!############################################################## 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_jaco_knownGood 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 ! real(pReal), dimension (:,:,:,:), allocatable :: GIA_rVect_new ! boundary relaxation vectors real(pReal), dimension (:,:,:,:), allocatable :: GIA_rVect_old ! boundary relaxation vectors real(pReal), dimension (:,:), allocatable :: GIA_bNorm ! grain boundary normals ! 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,b ! ! *** 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 allocate(CPFEM_jaco_knownGood(6,6,mesh_maxNips,mesh_NcpElems)) ; CPFEM_jaco_knownGood = 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 ! allocate(GIA_rVect_new(3,12,mesh_maxNips,mesh_NcpElems)) ; GIA_rVect_new = 0.0_pReal allocate(GIA_rVect_old(3,12,mesh_maxNips,mesh_NcpElems)) ; GIA_rVect_old = 0.0_pReal allocate(GIA_bNorm(3,12)) ; GIA_bNorm = 0.0_pReal do b = 1,4 GIA_bNorm(1,b) = 1.0_pReal GIA_bNorm(2,b+4) = 1.0_pReal GIA_bNorm(3,b+8) = 1.0_pReal enddo ! ! *** 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_jaco_knownGood: ', shape(CPFEM_jaco_knownGood) 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,*) 'GIA_rVect_new: ', shape(GIA_rVect_new) write(6,*) 'GIA_rVect_old: ', shape(GIA_rVect_old) write(6,*) 'GIA_bNorm: ', shape(GIA_bNorm) 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 lattice, only: lattice_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 with aged results& ! 2: regular computation& ! 3: collection of FEM data& ! 4: recycling of former results (MARC speciality)& ! 5: record tangent from former converged inc& ! 6: restore tangent from former converged inc logical CPFEM_updateJaco ! if (.not. CPFEM_init_done) then ! initialization step (three dimensional stress state check missing?) call math_init() call mesh_init() call lattice_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,f8.4,x,a10,x,i2,x,a10,x,i2,x,a10,x,i2,x,a10,x,i2)') & 'elem',cp_en,'IP',CPFEM_in,& 'theTime',theTime,'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 GIA_rVect_old = GIA_rVect_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) case (5) ! record consistent tangent at beginning of new increment CPFEM_jaco_knownGood = CPFEM_jaco_bar case (6) ! restore consistent tangent after cutback CPFEM_jaco_bar = CPFEM_jaco_knownGood 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 ! if (cp_en == 1 .and. CPFEM_in == 1 .and. CPFEM_updateJaco) write (6,*) 'stiffness',CPFEM_jaco ! if (cp_en == 1 .and. CPFEM_in == 1) write (6,*) 'vector',GIA_rVect_new(:,:,1,1) ! 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 use FEsolving, only: theCycle use debug use math, only: math_pDecomposition,math_RtoEuler,inDeg,math_I3,math_invert3x3,math_permut,math_invert,math_delta use IO, only: IO_error use mesh, only: mesh_element use crystallite use constitutive implicit none ! character(len=128) msg integer(pInt) cp_en,CPFEM_in,grain,max_cutbacks,i,j,k,l,m,n,iBoun,NRiter,dummy,ii,jj,kk,ll,ip,jp logical updateJaco,error,NRconvergent,failed real(pReal) CPFEM_dt,volfrac,dTime,shMod,C_kb,resNorm,resMax,subStep,subFrac,temp1,temp2 real(pReal), dimension(3,3) :: F0_bar,F1_bar,dF_bar,PK1_per,F1_per real(pReal), dimension(3,3) :: U,R real(pReal), dimension(3,3,8) :: PK1,Fp0,Fp1,Fe1,F1,F0 real(pReal), dimension(3,3,12) :: GPK1,GF1,Nye,GRB1 real(pReal), dimension(3,3,3,3,8) :: dPdF real(pReal), dimension(3,3,3,3,12) :: dRdX1 real(pReal), dimension(36) :: var,res real(pReal), dimension(36,36) :: dresdvar,dvardres real(pReal), dimension(3,12) :: rx,rVect real(pReal), dimension(12) :: NyeNorm real(pReal), dimension(constitutive_maxNstatevars,8) :: state0,state1 ! if (texture_Ngrains(mesh_element(4,cp_en)) /= 8_pInt) then call IO_error(800) return endif ! 