!############################################################## 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_stress_all real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobi_all real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn_all real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ffn1_all real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_results real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_ini_ori real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_old real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_sigma_new real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_old real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_jacobian real(pReal), parameter :: CPFEM_odd_stress = 1e15_pReal, CPFEM_odd_jacobian = 1e50_pReal integer(pInt) :: CPFEM_inc_old = 0_pInt integer(pInt) :: CPFEM_subinc_old = 1_pInt integer(pInt) :: CPFEM_cycle_old = -1_pInt integer(pInt) :: CPFEM_Nresults = 4_pInt ! three Euler angles plus volume fraction logical :: CPFEM_first_call = .true. CONTAINS !********************************************************* !*** allocate the arrays defined in module CPFEM *** !*** and initialize them *** !********************************************************* SUBROUTINE CPFEM_init() ! use prec use math, only: math_EulertoR, math_I3, math_identity2nd use mesh use constitutive ! implicit none integer(pInt) e,i,g ! ! *** mpie.marc parameters *** allocate(CPFEM_Temperature (mesh_maxNips,mesh_NcpElems)) ; CPFEM_Temperature = 0.0_pReal allocate(CPFEM_ffn_all (3,3,mesh_maxNips,mesh_NcpElems)) forall(e=1:mesh_NcpElems,i=1:mesh_maxNips) CPFEM_ffn_all(:,:,i,e) = math_I3 allocate(CPFEM_ffn1_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_all = CPFEM_ffn_all allocate(CPFEM_stress_all( 6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_stress_all = 0.0_pReal allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobi_all = 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 ! ! *** Second Piola-Kirchoff stress tensor at (t=t0) and (t=t1) *** allocate(CPFEM_sigma_old(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_old = 0.0_pReal allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_sigma_new = 0.0_pReal ! ! *** Plastic deformation gradient at (t=t0) and (t=t1) *** 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 allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal ! ! *** FEM jacobian (consistent tangent) *** allocate(CPFEM_jacobian(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jacobian = 0.0_pReal ! ! ! *** Output to MARC output file *** write(6,*) write(6,*) 'Arrays allocated:' write(6,*) 'CPFEM_Temperature: ', shape(CPFEM_Temperature) write(6,*) 'CPFEM_ffn_all: ', shape(CPFEM_ffn_all) write(6,*) 'CPFEM_ffn1_all: ', shape(CPFEM_ffn1_all) write(6,*) 'CPFEM_stress_all: ', shape(CPFEM_stress_all) write(6,*) 'CPFEM_jacobi_all: ', shape(CPFEM_jacobi_all) write(6,*) 'CPFEM_results: ', shape(CPFEM_results) write(6,*) 'CPFEM_sigma_old: ', shape(CPFEM_sigma_old) write(6,*) 'CPFEM_sigma_new: ', shape(CPFEM_sigma_new) write(6,*) 'CPFEM_Fp_old: ', shape(CPFEM_Fp_old) write(6,*) 'CPFEM_Fp_new: ', shape(CPFEM_Fp_new) write(6,*) 'CPFEM_jacobian: ', shape(CPFEM_jacobian) write(6,*) call flush(6) return END SUBROUTINE ! ! !*********************************************************************** !*** perform initialization at first call, update variables and *** !*** call the actual material model *** !*********************************************************************** SUBROUTINE CPFEM_general(ffn, ffn1, Temperature, CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_stress_recovery, CPFEM_dt,& CPFEM_en, CPFEM_in, CPFEM_stress, CPFEM_jaco, CPFEM_ngens) ! use prec, only: pReal,pInt use debug use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33 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_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l, e real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens) logical CPFEM_stress_recovery ! calculate only every second cycle if (mod(CPFEM_cn,2) /= 