, phase_Nkinematics(phase) !< Warning: small initial strain assumption
kinematicsType: select case (phase_kinematics(k,phase))
case (KINEMATICS_thermal_expansion_ID) kinematicsType
homog = material_homogenizationAt(el)
offset = thermalMapping(homog)%p(ip,el)
constitutive_initialFi = &
constitutive_initialFi + kinematics_thermal_expansion_initialStrain(homog,phase,offset)
end select kinematicsType
enddo KinematicsLoop
add pheno+ module in
2015-10-14 00:22:01 +05:30
initialise Fi correctly for initial field values away from equilibrium
2015-07-24 20:17:18 +05:30
end function constitutive_initialFi
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
add pheno+ module in
2015-10-14 00:22:01 +05:30
!> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
rename according to paper
2018-08-28 18:24:36 +05:30
!> the elastic/intermediate deformation gradients depending on the selected elastic law
!! (so far no case switch because only Hooke is implemented)
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
rename according to paper
2018-08-28 18:24:36 +05:30
subroutine constitutive_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el)
changed to new state, please report bugs to Luv or Martin
2014-07-02 17:57:39 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
Fe, & !< elastic deformation gradient
Fi !< intermediate deformation gradient
real(pReal), intent(out), dimension(3,3) :: &
S !< 2nd Piola-Kirchhoff stress tensor
real(pReal), intent(out), dimension(3,3,3,3) :: &
dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
add pheno+ module in
2015-10-14 00:22:01 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, Fe, Fi, ipc, ip, el)
removed a bunch of dummy functions (delta state for all constitutive_XXX except nonlocal, microstructure for none, j2 and phenopowerla), additional simplifications for none, averageBurgers is only relevant for RGC
2013-10-14 16:24:45 +05:30
add pheno+ module in
2015-10-14 00:22:01 +05:30
rename according to paper
2018-08-28 18:24:36 +05:30
end subroutine constitutive_SandItsTangents
shifted location of elasticity part closer to plasticity... (constitutive has been shaken back and forth quite a bit today ;-] )
2012-03-15 15:21:33 +05:30
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
add pheno+ module in
2015-10-14 00:22:01 +05:30
!> @brief returns the 2nd Piola-Kirchhoff stress tensor and its tangent with respect to
rename according to paper
2018-08-28 18:24:36 +05:30
!> the elastic and intermeidate deformation gradients using Hookes law
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
move stress conversion one level up should be totally avoided
2019-02-18 11:54:56 +05:30
subroutine constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
Fe, Fi, ipc, ip, el)
fixed bug in crystallite_FPI: stateDamper always has to be defined for each grain added some OMP FLUSH statements were necessary replaced openmp do by forall construct where possible; this is much safer and perhaps even as fast for small loops
2012-11-07 21:13:29 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
Fe, & !< elastic deformation gradient
Fi !< intermediate deformation gradient
real(pReal), intent(out), dimension(3,3) :: &
S !< 2nd Piola-Kirchhoff stress tensor in lattice configuration
real(pReal), intent(out), dimension(3,3,3,3) :: &
dS_dFe, & !< derivative of 2nd P-K stress with respect to elastic deformation gradient
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
real(pReal), dimension(3,3) :: E
real(pReal), dimension(3,3,3,3) :: C
integer :: &
ho, & !< homogenization
d !< counter in degradation loop
