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Philip Eisenlohr 2009-03-05 16:49:13 +00:00
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!*****************************************************
!* Module: CONSTITUTIVE_J2 *
!*****************************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!*****************************************************
MODULE constitutive_j2
!*** Include other modules ***
use prec, only: pReal,pInt
implicit none
character (len=*), parameter :: constitutive_j2_label = 'j2'
integer(pInt), dimension(:), allocatable :: constitutive_j2_sizeDotState, &
constitutive_j2_sizeState, &
constitutive_j2_sizePostResults
character(len=64), dimension(:,:), allocatable :: constitutive_j2_output
integer(pInt), dimension(:), allocatable :: constitutive_j2_structure
real(pReal), dimension(:), allocatable :: constitutive_j2_mu
real(pReal), dimension(:), allocatable :: constitutive_j2_lambda
real(pReal), dimension(:,:,:), allocatable :: constitutive_j2_Cslip_66
!* Visco-plastic constitutive_j2 parameters
real(pReal), dimension(:), allocatable :: constitutive_j2_fTaylor
real(pReal), dimension(:), allocatable :: constitutive_j2_s0_slip
real(pReal), dimension(:), allocatable :: constitutive_j2_gdot0_slip
real(pReal), dimension(:), allocatable :: constitutive_j2_n_slip
real(pReal), dimension(:), allocatable :: constitutive_j2_h0
real(pReal), dimension(:), allocatable :: constitutive_j2_s_sat
real(pReal), dimension(:), allocatable :: constitutive_j2_w0
CONTAINS
!****************************************
!* - constitutive_init
!* - constitutive_homogenizedC
!* - constitutive_microstructure
!* - constitutive_LpAndItsTangent
!* - consistutive_dotState
!* - consistutive_postResults
!****************************************
subroutine constitutive_j2_init(file)
!**************************************
!* Module initialization *
!**************************************
use prec, only: pInt, pReal
use math, only: math_Mandel3333to66, math_Voigt66to3333
use IO
use material
integer(pInt), intent(in) :: file
integer(pInt), parameter :: maxNchunks = 7
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section, maxNinstance, i,j,k,l, output
character(len=64) tag
character(len=1024) line
maxNinstance = count(phase_constitution == constitutive_j2_label)
if (maxNinstance == 0) return
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_output(maxval(phase_Noutput), &
maxNinstance)) ; constitutive_j2_output = ''
allocate(constitutive_j2_mu(maxNinstance)) ; constitutive_j2_mu = 0.0_pReal
allocate(constitutive_j2_lambda(maxNinstance)) ; constitutive_j2_lambda = 0.0_pReal
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_s0_slip(maxNinstance)) ; constitutive_j2_s0_slip = 0.0_pReal
allocate(constitutive_j2_gdot0_slip(maxNinstance)) ; constitutive_j2_gdot0_slip = 0.0_pReal
allocate(constitutive_j2_n_slip(maxNinstance)) ; constitutive_j2_n_slip = 0.0_pReal
allocate(constitutive_j2_h0(maxNinstance)) ; constitutive_j2_h0 = 0.0_pReal
allocate(constitutive_j2_s_sat(maxNinstance)) ; constitutive_j2_s_sat = 0.0_pReal
allocate(constitutive_j2_w0(maxNinstance)) ; constitutive_j2_w0 = 0.0_pReal
allocate(constitutive_j2_latent(maxNinstance)) ; constitutive_j2_latent = 1.0_pReal
rewind(file)
line = ''
section = 0
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
read(file,'(a1024)',END=100) line
enddo
do ! read thru sections of phase part
read(file,'(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
output = 0 ! reset output counter
endif
if (section > 0 .and. phase_constitution(section) == constitutive_j2_label) then ! one of my sections
i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
select case(tag)
case ('(output)')
output = output + 1
constitutive_j2_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
case ('nslip')
constitutive_j2_Nslip(i) = IO_intValue(line,positions,2)
case ('mu')
constitutive_j2_mu(i) = IO_floatValue(line,positions,2)
case ('lambda')
constitutive_j2_lambda(i) = IO_floatValue(line,positions,2)
case ('s0_slip')
constitutive_j2_s0_slip(i) = IO_floatValue(line,positions,2)
case ('gdot0_slip')
constitutive_j2_gdot0_slip(i) = IO_floatValue(line,positions,2)
case ('n_slip')
constitutive_j2_n_slip(i) = IO_floatValue(line,positions,2)
case ('h0')
constitutive_j2_h0(i) = IO_floatValue(line,positions,2)
case ('s_sat')
constitutive_j2_s_sat(i) = IO_floatValue(line,positions,2)
case ('w0')
constitutive_j2_w0(i) = IO_floatValue(line,positions,2)
case ('taylor')
constitutive_j2_fTaylor(i) = IO_floatValue(line,positions,2)
end select
endif
enddo
100 do i = 1,maxNinstance ! sanity checks
if (constitutive_j2_s0_slip(i) < 0.0_pReal) call IO_error(203)
if (constitutive_j2_gdot0_slip(i) <= 0.0_pReal) call IO_error(204)
if (constitutive_j2_n_slip(i) <= 0.0_pReal) call IO_error(205)
if (constitutive_j2_h0(i) <= 0.0_pReal) call IO_error(206)
if (constitutive_j2_s_sat(i) <= 0.0_pReal) call IO_error(207)
if (constitutive_j2_w0(i) <= 0.0_pReal) call IO_error(208)
if (constitutive_j2_fTaylor(i) <= 0.0_pReal) call IO_error(240)
enddo
do i = 1,maxNinstance
constitutive_j2_sizeDotState(i) = 1
constitutive_j2_sizeState(i) = 1
do j = 1,maxval(phase_Noutput)
select case(constitutive_j2_output(j,i))
case('flowstress')
constitutive_j2_sizePostResults(i) = &
constitutive_j2_sizePostResults(i) + 1
case('strainrate')
constitutive_j2_sizePostResults(i) = &
constitutive_j2_sizePostResults(i) + 1
end select
enddo
forall(k=1:3)
forall(j=1:3) &
constitutive_j2_Cslip_66(k,j,i) = constitutive_j2_C12(i)
constitutive_j2_Cslip_66(k,k,i) = constitutive_j2_C11(i)
constitutive_j2_Cslip_66(k+3,k+3,i) = constitutive_j2_C44(i)
end forall
constitutive_j2_Cslip_66(:,:,i) = &
math_Mandel3333to66(math_Voigt66to3333(constitutive_j2_Cslip_66(:,:,i)))
enddo
return
end subroutine
function constitutive_j2_stateInit(ipc,ip,el)
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
use prec, only: pReal,pInt
use material, only: material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt), intent(in) :: ipc,ip,el
integer(pInt) matID
real(pReal), dimension(1) :: &
constitutive_j2_stateInit
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
constitutive_j2_stateInit = constitutive_j2_s0_slip(matID)
return
end function
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: pReal,pInt,p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt), intent(in) :: ipc,ip,el
integer(pInt) matID
real(pReal), dimension(6,6) :: constitutive_j2_homogenizedC
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
constitutive_j2_homogenizedC = constitutive_j2_Cslip_66(:,:,matID)
return
end function
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: pReal,pInt,p_vec
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el, matID
real(pReal) Temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
end subroutine
subroutine constitutive_j2_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
!*********************************************************************
!* plastic velocity gradient and its tangent *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - ipc : component-ID at current integration point *
!* - ip : current integration point *
!* - el : current element *
!* OUTPUT: *
!* - Lp : plastic velocity gradient *
!* - dLp_dTstar : derivative of Lp (4th-rank tensor) *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use math, only: math_mul6x6,math_Mandel6to33,math_Plain3333to99
use lattice, only: lattice_Sslip,lattice_Sslip_v
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,k,l,m,n
real(pReal) Temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(3,3) :: Lp
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
real(pReal), dimension(9,9) :: dLp_dTstar
real(pReal), norm_Tstar
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v))
!* Calculation of Lp
Lp = math_Mandel6to33(Tstar_v)/norm_Tstar*constitutive_j2_gdot0_slip(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))**constitutive_j2_n_slip(matID)
!* Calculation of the tangent of Lp
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar = 0.0_pReal
do i = 1,constitutive_phenomenological_Nslip(matID)
dgdot_dtauslip(i) = constitutive_phenomenological_gdot0_slip(matID)*(abs(tau_slip(i))/state(ipc,ip,el)%p(i))**&
(constitutive_phenomenological_n_slip(matID)-1.0_pReal)*&
constitutive_phenomenological_n_slip(matID)/state(ipc,ip,el)%p(i)
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
dgdot_dtauslip(i)*lattice_Sslip(k,l,i,constitutive_phenomenological_structure(matID))* &
lattice_Sslip(m,n,i,constitutive_phenomenological_structure(matID))
enddo
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
return
end subroutine
function constitutive_j2_dotState(Tstar_v,Temperature,state,ipc,ip,el)
!*********************************************************************
!* rate of change of microstructure *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - ipc : component-ID at current integration point *
!* - ip : current integration point *
!* - el : current element *
!* OUTPUT: *
!* - constitutive_dotState : evolution of state variable *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use math, only: math_mul6x6
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,n
real(pReal) Temperature,tau_slip,gdot_slip
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(1) :: &
constitutive_phenomenological_dotState,self_hardening
real(pReal), norm_Tstar
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v))
constitutive_j2_dotState = constitutive_j2_gdot0_slip(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** &
constitutive_j2_n_slip(matID) * &
constitutive_j2_h0(matID)*(1.0_pReal-state(ipc,ip,el)%p(1)/constitutive_j2_s0_sat(matID))** &
constitutive_j2_w0(matID)
return
end function
pure function constitutive_phenomenological_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
!*********************************************************************
!* return array of constitutive results *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - dt : current time increment *
!* - ipc : component-ID at current integration point *
!* - ip : current integration point *
!* - el : current element *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use math, only: math_mul6x6
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
implicit none
!* Definition of variables
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: dt,Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
integer(pInt) matID,o,i,c,n
real(pReal) norm_Tstar
real(pReal), dimension(constitutive_j2_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
constitutive_phenomenological_postResults
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v))
c = 0_pInt
constitutive_j2_postResults = 0.0_pReal
do o = 1,phase_Noutput(material_phase(ipc,ip,el))
select case(constitutive_j2_output(o,matID))
case ('flowstress')
constitutive_j2_postResults(c+1) = state(ipc,ip,el)%p(1)
c = c + 1
case ('strainrate')
constitutive_j2_postResults(c+1) = constitutive_j2_gdot0_slip(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** &
constitutive_j2_n_slip(matID)
c = c + 1
end select
enddo
return
end function
END MODULE