0) then ! odd cycle: record data for use in even cycle and return stiff result for this odd cycle cp_en = mesh_FEasCP('elem',CPFEM_en) CPFEM_Temperature(CPFEM_in, cp_en) = Temperature CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1 CPFEM_stress(1:CPFEM_ngens) = CPFEM_odd_stress CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_odd_jacobian*math_identity2nd(CPFEM_ngens) CPFEM_cycle_old = CPFEM_cn else ! even cycle: really calculate only in first call of new cycle and when in stress recovery if (CPFEM_cn /= CPFEM_cycle_old .and. CPFEM_stress_recovery) then if (CPFEM_first_call) then ! initialization step ! three dimensional stress state ? call math_init() call mesh_init() call crystal_Init() call constitutive_init() call CPFEM_init() CPFEM_Temperature = Temperature CPFEM_first_call = .false. endif if (CPFEM_inc == CPFEM_inc_old) then ! not a new increment if (CPFEM_subinc > CPFEM_subinc_old) then ! new subincrement: update starting with subinc 2 CPFEM_sigma_old = CPFEM_sigma_new CPFEM_Fp_old = CPFEM_Fp_new constitutive_state_old = constitutive_state_new CPFEM_subinc_old = CPFEM_subinc endif else ! new increment CPFEM_sigma_old = CPFEM_sigma_new CPFEM_Fp_old = CPFEM_Fp_new constitutive_state_old = constitutive_state_new CPFEM_inc_old = CPFEM_inc CPFEM_subinc_old = 1_pInt endif CPFEM_cycle_old = CPFEM_cn debug_cutbackDistribution = 0_pInt ! initialize debugging data debug_InnerLoopDistribution = 0_pInt debug_OuterLoopDistribution = 0_pInt ! this shall be done in a parallel loop in the future do e=1,mesh_NcpElems do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e))) debugger = (e==1 .and. i==1) call CPFEM_stressIP(CPFEM_cn, CPFEM_dt, i, e) enddo enddo call debug_info() ! output of debugging/performance statistics end if ! return stress and jacobi cp_en = mesh_FEasCP('elem', CPFEM_en) CPFEM_stress(1:CPFEM_ngens) = CPFEM_stress_all(1:CPFEM_ngens, CPFEM_in, cp_en) CPFEM_jaco(1:CPFEM_ngens,1:CPFEM_ngens) = CPFEM_jacobian(1:CPFEM_ngens,1:CPFEM_ngens, CPFEM_in, cp_en) end if return END SUBROUTINE !********************************************************** !*** calculate the material behaviour at IP level *** !********************************************************** SUBROUTINE CPFEM_stressIP(& CPFEM_cn,& ! Cycle number 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) CPFEM_cn,cp_en,CPFEM_in,grain,i,max_cutbacks logical updateJaco,error,cutback real(pReal) CPFEM_dt,dt,t,volfrac,det real(pReal), dimension(6) :: cs,Tstar_v real(pReal), dimension(6,6) :: cd 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 updateJaco = (mod(CPFEM_cn,2_pInt*ijaco)==0) ! update consistent tangent every ijaco'th iteration CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = 0.0_pReal ! average consistent tangent ! -------------- grain loop ----------------- do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) ! ------------------------------------------- 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_all(:,:,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_all(:,:,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_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en) Tstar_v = CPFEM_sigma_old(:,grain,CPFEM_in,cp_en) ! use last result as initial guess 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 ! ------- crystallite integration ----------- do ! ------------------------------------------- if (t+dt < CPFEM_dt) then ! intermediate solution t = t+dt ! next time inc Fg(:,:,i_then) = Fg(:,:,i_then)+deltaFg ! corresponding Fg else ! full step solution t = CPFEM_dt ! final time Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg endif call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Lp,Fp(:,:,i_then),Fe,state(:,i_then),& t,cp_en,CPFEM_in,grain,updateJaco .and. t==CPFEM_dt,& Fg(:,:,i_now),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 (cutback == .false.) 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 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,i6,x,a,x,i2,x,a,x,i2)') '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) ! ---- 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) CPFEM_sigma_new(:,grain,CPFEM_in,cp_en) = Tstar_v ! ---- contribute to IP result ---- volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en) CPFEM_stress_all(:,CPFEM_in,cp_en) = CPFEM_stress_all(:,CPFEM_in,cp_en)+volfrac*cs ! average Cauchy stress if (updateJaco) CPFEM_jacobian(:,:,CPFEM_in,cp_en) = CPFEM_jacobian(:,:,CPFEM_in,cp_en)+volfrac*cd ! average consistent tangent ! ---- update results plotted in MENTAT ---- call math_pDecomposition(Fe,U,R,error) ! polar decomposition if (error) then 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) = & constitutive_post_results(Tstar_v,state(:,i_then),CPFEM_dt,CPFEM_Temperature(CPFEM_in,cp_en),grain,CPFEM_in,cp_en) enddo ! grain loop return END SUBROUTINE !******************************************************************** ! Calculates the stress for a single component !******************************************************************** subroutine CPFEM_stressCrystallite(& msg,& ! return message cs,& ! Cauchy stress vector dcs_de,& ! consistent tangent Tstar_v,& ! second Piola-Kirchhoff stress tensor 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_old,& ! old global deformation gradient 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 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 integer(pInt) cp_en,CPFEM_in,grain,i,j,k,l,m,n real(pReal) dt,invJ,det real(pReal), dimension(3,3,3,3) :: A,H 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(6) :: cs,Tstar_v,Tstar_v_pert real(pReal), dimension(6,6) :: dcs_de real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en)) :: state_old,state_new,state_pert call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step dt,cp_en,CPFEM_in,grain,Fg_new,Fg_old,Fp_old,state_old) if (msg /= 'ok') return ! solution not reached --> report back Tstar = math_Mandel6to33(Tstar_v) ! second PK in intermediate tau = matmul(Fe_new,matmul(Tstar,transpose(Fe_new))) ! Kirchhoff stress invJ = 1.0_pReal/math_det3x3(Fe_new) ! inverse dilatation of Fe cs = math_Mandel33to6(invJ*tau) ! Cauchy stress 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 P = matmul(Fe_new,& matmul(Tstar,transpose(invFp_new))) ! first PK at center 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,Tstar_v_pert,state_pert, & dt,cp_en,CPFEM_in,grain,Fg_pert,Fg_old,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 P_pert = matmul(Fe_pert,& matmul(math_mandel6to33(Tstar_v_pert),transpose(invFp_pert))) ! perturbed first PK A(:,:,k,l) = (P_pert-P)/pert_Fg ! dP_ij/dFg_kl enddo enddo H = 0.0_pReal forall(i=1:3,j=1:3,k=1:3,l=1:3,m=1:3,n=1:3) & H(i,j,k,l) = H(i,j,k,l) + & (Fg_new(j,m)*Fg_new(l,n)*A(i,m,k,n) - math_I3(j,l)*Fg_new(i,m)*P(k,m)) + & 0.5_pReal*(math_I3(i,k)*tau(j,l) + math_I3(j,l)*tau(i,k) + & math_I3(i,l)*tau(j,k) + math_I3(j,k)*tau(i,l)) dcs_de = math_Mandel3333to66(invJ*H) ! Mandel version of stiffness tensor 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 Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0) state,& ! current microstructure at end of time inc (taken as guess if /= 0) ! dt,& ! time increment cp_en,& ! element number CPFEM_in,& ! integration point number grain,& ! grain number Fg_new,& ! new total def gradient Fg_old,& ! old 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_Microstructure use math implicit none character(len=*) msg integer(pInt) cp_en, CPFEM_in, grain integer(pInt) iOuter,iInner,dummy, i,j,k,l,m,n real(pReal) dt, det, p_hydro, max_dlnLp, max_deltalnLp, leapfrog,maxleap real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(9) :: deltaLp,deltaR 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,Fg_old,Fp_new,invFp_new,Fp_old,invFp_old,Fe_new,Fe_old real(pReal), dimension(3,3) :: Tstar real(pReal), dimension(3,3) :: Lp,Lpguess,Lpguess_old,dLpguess,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 logical failed 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' 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 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 return END SUBROUTINE END MODULE