only relevant for mechanics
This commit is contained in:
Martin Diehl
parent
2ceb000002
commit
5fce37fb3e
|
|
@ -392,6 +392,26 @@ end function constitutive_deltaState
|
||||||
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
|
dS_dFi !< derivative of 2nd P-K stress with respect to intermediate deformation gradient
|
||||||
end subroutine constitutive_hooke_SandItsTangents
|
end subroutine constitutive_hooke_SandItsTangents
|
||||||
|
|
||||||
|
module subroutine integrateStateFPI(g,i,e)
|
||||||
|
integer, intent(in) :: e, i, g
|
||||||
|
end subroutine integrateStateFPI
|
||||||
|
|
||||||
|
module subroutine integrateStateEuler(g,i,e)
|
||||||
|
integer, intent(in) :: e, i, g
|
||||||
|
end subroutine integrateStateEuler
|
||||||
|
|
||||||
|
module subroutine integrateStateAdaptiveEuler(g,i,e)
|
||||||
|
integer, intent(in) :: e, i, g
|
||||||
|
end subroutine integrateStateAdaptiveEuler
|
||||||
|
|
||||||
|
module subroutine integrateStateRK4(g,i,e)
|
||||||
|
integer, intent(in) :: e, i, g
|
||||||
|
end subroutine integrateStateRK4
|
||||||
|
|
||||||
|
module subroutine integrateStateRKCK45(g,i,e)
|
||||||
|
integer, intent(in) :: e, i, g
|
||||||
|
end subroutine integrateStateRKCK45
|
||||||
|
|
||||||
end interface
|
end interface
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -414,9 +434,8 @@ end function constitutive_deltaState
|
||||||
plastic_nonlocal_updateCompatibility, &
|
plastic_nonlocal_updateCompatibility, &
|
||||||
plastic_active, &
|
plastic_active, &
|
||||||
source_active, &
|
source_active, &
|
||||||
kinematics_active
|
kinematics_active, &
|
||||||
|
converged, &
|
||||||
public :: &
|
|
||||||
crystallite_init, &
|
crystallite_init, &
|
||||||
crystallite_stress, &
|
crystallite_stress, &
|
||||||
crystallite_stressTangent, &
|
crystallite_stressTangent, &
|
||||||
|
|
@ -429,6 +448,7 @@ end function constitutive_deltaState
|
||||||
crystallite_initializeRestorationPoints, &
|
crystallite_initializeRestorationPoints, &
|
||||||
crystallite_windForward, &
|
crystallite_windForward, &
|
||||||
crystallite_restore
|
crystallite_restore
|
||||||
|
|
||||||
contains
|
contains
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -1562,338 +1582,6 @@ subroutine crystallite_results
|
||||||
end subroutine crystallite_results
|
end subroutine crystallite_results
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief calculation of stress (P) with time integration based on a residuum in Lp and
|
|
||||||
!> intermediate acceleration of the Newton-Raphson correction
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
function integrateStress(ipc,ip,el,timeFraction) result(broken)
|
|
||||||
|
|
||||||
integer, intent(in):: el, & ! element index
|
|
||||||
ip, & ! integration point index
|
|
||||||
ipc ! grain index
|
|
||||||
real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep
|
|
||||||
|
|
||||||
real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep
|
|
||||||
Fp_new, & ! plastic deformation gradient at end of timestep
|
|
||||||
invFp_new, & ! inverse of Fp_new
|
|
||||||
invFp_current, & ! inverse of Fp_current
|
|
||||||
Lpguess, & ! current guess for plastic velocity gradient
|
|
||||||
Lpguess_old, & ! known last good guess for plastic velocity gradient
|
|
||||||
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
|
|
||||||
residuumLp, & ! current residuum of plastic velocity gradient
|
|
||||||
residuumLp_old, & ! last residuum of plastic velocity gradient
|
|
||||||
deltaLp, & ! direction of next guess
|
|
||||||
Fi_new, & ! gradient of intermediate deformation stages
|
|
||||||
invFi_new, &
|
|
||||||
invFi_current, & ! inverse of Fi_current
|
|
||||||
Liguess, & ! current guess for intermediate velocity gradient
|
|
||||||
Liguess_old, & ! known last good guess for intermediate velocity gradient
|
|
||||||
Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law
|
|
||||||
residuumLi, & ! current residuum of intermediate velocity gradient
|
|
||||||
residuumLi_old, & ! last residuum of intermediate velocity gradient
|
|
||||||
deltaLi, & ! direction of next guess
|
|
||||||
Fe, & ! elastic deformation gradient
|
|
||||||
S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration
|
|
||||||
A, &
|
|
||||||
B, &
|
|
||||||
temp_33
|
|
||||||
real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK
|
|
||||||
integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK
|
|
||||||
real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme)
|
|
||||||
dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme)
|
|
||||||
real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress
|
|
||||||
dS_dFi, &
|
|
||||||
dFe_dLp, & ! partial derivative of elastic deformation gradient
|
|
||||||
dFe_dLi, &
|
|
||||||
dFi_dLi, &
|
|
||||||
dLp_dFi, &
|
|
||||||
dLi_dFi, &
|
|
||||||
dLp_dS, &
|
|
||||||
dLi_dS
|
|
||||||
real(pReal) steplengthLp, &
|
|
||||||
steplengthLi, &
|
|
||||||
dt, & ! time increment
|
|
||||||
atol_Lp, &
|
|
||||||
atol_Li, &
|
|
||||||
devNull
|
|
||||||
integer NiterationStressLp, & ! number of stress integrations
|
|
||||||
NiterationStressLi, & ! number of inner stress integrations
|
|
||||||
ierr, & ! error indicator for LAPACK
|
|
||||||
o, &
|
|
||||||
p, &
|
|
||||||
m, &
|
|
||||||
jacoCounterLp, &
|
|
||||||
jacoCounterLi ! counters to check for Jacobian update
|
|
||||||
logical :: error,broken
|
|
||||||
|
|
||||||
broken = .true.
