Stress integration now uses Armijo rule to find an appropriate correction of Lp: decreases step in case that residuum does not improve significantly, accelerates as usual in case of good convergence. This turned out to improve convergence behavior.
This commit is contained in:
Christoph Kords
parent
6f859e99de
commit
ef7405fe21
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@ -661,7 +661,7 @@ do while (any(crystallite_subStep(:,:,FEsolving_execELem(1):FEsolving_execElem(2
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enddo
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enddo
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!$OMP END PARALLEL DO
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!$OMP END PARALLEL DO
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! --- integrate ---
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! --- integrate --- requires fully defined state array (basic + dependent state)
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if (any(crystallite_todo)) then
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if (any(crystallite_todo)) then
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select case(numerics_integrator(numerics_integrationMode))
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select case(numerics_integrator(numerics_integrationMode))
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@ -2533,6 +2533,7 @@ use math, only: math_mul33x33, &
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math_invert3x3, &
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math_invert3x3, &
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math_invert, &
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math_invert, &
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math_det3x3, &
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math_det3x3, &
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math_norm33, &
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math_I3, &
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math_I3, &
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math_identity2nd, &
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math_identity2nd, &
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math_Mandel66to3333, &
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math_Mandel66to3333, &
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@ -2562,22 +2563,25 @@ real(pReal), dimension(3,3):: Fg_new, & ! deformation
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Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
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Lp_constitutive, & ! plastic velocity gradient resulting from constitutive law
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residuum, & ! current residuum of plastic velocity gradient
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residuum, & ! current residuum of plastic velocity gradient
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residuum_old, & ! last residuum of plastic velocity gradient
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residuum_old, & ! last residuum of plastic velocity gradient
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deltaLp, &
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expectedImprovement, &
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A, &
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A, &
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B, &
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B, &
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BT, &
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BT, &
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AB, &
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AB, &
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BTA
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BTA
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real(pReal), dimension(6):: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
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real(pReal), dimension(6):: Tstar_v ! 2nd Piola-Kirchhoff Stress in Mandel-Notation
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real(pReal), dimension(9,9):: dLpdT_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
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real(pReal), dimension(9,9):: dLp_dT_constitutive, & ! partial derivative of plastic velocity gradient calculated by constitutive law
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dTdLp, & ! partial derivative of 2nd Piola-Kirchhoff stress
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dT_dLp, & ! partial derivative of 2nd Piola-Kirchhoff stress
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dRdLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
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dR_dLp, & ! partial derivative of residuum (Jacobian for NEwton-Raphson scheme)
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invdRdLp ! inverse of dRdLp
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inv_dR_dLp ! inverse of dRdLp
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real(pReal), dimension(3,3,3,3):: C ! 4th rank elasticity tensor
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real(pReal), dimension(3,3,3,3):: C ! 4th rank elasticity tensor
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real(pReal), dimension(6,6):: C_66 ! simplified 2nd rank elasticity tensor
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real(pReal), dimension(6,6):: C_66 ! simplified 2nd rank elasticity tensor
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real(pReal) p_hydro, & ! volumetric part of 2nd Piola-Kirchhoff Stress
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real(pReal) p_hydro, & ! volumetric part of 2nd Piola-Kirchhoff Stress
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det, & ! determinant
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det, & ! determinant
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leapfrog, & ! acceleration factor for Newton-Raphson scheme
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steplength0, &
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maxleap, & ! maximum acceleration factor
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steplength, &
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steplength_max, &
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dt ! time increment
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dt ! time increment
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logical error ! flag indicating an error
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logical error ! flag indicating an error
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integer(pInt) NiterationStress, & ! number of stress integrations
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integer(pInt) NiterationStress, & ! number of stress integrations
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@ -2594,6 +2598,7 @@ integer(pLongInt) tick, &
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tickrate, &
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tickrate, &
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maxticks
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maxticks
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!* be pessimistic
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!* be pessimistic
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crystallite_integrateStress = .false.
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crystallite_integrateStress = .false.
