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corrected the constitutive law for j2-plasticity in Lp and its tangent and dotState.

This commit is contained in:
Christoph Kords 2009-06-23 10:39:29 +00:00
parent 0873231e78
commit 06ed8c8177
2 changed files with 236 additions and 148 deletions
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380
trunk/constitutive_j2.f90
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@ -14,11 +14,11 @@
! 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
! s0 31e6
! tau0 31e6
! gdot0 0.001
! n 20
! h0 75e6
! s_sat 63e6
! tau_sat 63e6
! w0 2.25
MODULE constitutive_j2
@ -38,11 +38,11 @@ MODULE constitutive_j2
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
real(pReal), dimension(:), allocatable :: constitutive_j2_tau0
real(pReal), dimension(:), allocatable :: constitutive_j2_gdot0
real(pReal), dimension(:), allocatable :: constitutive_j2_n
real(pReal), dimension(:), allocatable :: constitutive_j2_h0
real(pReal), dimension(:), allocatable :: constitutive_j2_s_sat
real(pReal), dimension(:), allocatable :: constitutive_j2_tau_sat
real(pReal), dimension(:), allocatable :: constitutive_j2_w0
@ -85,11 +85,11 @@ subroutine constitutive_j2_init(file)
allocate(constitutive_j2_C12(maxNinstance)) ; constitutive_j2_C12 = 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(maxNinstance)) ; constitutive_j2_s0 = 0.0_pReal
allocate(constitutive_j2_tau0(maxNinstance)) ; constitutive_j2_tau0 = 0.0_pReal
allocate(constitutive_j2_gdot0(maxNinstance)) ; constitutive_j2_gdot0 = 0.0_pReal
allocate(constitutive_j2_n(maxNinstance)) ; constitutive_j2_n = 0.0_pReal
allocate(constitutive_j2_h0(maxNinstance)) ; constitutive_j2_h0 = 0.0_pReal
allocate(constitutive_j2_s_sat(maxNinstance)) ; constitutive_j2_s_sat = 0.0_pReal
allocate(constitutive_j2_tau_sat(maxNinstance)) ; constitutive_j2_tau_sat = 0.0_pReal
allocate(constitutive_j2_w0(maxNinstance)) ; constitutive_j2_w0 = 0.0_pReal
rewind(file)
@ -120,16 +120,16 @@ subroutine constitutive_j2_init(file)
constitutive_j2_C11(i) = IO_floatValue(line,positions,2)
case ('c12')
constitutive_j2_C12(i) = IO_floatValue(line,positions,2)
case ('s0')
constitutive_j2_s0(i) = IO_floatValue(line,positions,2)
case ('tau0')
constitutive_j2_tau0(i) = IO_floatValue(line,positions,2)
case ('gdot0')
constitutive_j2_gdot0(i) = IO_floatValue(line,positions,2)
case ('n')
constitutive_j2_n(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 ('tau_sat')
constitutive_j2_tau_sat(i) = IO_floatValue(line,positions,2)
case ('w0')
constitutive_j2_w0(i) = IO_floatValue(line,positions,2)
case ('taylorfactor')
@ -139,11 +139,11 @@ subroutine constitutive_j2_init(file)
enddo
100 do i = 1,maxNinstance ! sanity checks
if (constitutive_j2_s0(i) < 0.0_pReal) call IO_error(203)
if (constitutive_j2_tau0(i) < 0.0_pReal) call IO_error(203)
if (constitutive_j2_gdot0(i) <= 0.0_pReal) call IO_error(204)
if (constitutive_j2_n(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_tau_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
@ -179,20 +179,31 @@ subroutine constitutive_j2_init(file)
endsubroutine
function constitutive_j2_stateInit(myInstance)
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
use prec, only: pReal,pInt
implicit none
pure function constitutive_j2_stateInit(myInstance)
!*** variables and functions from other modules ***!
use prec, only: pReal,pInt
implicit none
!*** input variables ***!
integer(pInt), intent(in) :: myInstance
!*** output variables ***!
real(pReal), dimension(1) :: constitutive_j2_stateInit
!*** local variables ***!
!*** global variables ***!
