!############################################################## MODULE CPFEM !############################################################## ! *** CPFEM engine *** ! use prec, only: pReal,pInt implicit none ! ! **************************************************************** ! *** General variables for the material behaviour calculation *** ! **************************************************************** real(pReal), dimension (:,:), allocatable :: CPFEM_Temperature real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar real(pReal), dimension (:,:,:,:,:,:),allocatable :: CPFEM_dPdF_bar real(pReal), dimension (:,:,:), allocatable :: CPFEM_stress_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jaco_bar real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction logical :: CPFEM_init_done = .false. ! remember if init has been done already logical :: CPFEM_calc_done = .false. ! remember if first IP has already calced the results ! CONTAINS ! !********************************************************* !*** allocate the arrays defined in module CPFEM *** !*** and initialize them *** !********************************************************* SUBROUTINE CPFEM_init(Temperature) ! use prec use math, only: math_EulertoR, math_I3, math_identity2nd use mesh use constitutive ! implicit none ! real(pReal) Temperature integer(pInt) e,i,g ! ! *** mpie.marc parameters *** allocate(CPFEM_Temperature (mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = Temperature allocate(CPFEM_ffn_bar (3,3,mesh_maxNips,mesh_NcpElems)) forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_bar(:,:,i,e) = math_I3 allocate(CPFEM_ffn1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_bar = CPFEM_ffn_bar allocate(CPFEM_PK1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_bar = 0.0_pReal allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal allocate(CPFEM_stress_bar(6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_bar = 0.0_pReal allocate(CPFEM_jaco_bar(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_bar = 0.0_pReal ! ! *** User defined results !!! MISSING incorporate consti_Nresults *** allocate(CPFEM_results(CPFEM_Nresults+constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) CPFEM_results = 0.0_pReal ! ! *** Plastic deformation gradient at (t=t0) and (t=t1) *** allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal allocate(CPFEM_Fp_old(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) forall (e=1:mesh_NcpElems,i=1:mesh_maxNips,g=1:constitutive_maxNgrains) & CPFEM_Fp_old(:,:,g,i,e) = math_EulerToR(constitutive_EulerAngles(:,g,i,e)) ! plastic def gradient reflects init orientation ! ! *** Output to MARC output file *** write(6,*) write(6,*) 'CPFEM Initialization' write(6,*) write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature) write(6,*) 'CPFEM_ffn_bar: ', shape(CPFEM_ffn_bar) write(6,*) 'CPFEM_ffn1_bar: ', shape(CPFEM_ffn1_bar) write(6,*) 'CPFEM_PK1_bar: ', shape(CPFEM_PK1_bar) write(6,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar) write(6,*) 'CPFEM_stress_bar: ', shape(CPFEM_stress_bar) write(6,*) 'CPFEM_jaco_bar: ', shape(CPFEM_jaco_bar) write(6,*) 'CPFEM_results: ', shape(CPFEM_results) write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old) write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new) write(6,*) call flush(6) return ! END SUBROUTINE ! ! !*********************************************************************** !*** perform initialization at first call, update variables and *** !*** call the actual material model *** ! ! CPFEM_mode computation mode (regular, collection, recycle) ! ffn deformation gradient for t=t0 ! ffn1 deformation gradient for t=t1 ! Temperature temperature ! CPFEM_dt time increment ! CPFEM_en element number ! CPFEM_in intergration point number ! CPFEM_stress stress vector in Mandel notation ! CPFEM_updateJaco flag to initiate computation of Jacobian ! CPFEM_jaco jacobian in Mandel notation ! CPFEM_ngens size of stress strain law !*********************************************************************** SUBROUTINE CPFEM_general(CPFEM_mode, ffn, ffn1, Temperature, CPFEM_dt,& CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_updateJaco, CPFEM_jaco, CPFEM_ngens) ! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de ! use prec, only: pReal,pInt use FEsolving use debug use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33,math_det3x3,math_I3 use mesh, only: mesh_init,mesh_FEasCP, mesh_NcpElems, FE_Nips, FE_mapElemtype, mesh_element use crystal, only: crystal_Init use constitutive, only: constitutive_init,constitutive_state_old,constitutive_state_new,material_Cslip_66 implicit none ! integer(pInt) CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n, e real(pReal), dimension (3,3) :: ffn,ffn1,Kirchhoff_bar real(pReal), dimension (3,3,3,3) :: H_bar real(pReal), dimension(CPFEM_ngens) :: CPFEM_stress real(pReal), dimension(CPFEM_ngens,CPFEM_ngens) :: CPFEM_jaco real(pReal) Temperature,CPFEM_dt,J_inverse integer(pInt) CPFEM_mode ! 1: regular computation, 2: collection, 3: recycling logical CPFEM_updateJaco ! if (.not. CPFEM_init_done) then ! initialization step ! three dimensional stress state check missing? call math_init() call mesh_init() call crystal_init() call constitutive_init() call CPFEM_init(Temperature) CPFEM_init_done = .true. endif cp_en = mesh_FEasCP('elem',CPFEM_en) if (cp_en == 1 .and. CPFEM_in == 1) & write(6,'(a6,x,i4,x,a4,x,i4,x,a10,x,i2,x,a10,x,i2,x,a10,x,i2)') & 'elem',cp_en,'IP',CPFEM_in,'theInc',theInc,'theCycle',theCycle,'theLovl',theLovl,'mode',CPFEM_mode select case (CPFEM_mode) case (2,1) ! regular computation (with aging of results) if (.not. CPFEM_calc_done) then ! puuh, me needs doing all the work... write (6,*) 'puuh me needs doing all the work', cp_en if (CPFEM_mode == 1) then ! age results at start of new increment CPFEM_Fp_old = CPFEM_Fp_new constitutive_state_old = constitutive_state_new write (6,*) '#### aged results' endif debug_cutbackDistribution = 0_pInt ! initialize debugging data debug_InnerLoopDistribution = 0_pInt debug_OuterLoopDistribution = 0_pInt do e=1,mesh_NcpElems ! ## this shall be done in a parallel loop in the future ## do i=1,FE_Nips(mesh_element(2,e)) ! iterate over all IPs of this element's type debugger = (e==1 .and. i==1) ! switch on debugging for first IP in first element call CPFEM_MaterialPoint(CPFEM_updateJaco, CPFEM_dt, i, e) enddo enddo call debug_info() ! output of debugging/performance statistics CPFEM_calc_done = .true. ! now calc is done endif ! translate from P and dP/dF to CS and dCS/dE Kirchhoff_bar = matmul(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en))) J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_bar(:,:,CPFEM_in, cp_en)) CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel33to6(J_inverse*Kirchhoff_bar) ! H_bar = 0.0_pReal forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) & H_bar(i,j,k,l) = H_bar(i,j,k,l) + & (CPFEM_ffn1_bar(j,m,CPFEM_in, cp_en)*CPFEM_ffn1_bar(l,n,CPFEM_in, cp_en)*CPFEM_dPdF_bar(i,m,k,n,CPFEM_in, cp_en) - & math_I3(j,l)*CPFEM_ffn1_bar(i,m,CPFEM_in, cp_en)*CPFEM_PK1_bar(k,m, CPFEM_in, cp_en)) + & 0.5_pReal*(math_I3(i,k)*Kirchhoff_bar(j,l) + math_I3(j,l)*Kirchhoff_bar(i,k) + & math_I3(i,l)*Kirchhoff_bar(j,k) + math_I3(j,k)*Kirchhoff_bar(i,l)) CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = math_Mandel3333to66(J_inverse*H_bar) case (3) ! collect and return odd result CPFEM_Temperature(CPFEM_in,cp_en) = Temperature CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) = ffn CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) = ffn1 CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_stress CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens) CPFEM_calc_done = .false. case (4) ! do nothing since we can recycle the former results (MARC specialty) end select ! ! return the local stress and the jacobian from storage CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_bar(1:CPFEM_ngens,CPFEM_in,cp_en) CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jaco_bar(1:CPFEM_ngens,1:CPFEM_ngens,CPFEM_in,cp_en) if (cp_en == 1 .and. CPFEM_in == 1) write (6,*) 'stress',CPFEM_stress ! return ! END SUBROUTINE ! !********************************************************** !*** calculate the material point behaviour *** !********************************************************** SUBROUTINE CPFEM_MaterialPoint(& updateJaco,& ! flag to initiate Jacobian updating CPFEM_dt,& ! Time increment (dt) CPFEM_in,& ! Integration point number cp_en) ! Element number ! use prec, only: pReal,pInt,ijaco,nCutback use debug use math, only: math_pDecomposition,math_RtoEuler, inDeg, math_I3, math_invert3x3 use IO, only: IO_error use mesh, only: mesh_element use constitutive implicit none ! integer(pInt), parameter :: i_now = 1_pInt,i_then = 2_pInt character(len=128) msg integer(pInt) cp_en,CPFEM_in,grain,i,max_cutbacks logical updateJaco,error,cutback,post_flag real(pReal) CPFEM_dt,dt,t,volfrac,det real(pReal), dimension(3,3) :: PK1 real(pReal), dimension(3,3,3,3) :: dPdF real(pReal), dimension(3,3) :: Fe,U,R,deltaFg,invFgthen,invFpnow,Lp real(pReal), dimension(3,3,2) :: Fg,Fp real(pReal), dimension(constitutive_maxNstatevars,2) :: state real(pReal), dimension (:), allocatable :: post_results ! CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average first PK stress if (updateJaco) CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = 0.0_pReal ! zero out average consistent tangent ! ! -------------- grain loop ----------------- do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) allocate(post_results(constitutive_Nresults(grain,CPFEM_in,cp_en))) ; post_results = 0.0_pReal ! i = 0_pInt ! cutback counter max_cutbacks = 0_pInt ! maximum depth of cut backing dt = CPFEM_dt state(:,i_now) = constitutive_state_old(:,grain,CPFEM_in,cp_en) Fg(:,:,i_now) = CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) Fp(:,:,i_now) = CPFEM_Fp_old(:,:,grain,CPFEM_in,cp_en) invFgthen = 0.0_pReal invFpnow = 0.0_pReal call math_invert3x3(CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en),invFgthen,det,error) call math_invert3x3(Fp(:,:,i_now),invFpnow,det,error) if (dt /= 0.0_pReal) then Lp = (math_I3-matmul(Fp(:,:,i_now),matmul(invFgthen,matmul(Fg(:,:,i_now),invFpnow))))/dt ! fully plastic initial guess else Lp = 0.0_pReal ! fully elastic guess endif ! deltaFg = CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en)-CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) Fg(:,:,i_then) = Fg(:,:,i_now) Fp(:,:,i_then) = Fp(:,:,i_now) state(:,i_then) = 0.0_pReal ! state_old as initial guess t = 0.0_pReal cutback = .false. ! no cutback has happened so far msg = '' if (debugger) then write(6,*) 'required Fg from FEM' write(6,'(3(3(f5.3,x),/))') CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) write(6,*) 'my Fp_old' write(6,'(3(3(f5.3,x),/))') CPFEM_Fp_old(:,:,grain,CPFEM_in,cp_en) write(6,*) 'my Fp_new' write(6,'(3(3(f5.3,x),/))') CPFEM_Fp_new(:,:,grain,CPFEM_in,cp_en) write(6,*) 'my state old' write(6,*) constitutive_state_old(:,grain,CPFEM_in,cp_en) endif ! ! ------- crystallite integration ----------- do while ((t < CPFEM_dt) .or. (msg /= 'ok')) ! if (t+dt < CPFEM_dt) then ! intermediate solution t = t+dt ! next time inc Fg(:,:,i_then) = Fg(:,:,i_then)+deltaFg ! corresponding Fg post_flag = .false. else ! full step solution t = CPFEM_dt ! final time Fg(:,:,i_then) = CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) ! final Fg post_flag = .true. endif ! if (debugger .and. CPFEM_dt > 0.0_pReal) & write (6,'(a,x,f7.5,x,a,x,f7.5,x,a,i2)') 'calculating from',(t-dt)/CPFEM_dt,'to',t/CPFEM_dt,'for grain',grain call CPFEM_Crystallite(msg,PK1,dPdF,post_results,post_flag,Lp,Fp(:,:,i_then),Fe,state(:,i_then),& t,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,& Fg(:,:,i_then),Fp(:,:,i_now),state(:,i_now)) if (msg == 'ok') then ! solution converged ! if (t == CPFEM_dt) then ! debug_cutbackDistribution(max_cutbacks+1) = debug_cutbackDistribution(max_cutbacks+1)+1 ! exit ! reached final "then" ! endif if (.not. cutback) then ! stable solution at current speed? dt = 2.0_pReal*dt ! double time-step i = i-1_pInt ! dec cutback counter endif cutback = .false. ! solution in next step does not derive from a cutback else ! solution not found if (debugger) write (6,*) msg i = i+1_pInt ! inc cutback counter max_cutbacks = max(i,max_cutbacks) cutback = .true. if (i > nCutback) then ! limit exceeded? debug_cutbackDistribution(nCutback+1) = debug_cutbackDistribution(nCutback+1)+1 write(6,'(x,a,x,f10.8,x,a,x,f10.8,x,a,x,i6,x,a,x,i2,x,a,x,i2)') & 'inc fraction:',t/CPFEM_dt,'from',(t-dt)/CPFEM_dt,'element:',cp_en,'IP:',CPFEM_in,'grain:',grain write(6,*) 'cutback limit --> '//msg call IO_error(600) return ! byebye else t = t-dt ! rewind time Fg(:,:,i_then) = Fg(:,:,i_then)-deltaFg ! rewind Fg dt = 0.5_pReal*dt ! cut time-step in half deltaFg = 0.5_pReal*deltaFg ! cut Fg-step in half endif endif enddo ! crystallite integration (cutback loop) debug_cutbackDistribution(max_cutbacks+1) = debug_cutbackDistribution(max_cutbacks+1)+1 ! ! update crystallite matrices at t = t1 CPFEM_Fp_new(:,:,grain,CPFEM_in,cp_en) = Fp(:,:,i_then) constitutive_state_new(:,grain,CPFEM_in,cp_en) = state(:,i_then) ! ! contribute to IP result volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en) CPFEM_PK1_bar(:,:,CPFEM_in,cp_en) = CPFEM_PK1_bar(:,:,CPFEM_in,cp_en)+volfrac*PK1 ! average Cauchy stress if (updateJaco) CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en)+volfrac*dPdF ! consistent tangent ! ! update results plotted in MENTAT call math_pDecomposition(Fe,U,R,error) ! polar decomposition if (error) then write(6,*) Fe write(6,*) 'polar decomposition' write(6,*) 'Grain: ',grain write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',mesh_element(1,cp_en) call IO_error(650) return endif CPFEM_results(1:3,grain,CPFEM_in,cp_en) = math_RtoEuler(transpose(R))*inDeg ! orientation CPFEM_results(4 ,grain,CPFEM_in,cp_en) = volfrac ! volume fraction of orientation CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = post_results ! deallocate(post_results) enddo ! grain loop ! return ! END SUBROUTINE ! !******************************************************************** ! Calculates the stress for a single component !******************************************************************** subroutine CPFEM_Crystallite(& msg,& ! return message P,& ! first PK stress dPdF,& ! consistent tangent post_results,& ! plot results from constitutive model post_flag,& ! its flag Lp,& ! guess of 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 CPFEM_in,& ! integration point number grain,& ! grain number updateJaco,& ! boolean to calculate Jacobi matrix Fg_new,& ! new global deformation gradient Fp_old,& ! old plastic deformation gradient state_old) ! old state variable array ! use prec, only: pReal,pInt,pert_Fg 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,post_flag integer(pInt) cp_en,CPFEM_in,grain,i,j,k,l,m,n real(pReal) dt,invJ,det real(pReal), dimension(3,3) :: Lp,Lp_pert,Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,invFp_new,Fp_pert,invFp_pert real(pReal), dimension(3,3) :: Fe_new,Fe_pert,Tstar,tau,P,P_pert,E_pert real(pReal), dimension(3,3,3,3) :: dPdF real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert real(pReal), dimension(constitutive_Nresults(grain,CPFEM_in,cp_en)) :: post_results ! call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,P,state_new,post_results,post_flag, & ! def gradients and PK2 at end of time step dt,cp_en,CPFEM_in,grain,Fg_new,Fp_old,state_old) if (msg /= 'ok') return ! solution not reached --> report back if (updateJaco) then ! consistent tangent using ! numerical perturbation of Fg (D. Tjahjanto Diss p.106) call math_invert3x3(Fp_new,invFp_new,det,error) if (error) then msg = 'inversion of Fp_new' return endif 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 CPFEM_timeIntegration(msg,Lp_pert,Fp_pert,Fe_pert,P_pert,state_pert,post_results,.false., & dt,cp_en,CPFEM_in,grain,Fg_pert,Fp_old,state_old) if (msg /= 'ok') then msg = 'consistent tangent --> '//msg return endif ! call math_invert3x3(Fp_pert,invFp_pert,det,error) if (error) then msg = 'inversion of Fp_pert' return endif ! dPdF(:,:,k,l) = (P_pert-P)/pert_Fg ! constructin the tangent dP_ij/dFg_kl 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 CPFEM_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 CPFEM_in,& ! integration point number grain,& ! grain number Fg_new,& ! new total def gradient Fp_old,& ! former plastic def gradient state_old) ! former microstructure ! 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 implicit none ! character(len=*) msg logical failed,wantsConstitutiveResults integer(pInt) cp_en, CPFEM_in, grain integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n real(pReal) dt, 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,invFg_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, CPFEM_in, cp_en)) :: state_old,state,ROuter real(pReal), dimension(constitutive_Nresults(grain,CPFEM_in,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 call math_invert3x3(Fg_new,invFg_new,det,failed) ! inversion of Fg_new if (failed) then msg = 'inversion Fg_new' return endif ! Fe_old = matmul(Fg_new,invFp_old) A = matmul(transpose(Fe_old), Fe_old) ! if (all(state == 0.0_pReal)) state = state_old ! former state guessed, if none specified iOuter = 0_pInt ! outer counter ! ! Outer: do ! outer iteration: State iOuter = iOuter+1 if (iOuter > nOuter) then msg = 'limit Outer iteration' debug_OuterLoopDistribution(nOuter) = debug_OuterLoopDistribution(nOuter)+1 return endif call constitutive_Microstructure(state,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) C_66 = constitutive_HomogenizedC(state, grain, CPFEM_in, 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 ! Inner: do ! inner iteration: Lp iInner = iInner+1 if (iInner > nInner) then ! too many loops required msg = 'limit Inner iteration' debug_InnerLoopDistribution(nInner) = debug_InnerLoopDistribution(nInner)+1 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,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) Rinner = Lpguess - Lp ! update current residuum if ((maxval(abs(Rinner)) < abstol_Inner) .or. & (any(abs(dt*Lpguess) > relevantStrain) .and. & maxval(abs(Rinner/Lpguess),abs(dt*Lpguess) > relevantStrain) < reltol_Inner)) & exit Inner ! ! check for acceleration/deceleration in Newton--Raphson correction if (leapfrog > 1.0_pReal .and. & (sum(Rinner*Rinner) > sum(Rinner_old*Rinner_old) .or. & ! worse residuum sum(Rinner*Rinner_old) < 0.0_pReal)) then ! residuum changed sign (overshoot) 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 write (6,*) msg write (6,*) 'dRdLp',dRdLp write (6,*) 'state',state write (6,*) 'Lpguess',Lpguess write (6,*) 'Tstar',Tstar_v 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 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 ! debug_InnerLoopDistribution(iInner) = debug_InnerLoopDistribution(iInner)+1 ROuter = state - state_old - & dt*constitutive_dotState(Tstar_v,state,CPFEM_Temperature(CPFEM_in,cp_en),& grain,CPFEM_in,cp_en) ! residuum from evolution of microstructure state = state - ROuter ! update of microstructure if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer enddo Outer ! debug_OuterLoopDistribution(iOuter) = debug_OuterLoopDistribution(iOuter)+1 invFp_new = matmul(invFp_old,B) call math_invert3x3(invFp_new,Fp_new,det,failed) if (failed) then msg = 'inversion Fp_new' return endif ! if (wantsConstitutiveResults) then ! get the post_results upon request results = 0.0_pReal results = constitutive_post_results(Tstar_v,state,dt,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) endif ! 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 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 !##############################################################