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@ -2647,11 +2652,12 @@ C_66 = constitutive_homogenizedC(g,i,e)
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C = math_Mandel66to3333(C_66)
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C = math_Mandel66to3333(C_66)
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!* start LpLoop with no acceleration
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!* start LpLoop with normal step length
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NiterationStress = 0_pInt
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NiterationStress = 0_pInt
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leapfrog = 1.0_pReal
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steplength0 = 1.0_pReal
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maxleap = 16.0_pReal
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steplength = steplength0
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steplength_max = 16.0_pReal
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jacoCounter = 0_pInt
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jacoCounter = 0_pInt
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LpLoop: do
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LpLoop: do
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@ -2688,7 +2694,7 @@ LpLoop: do
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0) then
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call system_clock(count=tick,count_rate=tickrate,count_max=maxticks)
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call system_clock(count=tick,count_rate=tickrate,count_max=maxticks)
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endif
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endif
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call constitutive_LpAndItsTangent(Lp_constitutive, dLpdT_constitutive, Tstar_v, crystallite_Temperature(g,i,e), g, i, e)
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call constitutive_LpAndItsTangent(Lp_constitutive, dLp_dT_constitutive, Tstar_v, crystallite_Temperature(g,i,e), g, i, e)
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if (debug_verbosity > 4) then
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if (debug_verbosity > 4) then
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call system_clock(count=tock,count_rate=tickrate,count_max=maxticks)
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call system_clock(count=tock,count_rate=tickrate,count_max=maxticks)
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!$OMP CRITICAL (debugTimingLpTangent)
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!$OMP CRITICAL (debugTimingLpTangent)
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@ -2713,10 +2719,10 @@ LpLoop: do
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!* update current residuum and check for convergence of loop
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!* update current residuum and check for convergence of loop
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residuum = Lpguess - Lp_constitutive
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residuum = Lpguess - Lp_constitutive
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if (.not.(any(residuum/=residuum)) .and. & ! exclude any NaN in residuum
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if (.not.(any(residuum /= residuum)) .and. & ! exclude any NaN in residuum
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( maxval(abs(residuum)) < aTol_crystalliteStress .or. & ! below absolute tolerance .or.
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( maxval(abs(residuum)) < aTol_crystalliteStress .or. & ! below absolute tolerance .or.
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( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and.
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( any(abs(dt * Lpguess) > relevantStrain) .and. & ! worth checking? .and.
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maxval(abs(residuum/Lpguess), abs(dt*Lpguess) > relevantStrain) < rTol_crystalliteStress & ! below relative tolerance
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maxval(abs(residuum / Lpguess), abs(dt*Lpguess) > relevantStrain) < rTol_crystalliteStress & ! below relative tolerance
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) &
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) &
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) &
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) &
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) then
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) then
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@ -2724,9 +2730,8 @@ LpLoop: do
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endif
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endif
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!* NaN occured at regular speed? -> return
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!* NaN occured at regular speed -> return
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if (steplength >= steplength0 .and. any(residuum /= residuum)) then
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if (any(residuum/=residuum) .and. leapfrog == 1.0) then
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#ifndef _OPENMP
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#ifndef _OPENMP
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if (debug_verbosity > 4) then
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if (debug_verbosity > 4) then
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write(6,'(a,i8,x,i2,x,i3,a,i3,a)') '<< CRYST >> integrateStress encountered NaN at el ip g ',e,i,g,&
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write(6,'(a,i8,x,i2,x,i3,a,i3,a)') '<< CRYST >> integrateStress encountered NaN at el ip g ',e,i,g,&
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@ -2735,82 +2740,116 @@ LpLoop: do
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endif
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endif
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#endif
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#endif
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return
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return
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!* something went wrong at accelerated speed? -> restore old residuum and Lp
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elseif (leapfrog > 1.0_pReal .and. & ! at fast pace .and.
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( sum(residuum*residuum) > sum(residuum_old*residuum_old) .or. & ! worse residuum .or.
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sum(residuum*residuum_old) < 0.0_pReal .or. & ! residuum changed sign (overshoot) .or.
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any(residuum/=residuum) & ! NaN occured
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) &
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) then
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#ifndef _OPENMP
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if (debug_verbosity > 5) then
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write(6,'(a,i8,x,i2,x,i3,x,a,i3)') '<< CRYST >> integrateStress encountered high-speed crash at el ip g ',e,i,g,&
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'; iteration ', NiterationStress
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endif
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#endif
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maxleap = 0.5_pReal * leapfrog ! limit next acceleration
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leapfrog = 1.0_pReal ! grinding halt
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jacoCounter = 0_pInt ! reset counter for Jacobian update (we want to do an update next time!)