|
|
||||||
|
|
||||||
if (present(timeFraction)) then
|
|
||||||
dt = crystallite_subdt(ipc,ip,el) * timeFraction
|
|
||||||
F = crystallite_subF0(1:3,1:3,ipc,ip,el) &
|
|
||||||
+ (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction
|
|
||||||
else
|
|
||||||
dt = crystallite_subdt(ipc,ip,el)
|
|
||||||
F = crystallite_subF(1:3,1:3,ipc,ip,el)
|
|
||||||
endif
|
|
||||||
|
|
||||||
call constitutive_plastic_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), &
|
|
||||||
crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el)
|
|
||||||
|
|
||||||
p = material_phaseAt(ipc,el)
|
|
||||||
m = material_phaseMemberAt(ipc,ip,el)
|
|
||||||
|
|
||||||
Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess
|
|
||||||
Liguess = constitutive_mech_Li(p)%data(1:3,1:3,m) ! take as first guess
|
|
||||||
|
|
||||||
call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el))
|
|
||||||
if (error) return ! error
|
|
||||||
call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el))
|
|
||||||
if (error) return ! error
|
|
||||||
|
|
||||||
A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp
|
|
||||||
|
|
||||||
jacoCounterLi = 0
|
|
||||||
steplengthLi = 1.0_pReal
|
|
||||||
residuumLi_old = 0.0_pReal
|
|
||||||
Liguess_old = Liguess
|
|
||||||
|
|
||||||
NiterationStressLi = 0
|
|
||||||
LiLoop: do
|
|
||||||
NiterationStressLi = NiterationStressLi + 1
|
|
||||||
if (NiterationStressLi>num%nStress) return ! error
|
|
||||||
|
|
||||||
invFi_new = matmul(invFi_current,math_I3 - dt*Liguess)
|
|
||||||
Fi_new = math_inv33(invFi_new)
|
|
||||||
|
|
||||||
jacoCounterLp = 0
|
|
||||||
steplengthLp = 1.0_pReal
|
|
||||||
residuumLp_old = 0.0_pReal
|
|
||||||
Lpguess_old = Lpguess
|
|
||||||
|
|
||||||
NiterationStressLp = 0
|
|
||||||
LpLoop: do
|
|
||||||
NiterationStressLp = NiterationStressLp + 1
|
|
||||||
if (NiterationStressLp>num%nStress) return ! error
|
|
||||||
|
|
||||||
B = math_I3 - dt*Lpguess
|
|
||||||
Fe = matmul(matmul(A,B), invFi_new)
|
|
||||||
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
|
||||||
Fe, Fi_new, ipc, ip, el)
|
|
||||||
|
|
||||||
call constitutive_plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, &
|
|
||||||
S, Fi_new, ipc, ip, el)
|
|
||||||
|
|
||||||
!* update current residuum and check for convergence of loop
|
|
||||||
atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
||||||
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
||||||
residuumLp = Lpguess - Lp_constitutive
|
|
||||||
|
|
||||||
if (any(IEEE_is_NaN(residuumLp))) then
|
|
||||||
return ! error
|
|
||||||
elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance
|
|
||||||
exit LpLoop
|
|
||||||
elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
||||||
residuumLp_old = residuumLp ! ...remember old values and...
|
|
||||||
Lpguess_old = Lpguess
|
|
||||||
steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
||||||
else ! not converged and residuum not improved...
|
|
||||||
steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction
|
|
||||||
Lpguess = Lpguess_old &
|
|
||||||
+ deltaLp * stepLengthLp
|
|
||||||
cycle LpLoop
|
|
||||||
endif
|
|
||||||
|
|
||||||
calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then
|
|
||||||
jacoCounterLp = jacoCounterLp + 1
|
|
||||||
|
|
||||||
do o=1,3; do p=1,3
|
|
||||||
dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
||||||
enddo; enddo
|
|
||||||
dRLp_dLp = math_eye(9) &
|
|
||||||
- math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp))
|
|
||||||
temp_9 = math_33to9(residuumLp)
|
|
||||||
call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp
|
|
||||||
if (ierr /= 0) return ! error
|
|
||||||
deltaLp = - math_9to33(temp_9)
|
|
||||||
endif calculateJacobiLi
|
|
||||||
|
|
||||||
Lpguess = Lpguess &
|
|
||||||
+ deltaLp * steplengthLp
|
|
||||||
enddo LpLoop
|
|
||||||
|
|
||||||
call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, &
|
|
||||||
S, Fi_new, ipc, ip, el)
|
|
||||||
|
|
||||||
!* update current residuum and check for convergence of loop
|
|
||||||
atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
|
||||||
num%atol_crystalliteStress) ! minimum lower cutoff
|
|
||||||
residuumLi = Liguess - Li_constitutive
|
|
||||||
if (any(IEEE_is_NaN(residuumLi))) then
|
|
||||||
return ! error
|
|
||||||
elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance
|
|
||||||
exit LiLoop
|
|
||||||
elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
|
||||||
residuumLi_old = residuumLi ! ...remember old values and...
|
|
||||||
Liguess_old = Liguess
|
|
||||||
steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
|
||||||
else ! not converged and residuum not improved...
|
|
||||||
steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction
|
|
||||||
Liguess = Liguess_old &
|
|
||||||
+ deltaLi * steplengthLi
|
|
||||||
cycle LiLoop
|
|
||||||
endif
|
|
||||||
|
|
||||||
calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then
|
|
||||||
jacoCounterLi = jacoCounterLi + 1
|
|
||||||
|
|
||||||
temp_33 = matmul(matmul(A,B),invFi_current)
|
|
||||||
do o=1,3; do p=1,3
|
|
||||||
dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
|
||||||
dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current
|
|
||||||
enddo; enddo
|
|
||||||
do o=1,3; do p=1,3
|
|
||||||
dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new)
|
|
||||||
enddo; enddo
|
|
||||||
dRLi_dLi = math_eye(9) &
|
|
||||||
- math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) &
|
|
||||||
+ math_mul3333xx3333(dS_dFi, dFi_dLi))) &
|
|
||||||
- math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi))
|
|
||||||
temp_9 = math_33to9(residuumLi)
|
|
||||||
call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li
|
|
||||||
if (ierr /= 0) return ! error
|
|
||||||
deltaLi = - math_9to33(temp_9)
|
|
||||||
endif calculateJacobiLp
|
|
||||||
|
|
||||||
Liguess = Liguess &
|
|
||||||
+ deltaLi * steplengthLi
|
|
||||||
enddo LiLoop
|
|
||||||
|
|
||||||
invFp_new = matmul(invFp_current,B)
|
|
||||||
call math_invert33(Fp_new,devNull,error,invFp_new)
|
|
||||||
if (error) return ! error
|
|
||||||
|
|
||||||
p = material_phaseAt(ipc,el)
|
|
||||||
m = material_phaseMemberAt(ipc,ip,el)
|
|
||||||
|
|
||||||
crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new)))
|
|
||||||
crystallite_S (1:3,1:3,ipc,ip,el) = S
|
|
||||||
crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess
|
|
||||||
constitutive_mech_Li(p)%data(1:3,1:3,m) = Liguess
|
|
||||||
crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,m) = Fi_new
|
|
||||||
crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new)
|
|
||||||
broken = .false.