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 ! ! ------------- GIA loop -------------------- ! ! collect information shMod = 0.2_pReal*(material_C11(1) - material_C12(1)) + 0.3_pReal*material_C44(1) ! equivalent shear modulus C_kb = material_bg(1)*shMod/material_GrainSize(1) ! equivalent boundary stiffness ! F0_bar = CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) ! effective deformation gradient at t_n state0 = constitutive_state_old(:,:,CPFEM_in,cp_en) ! state variables at t_n Fp0 = CPFEM_Fp_old(:,:,:,CPFEM_in,cp_en) ! grain plastic def. gradient at t_n rVect = GIA_rVect_old(:,:,CPFEM_in,cp_en) ! relaxation vectors from previous convergent step ! dF_bar = CPFEM_ffn1_bar(:,:,CPFEM_in,cp_en) - CPFEM_ffn_bar(:,:,CPFEM_in,cp_en) ! deformation gradient increment subFrac = 0.0_pReal subStep = 1.0_pReal ! ! Substepping procedure to improve N-R iteration SubStepping: do dTime = subStep*CPFEM_dt call GIA_RelaxedDeformation(F0,F0_bar,rVect) ! def. gradient of indiv. grains at t_n F1_bar = F0_bar + subStep*dF_bar ! effective def. gradient at t_n+1 forall (iBoun=1:12,i=1:3) var(3_pInt*(iBoun-1_pInt)+i) = rVect(i,iBoun) ! primary variable: relaxation vector ! ! Newton-Raphson iteration block NRiter = 1_pInt NRIteration: do forall (iBoun=1:12,i=1:3) rx(i,iBoun) = var(3_pInt*(iBoun-1_pInt)+i) ! relaxation vectors (guess) ! ! deformation gradients of grains at t_n+1 (guess) call GIA_RelaxedDeformation(F1,F1_bar,rx) ! ! -------------- grain loop ----------------- do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) call SingleCrystallite(msg,PK1(:,:,grain),dPdF(:,:,:,:,grain),& CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en),& Fp1(:,:,grain),Fe1(:,:,grain),state1(:,grain),& ! output up to here dTime,cp_en,CPFEM_in,grain,.true.,& CPFEM_Temperature(CPFEM_in,cp_en),F1(:,:,grain),F0(:,:,grain),Fp0(:,:,grain),state0(:,grain)) if (msg /= 'ok') then ! solution not reached --> exit NRIteration write(6,*) 'GIA: grain loop failed to converge @ EL:',cp_en,' IP:',CPFEM_in NRconvergent = .false. exit NRiteration endif enddo ! grain loop ! ! calculate the deformation jump and stress jump across the boundaries call GIA_BoundaryJump(GF1,F1) call GIA_BoundaryJump(GPK1,PK1) ! ! compute the Nye tensor at the boundary Nye = 0.0_pReal NyeNorm = 0.0_pReal do iBoun = 1,12 do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 Nye(i,j,iBoun) = Nye(i,j,iBoun) - 0.5_pReal*math_permut(j,k,l)*GIA_bNorm(k,iBoun)*GF1(i,l,iBoun) enddo enddo NyeNorm(iBoun) = NyeNorm(iBoun) + Nye(i,j,iBoun)*Nye(i,j,iBoun) enddo enddo NyeNorm(iBoun) = sqrt(NyeNorm(iBoun)) if (NyeNorm(iBoun) > 1.0e-8_pReal) Nye(:,:,iBoun) = Nye(:,:,iBoun)/NyeNorm(iBoun) enddo ! ! compute the stress-like penalty at the boundary GRB1 = 0.0_pReal do iBoun = 1,12 do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 GRB1(i,j,iBoun) = GRB1(i,j,iBoun) + Nye(i,k,iBoun)*GIA_bNorm(l,iBoun)*math_permut(k,l,j) enddo enddo enddo enddo GRB1(:,:,iBoun) = 0.5_pReal*(C_kb + C_kb)*GRB1(:,:,iBoun) enddo ! ! compute the resiudal of stress at the boundary res = 0.0_pReal resNorm = 0.0_pReal do iBoun = 1,12 do j = 1,3 do i = 1,3 res(3_pInt*(iBoun-1_pInt)+j) = res(3_pInt*(iBoun-1_pInt)+j) - & GIA_bNorm(i,iBoun)*(GPK1(i,j,iBoun) - GRB1(i,j,iBoun)) enddo