!############################################################## MODULE crystallite !############################################################## ! *** Solution at single crystallite level *** ! CONTAINS ! ! !******************************************************************** ! Calculates the stress for a single component !******************************************************************** !*********************************************************************** !*** calculation of stress (P), stiffness (dPdF), *** !*** and announcment of any *** !*** acceleration of the Newton-Raphson correction *** !*********************************************************************** subroutine SingleCrystallite(& msg,& ! return message P,& ! first PK stress dPdF,& ! consistent tangent post_results,& ! plot results from constitutive model Lp,& ! plastic velocity gradient Fp_new,& ! new plastic deformation gradient Fe_new,& ! new "elastic" deformation gradient state_new,& ! new state variable array ! dt,& ! time increment cp_en,& ! element number ip,& ! integration point number grain,& ! grain number updateJaco,& ! update of Jacobian required Temperature,& ! temperature of crystallite Fg_new,& ! new global deformation gradient Fg_old,& ! old global deformation gradient Fp_old,& ! old plastic deformation gradient state_old) ! old state variable array ! use prec, only: pReal,pInt,pert_Fg,subStepMin use debug use constitutive, only: constitutive_Nstatevars,constitutive_Nresults use mesh, only: mesh_element use math, only: math_Mandel6to33,math_Mandel33to6,math_Mandel3333to66,& math_I3,math_det3x3,math_invert3x3 implicit none ! character(len=*) msg logical updateJaco,error,cuttedBack,guessNew integer(pInt) cp_en,ip,grain,i,j,k,l,m,n, nCutbacks real(pReal) Temperature real(pReal) dt,dt_aim,subFrac,subStep,invJ,det real(pReal), dimension(3,3) :: Lp,Lp_pert,inv real(pReal), dimension(3,3) :: Fg_old,Fg_current,Fg_new,Fg_pert,Fg_aim,deltaFg real(pReal), dimension(3,3) :: Fp_old,Fp_current,Fp_new,Fp_pert real(pReal), dimension(3,3) :: Fe_old,Fe_current,Fe_new,Fe_pert real(pReal), dimension(3,3) :: Tstar,tau,P,P_pert real(pReal), dimension(3,3,3,3) :: dPdF real(pReal), dimension(constitutive_Nstatevars(grain,ip,cp_en)) :: state_old,state_new real(pReal), dimension(constitutive_Nstatevars(grain,ip,cp_en)) :: state_current,state_bestguess,state_pert real(pReal), dimension(constitutive_Nresults(grain,ip,cp_en)) :: post_results ! deltaFg = Fg_new-Fg_old subFrac = 0.0_pReal subStep = 1.0_pReal nCutbacks = 0_pInt ! Fg_aim = Fg_old ! make "new", "aim" a synonym for "old" !$OMP CRITICAL (fpnew) Fp_new = Fp_old !$OMP END CRITICAL (fpnew) call math_invert3x3(Fp_old,inv,det,error) Fe_new = matmul(Fg_old,inv) !$OMP CRITICAL (statenew) state_bestguess = state_new ! remember potentially available state guess state_new = state_old !$OMP END CRITICAL (statenew) ! cuttedBack = .false. guessNew = .true. ! ! begin the cutback loop do while (subStep > subStepMin) ! continue until finished or too much cut backing if (.not. cuttedBack) then Fg_current = Fg_aim ! wind forward Fp_current = Fp_new Fe_current = Fe_new state_current = state_new endif ! Fg_aim = Fg_current + subStep*deltaFg ! aim for Fg dt_aim = subStep*dt ! aim for dt if (guessNew) & state_new = state_bestguess ! try best available guess for state call TimeIntegration(msg,Lp,Fp_new,Fe_new,P,state_new,post_results,.true., & ! def gradients and PK2 at end of time step dt_aim,cp_en,ip,grain,Temperature,Fg_aim,Fp_current,state_current,0_pInt) ! if (msg == 'ok') then cuttedBack = .false. ! no cut back required guessNew = .false. ! keep the Lp subFrac = subFrac + subStep subStep = 1.0_pReal - subFrac ! try one go if (debugger) write (6,*) '--------- one go -----------++##' else nCutbacks = nCutbacks + 1 ! record additional cutback cuttedBack = .true. ! encountered problems --> guessNew = .true. ! redo plastic Lp guess subStep = subStep / 2.0_pReal ! cut time step in half state_bestguess = state_current ! current state is then best guess if (debugger) write (6,*) '>>>>>>>>>>>>>>>>>>>> cutback <<<<<<<<<<<<<<<<<<<<<<' endif enddo ! potential substepping ! !$OMP CRITICAL (cutback) debug_cutbackDistribution(min(nCutback,nCutbacks)+1) = debug_cutbackDistribution(min(nCutback,nCutbacks)+1)+1 !$OMP END CRITICAL (cutback) ! if (msg /= 'ok') return ! solution not reached --> report back !!$OMP CRITICAL (write2out) ! write(6,*) '*************************' ! write(6,*) '*************************' ! write(6,*) 'updateJaco', updateJaco, cp_en, ip ! write(6,*) '*************************' ! write(6,*) '*************************' !!$OMP END CRITICAL (write2out) if (updateJaco) then ! consistent tangent using do k=1,3 do l=1,3 Fg_pert = Fg_new ! initialize perturbed Fg Fg_pert(k,l) = Fg_pert(k,l) + pert_Fg ! perturb single component Lp_pert = Lp state_pert = state_new ! initial guess from end of time step call TimeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,P_pert,state_pert,post_results,.false., & ! def gradients and PK2 at end of time step dt_aim,cp_en,ip,grain,Temperature,Fg_pert,Fp_current,state_current,1_pInt) if (msg == 'ok') & dPdF(:,:,k,l) = (P_pert-P)/pert_Fg ! constructing tangent dP_ij/dFg_kl only if valid forward difference ! otherwise leave component unchanged !!$OMP CRITICAL (write2out) ! write(6,*) '*************************' ! write(6,*) cp_en, ip ! write(6,*) 'dPdF_kl', k, l ! write(6,*) dPdF(:,:,k,l) ! write(6,*) '*************************' !!$OMP END CRITICAL (write2out) enddo enddo endif ! return ! END SUBROUTINE ! !*********************************************************************** !*** fully-implicit two-level time integration *** !*** based on a residuum in Lp and intermediate *** !*** acceleration of the Newton-Raphson correction *** !*********************************************************************** SUBROUTINE TimeIntegration(& msg,& ! return message Lpguess,& ! guess of plastic velocity gradient Fp_new,& ! new plastic deformation gradient Fe_new,& ! new "elastic" deformation gradient P,& ! 1nd PK stress (taken as initial guess if /= 0) state,& ! current microstructure at end of time inc (taken as guess if /= 0) results,& ! post results from constitutive wantsConstitutiveResults,& ! its flag ! dt,& ! time increment cp_en,& ! element number ip,& ! integration point number grain,& ! grain number Temperature,& ! temperature Fg_new,& ! new total def gradient Fp_old,& ! former plastic def gradient state_old,& ! former microstructure flag) use prec use debug use mesh, only: mesh_element use constitutive, only: constitutive_Nstatevars,& constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent,& constitutive_Nresults,constitutive_Microstructure,constitutive_post_results use math use IO implicit none ! character(len=*) msg logical failed,wantsConstitutiveResults integer(pInt) cp_en, ip, grain integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n,flag real(pReal) dt, Temperature, det, p_hydro, leapfrog,maxleap real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(9,9) :: dLp,dTdLp,dRdLp,invdRdLp,eye2 real(pReal), dimension(6,6) :: C_66 real(pReal), dimension(3,3) :: Fg_new,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new,Fe_old real(pReal), dimension(3,3) :: P,Tstar real(pReal), dimension(3,3) :: Lp,Lpguess,Lpguess_old,Rinner,Rinner_old,A,B,BT,AB,BTA real(pReal), dimension(3,3,3,3) :: C real(pReal), dimension(constitutive_Nstatevars(grain, ip, cp_en)) :: state_old,state,ROuter real(pReal), dimension(constitutive_Nresults(grain,ip,cp_en)) :: results ! msg = 'ok' ! error-free so far eye2 = math_identity2nd(9) call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp_old if (failed) then msg = 'inversion Fp_old' return endif A = matmul(transpose(invFp_old), matmul(transpose(Fg_new),matmul(Fg_new,invFp_old))) ! if (all(state == 0.0_pReal)) then !$OMP CRITICAL (statenew) state = state_old ! former state guessed, if none specified !$OMP END CRITICAL (statenew) endif iOuter = 0_pInt ! outer counter ! ! Outer: do ! outer iteration: State iOuter = iOuter+1 if (iOuter > nOuter) then msg = 'limit Outer iteration' !$OMP CRITICAL (out) debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1 !$OMP END CRITICAL (out) return endif call constitutive_Microstructure(state,Temperature,grain,ip,cp_en) C_66 = constitutive_HomogenizedC(state, grain, ip, cp_en) C = math_Mandel66to3333(C_66) ! 4th rank elasticity tensor ! iInner = 0_pInt leapfrog = 1.0_pReal ! correction as suggested by invdRdLp-step maxleap = 1024.0_pReal ! preassign maximum acceleration level ! Lpguess_old = Lpguess ! consider present Lpguess good ! Inner: do ! inner iteration: Lp iInner = iInner+1 if (iInner > nInner) then ! too many loops required msg = 'limit Inner iteration' !$OMP CRITICAL (in) debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1 !$OMP END CRITICAL (in) return endif ! B = math_i3 - dt*Lpguess BT = transpose(B) AB = matmul(A,B) BTA = matmul(BT,A) Tstar_v = 0.5_pReal*matmul(C_66,math_mandel33to6(matmul(BT,AB)-math_I3)) Tstar = math_Mandel6to33(Tstar_v) p_hydro=(Tstar_v(1)+Tstar_v(2)+Tstar_v(3))/3.0_pReal forall(i=1:3) Tstar_v(i) = Tstar_v(i)-p_hydro ! subtract hydrostatic pressure call constitutive_LpAndItsTangent(Lp,dLp, & Tstar_v,state,Temperature,grain,ip,cp_en) !!$OMP CRITICAL (write2out) ! write(6,*) ! write(6,*) '*************************' ! write(6,*) cp_en, ip ! write(6,*) 'Tstar_v' ! write(6,*) Tstar_v ! write(6,*) 'A' ! write(6,*) A ! write(6,*) 'B' ! write(6,*) B ! write(6,*) 'AB' ! write(6,*) AB ! write(6,*) 'BTA' ! write(6,*) BTA ! write(6,*) 'C_66' ! write(6,*) C_66 ! write(6,*) '*************************' ! write(6,*) !$OMP END CRITICAL (write2out) ! Rinner = Lpguess - Lp ! update current residuum ! if (.not.(any(Rinner/=Rinner)) .and. & ! exclude any NaN in residuum ( (maxval(abs(Rinner)) < abstol_Inner) .or. & ! below abs tol .or. ( any(abs(dt*Lpguess) > relevantStrain) .and. & ! worth checking? .and. maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner & ! below rel tol ) & ) & ) & exit Inner ! convergence ! ! check for acceleration/deceleration in Newton--Raphson correction ! if (any(Rinner/=Rinner) .and. & ! NaN occured at regular speed leapfrog == 1.0) then Lpguess = Lpguess_old ! restore known good guess msg = 'NaN present' ! croak for cutback return elseif (leapfrog > 1.0_pReal .and. & ! at fast pace ? (sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum sum(Rinner*Rinner_old) < 0.0_pReal) .or. & ! residuum changed sign (overshoot) any(Rinner/=Rinner) ) then ! NaN maxleap = 0.5_pReal * leapfrog ! limit next acceleration leapfrog = 1.0_pReal ! grinding halt else ! better residuum dTdLp = 0.0_pReal ! calc dT/dLp forall (i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) & dTdLp(3*(i-1)+j,3*(k-1)+l) = dTdLp(3*(i-1)+j,3*(k-1)+l) + & C(i,j,l,n)*AB(k,n)+C(i,j,m,l)*BTA(m,k) dTdLp = -0.5_pReal*dt*dTdLp dRdLp = eye2 - matmul(dLp,dTdLp) ! calc dR/dLp invdRdLp = 0.0_pReal call math_invert(9,dRdLp,invdRdLp,dummy,failed) ! invert dR/dLp --> dLp/dR if (failed) then msg = 'inversion dR/dLp' if (debugger) then !$OMP CRITICAL (write2out) write (6,*) msg write (6,'(a,/,9(9(e9.3,x)/))') 'dRdLp', dRdLp(1:9,:) write (6,*) 'state',state write (6,'(a,/,3(3(f12.7,x)/))') 'Lpguess',Lpguess(1:3,:) write (6,*) 'Tstar',Tstar_v !$OMP END CRITICAL (write2out) endif return endif ! Rinner_old = Rinner ! remember current residuum Lpguess_old = Lpguess ! remember current Lp guess if (iInner > 1 .and. leapfrog < maxleap) & leapfrog = 2.0_pReal * leapfrog ! accelerate if ok endif ! Lpguess = Lpguess_old ! start from current guess Rinner = Rinner_old ! use current residuum forall (i=1:3,j=1:3,k=1:3,l=1:3) & ! leapfrog to updated Lpguess Lpguess(i,j) = Lpguess(i,j) - leapfrog*invdRdLp(3*(i-1)+j,3*(k-1)+l)*Rinner(k,l) enddo Inner ! !$OMP CRITICAL (in) debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1 !$OMP END CRITICAL (in) ROuter = state - state_old - & dt*constitutive_dotState(Tstar_v,state,Temperature,& grain,ip,cp_en) ! residuum from evolution of microstructure !$OMP CRITICAL (statenew) state = state - ROuter ! update of microstructure !$OMP END CRITICAL (statenew) if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer enddo Outer ! !$OMP CRITICAL (out) debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1 !$OMP END CRITICAL (out) invFp_new = matmul(invFp_old,B) !$OMP CRITICAL (fpnew) call math_invert3x3(invFp_new,Fp_new,det,failed) !$OMP END CRITICAL (fpnew) if (failed) then msg = 'inversion Fp_new^-1' return endif ! if (wantsConstitutiveResults) then ! get the post_results upon request !$OMP CRITICAL (res) results = 0.0_pReal results = constitutive_post_results(Tstar_v,state,Temperature,dt,grain,ip,cp_en) !$OMP END CRITICAL (res) endif ! !$OMP CRITICAL (fpnew) Fp_new = Fp_new*det**(1.0_pReal/3.0_pReal) ! regularize Fp by det = det(InvFp_new) !! Fe_new = matmul(Fg_new,invFp_new) ! calc resulting Fe !$OMP END CRITICAL (fpnew) forall (i=1:3) Tstar_v(i) = Tstar_v(i)+p_hydro ! add hydrostatic component back P = matmul(Fe_new,matmul(Tstar,transpose(invFp_new))) ! first PK stress ! return ! END SUBROUTINE ! ! END MODULE !##############################################################