|
|
||||||
|
|
||||||
end function integrateStress
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
|
||||||
!> using Fixed Point Iteration to adapt the stepsize
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateFPI(g,i,e)
|
|
||||||
|
|
||||||
integer, intent(in) :: &
|
|
||||||
e, & !< element index in element loop
|
|
||||||
i, & !< integration point index in ip loop
|
|
||||||
g !< grain index in grain loop
|
|
||||||
integer :: &
|
|
||||||
NiterationState, & !< number of iterations in state loop
|
|
||||||
p, &
|
|
||||||
c, &
|
|
||||||
s, &
|
|
||||||
size_pl
|
|
||||||
integer, dimension(maxval(phase_Nsources)) :: &
|
|
||||||
size_so
|
|
||||||
real(pReal) :: &
|
|
||||||
zeta
|
|
||||||
real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: &
|
|
||||||
r ! state residuum
|
|
||||||
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,2) :: &
|
|
||||||
plastic_dotState
|
|
||||||
real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState
|
|
||||||
logical :: &
|
|
||||||
broken
|
|
||||||
|
|
||||||
p = material_phaseAt(g,e)
|
|
||||||
c = material_phaseMemberAt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
size_pl = plasticState(p)%sizeDotState
|
|
||||||
plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) &
|
|
||||||
+ plasticState(p)%dotState (1:size_pl,c) &
|
|
||||||
* crystallite_subdt(g,i,e)
|
|
||||||
plastic_dotState(1:size_pl,2) = 0.0_pReal
|
|
||||||
|
|
||||||
iteration: do NiterationState = 1, num%nState
|
|
||||||
|
|
||||||
if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1)
|
|
||||||
plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c)
|
|
||||||
|
|
||||||
broken = integrateStress(g,i,e)
|
|
||||||
if(broken) exit iteration
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) exit iteration
|
|
||||||
|
|
||||||
zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),&
|
|
||||||
plastic_dotState(1:size_pl,2))
|
|
||||||
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta &
|
|
||||||
+ plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta)
|
|
||||||
r(1:size_pl) = plasticState(p)%state (1:size_pl,c) &
|
|
||||||
- plasticState(p)%subState0(1:size_pl,c) &
|
|
||||||
- plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e)
|
|
||||||
plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) &
|
|
||||||
- r(1:size_pl)
|
|
||||||
crystallite_converged(g,i,e) = converged(r(1:size_pl), &
|
|
||||||
plasticState(p)%state(1:size_pl,c), &
|
|
||||||
plasticState(p)%atol(1:size_pl))
|
|
||||||
|
|
||||||
if(crystallite_converged(g,i,e)) then
|
|
||||||
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
||||||
exit iteration
|
|
||||||
endif
|
|
||||||
|
|
||||||
enddo iteration
|
|
||||||
|
|
||||||
|
|
||||||
contains
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief calculate the damping for correction of state and dot state
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
real(pReal) pure function damper(current,previous,previous2)
|
|
||||||
|
|
||||||
real(pReal), dimension(:), intent(in) ::&
|
|
||||||
current, previous, previous2
|
|
||||||
|
|
||||||
real(pReal) :: dot_prod12, dot_prod22
|
|
||||||
|
|
||||||
dot_prod12 = dot_product(current - previous, previous - previous2)
|
|
||||||
dot_prod22 = dot_product(previous - previous2, previous - previous2)
|
|
||||||
if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then
|
|
||||||
damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22)
|
|
||||||
else
|
|
||||||
damper = 1.0_pReal
|
|
||||||
endif
|
|
||||||
|
|
||||||
end function damper
|
|
||||||
|
|
||||||
end subroutine integrateStateFPI
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
||||||
!> using Fixed Point Iteration to adapt the stepsize
|
!> using Fixed Point Iteration to adapt the stepsize
|
||||||
|
|
@ -1993,248 +1681,6 @@ subroutine integrateSourceState(g,i,e)
|
||||||
|
|
||||||
end subroutine integrateSourceState
|
end subroutine integrateSourceState
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief integrate state with 1st order explicit Euler method
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateEuler(g,i,e)
|
|
||||||
|
|
||||||
integer, intent(in) :: &
|
|
||||||
e, & !< element index in element loop
|
|
||||||
i, & !< integration point index in ip loop
|
|
||||||
g !< grain index in grain loop
|
|
||||||
integer :: &
|
|
||||||
p, &
|
|
||||||
c, &
|
|
||||||
sizeDotState
|
|
||||||
logical :: &
|
|
||||||
broken
|
|
||||||
|
|
||||||
p = material_phaseAt(g,e)
|
|
||||||
c = material_phaseMemberAt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
||||||
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
||||||
* crystallite_subdt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
broken = integrateStress(g,i,e)
|
|
||||||
crystallite_converged(g,i,e) = .not. broken
|
|
||||||
|
|
||||||
end subroutine integrateStateEuler
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief integrate stress, state with 1st order Euler method with adaptive step size
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateAdaptiveEuler(g,i,e)
|
|
||||||
|
|
||||||
integer, intent(in) :: &
|
|
||||||
e, & !< element index in element loop
|
|
||||||
i, & !< integration point index in ip loop
|
|
||||||
g !< grain index in grain loop
|
|
||||||
integer :: &
|
|
||||||
p, &
|
|
||||||
c, &
|
|
||||||
sizeDotState
|
|
||||||
logical :: &
|
|
||||||
broken
|
|
||||||
|
|
||||||
real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic
|
|
||||||
|
|
||||||
|
|
||||||
p = material_phaseAt(g,e)
|
|
||||||
c = material_phaseMemberAt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
|
|
||||||
residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e)
|
|
||||||
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
||||||
+ plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
broken = integrateStress(g,i,e)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) &
|
|
||||||
+ 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), &
|
|
||||||
plasticState(p)%state(1:sizeDotState,c), &
|
|
||||||
plasticState(p)%atol(1:sizeDotState))