resNorm = resNorm + res(3_pInt*(iBoun-1_pInt)+j)*res(3_pInt*(iBoun-1_pInt)+j) enddo enddo resNorm = sqrt(resNorm) ! if (debugger) write(6,'(x,a,i3,a,i3,a,i3,a,e10.4)')'EL:',cp_en,' IP:',CPFEM_in,' Iter:',NRiter,' RNorm:',resNorm if (NRiter == 1_pInt) resMax = resNorm if ((resNorm < resToler*resMax) .or. (resNorm < resAbsol)) then ! resNorm < tolerance ===> convergent NRconvergent = .true. exit NRiteration elseif ((NRiter > NRiterMax) .or. (resNorm > resBound*resMax)) then ! resNorm > up. bound ===> substepping NRconvergent = .false. exit NRiteration else ! update the residual dRdX1 = 0.0_pReal do iBoun = 1,12 if (NyeNorm(iBoun) < 1.0e-8_pReal) NyeNorm(iBoun) = 1.0e-8_pReal do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 temp1 = 0.0_pReal temp2 = 0.0_pReal do ii = 1,3 do jj = 1,3 do kk = 1,3 temp1 = temp1 + GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)*math_delta(i,k)* & GIA_bNorm(kk,iBoun)*math_permut(ii,kk,l) do ll = 1,3 temp2 = temp2 + Nye(i,ii,iBoun)*GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)* & Nye(k,kk,iBoun)*GIA_bNorm(ll,iBoun)*math_permut(kk,ll,l) enddo enddo enddo enddo dRdX1(i,j,k,l,iBoun) = 0.25_pReal*(C_kb + C_kb)*(temp1 - temp2)/NyeNorm(iBoun) enddo enddo enddo enddo enddo call GIA_JacobianMatrix(dresdvar,dPdF,dRdX1) dvardres = 0.0_pReal call math_invert(36,dresdvar,dvardres,dummy,failed) if (failed) then write(6,*) 'GIA: failed to invert the Jacobian @ EL:',cp_en,' IP:',CPFEM_in NRconvergent = .false. exit NRiteration endif forall (i=1:36,j=1:36) var(i) = var(i) - dvardres(i,j)*res(j) endif ! NRiter = NRiter + 1_pInt enddo NRIteration ! End of N-R iteration blok ! if (.not. NRconvergent) then subStep = 0.5_pReal*subStep else subFrac = subFrac + subStep subStep = 1.0_pReal - subFrac Fp0 = Fp1 F0_bar = F1_bar state0 = state1 rVect = rx endif ! if (subStep < subStepMin) exit SubStepping enddo SubStepping ! End of substepping blok ! ! ------------- GIA loop (end) -------------- ! ! return to the general subroutine when convergence is not reached if (.not. NRconvergent) then write(6,'(x,a)') 'GIA: convergence is not reached @ EL:',cp_en,' IP:',CPFEM_in call IO_error(600) return endif ! ! updates all variables, deformation gradients, and vectors GIA_rVect_new(:,:,CPFEM_in,cp_en) = rVect CPFEM_Fp_new(:,:,:,CPFEM_in,cp_en) = Fp1 constitutive_state_new(:,:,CPFEM_in,cp_en) = state1 ! ! compute the effective stress and consistent tangent do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) 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(:,:,grain) ! average Cauchy stress ! ! update results plotted in MENTAT call math_pDecomposition(Fe1(:,:,grain),U,R,error) ! polar decomposition if (error) then write(6,*) Fe1(:,:,grain) 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 enddo ! if (theCycle >= 0_pInt) then forall (grain=1:texture_Ngrains(mesh_element(4,cp_en))) & CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) = CPFEM_dPdF_bar(:,:,:,:,CPFEM_in,cp_en) + volfrac*dPdF(:,:,:,:,grain) else do ip = 1,3 do jp = 1,3 F1_per = F1_bar F1_per(ip,jp) = F1_per(ip,jp) + 1.0e-5_pReal forall (iBoun=1:12,i=1:3) var(3_pInt*(iBoun-1_pInt)+i) = rVect(i,iBoun) NRiter = 1_pInt ! NRPerturbation: do forall (iBoun=1:12,i=1:3) rx(i,iBoun) = var(3_pInt*(iBoun-1_pInt)+i) ! relaxation vectors (guess) call GIA_RelaxedDeformation(F1,F1_bar,rx) do grain = 1,8 call SingleCrystallite(msg,PK1(:,:,grain),dPdF(:,:,:,:,grain),& CPFEM_results(5:4+constitutive_Nresults(grain,CPFEM_in,cp_en),grain,CPFEM_in,cp_en),& Fp1(:,:,grain),Fe1(:,:,grain),state1(:,grain),& ! output up to here dTime,cp_en,CPFEM_in,grain,.true.,& CPFEM_Temperature(CPFEM_in,cp_en),F1(:,:,grain),F0(:,:,grain),Fp0(:,:,grain),state0(:,grain)) if (msg /= 'ok') then ! solution not reached --> exit NRIteration write(6,*) 'GIA: perturbation grain loop failed to converge within allowable step-size' NRconvergent = .false. exit NRPerturbation endif enddo call GIA_BoundaryJump(GF1,F1) call GIA_BoundaryJump(GPK1,PK1) ! Nye = 0.0_pReal NyeNorm = 0.0_pReal do iBoun = 1,12 do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 Nye(i,j,iBoun) = Nye(i,j,iBoun) - 0.5_pReal*math_permut(j,k,l)*GIA_bNorm(k,iBoun)*GF1(i,l,iBoun) enddo enddo NyeNorm(iBoun) = NyeNorm(iBoun) + Nye(i,j,iBoun)*Nye(i,j,iBoun) enddo enddo NyeNorm(iBoun) = sqrt(NyeNorm(iBoun)) if (NyeNorm(iBoun) > 1.0e-8_pReal) Nye(:,:,iBoun) = Nye(:,:,iBoun)/NyeNorm(iBoun) enddo ! GRB1 = 0.0_pReal do iBoun = 1,12 do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 GRB1(i,j,iBoun) = GRB1(i,j,iBoun) + Nye(i,k,iBoun)*GIA_bNorm(l,iBoun)*math_permut(k,l,j) enddo enddo enddo enddo GRB1(:,:,iBoun) = 0.5_pReal*(C_kb + C_kb)*GRB1(:,:,iBoun) enddo ! res = 0.0_pReal resNorm = 0.0_pReal do iBoun = 1,12 do j = 1,3 do i = 1,3 res(3_pInt*(iBoun-1_pInt)+j) = res(3_pInt*(iBoun-1_pInt)+j) - & GIA_bNorm(i,iBoun)*(GPK1(i,j,iBoun) - GRB1(i,j,iBoun)) enddo resNorm = resNorm + res(3_pInt*(iBoun-1_pInt)+j)*res(3_pInt*(iBoun-1_pInt)+j) enddo enddo resNorm = sqrt(resNorm) ! ! if (debugger) write(6,'(x,a,i3,a,i3,a,i3,a,i3,a,e10.4)')'EL = ',cp_en,':IP = ',CPFEM_in,':pert = ',3*(ip-1)+jp,':Iter = ',NRiter,':RNorm = ',resNorm if (NRiter == 1_pInt) resMax = resNorm if ((resNorm < resToler*resMax) .or. (resNorm < resAbsol)) then ! resNorm < tolerance ===> convergent NRconvergent = .true. exit NRPerturbation elseif ((NRiter > NRiterMax) .or. (resNorm > resBound*resMax)) then ! resNorm > up. bound ===> substepping NRconvergent = .false. exit NRPerturbation else ! update the residual dRdX1 = 0.0_pReal do iBoun = 1,12 if (NyeNorm(iBoun) < 1.0e-8_pReal) NyeNorm(iBoun) = 1.0e-8_pReal do i = 1,3 do j = 1,3 do k = 1,3 do l = 1,3 temp1 = 0.0_pReal temp2 = 0.0_pReal do ii = 1,3 do jj = 1,3 do kk = 1,3 temp1 = temp1 + GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)*math_delta(i,k)* & GIA_bNorm(kk,iBoun)*math_permut(ii,kk,l) do ll = 1,3 temp2 = temp2 + Nye(i,ii,iBoun)*GIA_bNorm(jj,iBoun)*math_permut(ii,jj,j)* & Nye(k,kk,iBoun)*GIA_bNorm(ll,iBoun)*math_permut(kk,ll,l) enddo enddo enddo enddo dRdX1(i,j,k,l,iBoun) = 0.25_pReal*(C_kb + C_kb)*(temp1 - temp2)/NyeNorm(iBoun) enddo enddo enddo enddo enddo call GIA_JacobianMatrix(dresdvar,dPdF,dRdX1) dvardres = 0.0_pReal call math_invert(36,dresdvar,dvardres,dummy,failed) if (failed) then write(6,*) 'GIA: perturbation failed to invert the Jacobian' NRconvergent = .false. exit NRPerturbation endif forall (i=1:36,j=1:36) var(i) = var(i) - dvardres(i,j)*res(j) endif NRiter = NRiter + 1_pInt enddo NRPerturbation ! End of N-R iteration blok ! PK1_per = 0.0_pReal do grain = 1,texture_Ngrains(mesh_element(4,cp_en)) volfrac = constitutive_matVolFrac(grain,CPFEM_in,cp_en)*constitutive_texVolFrac(grain,CPFEM_in,cp_en) PK1_per = PK1_per + volfrac*PK1(:,:,grain) enddo CPFEM_dPdF_bar(:,:,ip,jp,CPFEM_in,cp_en) = (PK1_per - CPFEM_PK1_bar(:,:,CPFEM_in,cp_en))/1.0e-5_pReal enddo enddo endif ! return ! END SUBROUTINE ! ! !******************************************************************** ! Calculates the relaxed deformation gradients of grains !******************************************************************** subroutine GIA_RelaxedDeformation(& F,& ! relaxed deformation gradient of grains F_bar,& ! effective deformation gradient r) ! relaxation vectors at boundary ! implicit none ! real(pReal), dimension(3,3) :: F_bar real(pReal), dimension(3,3,8) :: F real(pReal), dimension(3,12) :: r,n integer(pInt) i,j,iBoun,grain ! n = GIA_bNorm do i = 1,3 do j = 1,3 F(i,j,1) = F_bar(i,j) + n(i, 1)*r(j, 1) + n(i, 5)*r(j, 5) + n(i, 9)*r(j, 9) F(i,j,2) = F_bar(i,j) - n(i, 1)*r(j, 1) + n(i, 6)*r(j, 6) + n(i,10)*r(j,10) F(i,j,3) = F_bar(i,j) + n(i, 2)*r(j, 2) - n(i, 5)*r(j, 5) + n(i,11)*r(j,11) F(i,j,4) = F_bar(i,j) - n(i, 2)*r(j, 2) - n(i, 6)*r(j, 6) + n(i,12)*r(j,12) F(i,j,5) = F_bar(i,j) + n(i, 3)*r(j, 3) + n(i, 7)*r(j, 7) - n(i, 9)*r(j, 9) F(i,j,6) = F_bar(i,j) - n(i, 3)*r(j, 3) + n(i, 8)*r(j, 8) - n(i,10)*r(j,10) F(i,j,7) = F_bar(i,j) + n(i, 4)*r(j, 4) - n(i, 7)*r(j, 7) - n(i,11)*r(j,11) F(i,j,8) = F_bar(i,j) - n(i, 4)*r(j, 4) - n(i, 8)*r(j, 8) - n(i,12)*r(j,12) enddo enddo ! return ! END SUBROUTINE ! ! !******************************************************************** ! Calculates the jump of tensors across the grain boundary !******************************************************************** subroutine GIA_BoundaryJump(& F_boun,& ! tensor jump across the boundary F_bulk) ! bulk tensor ! implicit none ! real(pReal), dimension(3,3,12) :: F_boun real(pReal), dimension(3,3,8) :: F_bulk integer(pInt) i,j,iBoun,grain ! F_boun(:,:, 1) = F_bulk(:,:,2) - F_bulk(:,:,1) F_boun(:,:, 2) = F_bulk(:,:,4) - F_bulk(:,:,3) F_boun(:,:, 3) = F_bulk(:,:,6) - F_bulk(:,:,5) F_boun(:,:, 4) = F_bulk(:,:,8) - F_bulk(:,:,7) F_boun(:,:, 5) = F_bulk(:,:,3) - F_bulk(:,:,1) F_boun(:,:, 6) = F_bulk(:,:,4) - F_bulk(:,:,2) F_boun(:,:, 7) = F_bulk(:,:,7) - F_bulk(:,:,5) F_boun(:,:, 8) = F_bulk(:,:,8) - F_bulk(:,:,6) F_boun(:,:, 9) = F_bulk(:,:,5) - F_bulk(:,:,1) F_boun(:,:,10) = F_bulk(:,:,6) - F_bulk(:,:,2) F_boun(:,:,11) = F_bulk(:,:,7) - F_bulk(:,:,3) F_boun(:,:,12) = F_bulk(:,:,8) - F_bulk(:,:,4) ! return ! END SUBROUTINE ! ! !******************************************************************** ! Calculates the jump of tensors across the grain boundary !******************************************************************** subroutine GIA_JacobianMatrix(& dresdvar,& ! Jacobian matrix dPdF,& ! stress consistent tangent of bulk dRdX) ! stress-like penalty tangent at boundary ! implicit none ! real(pReal), dimension(3,3,3,3,8) :: dPdF real(pReal), dimension(3,3,3,3,12) :: dRdX real(pReal), dimension(36,36) :: dresdvar real(pReal), dimension(3,12) :: n integer(pInt) i,j,k,l ! n = GIA_bNorm dresdvar = 0.0_pReal do i = 1,3 do k = 1,3 do l = 1,3 do j = 1,3 ! ! at boundary 1, influenced by boundary +5, -6, +9, -10 dresdvar(( 1-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 1-1)*3 + l) & + (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 2))*n(i, 1)*n(k, 1) & + (dRdX(i,j,k,l, 1) + dRdX(i,j,k,l, 1))*n(i, 1)*n(k, 1) dresdvar(( 1-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 5-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 1)*n(k, 5) & + dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 5) dresdvar(( 1-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 6-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 1)*n(k, 6) & - dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 6) dresdvar(( 1-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 1-1)*3 + j,( 9-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 