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Lpguess = Lpguess_old
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residuum = residuum_old
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if (debug_verbosity > 4) then
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!$OMP CRITICAL (distributionLeapfrogBreak)
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debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) = &
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debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) + 1
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!$OMP END CRITICAL (distributionLeapfrogBreak)
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endif
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!* residuum got better? -> calculate Jacobian for correction term and remember current residuum and Lpguess
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else
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if (mod(jacoCounter, iJacoLpresiduum) == 0_pInt) then
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dTdLp = 0.0_pReal
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do h=1,3; do j=1,3; do k=1,3; do l=1,3; do m=1,3
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dTdLp(3*(h-1)+j,3*(k-1)+l) = dTdLp(3*(h-1)+j,3*(k-1)+l) + C(h,j,l,m)*AB(k,m)+C(h,j,m,l)*BTA(m,k)
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enddo; enddo; enddo; enddo; enddo
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dTdLp = -0.5_pReal*dt*dTdLp
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dRdLp = math_identity2nd(9) - math_mul99x99(dLpdT_constitutive,dTdLp)
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invdRdLp = 0.0_pReal
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call math_invert(9,dRdLp,invdRdLp,dummy,error) ! invert dR/dLp --> dLp/dR
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if (error) then
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#ifndef _OPENMP
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if (debug_verbosity > 4) then
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write(6,'(a,i8,x,i2,x,i3,a,i3)') '<< CRYST >> integrateStress failed on dR/dLp inversion at el ip g ',e,i,g,&
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' ; iteration ', NiterationStress
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if (debug_verbosity > 5 &
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.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
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write(6,*)
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write(6,'(a,/,9(12(x),9(e15.3,x)/))') '<< CRYST >> dRdLp',transpose(dRdLp)
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write(6,'(a,/,9(12(x),9(e15.3,x)/))') '<< CRYST >> dLpdT_constitutive',transpose(dLpdT_constitutive)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> Lp_constitutive',math_transpose3x3(Lp_constitutive)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> Lpguess',math_transpose3x3(Lpguess)
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endif
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endif
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#endif
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return
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endif
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endif
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jacoCounter = jacoCounter + 1_pInt ! increase counter for jaco update
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residuum_old = residuum
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Lpguess_old = Lpguess
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!* accelerate?
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if (NiterationStress > 1 .and. leapfrog+1.0_pReal <= maxleap) leapfrog = leapfrog + 1.0_pReal
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endif
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endif
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!* leapfrog to updated Lp
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if (NiterationStress > 1_pInt) then
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do k=1,3; do l=1,3; do m=1,3; do n=1,3
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!* not at regular speed
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Lpguess(k,l) = Lpguess(k,l) - leapfrog * invdRdLp(3*(k-1)+l,3*(m-1)+n) * residuum(m,n)
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if (steplength <= steplength0) then
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enddo; enddo; enddo; enddo
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!* Armijo rule is fullfilled (norm of residuum was reduced by at least 0.01 of what was expected)
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if (math_norm33(residuum) <= math_norm33(residuum_old + 0.01_pReal * steplength * expectedImprovement)) then
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!* reduced step length -> return to normal step length
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if (steplength < steplength0) then
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steplength = steplength0
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!* normal step length without change in sign of residuum -> accelerate if not yet at maximum speed
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elseif (sum(residuum * residuum_old) >= 0.0_pReal .and. steplength + 1_pInt <= steplength_max) then
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steplength = steplength + 1.0_pReal
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endif
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!* Armijo rule not fullfilled -> try smaller step size in same direction
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else
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steplength = 0.5_pReal * steplength
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Lpguess = Lpguess_old + steplength * deltaLp
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cycle LpLoop
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endif
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!* at high-speed
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else
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!* no NaN, Armijo rule fullfilled, and sign of residuum did not change -> accelerate if not yet at maximum speed
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if (.not. any(residuum /= residuum) &
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.and. math_norm33(residuum) <= math_norm33(residuum_old + 0.01_pReal * steplength * expectedImprovement) &
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.and. sum(residuum * residuum_old) >= 0.0_pReal) then
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if (steplength + 1_pInt <= steplength_max) then
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steplength = steplength + 1.0_pReal
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endif
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!* something went wrong at accelerated speed? -> return to regular speed and try again
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else
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#ifndef _OPENMP
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if (debug_verbosity > 5) then
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write(6,'(a,i8,x,i2,x,i3,x,a,i3)') '<< CRYST >> integrateStress encountered high-speed crash at el ip g ',e,i,g,&
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'; iteration ', NiterationStress
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endif
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#endif
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!* NaN occured -> use old guess and residuum
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if (any(residuum /= residuum)) then
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Lpguess = Lpguess_old
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residuum = residuum_old
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endif
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steplength_max = steplength - 1.0_pReal ! limit acceleration
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steplength = steplength0 ! grinding halt
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jacoCounter = 0_pInt ! reset counter for Jacobian update (we want to do an update next time!)