|
|
||||||
|
|
||||||
end subroutine integrateStateAdaptiveEuler
|
|
||||||
|
|
||||||
|
|
||||||
!---------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
|
|
||||||
!---------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateRK4(g,i,e)
|
|
||||||
|
|
||||||
integer, intent(in) :: g,i,e
|
|
||||||
|
|
||||||
real(pReal), dimension(3,3), parameter :: &
|
|
||||||
A = reshape([&
|
|
||||||
0.5_pReal, 0.0_pReal, 0.0_pReal, &
|
|
||||||
0.0_pReal, 0.5_pReal, 0.0_pReal, &
|
|
||||||
0.0_pReal, 0.0_pReal, 1.0_pReal],&
|
|
||||||
shape(A))
|
|
||||||
real(pReal), dimension(3), parameter :: &
|
|
||||||
C = [0.5_pReal, 0.5_pReal, 1.0_pReal]
|
|
||||||
real(pReal), dimension(4), parameter :: &
|
|
||||||
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
|
|
||||||
|
|
||||||
call integrateStateRK(g,i,e,A,B,C)
|
|
||||||
|
|
||||||
end subroutine integrateStateRK4
|
|
||||||
|
|
||||||
|
|
||||||
!---------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief Integrate state (including stress integration) with the Cash-Carp method
|
|
||||||
!---------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateRKCK45(g,i,e)
|
|
||||||
|
|
||||||
integer, intent(in) :: g,i,e
|
|
||||||
|
|
||||||
real(pReal), dimension(5,5), parameter :: &
|
|
||||||
A = reshape([&
|
|
||||||
1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
||||||
3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, &
|
|
||||||
3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, &
|
|
||||||
-11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, &
|
|
||||||
1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],&
|
|
||||||
shape(A))
|
|
||||||
real(pReal), dimension(5), parameter :: &
|
|
||||||
C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal]
|
|
||||||
real(pReal), dimension(6), parameter :: &
|
|
||||||
B = &
|
|
||||||
[37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, &
|
|
||||||
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], &
|
|
||||||
DB = B - &
|
|
||||||
[2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,&
|
|
||||||
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal]
|
|
||||||
|
|
||||||
call integrateStateRK(g,i,e,A,B,C,DB)
|
|
||||||
|
|
||||||
end subroutine integrateStateRKCK45
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
!> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
|
|
||||||
!! embedded explicit Runge-Kutta method
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
|
||||||
subroutine integrateStateRK(g,i,e,A,B,CC,DB)
|
|
||||||
|
|
||||||
|
|
||||||
real(pReal), dimension(:,:), intent(in) :: A
|
|
||||||
real(pReal), dimension(:), intent(in) :: B, CC
|
|
||||||
real(pReal), dimension(:), intent(in), optional :: DB
|
|
||||||
|
|
||||||
integer, intent(in) :: &
|
|
||||||
e, & !< element index in element loop
|
|
||||||
i, & !< integration point index in ip loop
|
|
||||||
g !< grain index in grain loop
|
|
||||||
integer :: &
|
|
||||||
stage, & ! stage index in integration stage loop
|
|
||||||
n, &
|
|
||||||
p, &
|
|
||||||
c, &
|
|
||||||
sizeDotState
|
|
||||||
logical :: &
|
|
||||||
broken
|
|
||||||
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
|
|
||||||
|
|
||||||
p = material_phaseAt(g,e)
|
|
||||||
c = material_phaseMemberAt(g,i,e)
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e), g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
do stage = 1,size(A,1)
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
|
|
||||||
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1)
|
|
||||||
|
|
||||||
do n = 2, stage
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
|
|
||||||
+ A(n,stage) * plastic_RKdotState(1:sizeDotState,n)
|
|
||||||
enddo
|
|
||||||
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
||||||
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
||||||
* crystallite_subdt(g,i,e)
|
|
||||||
|
|
||||||
broken = integrateStress(g,i,e,CC(stage))
|
|
||||||
if(broken) exit
|
|
||||||
|
|
||||||
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
crystallite_partitionedF0, &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
|
||||||
crystallite_partitionedFp0, &
|
|
||||||
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
|
|
||||||
if(broken) exit
|
|
||||||
|
|
||||||
enddo
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
sizeDotState = plasticState(p)%sizeDotState
|
|
||||||
|
|
||||||
plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c)
|
|
||||||
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B)
|
|
||||||
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
|
||||||
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
|
||||||
* crystallite_subdt(g,i,e)
|
|
||||||
if(present(DB)) &
|
|
||||||
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) &
|
|
||||||
* crystallite_subdt(g,i,e), &
|
|
||||||
plasticState(p)%state(1:sizeDotState,c), &
|
|
||||||
plasticState(p)%atol(1:sizeDotState))
|
|
||||||
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
|
||||||
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
|
||||||
if(broken) return
|
|
||||||
|
|
||||||
broken = integrateStress(g,i,e)
|
|
||||||
crystallite_converged(g,i,e) = .not. broken
|
|
||||||
|
|
||||||
|
|
||||||
end subroutine integrateStateRK
|
|
||||||
|
|
||||||
|
|
||||||
!--------------------------------------------------------------------------------------------------
|
!--------------------------------------------------------------------------------------------------
|
||||||
!> @brief determines whether a point is converged
|
!> @brief determines whether a point is converged
|
||||||
|
|
|
||||||
|
|
@ -691,5 +691,581 @@ module subroutine plastic_results
|
||||||
|
|
||||||
end subroutine plastic_results
|
end subroutine plastic_results
|
||||||
|
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief calculation of stress (P) with time integration based on a residuum in Lp and
|
||||||
|
!> intermediate acceleration of the Newton-Raphson correction
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
function integrateStress(ipc,ip,el,timeFraction) result(broken)
|
||||||
|
|
||||||
|
integer, intent(in):: el, & ! element index
|
||||||
|
ip, & ! integration point index
|
||||||
|
ipc ! grain index
|
||||||
|
real(pReal), optional, intent(in) :: timeFraction ! fraction of timestep
|
||||||
|
|
||||||
|
real(pReal), dimension(3,3):: F, & ! deformation gradient at end of timestep
|
||||||
|
Fp_new, & ! plastic deformation gradient at end of timestep
|
||||||
|
invFp_new, & ! inverse of Fp_new
|
||||||
|
invFp_current, & ! inverse of Fp_current
|
||||||
|
Lpguess, & ! current guess for plastic velocity gradient
|
||||||
|
Lpguess_old, & ! known last good guess for plastic velocity gradient
|
||||||
|
Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
|
||||||
|
residuumLp, & ! current residuum of plastic velocity gradient
|
||||||
|
residuumLp_old, & ! last residuum of plastic velocity gradient
|
||||||
|
deltaLp, & ! direction of next guess
|
||||||
|
Fi_new, & ! gradient of intermediate deformation stages
|
||||||
|
invFi_new, &
|
||||||
|
invFi_current, & ! inverse of Fi_current
|
||||||
|
Liguess, & ! current guess for intermediate velocity gradient
|
||||||
|
Liguess_old, & ! known last good guess for intermediate velocity gradient
|
||||||
|
Li_constitutive, & ! intermediate velocity gradient resulting from constitutive law
|
||||||
|
residuumLi, & ! current residuum of intermediate velocity gradient
|
||||||
|
residuumLi_old, & ! last residuum of intermediate velocity gradient
|
||||||
|
deltaLi, & ! direction of next guess
|
||||||
|
Fe, & ! elastic deformation gradient
|
||||||
|
S, & ! 2nd Piola-Kirchhoff Stress in plastic (lattice) configuration
|
||||||
|
A, &
|
||||||
|
B, &
|
||||||
|
temp_33
|
||||||
|
real(pReal), dimension(9) :: temp_9 ! needed for matrix inversion by LAPACK
|
||||||
|
integer, dimension(9) :: devNull_9 ! needed for matrix inversion by LAPACK
|
||||||
|
real(pReal), dimension(9,9) :: dRLp_dLp, & ! partial derivative of residuum (Jacobian for Newton-Raphson scheme)
|
||||||
|
dRLi_dLi ! partial derivative of residuumI (Jacobian for Newton-Raphson scheme)
|
||||||
|
real(pReal), dimension(3,3,3,3):: dS_dFe, & ! partial derivative of 2nd Piola-Kirchhoff stress
|
||||||
|
dS_dFi, &
|
||||||
|
dFe_dLp, & ! partial derivative of elastic deformation gradient
|
||||||
|
dFe_dLi, &
|
||||||
|
dFi_dLi, &
|
||||||
|
dLp_dFi, &
|
||||||
|
dLi_dFi, &
|
||||||
|
dLp_dS, &
|
||||||
|
dLi_dS
|
||||||
|
real(pReal) steplengthLp, &
|
||||||
|
steplengthLi, &
|
||||||
|
dt, & ! time increment
|
||||||
|
atol_Lp, &
|
||||||
|
atol_Li, &
|
||||||
|
devNull
|
||||||
|
integer NiterationStressLp, & ! number of stress integrations
|
||||||
|
NiterationStressLi, & ! number of inner stress integrations
|
||||||
|
ierr, & ! error indicator for LAPACK
|
||||||
|
o, &
|
||||||
|
p, &
|
||||||
|
m, &
|
||||||
|
jacoCounterLp, &
|
||||||
|
jacoCounterLi ! counters to check for Jacobian update
|
||||||
|
logical :: error,broken
|
||||||
|
|
||||||
|
broken = .true.
|
||||||
|
|
||||||
|
if (present(timeFraction)) then
|
||||||
|
dt = crystallite_subdt(ipc,ip,el) * timeFraction
|
||||||
|
F = crystallite_subF0(1:3,1:3,ipc,ip,el) &
|
||||||
|
+ (crystallite_subF(1:3,1:3,ipc,ip,el) - crystallite_subF0(1:3,1:3,ipc,ip,el)) * timeFraction
|
||||||
|
else
|
||||||
|
dt = crystallite_subdt(ipc,ip,el)
|
||||||
|
F = crystallite_subF(1:3,1:3,ipc,ip,el)
|
||||||
|
endif
|
||||||
|
|
||||||
|
call constitutive_plastic_dependentState(crystallite_partitionedF(1:3,1:3,ipc,ip,el), &
|
||||||
|
crystallite_Fp(1:3,1:3,ipc,ip,el),ipc,ip,el)
|
||||||
|
|
||||||
|
p = material_phaseAt(ipc,el)
|
||||||
|
m = material_phaseMemberAt(ipc,ip,el)
|
||||||
|
|
||||||
|
Lpguess = crystallite_Lp(1:3,1:3,ipc,ip,el) ! take as first guess
|
||||||
|
Liguess = constitutive_mech_Li(p)%data(1:3,1:3,m) ! take as first guess
|
||||||
|
|
||||||
|
call math_invert33(invFp_current,devNull,error,crystallite_subFp0(1:3,1:3,ipc,ip,el))
|
||||||
|
if (error) return ! error
|
||||||
|
call math_invert33(invFi_current,devNull,error,crystallite_subFi0(1:3,1:3,ipc,ip,el))
|
||||||
|
if (error) return ! error
|
||||||
|
|
||||||
|
A = matmul(F,invFp_current) ! intermediate tensor needed later to calculate dFe_dLp
|
||||||
|
|
||||||
|
jacoCounterLi = 0
|
||||||
|
steplengthLi = 1.0_pReal
|
||||||
|
residuumLi_old = 0.0_pReal
|
||||||
|
Liguess_old = Liguess
|
||||||
|
|
||||||
|
NiterationStressLi = 0
|
||||||
|
LiLoop: do
|
||||||
|
NiterationStressLi = NiterationStressLi + 1
|
||||||
|
if (NiterationStressLi>num%nStress) return ! error
|
||||||
|
|
||||||
|
invFi_new = matmul(invFi_current,math_I3 - dt*Liguess)
|
||||||
|
Fi_new = math_inv33(invFi_new)
|
||||||
|
|
||||||
|
jacoCounterLp = 0
|
||||||
|
steplengthLp = 1.0_pReal
|
||||||
|
residuumLp_old = 0.0_pReal
|
||||||
|
Lpguess_old = Lpguess
|
||||||
|
|
||||||
|
NiterationStressLp = 0
|
||||||
|
LpLoop: do
|
||||||
|
NiterationStressLp = NiterationStressLp + 1
|
||||||
|
if (NiterationStressLp>num%nStress) return ! error
|
||||||
|
|
||||||
|
B = math_I3 - dt*Lpguess
|
||||||
|
Fe = matmul(matmul(A,B), invFi_new)
|
||||||
|
call constitutive_hooke_SandItsTangents(S, dS_dFe, dS_dFi, &
|
||||||
|
Fe, Fi_new, ipc, ip, el)
|
||||||
|
|
||||||
|
call constitutive_plastic_LpAndItsTangents(Lp_constitutive, dLp_dS, dLp_dFi, &
|
||||||
|
S, Fi_new, ipc, ip, el)
|
||||||
|
|
||||||
|
!* update current residuum and check for convergence of loop
|
||||||
|
atol_Lp = max(num%rtol_crystalliteStress * max(norm2(Lpguess),norm2(Lp_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
||||||
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
||||||
|
residuumLp = Lpguess - Lp_constitutive
|
||||||
|
|
||||||
|
if (any(IEEE_is_NaN(residuumLp))) then
|
||||||
|
return ! error
|
||||||
|
elseif (norm2(residuumLp) < atol_Lp) then ! converged if below absolute tolerance
|
||||||
|
exit LpLoop
|
||||||
|
elseif (NiterationStressLp == 1 .or. norm2(residuumLp) < norm2(residuumLp_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
||||||
|
residuumLp_old = residuumLp ! ...remember old values and...