! constitutive_j2_tau0
!* Definition of variables
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(1) :: constitutive_j2_stateInit
constitutive_j2_stateInit = constitutive_j2_tau0(myInstance)
constitutive_j2_stateInit = constitutive_j2_s0(myInstance)
return
return
endfunction
@ -248,156 +259,233 @@ subroutine constitutive_j2_microstructure(Temperature,state,ipc,ip,el)
endsubroutine
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
!****************************************************************
!* calculates plastic velocity gradient and its tangent *
!****************************************************************
pure subroutine constitutive_j2_LpAndItsTangent(Lp, dLp_dTstar_99, Tstar_dev_v, Temperature, state, g, ip, el)
implicit none
!*** variables and functions from other modules ***!
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6, &
math_Mandel6to33, &
math_Plain3333to99, &
math_spectral1
use lattice, only: lattice_Sslip, &
lattice_Sslip_v
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
!* 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) :: Tstar33
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, squarenorm_Tstar, factor
implicit none
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in):: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar_99 ! derivative of Lp with respect to Tstar (9x9 matrix)
!*** local variables ***!
real(pReal), dimension(3,3) :: Tstar_dev_33 ! deviatoric part of the 2nd Piola Kirchhoff stress tensor as 2nd order tensor
real(pReal), dimension(3,3,3,3) :: dLp_dTstar_3333 ! derivative of Lp with respect to Tstar as 4th order tensor
real(pReal) gamma_dot, & ! strainrate
norm_Tstar_dev, & ! euclidean norm of Tstar_dev
squarenorm_Tstar_dev ! square of the euclidean norm of Tstar_dev
integer(pInt) matID, &
k, &
l, &
m, &
n
!*** global variables ***!
! constitutive_j2_gdot0
! constitutive_j2_fTaylor
! constitutive_j2_n
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
matID = phase_constitutionInstance(material_phase(g,ip,el))
Tstar33 = math_Mandel6to33(Tstar_v)
squarenorm_Tstar = math_mul6x6(Tstar_v,Tstar_v)
norm_Tstar = dsqrt(squarenorm_Tstar)
! convert Tstar to matrix and calculate euclidean norm
Tstar_dev_33 = math_Mandel6to33(Tstar_dev_v)
squarenorm_Tstar_dev = math_mul6x6(Tstar_dev_v,Tstar_dev_v)
norm_Tstar_dev = dsqrt(squarenorm_Tstar_dev)
!* Initialization of Lp and dLp_dTstar
Lp = 0.0_pReal
dLp_dTstar = 0.0_pReal
! Initialization of Lp and dLp_dTstar
Lp = 0.0_pReal
dLp_dTstar_99 = 0.0_pReal
!* for Tstar==0 both Lp and dLp_dTstar are zero (if not n==1)
if (norm_Tstar > 0) then
!* Calculation of Lp
Lp = dsqrt(1.5_pReal)*Tstar33/norm_Tstar*constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))**constitutive_j2_n(matID)
! for Tstar==0 both Lp and dLp_dTstar are zero (if not n==1)
if (norm_Tstar_dev > 0) then
! Calculation of gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) **constitutive_j2_n(matID)
!* Calculation of the tangent of Lp
factor = dsqrt(1.5_pReal)*constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)/state(ipc,ip,el)%p(1))**constitutive_j2_n(matID) * &
norm_Tstar**(constitutive_j2_n(matID)-1.0_pReal)
dLp_dTstar3333 = 0.0_pReal
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dTstar3333(k,l,m,n) = Tstar33(k,l)*Tstar33(m,n) * (constitutive_j2_n(matID)-1.0_pReal)/squarenorm_Tstar
forall (k=1:3,l=1:3) &
dLp_dTstar3333(k,l,k,l) = dLp_dTstar3333(k,l,k,l) + 1.0_pReal
dLp_dTstar = math_Plain3333to99(factor * dLp_dTstar3333)
end if
return
! Calculation of Lp
Lp = Tstar_dev_33/norm_Tstar_dev * gamma_dot/constitutive_j2_fTaylor(matID)
!* Calculation of the tangent of Lp
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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=1:3,l=1:3) &
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
return
endsubroutine
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
!****************************************************************
!* calculates the rate of change of microstructure *
!****************************************************************
pure function constitutive_j2_dotState(Tstar_v, Temperature, state, g, ip, el)
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID
real(pReal) Temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(1) :: constitutive_j2_dotState
real(pReal) norm_Tstar
!*** variables and functions from other modules ***!
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
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
!*** input variables ***!
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: Temperature
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(1) :: constitutive_j2_dotState ! evolution of state variable
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) gamma_dot, & ! strainrate
hardening, & ! hardening coefficient
norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID
norm_Tstar = dsqrt(math_mul6x6(Tstar_v,Tstar_v))
constitutive_j2_dotState = constitutive_j2_h0(matID)*(1.0_pReal-state(ipc,ip,el)%p(1)/constitutive_j2_s_sat(matID))** &
constitutive_j2_w0(matID) * &
constitutive_j2_gdot0(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** &
constitutive_j2_n(matID)
!*** global variables ***!
! constitutive_j2_gdot0
! constitutive_j2_fTaylor
! constitutive_j2_n
! constitutive_j2_h0
! constitutive_j2_tau_sat
! constitutive_j2_w0
matID = phase_constitutionInstance(material_phase(g,ip,el))
return
! caclulate deviatoric part of 2nd Piola-Kirchhoff stress
Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3_pReal
Tstar_dev_v(4:6) = Tstar_v(4:6)
norm_Tstar_dev = dsqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
! Calculation of gamma_dot
gamma_dot = constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
! calculate hardening coefficient
hardening = constitutive_j2_h0(matID) * &
( 1.0_pReal - state(g,ip,el)%p(1) / constitutive_j2_tau_sat(matID) ) ** constitutive_j2_w0(matID)
! finally calculate dotState
constitutive_j2_dotState = hardening * gamma_dot
return
endfunction
pure function constitutive_j2_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
pure function constitutive_j2_postResults(Tstar_v, Temperature, dt, state, g, ip, el)
!* 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_j2_postResults
!*** variables and functions from other modules ***!
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
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
implicit none
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(matID)/constitutive_j2_fTaylor(matID)* &
(dsqrt(1.5_pReal)/constitutive_j2_fTaylor(matID)*norm_Tstar/state(ipc,ip,el)%p(1))** &
constitutive_j2_n(matID)
c = c + 1
end select
enddo
!*** input variables ***!
real(pReal), dimension(6), intent(in):: Tstar_v ! 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in):: Temperature, &
dt ! current time increment
integer(pInt), intent(in):: g, & ! grain number
ip, & ! integration point number
el ! element number
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! state of the current microstructure
!*** output variables ***!
real(pReal), dimension(constitutive_j2_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
constitutive_j2_postResults
!*** local variables ***!
real(pReal), dimension(6) :: Tstar_dev_v ! deviatoric part of the 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal) norm_Tstar_dev ! euclidean norm of Tstar_dev
integer(pInt) matID, &
o, &
c
!*** global variables ***!
! constitutive_j2_gdot0
! constitutive_j2_fTaylor
! constitutive_j2_n
matID = phase_constitutionInstance(material_phase(g,ip,el))
! calculate deviatoric part of 2nd Piola-Kirchhoff stress and its norm
Tstar_dev_v(1:3) = Tstar_v(1:3) - sum(Tstar_v(1:3))/3_pReal
Tstar_dev_v(4:6) = Tstar_v(4:6)
norm_Tstar_dev = dsqrt(math_mul6x6(Tstar_dev_v,Tstar_dev_v))
c = 0_pInt
constitutive_j2_postResults = 0.0_pReal
do o = 1,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_j2_output(o,matID))
case ('flowstress')
constitutive_j2_postResults(c+1) = state(g,ip,el)%p(1)
c = c + 1
case ('strainrate')
constitutive_j2_postResults(c+1) = &
constitutive_j2_gdot0(matID) * ( dsqrt(1.5_pReal) * norm_Tstar_dev &
/ &!---------------------------------------------------
(constitutive_j2_fTaylor(matID) * state(g,ip,el)%p(1)) ) ** constitutive_j2_n(matID)
c = c + 1
end select
enddo
return

4
trunk/material.config
View File

@ -41,11 +41,11 @@ c12 58.34e9
(output) flowstress
(output) strainrate
taylorfactor 3
s0 31e6
tau0 31e6
gdot0 0.001
n 20
h0 75e6
s_sat 63e6
tau_sat 63e6
w0 2.25
constitution phenomenological