From 6950eee59bc9df2fd5364d9f20e9e90b77076111 Mon Sep 17 00:00:00 2001 From: Denny Tjahjanto Date: Fri, 14 Mar 2008 14:19:10 +0000 Subject: [PATCH] altered stress and strain "language" to first PK and deformation gradient. plot_results are now part of the crystallite result and not explicitly called from the homogenization layer. --- trunk/CPFEM.f90 | 428 +++++++++++++++++++++++------------------------- 1 file changed, 205 insertions(+), 223 deletions(-) diff --git a/trunk/CPFEM.f90 b/trunk/CPFEM.f90 index 72af62559..eeb93f1ea 100644 --- a/trunk/CPFEM.f90 +++ b/trunk/CPFEM.f90 @@ -1,4 +1,3 @@ - !############################################################## MODULE CPFEM !############################################################## @@ -10,27 +9,24 @@ ! **************************************************************** ! *** 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), dimension (:,:), allocatable :: CPFEM_Temperature + real(pReal), dimension (:,:,:,:), allocatable :: CPFEM_PK1_bar + 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_Fp_old + real(pReal), dimension (:,:,:,:,:), allocatable :: CPFEM_Fp_new + real(pReal), dimension (:,:,:,:,:,:),allocatable :: CPFEM_dPdF_bar 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 *** @@ -43,7 +39,7 @@ use constitutive ! implicit none - +! integer(pInt) e,i,g ! ! *** mpie.marc parameters *** @@ -51,17 +47,12 @@ 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 + allocate(CPFEM_PK1_bar (3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_PK1_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 ! -! *** 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) & @@ -69,8 +60,7 @@ 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 -! + allocate(CPFEM_dPdF_bar(3,3,3,3,mesh_maxNips,mesh_NcpElems)) ; CPFEM_dPdF_bar = 0.0_pReal ! ! *** Output to MARC output file *** write(6,*) @@ -78,18 +68,15 @@ 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_PK1_bar: ', shape(CPFEM_PK1_bar) 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,*) 'CPFEM_dPdF_bar: ', shape(CPFEM_dPdF_bar) write(6,*) call flush(6) return - +! END SUBROUTINE ! ! @@ -99,21 +86,22 @@ !*********************************************************************** 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) +! note: CPFEM_stress = Cauchy stress cs(6) and CPFEM_jaco = Consistent tangent dcs/de ! use prec, only: pReal,pInt use debug - use math, only: math_init, invnrmMandel, math_identity2nd, math_Mandel3333to66,math_Mandel33to6,math_Mandel6to33 + 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_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i, e - real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens) +! + integer(pInt) CPFEM_inc, CPFEM_subinc, CPFEM_cn, CPFEM_en, CPFEM_in, cp_en, CPFEM_ngens, i,j,k,l,m,n, e + real(pReal) ffn(3,3),ffn1(3,3),Temperature,CPFEM_dt,CPFEM_stress(CPFEM_ngens),CPFEM_jaco(CPFEM_ngens,CPFEM_ngens),Kirchhoff_bar(3,3), & + H_bar(3,3,3,3),J_inverse 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 @@ -122,9 +110,8 @@ 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 ? @@ -135,51 +122,55 @@ 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_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 +! +! return stress and the jacobian 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) + Kirchhoff_bar = matmul(CPFEM_PK1_bar(:,:,CPFEM_in, cp_en),transpose(CPFEM_ffn1_all(:,:,CPFEM_in, cp_en))) + J_inverse = 1.0_pReal/math_det3x3(CPFEM_ffn1_all(:,:,CPFEM_in, cp_en)) + CPFEM_stress(1:CPFEM_ngens) = 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_all(j,m,CPFEM_in, cp_en)*CPFEM_ffn1_all(l,n,CPFEM_in, cp_en)*CPFEM_dPdF_bar(i,m,k,n,CPFEM_in, cp_en) - & + math_I3(j,l)*CPFEM_ffn1_all(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(1:CPFEM_ngens,1:CPFEM_ngens) = math_Mandel3333to66(J_inverse*H_bar) end if +! return - +! END SUBROUTINE - - +! !********************************************************** !*** calculate the material behaviour at IP level *** !********************************************************** @@ -188,36 +179,36 @@ 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 + logical updateJaco,error,cutback,post_flag 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(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 +! 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 - +! + 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 @@ -233,35 +224,37 @@ 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 + msg = '' +! ! ------- crystallite integration ----------- - do -! ------------------------------------------- + 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_all(:,:,CPFEM_in,cp_en) ! final Fg + Fg(:,:,i_then) = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! final Fg + post_flag = .true. endif - - call CPFEM_stressCrystallite(msg,cs,cd,Tstar_v,Lp,Fp(:,:,i_then),Fe,state(:,i_then),& +! + call CPFEM_stressCrystallite(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 (cutback == .false.) then ! stable solution at current speed? +! 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 @@ -271,8 +264,9 @@ 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 + 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 @@ -284,18 +278,21 @@ endif endif enddo ! crystallite integration (cutback loop) - -! ---- update crystallite matrices at t = t1 ---- + 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) - CPFEM_sigma_new(:,grain,CPFEM_in,cp_en) = Tstar_v -! ---- contribute to IP result ---- +! +! 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 ---- + 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 @@ -305,23 +302,24 @@ 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) - + 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_stressCrystallite(& msg,& ! return message - cs,& ! Cauchy stress vector - dcs_de,& ! consistent tangent - Tstar_v,& ! second Piola-Kirchhoff stress tensor + 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 @@ -335,33 +333,28 @@ 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 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 + 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(3,3,3,3) :: A,H - real(pReal), dimension(3,3) :: Lp,Lp_pert,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 - real(pReal), dimension(6) :: cs,Tstar_v,Tstar_v_pert - real(pReal), dimension(6,6) :: dcs_de + 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 - - call CPFEM_timeIntegration(msg,Lp,Fp_new,Fe_new,Tstar_v,state_new, & ! def gradients and PK2 at end of time step + 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 - 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) @@ -369,46 +362,34 @@ 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, & + 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 - 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 +! + dPdF(:,:,k,l) = (P_pert-P)/pert_Fg ! constructin the tangent 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 *** @@ -419,8 +400,10 @@ 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) + 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 @@ -429,33 +412,32 @@ 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_Microstructure + 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) :: Tstar + 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 - logical failed - + 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 @@ -467,113 +449,113 @@ 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 + 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) + 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 +! +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 - 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 - +! + 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 + 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 - + 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 + 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 +!############################################################## +