1)*n(k, 9) & + dRdX(i,j,k,l, 1)*n(i, 1)*n(k, 9) dresdvar(( 1-1)*3 + j,(10-1)*3 + l) = dresdvar(( 1-1)*3 + j,(10-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 1)*n(k,10) & - dRdX(i,j,k,l, 1)*n(i, 1)*n(k,10) ! ! at boundary 2, influenced by boundary -5, +6, +11, -12 dresdvar(( 2-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 2-1)*3 + l) & + (dPdF(i,j,k,l, 3) + dPdF(i,j,k,l, 4))*n(i, 2)*n(k, 2) & + (dRdX(i,j,k,l, 2) + dRdX(i,j,k,l, 2))*n(i, 2)*n(k, 2) dresdvar(( 2-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 5-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 2)*n(k, 5) & - dRdX(i,j,k,l, 2)*n(i, 2)*n(k, 5) dresdvar(( 2-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 2-1)*3 + j,( 6-1)*3 + l) + dPdF(i,j,k,l, 4)*n(i, 2)*n(k, 6) & + dRdX(i,j,k,l, 2)*n(i, 2)*n(k, 6) dresdvar(( 2-1)*3 + j,(11-1)*3 + l) = dresdvar(( 2-1)*3 + j,(11-1)*3 + l) + dPdF(i,j,k,l, 3)*n(i, 2)*n(k,11) & + dRdX(i,j,k,l, 2)*n(i, 2)*n(k,11) dresdvar(( 2-1)*3 + j,(12-1)*3 + l) = dresdvar(( 2-1)*3 + j,(12-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i, 2)*n(k,12) & - dRdX(i,j,k,l, 2)*n(i, 2)*n(k,12) ! ! at boundary 3, influenced by boundary +7, -8, -9, +10 dresdvar(( 3-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 3-1)*3 + l) & + (dPdF(i,j,k,l, 5) + dPdF(i,j,k,l, 6))*n(i, 3)*n(k, 3) & + (dRdX(i,j,k,l, 3) + dRdX(i,j,k,l, 3))*n(i, 3)*n(k, 3) dresdvar(( 3-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 7-1)*3 + l) + dPdF(i,j,k,l, 5)*n(i, 3)*n(k, 7) & + dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 7) dresdvar(( 3-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 8-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 3)*n(k, 8) & - dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 8) dresdvar(( 3-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 3-1)*3 + j,( 9-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 3)*n(k, 9) & - dRdX(i,j,k,l, 3)*n(i, 3)*n(k, 9) dresdvar(( 3-1)*3 + j,(10-1)*3 + l) = dresdvar(( 3-1)*3 + j,(10-1)*3 + l) + dPdF(i,j,k,l, 6)*n(i, 3)*n(k,10) & + dRdX(i,j,k,l, 3)*n(i, 3)*n(k,10) ! ! at boundary 4, influenced by boundary -7, +8, -11, +12 dresdvar(( 4-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 4-1)*3 + l) & + (dPdF(i,j,k,l, 7) + dPdF(i,j,k,l, 8))*n(i, 4)*n(k, 4) & + (dRdX(i,j,k,l, 4) + dRdX(i,j,k,l, 4))*n(i, 4)*n(k, 4) dresdvar(( 4-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 7-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 4)*n(k, 7) & - dRdX(i,j,k,l, 4)*n(i, 4)*n(k, 7) dresdvar(( 4-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 4-1)*3 + j,( 8-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 4)*n(k, 8) & + dRdX(i,j,k,l, 4)*n(i, 4)*n(k, 8) dresdvar(( 4-1)*3 + j,(11-1)*3 + l) = dresdvar(( 4-1)*3 + j,(11-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 4)*n(k,11) & - dRdX(i,j,k,l, 4)*n(i, 4)*n(k,11) dresdvar(( 4-1)*3 + j,(12-1)*3 + l) = dresdvar(( 4-1)*3 + j,(12-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 4)*n(k,12) & + dRdX(i,j,k,l, 4)*n(i, 4)*n(k,12) ! ! at boundary 5, influenced by boundary +1, -2, +9, -11 dresdvar(( 5-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 5-1)*3 + l) & + (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 3))*n(i, 5)*n(k, 5) & + (dRdX(i,j,k,l, 5) + dRdX(i,j,k,l, 5))*n(i, 5)*n(k, 5) dresdvar(( 5-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 1-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 5)*n(k, 1) & + dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 1) dresdvar(( 