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if (debug_verbosity > 4) then
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!$OMP CRITICAL (distributionLeapfrogBreak)
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debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) = &
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debug_LeapfrogBreakDistribution(NiterationStress,numerics_integrationMode) + 1
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!$OMP END CRITICAL (distributionLeapfrogBreak)
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endif
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endif
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endif
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endif
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!* calculate Jacobian for correction term and remember current residuum and Lpguess
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if (mod(jacoCounter, iJacoLpresiduum) == 0_pInt) then
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dT_dLp = 0.0_pReal
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do h=1,3; do j=1,3; do k=1,3; do l=1,3; do m=1,3
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dT_dLp(3*(h-1)+j,3*(k-1)+l) = dT_dLp(3*(h-1)+j,3*(k-1)+l) + C(h,j,l,m) * AB(k,m) + C(h,j,m,l) * BTA(m,k)
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enddo; enddo; enddo; enddo; enddo
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dT_dLp = -0.5_pReal * dt * dT_dLp
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dR_dLp = math_identity2nd(9) - math_mul99x99(dLp_dT_constitutive, dT_dLp)
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inv_dR_dLp = 0.0_pReal
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call math_invert(9,dR_dLp,inv_dR_dLp,dummy,error) ! invert dR/dLp --> dLp/dR
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if (error) then
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#ifndef _OPENMP
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if (debug_verbosity > 4) then
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write(6,'(a,i8,x,i2,x,i3,a,i3)') '<< CRYST >> integrateStress failed on dR/dLp inversion at el ip g ',e,i,g
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if (debug_verbosity > 5 &
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.and. ((e == debug_e .and. i == debug_i .and. g == debug_g) .or. .not. debug_selectiveDebugger)) then
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write(6,*)
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write(6,'(a,/,9(12(x),9(e15.3,x)/))') '<< CRYST >> dR_dLp',transpose(dR_dLp)
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write(6,'(a,/,9(12(x),9(e15.3,x)/))') '<< CRYST >> dT_dLp',transpose(dT_dLp)
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write(6,'(a,/,9(12(x),9(e15.3,x)/))') '<< CRYST >> dLp_dT_constitutive',transpose(dLp_dT_constitutive)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> AB',math_transpose3x3(AB)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> BTA',math_transpose3x3(BTA)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> Lp_constitutive',math_transpose3x3(Lp_constitutive)
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write(6,'(a,/,3(12(x),3(e20.7,x)/))') '<< CRYST >> Lpguess',math_transpose3x3(Lpguess)
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endif
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endif
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#endif
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return
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endif
|
||||||
|
deltaLp = 0.0_pReal
|
||||||
|
do k=1,3; do l=1,3; do m=1,3; do n=1,3
|
||||||
|
deltaLp(k,l) = deltaLp(k,l) - inv_dR_dLp(3*(k-1)+l,3*(m-1)+n) * residuum(m,n)
|
||||||
|
enddo; enddo; enddo; enddo
|
||||||
|
|
||||||
|
expectedImprovement = 0.0_pReal
|
||||||
|
do k=1,3; do l=1,3; do m=1,3; do n=1,3
|
||||||
|
expectedImprovement(k,l) = expectedImprovement(k,l) - dR_dLp(3*(k-1)+l,3*(m-1)+n) * deltaLp(m,n)
|
||||||
|
enddo; enddo; enddo; enddo
|
||||||
|
endif
|
||||||
|
|
||||||
|
jacoCounter = jacoCounter + 1_pInt ! increase counter for jaco update
|
||||||
|
residuum_old = residuum
|
||||||
|
Lpguess_old = Lpguess
|
||||||
|
Lpguess = Lpguess + steplength * deltaLp
|
||||||
|
|
||||||
enddo LpLoop
|
enddo LpLoop
|
||||||
|
|
||||||
|
|
@ -2861,7 +2900,7 @@ if (debug_verbosity > 5 .and. ((e == debug_e .and. i == debug_i .and. g == debug
|
||||||
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Cauchy / MPa', &
|
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Cauchy / MPa', &
|
||||||
math_mul33x33(crystallite_P(1:3,1:3,g,i,e), math_transpose3x3(Fg_new)) / 1e6 / math_det3x3(Fg_new)
|
math_mul33x33(crystallite_P(1:3,1:3,g,i,e), math_transpose3x3(Fg_new)) / 1e6 / math_det3x3(Fg_new)
|
||||||
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Fe Lp Fe^-1', &
|
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Fe Lp Fe^-1', &
|
||||||
math_transpose3x3(math_mul33x33(Fe_new, math_mul33x33(crystallite_Lp(1:3,1:3,g,i,e), math_inv3x3(Fe_new)))) ! transpose to get correct print out order
|
math_transpose3x3(math_mul33x33(Fe_new, math_mul33x33(crystallite_Lp(1:3,1:3,g,i,e), math_inv3x3(Fe_new)))) ! transpose to get correct print out order
|
||||||
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Fp',math_transpose3x3(crystallite_Fp(1:3,1:3,g,i,e))
|
write(6,'(a,/,3(12(x),3(f12.7,x)/))') '<< CRYST >> Fp',math_transpose3x3(crystallite_Fp(1:3,1:3,g,i,e))
|
||||||
endif
|
endif
|
||||||
#endif
|
#endif
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue