!############################################################## MODULE CPFEM !############################################################## ! *** CPFEM engine *** ! use prec, only: pReal,pInt implicit none ! ! **************************************************************** ! *** General variables for the material behaviour calculation *** ! **************************************************************** 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_jaco_old integer(pInt) :: CPFEM_inc_old = 0_pInt integer(pInt) :: CPFEM_subinc_old = 1_pInt integer(pInt) :: CPFEM_Nresults = 3_pInt logical :: CPFEM_first_call = .true. CONTAINS !********************************************************* !*** allocate the arrays defined in module CPFEM *** !*** and initialize them *** !********************************************************* SUBROUTINE CPFEM_init() ! use prec, only: pReal,pInt ! use math, only: math_I3 use mesh use constitutive ! implicit none ! ! *** mpie.marc parameters *** allocate(CPFEM_ffn_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn_all = 0.0_pReal allocate(CPFEM_ffn1_all (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_ffn1_all = 0.0_pReal 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)) ; CPFEM_Fp_old = 0.0_pReal allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; CPFEM_Fp_new = 0.0_pReal ! ! *** Old jacobian (consistent tangent) *** allocate(CPFEM_jaco_old(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_old = 0.0_pReal ! ! *** Output to MARC output file *** write(6,*) write(6,*) 'Arrays allocated:' 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_jaco_old: ', shape(CPFEM_jaco_old) 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, CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_dt, cp_en, CPFEM_in) ! use prec, only: pReal,pInt use constitutive, only: constitutive_state_old, constitutive_state_new implicit none ! real(pReal) ffn(3,3), ffn1(3,3), CPFEM_dt integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, cp_en, CPFEM_in ! ! initialization step if (CPFEM_first_call) then ! three dimensional stress state ? call math_init() call mesh_init() call constitutive_init() call CPFEM_init() CPFEM_first_call = .false. endif if (CPFEM_inc==CPFEM_inc_old) then ! not a new increment ! case of a new subincrement:update starting with subinc 2 if (CPFEM_subinc > CPFEM_subinc_old) then 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_ffn_all(:,:,CPFEM_in, cp_en) = ffn CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1 call CPFEM_stressIP(CPFEM_cn, CPFEM_dt, cp_en, CPFEM_in) return END SUBROUTINE !********************************************************** !*** calculate the material behaviour at IP level *** !********************************************************** SUBROUTINE CPFEM_stressIP(& CPFEM_cn,& ! Cycle number CPFEM_dt,& ! Time increment (dt) cp_en,& ! Element number CPFEM_in) ! Integration point number use prec, only: pReal,pInt,ijaco,nCutback 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 logical updateJaco real(pReal) CPFEM_dt,dt,t,volfrac real(pReal), dimension(6) :: cs,Tstar_v real(pReal), dimension(6,6) :: cd,cd_IP real(pReal), dimension(3,3) :: deltaFg real(pReal), dimension(3) :: Euler real(pReal), dimension(3,3,2) :: Fg,Fp real(pReal), dimension(constitutive_Nstatevars(grain,CPFEM_in,cp_en),2) :: state updateJaco = (mod(CPFEM_cn,ijaco)==0) ! update consistent tangent every ijaco'th iteration CPFEM_stress_all(:,CPFEM_in,cp_en) = 0.0_pReal ! average Cauchy stress cd_IP = 0.0_pReal ! average consistent tangent ! -------------- grain loop ----------------- do grain = 1,constitutive_Ngrains(CPFEM_in,cp_en) ! ------------------------------------------- i = 0_pInt ! cutback counter 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) deltaFg = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en)-CPFEM_ffn_all(:,:,CPFEM_in,cp_en) dt = CPFEM_dt Tstar_v = 0.0_pReal ! fully elastic initial guess Fg(:,:,i_then) = Fg(:,:,i_now) state(:,i_then) = 0.0_pReal ! state_old as initial guess t = 0.0_pReal ! ------- 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_ffn_all(:,:,CPFEM_in,cp_en) ! final Fg endif call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Fp(:,:,i_then),state(:,i_then),Euler,& dt,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) exit ! reached final "then" else ! solution not found i = i+1_pInt ! inc cutback counter if (i > nCutback) then ! limit exceeded? write(6,*) 'cutback limit --> '//msg write(6,*) 'Grain: ',grain write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',mesh_element(1,cp_en) 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 ! ---- update results plotted in MENTAT ---- CPFEM_results(1:3,grain,CPFEM_in,cp_en) = Euler CPFEM_results(4:3+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en) = & constitutive_results(1:constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en)!ÄÄÄÄ ! ---- 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) cd_IP = cd_IP+volfrac*cd ! average consistent tangent enddo ! grain loop return END SUBROUTINE !******************************************************************** ! Calculates the stress for a single component ! it is based on the paper by Kalidindi et al.: ! J. Mech. Phys, Solids Vol. 40, No. 3, pp. 537-569, 1992 ! it is modified to use anisotropic elasticity matrix !******************************************************************** subroutine CPFEM_stressCrystallite(& msg,& ! return message cs,& ! Cauchy stress vector dcs_de,& ! consistent tangent Tstar_v,& ! second Piola-Kirchoff stress tensor Fp_new,& ! new plastic deformation gradient state_new,& ! new state variable array Euler,& ! Euler angles ! 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_e use constitutive, only: constitutive_Nstatevars use math, only: math_Mandel6to33, mapMandel,math_pDecomposition,math_RtoEuler implicit none character(len=*) msg logical updateJaco,error integer(pInt) cp_en,CPFEM_in,grain,i real(pReal) dt real(pReal), dimension(3) :: Euler real(pReal), dimension(3,3) :: Fg_old,Fg_new,Fg_pert,Fp_old,Fp_new,Fp_pert,Fe_new,Fe_pert,R,U,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,Fp_new,Fe_new,Tstar_v,state_new, & dt,cp_en,CPFEM_in,grain,Fg_new,Fp_old,state_old) if (msg /= 'ok') return cs = CPFEM_CauchyStress(Tstar_v,Fe_new) ! Cauchy stress call math_pDecomposition(Fe_new,U,R,error) ! polar decomposition if (error) then msg = 'polar decomposition' return endif Euler = math_RtoEuler(transpose(R)) ! orientation if (updateJaco) then ! *** Calculation of the consistent tangent with perturbation *** ! *** Perturbation on the component of Fg *** do i = 1,6 E_pert = 0.0_pReal E_pert(mapMandel(1,i),mapMandel(2,i)) = E_pert(mapMandel(1,i),mapMandel(2,i)) + pert_e/2.0_pReal E_pert(mapMandel(2,i),mapMandel(1,i)) = E_pert(mapMandel(2,i),mapMandel(1,i)) + pert_e/2.0_pReal Fg_pert = Fg_new+matmul(E_pert,Fg_old) ! perturbated Fg Tstar_v_pert = Tstar_v ! initial guess at center state_pert = state_new ! initial guess at center call CPFEM_timeIntegration(msg,Fp_pert,Fe_pert,Tstar_v_pert,state_pert, & dt,cp_en,CPFEM_in,grain,Fg_pert,Fp_old,state_old) if (msg /= 'ok') then msg = 'consistent tangent --> '//msg return endif ! *** MISSING:Consistent tangent, (perturbated) Cauchy stress is Mandel hence dcs_de(:,4:6) is too large by sqrt(2) dcs_de(:,i) = (CPFEM_CauchyStress(Tstar_v_pert,Fe_pert)-cs)/pert_e enddo endif return END SUBROUTINE !*********************************************************************** !*** fully-implicit two-level time integration *** !*********************************************************************** SUBROUTINE CPFEM_timeIntegration(& msg,& ! return message Fp_new,& ! new plastic deformation gradient Fe_new,& ! new "elastic" deformation gradient Tstar_v,& ! 2nd PK stress (taken as initial guess if /= 0) state_new,& ! 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 Fp_old,& ! former plastic def gradient state_old) ! former microstructure use prec, only: pReal,pInt, nState,tol_State,nStress,tol_Stress, crite, nReg use constitutive, only: constitutive_Nstatevars,& constitutive_homogenizedC,constitutive_dotState,constitutive_LpAndItsTangent use math implicit none character(len=*) msg integer(pInt) cp_en, CPFEM_in, grain integer(pInt) iState,iStress,dummy, i,j,k,l,m real(pReal) dt,det real(pReal), dimension(6) :: Tstar_v,dTstar_v,Rstress real(pReal), dimension(6,6) :: C_66,Jacobi,invJacobi,help2 real(pReal), dimension(3,3) :: Fg_new,Fp_old,Fp_new,Fe_new,invFp_old,invFp_new,Lp,A,B,AB real(pReal), dimension(3,3,3,3) :: dLp, LTL real(pReal), dimension(constitutive_Nstatevars(grain, CPFEM_in, cp_en)) :: state_old,state_new,dstate,Rstate,RstateS logical failed msg = 'ok' ! error-free so far call math_invert3x3(Fp_old,invFp_old,det,failed) ! inversion of Fp if (failed) then msg = 'inversion Fp_old' return endif C_66 = constitutive_HomogenizedC(grain, CPFEM_in, cp_en) A = matmul(Fg_new,invFp_old) ! actually Fe A = matmul(transpose(A), A) ! former state guessed, if none specified if (all(state_new == 0.0_pReal)) state_new = state_old RstateS = state_new iState = 0_pInt ! fully elastic guess (Lp = 0), if none specified if (all(Tstar_v == 0.0_pReal)) Tstar_v = 0.5_pReal*matmul(C_66,math_Mandel33to6(A-math_I3)) ! QUESTION follow former plastic slope to guess better? Rstress = Tstar_v iStress = 0_pInt state: do ! outer iteration: state iState = iState+1 if (iState > nState) then msg = 'limit state iteration' return endif stress: do ! inner iteration: stress iStress = iStress+1 if (iStress > nStress) then ! too many loops required msg = 'limit stress iteration' return endif call constitutive_LpAndItsTangent(Lp,dLp, Tstar_v,state_new,grain,CPFEM_in,cp_en) B = math_I3-dt*Lp Rstress = Tstar_v - 0.5_pReal*matmul(C_66,math_Mandel33to6(matmul(transpose(B),matmul(A,B))-math_I3)) if (maxval(abs(Rstress/maxval(abs(Tstar_v)))) < tol_Stress) exit stress ! update stress guess using inverse of dRes/dTstar (Newton--Raphson) AB = matmul(A,B) LTL = 0.0_pReal do i=1,3 do j=1,3 do k=1,3 do l=1,3 do m=1,3 ! LTL(i,j,k,l) = LTL(i,j,k,l) + AB(i,m)*dLp(m,j,k,l) + AB(j,m)*dLp(m,i,l,k) ! old LTL(i,j,k,l) = LTL(i,j,k,l) + dLp(j,i,k,m)*AB(m,l) + AB(m,i)*dLp(m,j,k,l) ! new (and correct??) enddo enddo enddo enddo enddo Jacobi = math_identity2nd(6) + 0.5_pReal*dt*matmul(C_66,math_Mandel3333to66(LTL)) j = 0_pInt ; failed = .true. do while (failed .and. j <= nReg) call math_invert6x6(Jacobi,invJacobi,dummy,failed) forall (i=1:6) Jacobi(i,i) = 1.05_pReal*maxval(Jacobi(i,:)) ! regularization j = j+1 enddo if (failed) then msg = 'regularization Jacobi' return endif dTstar_v = matmul(invJacobi,Rstress) ! correction to Tstar forall(i=1:6, abs(dTstar_v(i)) > crite*maxval(abs(Tstar_v))) & dTstar_v(i) = sign(crite*maxval(abs(Tstar_v)),dTstar_v(i)) ! cap to maximum correction Tstar_v = Tstar_v-dTstar_v enddo stress dstate = dt*constitutive_dotState(Tstar_v,state_new,grain,CPFEM_in,cp_en) ! evolution of microstructure Rstate = state_new - (state_old+dstate) RstateS = 0.0_pReal forall (i=1:constitutive_Nstatevars(grain,CPFEM_in,cp_en), state_new(i)/=0.0_pReal) & RstateS(i) = Rstress(i)/state_new(i) if (maxval(abs(RstateS)) < tol_State) exit state state_new = state_old+dstate enddo state 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) ! det = det(InvFp_new) !! Fe_new = matmul(Fg_new,invFp_new) return END SUBROUTINE FUNCTION CPFEM_CauchyStress(PK_v,Fe) !*********************************************************************** !*** Cauchy stress calculation *** !*********************************************************************** use prec, only: pReal,pInt use math, only: math_Mandel33to6,math_Mandel6to33,math_det3x3 implicit none ! *** Subroutine parameters *** real(pReal) PK_v(6), Fe(3,3), CPFEM_CauchyStress(6) CPFEM_CauchyStress = math_Mandel33to6(matmul(matmul(Fe,math_Mandel6to33(PK_v)),transpose(Fe))/math_det3x3(Fe)) return END FUNCTION END MODULE