5-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 2-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 5)*n(k, 2) & - dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 2) dresdvar(( 5-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 5-1)*3 + j,( 9-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 5)*n(k, 9) & + dRdX(i,j,k,l, 5)*n(i, 5)*n(k, 9) dresdvar(( 5-1)*3 + j,(11-1)*3 + l) = dresdvar(( 5-1)*3 + j,(11-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i, 5)*n(k,11) & - dRdX(i,j,k,l, 5)*n(i, 5)*n(k,11) ! ! at boundary 6, influenced by boundary -1, +2, +10, -12 dresdvar(( 6-1)*3 + j,( 6-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 6-1)*3 + l) & + (dPdF(i,j,k,l, 2) + dPdF(i,j,k,l, 4))*n(i, 6)*n(k, 6) & + (dRdX(i,j,k,l, 6) + dRdX(i,j,k,l, 6))*n(i, 6)*n(k, 6) dresdvar(( 6-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 1-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i, 6)*n(k, 1) & - dRdX(i,j,k,l, 6)*n(i, 6)*n(k, 1) dresdvar(( 6-1)*3 + j,( 2-1)*3 + l) = dresdvar(( 6-1)*3 + j,( 2-1)*3 + l) + dPdF(i,j,k,l, 4)*n(i, 6)*n(k, 2) & + dRdX(i,j,k,l, 6)*n(i, 6)*n(k, 2) dresdvar(( 6-1)*3 + j,(10-1)*3 + l) = dresdvar(( 6-1)*3 + j,(10-1)*3 + l) + dPdF(i,j,k,l, 2)*n(i, 6)*n(k,10) & + dRdX(i,j,k,l, 6)*n(i, 6)*n(k,10) dresdvar(( 6-1)*3 + j,(12-1)*3 + l) = dresdvar(( 6-1)*3 + j,(12-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i, 6)*n(k,12) & - dRdX(i,j,k,l, 6)*n(i, 6)*n(k,12) ! ! at boundary 7, influenced by boundary +3, -4, -9, +11 dresdvar(( 7-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 7-1)*3 + l) & + (dPdF(i,j,k,l, 5) + dPdF(i,j,k,l, 7))*n(i, 7)*n(k, 7) & + (dRdX(i,j,k,l, 7) + dRdX(i,j,k,l, 7))*n(i, 7)*n(k, 7) dresdvar(( 7-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 3-1)*3 + l) + dPdF(i,j,k,l, 5)*n(i, 7)*n(k, 3) & + dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 3) dresdvar(( 7-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 4-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i, 7)*n(k, 4) & - dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 4) dresdvar(( 7-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 7-1)*3 + j,( 9-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 7)*n(k, 9) & - dRdX(i,j,k,l, 7)*n(i, 7)*n(k, 9) dresdvar(( 7-1)*3 + j,(11-1)*3 + l) = dresdvar(( 7-1)*3 + j,(11-1)*3 + l) + dPdF(i,j,k,l, 7)*n(i, 7)*n(k,11) & + dRdX(i,j,k,l, 7)*n(i, 7)*n(k,11) ! ! at boundary 8, influenced by boundary -3, +4, -10, +12 dresdvar(( 8-1)*3 + j,( 8-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 8-1)*3 + l) & + (dPdF(i,j,k,l, 6) + dPdF(i,j,k,l, 8))*n(i, 8)*n(k, 8) & + (dRdX(i,j,k,l, 8) + dRdX(i,j,k,l, 8))*n(i, 8)*n(k, 8) dresdvar(( 8-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 3-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 8)*n(k, 3) & - dRdX(i,j,k,l, 8)*n(i, 8)*n(k, 3) dresdvar(( 8-1)*3 + j,( 4-1)*3 + l) = dresdvar(( 8-1)*3 + j,( 4-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 8)*n(k, 4) & + dRdX(i,j,k,l, 8)*n(i, 8)*n(k, 4) dresdvar(( 8-1)*3 + j,(10-1)*3 + l) = dresdvar(( 8-1)*3 + j,(10-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i, 8)*n(k,10) & - dRdX(i,j,k,l, 8)*n(i, 8)*n(k,10) dresdvar(( 8-1)*3 + j,(12-1)*3 + l) = dresdvar(( 8-1)*3 + j,(12-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i, 8)*n(k,12) & + dRdX(i,j,k,l, 8)*n(i, 8)*n(k,12) ! ! at boundary 9, influenced by boundary +1, -3, +5, -7 dresdvar(( 9-1)*3 + j,( 9-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 9-1)*3 + l) & + (dPdF(i,j,k,l, 1) + dPdF(i,j,k,l, 5))*n(i, 9)*n(k, 9) & + (dRdX(i,j,k,l, 9) + dRdX(i,j,k,l, 9))*n(i, 9)*n(k, 9) dresdvar(( 9-1)*3 + j,( 1-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 1-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 9)*n(k, 1) & + dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 1) dresdvar(( 9-1)*3 + j,( 3-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 3-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 9)*n(k, 3) & - dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 3) dresdvar(( 9-1)*3 + j,( 5-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 5-1)*3 + l) + dPdF(i,j,k,l, 1)*n(i, 9)*n(k, 5) & + dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 5) dresdvar(( 9-1)*3 + j,( 7-1)*3 + l) = dresdvar(( 9-1)*3 + j,( 7-1)*3 + l) - dPdF(i,j,k,l, 5)*n(i, 9)*n(k, 7) & - dRdX(i,j,k,l, 9)*n(i, 9)*n(k, 7) ! ! at boundary 10, influenced by boundary -1, +3, +6, -8 dresdvar((10-1)*3 + j,(10-1)*3 + l) = dresdvar((10-1)*3 + j,(10-1)*3 + l) & + (dPdF(i,j,k,l, 2) + dPdF(i,j,k,l, 6))*n(i,10)*n(k,10) & + (dRdX(i,j,k,l,10) + dRdX(i,j,k,l,10))*n(i,10)*n(k,10) dresdvar((10-1)*3 + j,( 1-1)*3 + l) = dresdvar((10-1)*3 + j,( 1-1)*3 + l) - dPdF(i,j,k,l, 2)*n(i,10)*n(k, 1) & - dRdX(i,j,k,l,10)*n(i,10)*n(k, 1) dresdvar((10-1)*3 + j,( 3-1)*3 + l) = dresdvar((10-1)*3 + j,( 3-1)*3 + l) + dPdF(i,j,k,l, 6)*n(i,10)*n(k, 3) & + dRdX(i,j,k,l,10)*n(i,10)*n(k, 3) dresdvar((10-1)*3 + j,( 6-1)*3 + l) = dresdvar((10-1)*3 + j,( 6-1)*3 + l) + dPdF(i,j,k,l, 2)*n(i,10)*n(k, 6) & + dRdX(i,j,k,l,10)*n(i,10)*n(k, 6) dresdvar((10-1)*3 + j,( 8-1)*3 + l) = dresdvar((10-1)*3 + j,( 8-1)*3 + l) - dPdF(i,j,k,l, 6)*n(i,10)*n(k, 8) & - dRdX(i,j,k,l,10)*n(i,10)*n(k, 8) ! ! at boundary 11, influenced by boundary +2, -4, -5, +7 dresdvar((11-1)*3 + j,(11-1)*3 + l) = dresdvar((11-1)*3 + j,(11-1)*3 + l) & + (dPdF(i,j,k,l, 3) + dPdF(i,j,k,l, 7))*n(i,11)*n(k,11) & + (dRdX(i,j,k,l,11) + dRdX(i,j,k,l,11))*n(i,11)*n(k,11) dresdvar((11-1)*3 + j,( 2-1)*3 + l) = dresdvar((11-1)*3 + j,( 2-1)*3 + l) + dPdF(i,j,k,l, 3)*n(i,11)*n(k, 2) & + dRdX(i,j,k,l,11)*n(i,11)*n(k, 2) dresdvar((11-1)*3 + j,( 4-1)*3 + l) = dresdvar((11-1)*3 + j,( 4-1)*3 + l) - dPdF(i,j,k,l, 7)*n(i,11)*n(k, 4) & - dRdX(i,j,k,l,11)*n(i,11)*n(k, 4) dresdvar((11-1)*3 + j,( 5-1)*3 + l) = dresdvar((11-1)*3 + j,( 5-1)*3 + l) - dPdF(i,j,k,l, 3)*n(i,11)*n(k, 5) & - dRdX(i,j,k,l,11)*n(i,11)*n(k, 5) dresdvar((11-1)*3 + j,( 7-1)*3 + l) = dresdvar((11-1)*3 + j,( 7-1)*3 + l) + dPdF(i,j,k,l, 7)*n(i,11)*n(k, 7) & + dRdX(i,j,k,l,11)*n(i,11)*n(k, 7) ! ! at boundary 12, influenced by boundary -2, +4, -6, +8 dresdvar((12-1)*3 + j,(12-1)*3 + l) = dresdvar((12-1)*3 + j,(12-1)*3 + l) & + (dPdF(i,j,k,l, 4) + dPdF(i,j,k,l, 8))*n(i,12)*n(k,12) & + (dRdX(i,j,k,l,12) + dRdX(i,j,k,l,12))*n(i,12)*n(k,12) dresdvar((12-1)*3 + j,( 2-1)*3 + l) = dresdvar((12-1)*3 + j,( 2-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i,12)*n(k, 2) & - dRdX(i,j,k,l,12)*n(i,12)*n(k, 2) dresdvar((12-1)*3 + j,( 4-1)*3 + l) = dresdvar((12-1)*3 + j,( 4-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i,12)*n(k, 4) & + dRdX(i,j,k,l,12)*n(i,12)*n(k, 4) dresdvar((12-1)*3 + j,( 6-1)*3 + l) = dresdvar((12-1)*3 + j,( 6-1)*3 + l) - dPdF(i,j,k,l, 4)*n(i,12)*n(k, 6) & - dRdX(i,j,k,l,12)*n(i,12)*n(k, 6) dresdvar((12-1)*3 + j,( 8-1)*3 + l) = dresdvar((12-1)*3 + j,( 8-1)*3 + l) + dPdF(i,j,k,l, 8)*n(i,12)*n(k, 8) & + dRdX(i,j,k,l,12)*n(i,12)*n(k, 8) ! enddo enddo enddo enddo ! return ! END SUBROUTINE ! ! END MODULE !##############################################################