|
||||||
|
Lpguess_old = Lpguess
|
||||||
|
steplengthLp = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
||||||
|
else ! not converged and residuum not improved...
|
||||||
|
steplengthLp = num%subStepSizeLp * steplengthLp ! ...try with smaller step length in same direction
|
||||||
|
Lpguess = Lpguess_old &
|
||||||
|
+ deltaLp * stepLengthLp
|
||||||
|
cycle LpLoop
|
||||||
|
endif
|
||||||
|
|
||||||
|
calculateJacobiLi: if (mod(jacoCounterLp, num%iJacoLpresiduum) == 0) then
|
||||||
|
jacoCounterLp = jacoCounterLp + 1
|
||||||
|
|
||||||
|
do o=1,3; do p=1,3
|
||||||
|
dFe_dLp(o,1:3,p,1:3) = - dt * A(o,p)*transpose(invFi_new) ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
||||||
|
enddo; enddo
|
||||||
|
dRLp_dLp = math_eye(9) &
|
||||||
|
- math_3333to99(math_mul3333xx3333(math_mul3333xx3333(dLp_dS,dS_dFe),dFe_dLp))
|
||||||
|
temp_9 = math_33to9(residuumLp)
|
||||||
|
call dgesv(9,1,dRLp_dLp,9,devNull_9,temp_9,9,ierr) ! solve dRLp/dLp * delta Lp = -res for delta Lp
|
||||||
|
if (ierr /= 0) return ! error
|
||||||
|
deltaLp = - math_9to33(temp_9)
|
||||||
|
endif calculateJacobiLi
|
||||||
|
|
||||||
|
Lpguess = Lpguess &
|
||||||
|
+ deltaLp * steplengthLp
|
||||||
|
enddo LpLoop
|
||||||
|
|
||||||
|
call constitutive_LiAndItsTangents(Li_constitutive, dLi_dS, dLi_dFi, &
|
||||||
|
S, Fi_new, ipc, ip, el)
|
||||||
|
|
||||||
|
!* update current residuum and check for convergence of loop
|
||||||
|
atol_Li = max(num%rtol_crystalliteStress * max(norm2(Liguess),norm2(Li_constitutive)), & ! absolute tolerance from largest acceptable relative error
|
||||||
|
num%atol_crystalliteStress) ! minimum lower cutoff
|
||||||
|
residuumLi = Liguess - Li_constitutive
|
||||||
|
if (any(IEEE_is_NaN(residuumLi))) then
|
||||||
|
return ! error
|
||||||
|
elseif (norm2(residuumLi) < atol_Li) then ! converged if below absolute tolerance
|
||||||
|
exit LiLoop
|
||||||
|
elseif (NiterationStressLi == 1 .or. norm2(residuumLi) < norm2(residuumLi_old)) then ! not converged, but improved norm of residuum (always proceed in first iteration)...
|
||||||
|
residuumLi_old = residuumLi ! ...remember old values and...
|
||||||
|
Liguess_old = Liguess
|
||||||
|
steplengthLi = 1.0_pReal ! ...proceed with normal step length (calculate new search direction)
|
||||||
|
else ! not converged and residuum not improved...
|
||||||
|
steplengthLi = num%subStepSizeLi * steplengthLi ! ...try with smaller step length in same direction
|
||||||
|
Liguess = Liguess_old &
|
||||||
|
+ deltaLi * steplengthLi
|
||||||
|
cycle LiLoop
|
||||||
|
endif
|
||||||
|
|
||||||
|
calculateJacobiLp: if (mod(jacoCounterLi, num%iJacoLpresiduum) == 0) then
|
||||||
|
jacoCounterLi = jacoCounterLi + 1
|
||||||
|
|
||||||
|
temp_33 = matmul(matmul(A,B),invFi_current)
|
||||||
|
do o=1,3; do p=1,3
|
||||||
|
dFe_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*temp_33 ! dFe_dLp(i,j,k,l) = -dt * A(i,k) invFi(l,j)
|
||||||
|
dFi_dLi(1:3,o,1:3,p) = -dt*math_I3(o,p)*invFi_current
|
||||||
|
enddo; enddo
|
||||||
|
do o=1,3; do p=1,3
|
||||||
|
dFi_dLi(1:3,1:3,o,p) = matmul(matmul(Fi_new,dFi_dLi(1:3,1:3,o,p)),Fi_new)
|
||||||
|
enddo; enddo
|
||||||
|
dRLi_dLi = math_eye(9) &
|
||||||
|
- math_3333to99(math_mul3333xx3333(dLi_dS, math_mul3333xx3333(dS_dFe, dFe_dLi) &
|
||||||
|
+ math_mul3333xx3333(dS_dFi, dFi_dLi))) &
|
||||||
|
- math_3333to99(math_mul3333xx3333(dLi_dFi, dFi_dLi))
|
||||||
|
temp_9 = math_33to9(residuumLi)
|
||||||
|
call dgesv(9,1,dRLi_dLi,9,devNull_9,temp_9,9,ierr) ! solve dRLi/dLp * delta Li = -res for delta Li
|
||||||
|
if (ierr /= 0) return ! error
|
||||||
|
deltaLi = - math_9to33(temp_9)
|
||||||
|
endif calculateJacobiLp
|
||||||
|
|
||||||
|
Liguess = Liguess &
|
||||||
|
+ deltaLi * steplengthLi
|
||||||
|
enddo LiLoop
|
||||||
|
|
||||||
|
invFp_new = matmul(invFp_current,B)
|
||||||
|
call math_invert33(Fp_new,devNull,error,invFp_new)
|
||||||
|
if (error) return ! error
|
||||||
|
|
||||||
|
p = material_phaseAt(ipc,el)
|
||||||
|
m = material_phaseMemberAt(ipc,ip,el)
|
||||||
|
|
||||||
|
crystallite_P (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),matmul(S,transpose(invFp_new)))
|
||||||
|
crystallite_S (1:3,1:3,ipc,ip,el) = S
|
||||||
|
crystallite_Lp (1:3,1:3,ipc,ip,el) = Lpguess
|
||||||
|
constitutive_mech_Li(p)%data(1:3,1:3,m) = Liguess
|
||||||
|
crystallite_Fp (1:3,1:3,ipc,ip,el) = Fp_new / math_det33(Fp_new)**(1.0_pReal/3.0_pReal) ! regularize
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,m) = Fi_new
|
||||||
|
crystallite_Fe (1:3,1:3,ipc,ip,el) = matmul(matmul(F,invFp_new),invFi_new)
|
||||||
|
broken = .false.