integer :: &
i, j
ho = material_homogenizationAt(el)
C = math_66toSym3333(constitutive_homogenizedC(ipc,ip,el))
DegradationLoop: do d = 1, phase_NstiffnessDegradations(material_phaseAt(ipc,el))
degradationType: select case(phase_stiffnessDegradation(d,material_phaseAt(ipc,el)))
case (STIFFNESS_DEGRADATION_damage_ID) degradationType
C = C * damage(ho)%p(damageMapping(ho)%p(ip,el))**2
end select degradationType
enddo DegradationLoop
E = 0.5_pReal*(matmul(transpose(Fe),Fe)-math_I3) !< Green-Lagrange strain in unloaded configuration
S = math_mul3333xx33(C,matmul(matmul(transpose(Fi),E),Fi)) !< 2PK stress in lattice configuration in work conjugate with GL strain pulled back to lattice configuration
forall (i=1:3, j=1:3)
dS_dFe(i,j,1:3,1:3) = matmul(Fe,matmul(matmul(Fi,C(i,j,1:3,1:3)),transpose(Fi))) !< dS_ij/dFe_kl = C_ijmn * Fi_lm * Fi_on * Fe_ko
dS_dFi(i,j,1:3,1:3) = 2.0_pReal*matmul(matmul(E,Fi),C(i,j,1:3,1:3)) !< dS_ij/dFi_kl = C_ijln * E_km * Fe_mn
end forall
add pheno+ module in
2015-10-14 00:22:01 +05:30
rename according to paper
2018-08-28 18:24:36 +05:30
end subroutine constitutive_hooke_SandItsTangents
shifted location of elasticity part closer to plasticity... (constitutive has been shaken back and forth quite a bit today ;-] )
2012-03-15 15:21:33 +05:30
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
add pheno+ module in
2015-10-14 00:22:01 +05:30
!> @brief contains the constitutive equation for calculating the rate of change of microstructure
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
Merge branch 'development' into New-Thermal
2019-02-26 12:24:03 +05:30
subroutine constitutive_collectDotState(S, FeArray, Fi, FpArray, subdt, ipc, ip, el)
applied new State for nonlocal model and a trivial changes in crystallite
2014-06-14 02:23:17 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in) :: &
subdt !< timestep
real(pReal), intent(in), dimension(3,3,homogenization_maxNgrains,discretization_nIP,discretization_nElem) :: &
FeArray, & !< elastic deformation gradient
FpArray !< plastic deformation gradient
real(pReal), intent(in), dimension(3,3) :: &
Fi !< intermediate deformation gradient
real(pReal), intent(in), dimension(3,3) :: &
S !< 2nd Piola Kirchhoff stress (vector notation)
real(pReal), dimension(3,3) :: &
Mp
integer :: &
ho, & !< homogenization
tme, & !< thermal member position
i, & !< counter in source loop
instance, of
ho = material_homogenizationAt(el)
tme = thermalMapping(ho)%p(ip,el)
Mp = matmul(matmul(transpose(Fi),Fi),S)
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_ISOTROPIC_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_isotropic_dotState (Mp,instance,of)
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_phenopowerlaw_dotState(Mp,instance,of)
case (PLASTICITY_KINEHARDENING_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_kinehardening_dotState(Mp,instance,of)
case (PLASTICITY_DISLOTWIN_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_dislotwin_dotState (Mp,temperature(ho)%p(tme),instance,of)
case (PLASTICITY_DISLOUCLA_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_disloucla_dotState (Mp,temperature(ho)%p(tme),instance,of)
case (PLASTICITY_NONLOCAL_ID) plasticityType
call plastic_nonlocal_dotState (Mp,FeArray,FpArray,temperature(ho)%p(tme), &
subdt,ip,el)
end select plasticityType
SourceLoop: do i = 1, phase_Nsources(material_phaseAt(ipc,el))
sourceType: select case (phase_source(i,material_phaseAt(ipc,el)))
case (SOURCE_damage_anisoBrittle_ID) sourceType
call source_damage_anisoBrittle_dotState (S, ipc, ip, el) !< correct stress?
case (SOURCE_damage_isoDuctile_ID) sourceType
call source_damage_isoDuctile_dotState ( ipc, ip, el)
case (SOURCE_damage_anisoDuctile_ID) sourceType
call source_damage_anisoDuctile_dotState ( ipc, ip, el)
case (SOURCE_thermal_externalheat_ID) sourceType
of = material_phasememberAt(ipc,ip,el)
call source_thermal_externalheat_dotState(material_phaseAt(ipc,el),of)
end select sourceType
enddo SourceLoop
subsumed constitutive_damage/thermal into constitutive
2014-09-23 16:08:20 +05:30
added doxygen comments, some polishing, added "protected" statements where applicable
2012-10-02 18:23:25 +05:30
end subroutine constitutive_collectDotState
changed line endings to unix style
2009-03-06 15:32:36 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
added documentation and changed some names
2016-01-16 22:57:19 +05:30
!> @brief for constitutive models having an instantaneous change of state
removed delta state for J2 and phenopowerlaw when using new state
2014-06-17 12:24:49 +05:30
!> will return false if delta state is not needed/supported by the constitutive model
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
prepare for consistent use of full tensor representation
2019-01-24 11:26:43 +05:30
subroutine constitutive_collectDeltaState(S, Fe, Fi, ipc, ip, el)
add pheno+ module in
2015-10-14 00:22:01 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in), dimension(3,3) :: &
S, & !< 2nd Piola Kirchhoff stress
Fe, & !< elastic deformation gradient
Fi !< intermediate deformation gradient
real(pReal), dimension(3,3) :: &
Mp
integer :: &
i, &
instance, of
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
Mp = matmul(matmul(transpose(Fi),Fi),S)
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
case (PLASTICITY_KINEHARDENING_ID) plasticityType
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
call plastic_kinehardening_deltaState(Mp,instance,of)
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
case (PLASTICITY_NONLOCAL_ID) plasticityType
call plastic_nonlocal_deltaState(Mp,ip,el)
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
end select plasticityType
all constitutive modules now contain a new function "deltaState", which in the future allows to have an instantaneous and incremental change of the state (additional to the rate based evolution with dotState).
2012-05-16 20:13:26 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
sourceLoop: do i = 1, phase_Nsources(material_phaseAt(ipc,el))
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
sourceType: select case (phase_source(i,material_phaseAt(ipc,el)))
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
case (SOURCE_damage_isoBrittle_ID) sourceType
call source_damage_isoBrittle_deltaState (constitutive_homogenizedC(ipc,ip,el), Fe, &
ipc, ip, el)
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
end select sourceType
dotState and deltaState parse Mstar instead of Tstar requires to parse in Fi
2018-08-25 19:29:34 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
enddo SourceLoop
major restructuring of multi field handling in DAMASK and added some example config files for multi field simulations. please report bugs
2015-05-28 22:32:23 +05:30
changed up handling of delta states, and some bug fixes
2015-06-01 21:32:27 +05:30
end subroutine constitutive_collectDeltaState
corrected typos and some field related changes
2014-09-10 23:56:12 +05:30
polished field state related changes and brittle damage
2014-09-22 23:45:19 +05:30
added doxygen comments and unified naming scheme for ip, element and grain
2013-01-16 15:44:57 +05:30
!--------------------------------------------------------------------------------------------------
!> @brief returns array of constitutive results
!--------------------------------------------------------------------------------------------------
Merge branch 'development' into New-Thermal
2019-02-26 12:24:03 +05:30
function constitutive_postResults(S, Fi, ipc, ip, el)
subsumed constitutive_damage/thermal into constitutive
2014-09-23 16:08:20 +05:30
white space adjustments
2019-06-15 19:10:22 +05:30
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), dimension(plasticState(material_phaseAt(ipc,el))%sizePostResults + &
sum(sourceState(material_phaseAt(ipc,el))%p(:)%sizePostResults)) :: &
constitutive_postResults
real(pReal), intent(in), dimension(3,3) :: &
Fi !< intermediate deformation gradient
real(pReal), intent(in), dimension(3,3) :: &
S !< 2nd Piola Kirchhoff stress
real(pReal), dimension(3,3) :: &
Mp !< Mandel stress
integer :: &
startPos, endPos
integer :: &
ho, & !< homogenization
tme, & !< thermal member position
i, of, instance !< counter in source loop
constitutive_postResults = 0.0_pReal
Mp = matmul(matmul(transpose(Fi),Fi),S)
ho = material_homogenizationAt(el)
tme = thermalMapping(ho)%p(ip,el)
startPos = 1
endPos = plasticState(material_phaseAt(ipc,el))%sizePostResults
of = material_phasememberAt(ipc,ip,el)
instance = phase_plasticityInstance(material_phaseAt(ipc,el))