|
||||||
|
|
||||||
|
end function integrateStress
|
||||||
|
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief integrate stress, state with adaptive 1st order explicit Euler method
|
||||||
|
!> using Fixed Point Iteration to adapt the stepsize
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateFPI(g,i,e)
|
||||||
|
|
||||||
|
integer, intent(in) :: &
|
||||||
|
e, & !< element index in element loop
|
||||||
|
i, & !< integration point index in ip loop
|
||||||
|
g !< grain index in grain loop
|
||||||
|
integer :: &
|
||||||
|
NiterationState, & !< number of iterations in state loop
|
||||||
|
p, &
|
||||||
|
c, &
|
||||||
|
s, &
|
||||||
|
size_pl
|
||||||
|
integer, dimension(maxval(phase_Nsources)) :: &
|
||||||
|
size_so
|
||||||
|
real(pReal) :: &
|
||||||
|
zeta
|
||||||
|
real(pReal), dimension(max(constitutive_plasticity_maxSizeDotState,constitutive_source_maxSizeDotState)) :: &
|
||||||
|
r ! state residuum
|
||||||
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,2) :: &
|
||||||
|
plastic_dotState
|
||||||
|
real(pReal), dimension(constitutive_source_maxSizeDotState,2,maxval(phase_Nsources)) :: source_dotState
|
||||||
|
logical :: &
|
||||||
|
broken
|
||||||
|
|
||||||
|
p = material_phaseAt(g,e)
|
||||||
|
c = material_phaseMemberAt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
size_pl = plasticState(p)%sizeDotState
|
||||||
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%subState0(1:size_pl,c) &
|
||||||
|
+ plasticState(p)%dotState (1:size_pl,c) &
|
||||||
|
* crystallite_subdt(g,i,e)
|
||||||
|
plastic_dotState(1:size_pl,2) = 0.0_pReal
|
||||||
|
|
||||||
|
iteration: do NiterationState = 1, num%nState
|
||||||
|
|
||||||
|
if(nIterationState > 1) plastic_dotState(1:size_pl,2) = plastic_dotState(1:size_pl,1)
|
||||||
|
plastic_dotState(1:size_pl,1) = plasticState(p)%dotState(:,c)
|
||||||
|
|
||||||
|
broken = integrateStress(g,i,e)
|
||||||
|
if(broken) exit iteration
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) exit iteration
|
||||||
|
|
||||||
|
zeta = damper(plasticState(p)%dotState(:,c),plastic_dotState(1:size_pl,1),&
|
||||||
|
plastic_dotState(1:size_pl,2))
|
||||||
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) * zeta &
|
||||||
|
+ plastic_dotState(1:size_pl,1) * (1.0_pReal - zeta)
|
||||||
|
r(1:size_pl) = plasticState(p)%state (1:size_pl,c) &
|
||||||
|
- plasticState(p)%subState0(1:size_pl,c) &
|
||||||
|
- plasticState(p)%dotState (1:size_pl,c) * crystallite_subdt(g,i,e)
|
||||||
|
plasticState(p)%state(1:size_pl,c) = plasticState(p)%state(1:size_pl,c) &
|
||||||
|
- r(1:size_pl)
|
||||||
|
crystallite_converged(g,i,e) = converged(r(1:size_pl), &
|
||||||
|
plasticState(p)%state(1:size_pl,c), &
|
||||||
|
plasticState(p)%atol(1:size_pl))
|
||||||
|
|
||||||
|
if(crystallite_converged(g,i,e)) then
|
||||||
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
||||||
|
exit iteration
|
||||||
|
endif
|
||||||
|
|
||||||
|
enddo iteration
|
||||||
|
|
||||||
|
|
||||||
|
contains
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief calculate the damping for correction of state and dot state
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
real(pReal) pure function damper(current,previous,previous2)
|
||||||
|
|
||||||
|
real(pReal), dimension(:), intent(in) ::&
|
||||||
|
current, previous, previous2
|
||||||
|
|
||||||
|
real(pReal) :: dot_prod12, dot_prod22
|
||||||
|
|
||||||
|
dot_prod12 = dot_product(current - previous, previous - previous2)
|
||||||
|
dot_prod22 = dot_product(previous - previous2, previous - previous2)
|
||||||
|
if ((dot_product(current,previous) < 0.0_pReal .or. dot_prod12 < 0.0_pReal) .and. dot_prod22 > 0.0_pReal) then
|
||||||
|
damper = 0.75_pReal + 0.25_pReal * tanh(2.0_pReal + 4.0_pReal * dot_prod12 / dot_prod22)
|
||||||
|
else
|
||||||
|
damper = 1.0_pReal
|
||||||
|
endif
|
||||||
|
|
||||||
|
end function damper
|
||||||
|
|
||||||
|
end subroutine integrateStateFPI
|
||||||
|
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief integrate state with 1st order explicit Euler method
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateEuler(g,i,e)
|
||||||
|
|
||||||
|
integer, intent(in) :: &
|
||||||
|
e, & !< element index in element loop
|
||||||
|
i, & !< integration point index in ip loop
|
||||||
|
g !< grain index in grain loop
|
||||||
|
integer :: &
|
||||||
|
p, &
|
||||||
|
c, &
|
||||||
|
sizeDotState
|
||||||
|
logical :: &
|
||||||
|
broken
|
||||||
|
|
||||||
|
p = material_phaseAt(g,e)
|
||||||
|
c = material_phaseMemberAt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
||||||
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
||||||
|
* crystallite_subdt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
broken = integrateStress(g,i,e)
|
||||||
|
crystallite_converged(g,i,e) = .not. broken
|
||||||
|
|
||||||
|
end subroutine integrateStateEuler
|
||||||
|
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief integrate stress, state with 1st order Euler method with adaptive step size
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateAdaptiveEuler(g,i,e)
|
||||||
|
|
||||||
|
integer, intent(in) :: &
|
||||||
|
e, & !< element index in element loop
|
||||||
|
i, & !< integration point index in ip loop
|
||||||
|
g !< grain index in grain loop
|
||||||
|
integer :: &
|
||||||
|
p, &
|
||||||
|
c, &
|
||||||
|
sizeDotState
|
||||||
|
logical :: &
|
||||||
|
broken
|
||||||
|
|
||||||
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState) :: residuum_plastic
|
||||||
|
|
||||||
|
|
||||||
|
p = material_phaseAt(g,e)
|
||||||
|
c = material_phaseMemberAt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
|
||||||
|
residuum_plastic(1:sizeDotState) = - plasticState(p)%dotstate(1:sizeDotState,c) * 0.5_pReal * crystallite_subdt(g,i,e)
|
||||||
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
||||||
|