plasticityType: select case (phase_plasticity(material_phaseAt(ipc,el)))
case (PLASTICITY_ISOTROPIC_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_isotropic_postResults(Mp,instance,of)
case (PLASTICITY_PHENOPOWERLAW_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_phenopowerlaw_postResults(Mp,instance,of)
case (PLASTICITY_KINEHARDENING_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_kinehardening_postResults(Mp,instance,of)
case (PLASTICITY_DISLOTWIN_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_dislotwin_postResults(Mp,temperature(ho)%p(tme),instance,of)
case (PLASTICITY_DISLOUCLA_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_disloucla_postResults(Mp,temperature(ho)%p(tme),instance,of)
case (PLASTICITY_NONLOCAL_ID) plasticityType
constitutive_postResults(startPos:endPos) = &
plastic_nonlocal_postResults (material_phaseAt(ipc,el),instance,of)
end select plasticityType
SourceLoop: do i = 1, phase_Nsources(material_phaseAt(ipc,el))
startPos = endPos + 1
endPos = endPos + sourceState(material_phaseAt(ipc,el))%p(i)%sizePostResults
of = material_phasememberAt(ipc,ip,el)
sourceType: select case (phase_source(i,material_phaseAt(ipc,el)))
case (SOURCE_damage_isoBrittle_ID) sourceType
constitutive_postResults(startPos:endPos) = source_damage_isoBrittle_postResults(material_phaseAt(ipc,el),of)
case (SOURCE_damage_isoDuctile_ID) sourceType
constitutive_postResults(startPos:endPos) = source_damage_isoDuctile_postResults(material_phaseAt(ipc,el),of)
case (SOURCE_damage_anisoBrittle_ID) sourceType
constitutive_postResults(startPos:endPos) = source_damage_anisoBrittle_postResults(material_phaseAt(ipc,el),of)
case (SOURCE_damage_anisoDuctile_ID) sourceType
constitutive_postResults(startPos:endPos) = source_damage_anisoDuctile_postResults(material_phaseAt(ipc,el),of)
end select sourceType
enddo SourceLoop
implemented possibly diffusive vacancy physics. to be coupled with micro void nucleation and ductile damage
2014-10-11 02:25:09 +05:30
added doxygen comments, some polishing, added "protected" statements where applicable
2012-10-02 18:23:25 +05:30
end function constitutive_postResults
changed line endings to unix style
2009-03-06 15:32:36 +05:30
writing group structure in file root
2018-12-05 04:25:39 +05:30
!--------------------------------------------------------------------------------------------------
dummy structure to write plasticity results
2018-12-12 11:10:57 +05:30
!> @brief writes constitutive results to HDF5 output file
writing group structure in file root
2018-12-05 04:25:39 +05:30
!--------------------------------------------------------------------------------------------------
WIP: crystallite HDF5 results will be stored according to the phase sections
2019-04-06 10:01:02 +05:30
subroutine constitutive_results
white space adjustments
2019-06-15 19:10:22 +05:30
#if defined(PETSc) || defined(DAMASK_HDF5)
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
integer :: p
character(len=256) :: group
consistent names
2019-06-15 17:56:32 +05:30
do p=1,size(config_name_phase)
group = trim('current/constituent')//'/'//trim(config_name_phase(p))
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
call HDF5_closeGroup(results_addGroup(group))
adjustments for easier access to output data
2019-04-18 15:25:50 +05:30
group = trim(group)//'/plastic'
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
call HDF5_closeGroup(results_addGroup(group))
cleaning
2019-06-06 14:11:56 +05:30
select case(phase_plasticity(p))
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
case(PLASTICITY_ISOTROPIC_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_isotropic_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
case(PLASTICITY_PHENOPOWERLAW_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_phenopowerlaw_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
case(PLASTICITY_KINEHARDENING_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_kinehardening_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
case(PLASTICITY_DISLOTWIN_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_dislotwin_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
case(PLASTICITY_DISLOUCLA_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_disloUCLA_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
case(PLASTICITY_NONLOCAL_ID)
proper indentation
2019-04-06 13:26:47 +05:30
call plastic_nonlocal_results(phase_plasticityInstance(p),group)
dummy HDF5 output for all plasticity laws
2019-03-10 01:13:31 +05:30
end select
writing results out credits to Vitesh
2019-04-04 13:34:44 +05:30
enddo
dummy structure to write plasticity results
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#endif
writing group structure in file root
2018-12-05 04:25:39 +05:30
end subroutine constitutive_results
removed unused variables, added pure statements, and declared external functions as external (using gfortrans debug option)
2013-02-11 16:13:45 +05:30
end module constitutive