+ plasticState(p)%dotstate(1:sizeDotState,c) * crystallite_subdt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
broken = integrateStress(g,i,e)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
crystallite_converged(g,i,e) = converged(residuum_plastic(1:sizeDotState) &
|
||||||
|
+ 0.5_pReal * plasticState(p)%dotState(:,c) * crystallite_subdt(g,i,e), &
|
||||||
|
plasticState(p)%state(1:sizeDotState,c), &
|
||||||
|
plasticState(p)%atol(1:sizeDotState))
|
||||||
|
|
||||||
|
end subroutine integrateStateAdaptiveEuler
|
||||||
|
|
||||||
|
|
||||||
|
!---------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
|
||||||
|
!---------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateRK4(g,i,e)
|
||||||
|
|
||||||
|
integer, intent(in) :: g,i,e
|
||||||
|
|
||||||
|
real(pReal), dimension(3,3), parameter :: &
|
||||||
|
A = reshape([&
|
||||||
|
0.5_pReal, 0.0_pReal, 0.0_pReal, &
|
||||||
|
0.0_pReal, 0.5_pReal, 0.0_pReal, &
|
||||||
|
0.0_pReal, 0.0_pReal, 1.0_pReal],&
|
||||||
|
shape(A))
|
||||||
|
real(pReal), dimension(3), parameter :: &
|
||||||
|
C = [0.5_pReal, 0.5_pReal, 1.0_pReal]
|
||||||
|
real(pReal), dimension(4), parameter :: &
|
||||||
|
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
|
||||||
|
|
||||||
|
call integrateStateRK(g,i,e,A,B,C)
|
||||||
|
|
||||||
|
end subroutine integrateStateRK4
|
||||||
|
|
||||||
|
|
||||||
|
!---------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief Integrate state (including stress integration) with the Cash-Carp method
|
||||||
|
!---------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateRKCK45(g,i,e)
|
||||||
|
|
||||||
|
integer, intent(in) :: g,i,e
|
||||||
|
|
||||||
|
real(pReal), dimension(5,5), parameter :: &
|
||||||
|
A = reshape([&
|
||||||
|
1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, &
|
||||||
|
3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, &
|
||||||
|
3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, &
|
||||||
|
-11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, &
|
||||||
|
1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],&
|
||||||
|
shape(A))
|
||||||
|
real(pReal), dimension(5), parameter :: &
|
||||||
|
C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal]
|
||||||
|
real(pReal), dimension(6), parameter :: &
|
||||||
|
B = &
|
||||||
|
[37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, &
|
||||||
|
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], &
|
||||||
|
DB = B - &
|
||||||
|
[2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,&
|
||||||
|
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal]
|
||||||
|
|
||||||
|
call integrateStateRK(g,i,e,A,B,C,DB)
|
||||||
|
|
||||||
|
end subroutine integrateStateRKCK45
|
||||||
|
|
||||||
|
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
!> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
|
||||||
|
!! embedded explicit Runge-Kutta method
|
||||||
|
!--------------------------------------------------------------------------------------------------
|
||||||
|
subroutine integrateStateRK(g,i,e,A,B,CC,DB)
|
||||||
|
|
||||||
|
|
||||||
|
real(pReal), dimension(:,:), intent(in) :: A
|
||||||
|
real(pReal), dimension(:), intent(in) :: B, CC
|
||||||
|
real(pReal), dimension(:), intent(in), optional :: DB
|
||||||
|
|
||||||
|
integer, intent(in) :: &
|
||||||
|
e, & !< element index in element loop
|
||||||
|
i, & !< integration point index in ip loop
|
||||||
|
g !< grain index in grain loop
|
||||||
|
integer :: &
|
||||||
|
stage, & ! stage index in integration stage loop
|
||||||
|
n, &
|
||||||
|
p, &
|
||||||
|
c, &
|
||||||
|
sizeDotState
|
||||||
|
logical :: &
|
||||||
|
broken
|
||||||
|
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
|
||||||
|
|
||||||
|
p = material_phaseAt(g,e)
|
||||||
|
c = material_phaseMemberAt(g,i,e)
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e), g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
do stage = 1,size(A,1)
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
|
||||||
|
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1)
|
||||||
|
|
||||||
|
do n = 2, stage
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
|
||||||
|
+ A(n,stage) * plastic_RKdotState(1:sizeDotState,n)
|
||||||
|
enddo
|
||||||
|
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
||||||
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
||||||
|
* crystallite_subdt(g,i,e)
|
||||||
|
|
||||||
|
broken = integrateStress(g,i,e,CC(stage))
|
||||||
|
if(broken) exit
|
||||||
|
|
||||||
|
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
crystallite_partitionedF0, &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c), &
|
||||||
|
crystallite_partitionedFp0, &
|
||||||
|
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
|
||||||
|
if(broken) exit
|
||||||
|
|
||||||
|
enddo
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
sizeDotState = plasticState(p)%sizeDotState
|
||||||
|
|
||||||
|
plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c)
|
||||||
|
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B)
|
||||||
|
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
|
||||||
|
+ plasticState(p)%dotState (1:sizeDotState,c) &
|
||||||
|
* crystallite_subdt(g,i,e)
|
||||||
|
if(present(DB)) &
|
||||||
|
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) &
|
||||||
|
* crystallite_subdt(g,i,e), &
|
||||||
|
plasticState(p)%state(1:sizeDotState,c), &
|
||||||
|
plasticState(p)%atol(1:sizeDotState))
|
||||||
|
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
|
||||||
|
constitutive_mech_Fi(p)%data(1:3,1:3,c),g,i,e,p,c)
|
||||||
|
if(broken) return
|
||||||
|
|
||||||
|
broken = integrateStress(g,i,e)
|
||||||
|
crystallite_converged(g,i,e) = .not. broken
|
||||||
|
|
||||||
|
|
||||||
|
end subroutine integrateStateRK
|
||||||
|
|
||||||
|
|
||||||
end submodule constitutive_mech
|
end submodule constitutive_mech
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue