! last modified 26.03.07 ! --------------------------- 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 !*********************************************************************** !*** This routine checks for initialization, variables update and *** !*** calls 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 CPFEM, only: CPFEM_ffn_all, CPFEM_ffn1_all, CPFEM_inc_old use IO, only: IO_init 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 IO_init() call mesh_init() call constitutive_init() call math_init() call CPFEM_init() CPFEM_first_call = .false. endif ! not a new increment if (CPFEM_inc==CPFEM_inc_old) then ! 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 ! case of a new increment else 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 CPFEM_timefactor_max = 0.0_pReal endif ! ! get cp element number for fe element number CPFEM_ffn_all(:,:,CPFEM_in, cp_en) = ffn CPFEM_ffn1_all(:,:,CPFEM_in, cp_en) = ffn1 call CPFEM_general_material(CPFEM_cn, CPFEM_dt, cp_en, CPFEM_in) return end subroutine !*********************************************************************** !*** This routine allocates the arrays defined in module CPFEM *** !*** and initializes them *** !*********************************************************************** subroutine CPFEM_init() ! use prec, only: pReal,pInt use math, only: math_I3 use mesh use constitutive ! implicit none ! integer(pInt) i ! ! *** mpie.marc parameters *** allocate(CPFEM_ffn_all(3,3,mesh_maxNips,mesh_NcpElems)) allocate(CPFEM_ffn1_all(3,3,mesh_maxNips,mesh_NcpElems)) allocate(CPFEM_stress_all(6,mesh_maxNips,mesh_NcpElems)) allocate(CPFEM_jacobi_all(6,6,mesh_maxNips,mesh_NcpElems)) CPFEM_ffn_all = 0.0_pReal CPFEM_ffn1_all = 0.0_pReal CPFEM_stress_all = 0.0_pReal 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)) allocate(CPFEM_sigma_new(6,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) CPFEM_sigma_old = 0.0_pReal 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)) allocate(CPFEM_Fp_new(3,3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) CPFEM_Fp_old = math_I3 CPFEM_Fp_new = math_I3 ! ! *** 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_thickness: ', shape(CPFEM_thickness) 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 ! ! subroutine CPFEM_general_material(& CPFEM_cn,& ! Cycle number CPFEM_dt,& ! Time increment (dt) cp_en,& ! Element number CPFEM_in) ! Integration point number !*********************************************************************** !*** This routine calculates the material behaviour *** !*********************************************************************** use prec, only: pReal,pInt ! use IO, only: IO_error use math use mesh use constitutive ! implicit none ! ! *** Definition of variables *** ! *** Subroutine parameters *** real(pReal) CPFEM_cn, CPFEM_dt integer(pInt) cp_en ,CPFEM_in ! *** Local variables *** real(pReal) vf, cs(6), cd(6,6) integer(pInt) jpara,nori, iori, ising, icut, iconv ! *** Numerical parameters *** ! *** How often the jacobian is recalculated *** integer (pInt), parameter :: ijaco = 5_pInt ! *** Reference shear rate for the calculation of CPFEM_timefactor *** real (pReal), parameter :: dgs = 0.01_pReal ! ! *** Flag for recalculation of jacobian *** jpara = 1_pInt ! get number of grains from cp element number and integration point number nori = constitutive_Ngrains(CPFEM_in,cp_en) !ÄÄÄ ! CPFEM_en = mesh_element(1,cp_en) ! remap back to FE id ! CPFEM_s=0 CPFEM_d=0 ! ! *** Loop over all the components *** do iori=1,nori ! ! *** Initialization of the matrices for t=t0 *** ! data from constitutive? vf = constitutive_volfrac(iori,CPFEM_in,cp_en) !ÄÄÄ ! *** Calculation of the solution at t=t1 *** ! QUESTION use the mod() as flag parameter in the call ?? if (mod(CPFEM_cn,ijaco)==0) then !ÄÄÄ call CPFEM_stress(cs, cd, CPFEM_dt,cp_en,CPFEM_in, iori, ising, icut, iconv, 1_pInt) ! *** Evaluation of ising *** ! *** ising=2 => singular matrix in jacobi calculation *** ! *** => use old jacobi *** if (ising==2) jpara=0 ! *** Calculation of the consistent tangent *** CPFEM_d=CPFEM_d+vf*cd else call CPFEM_stress(cs, cd, CPFEM_dt,cp_en,CPFEM_in, iori, ising, icut, iconv, 0_pInt) jpara=0 endif ! *** Cases of unsuccessful calculations *** ! *** Evaluation of ising *** ! *** ising!=0 => singular matrix *** if (ising==1) then write(6,*) 'Singular matrix!' write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',CPFEM_en call IO_error(700) ! CPFEM_timefactor=1.e5_pReal return endif ! *** Evaluation of icut *** ! *** icut!=0 => too many cutbacks *** if (icut==1) then write(6,*) 'Too many cutbacks' write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',CPFEM_en call IO_error(600) ! CPFEM_timefactor=1.e5_pReal return endif ! *** Evaluation of iconv *** ! *** iconv!=0 => no convergence *** if (iconv==1) then write(6,*) 'Inner loop did not converge!' write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',CPFEM_en call IO_error(600) ! CPFEM_timefactor=1.e5_pReal return else if (iconv==2) then write(6,*) 'Outer loop did not converge!' write(6,*) 'Integration point: ',CPFEM_in write(6,*) 'Element: ',CPFEM_en call IO_error(600) ! CPFEM_timefactor=1.e5_pReal return endif ! *** Evaluation of the average Cauchy stress *** CPFEM_s=CPFEM_s+vf*cs enddo ! *** End of the loop over the components *** ! ************************************* ! *** End of the CP-FEM Calculation *** ! ************************************* ! *** Store the new stress *** CPFEM_stress_all(:,CPFEM_in,cp_en)=CPFEM_s ! *** Store the new jacobian *** if (jpara/=0) CPFEM_jaco_old(:,:,CPFEM_in,cp_en)=CPFEM_d return end subroutine ! ! subroutine CPFEM_stress(& cs,& ! stress vector cd,& ! Jacoby matrix CPFEM_dt,& ! Time increment (dt) cp_en,& ! Element number CPFEM_in,& ! Integration point number iori,& ! number of orintation ising,& ! flag for singular matrix icut,& ! flag for too many cut backs iconv,& ! flag for non convergence isjaco) ! flag whether to calculate Jacoby matrix !******************************************************************** ! This routine calculates the stress for a single component ! and manages the independent time incrmentation !******************************************************************** use prec, only: pReal,pInt use constitutive, only: constitutive_Nstatevars implicit none ! ! *** Definition of variables *** ! *** Subroutine parameters *** real(pReal) cs(6), cd(6,6), CPFEM_dt integer(pInt) cp_en ,CPFEM_in, iori, ising, icut, iconv, isjaco ! *** Local variables *** real(pReal) Fp_old(3,3), Fp_new(3,3), state_old(constitutive_Nstatevars) real(pReal) state_new(constitutive_Nstatevars), Tstar_v(6), CPFEM_ffn(3,3), CPFEM_ffn1(3,3) real(pReal) Tstar_v_h(6), state_new_h(constitutive_Nstatevars) ! *** Numerical parameters *** integer(pInt), parameter :: ncut=7_pInt ! icut=0 ! ! *** Initialization of the matrices for t=t0 *** Fp_old = CPFEM_Fp_old(:,:,iori,CPFEM_in,cp_en) Fp_new = 0_pReal state_old = constitutive_state_old(:,iori,CPFEM_in,cp_en) state_new = state_old Tstar_v = CPFEM_sigma_old(:,iori,CPFEM_in,cp_en) CPFEM_ffn = CPFEM_ffn_all(:,:,CPFEM_in,cp_en) CPFEM_ffn1 = CPFEM_ffn1_all(:,:,CPFEM_in,cp_en) ! ! *** First attempt to calculate Tstar and tauc with initial timestep *** ! save copies of Tstar_v and state_new Tstar_v_h = Tstar_v state_new_h = state_new call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, iori,, ising, icut, iconv, isjaco, phi1, PHI, phi2,& CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,g_old,g_new,state_old, state_new, Tstar_v) if ((iconv==0).AND.(ising==0)) then ! *** Update the differents matrices for t=t1 *** CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new constituitive_state_new(:,iori,CPFEM_in,cp_en) = state_new CPFEM_g_new(:,iori,CPFEM_in,cp_en) = g_new CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v ! *** Update the results plotted in MENTAT *** CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1 CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2 CPFEM_results(4:3+constitutive_Nresults(iori,CPFEM_in,cp_en),iori,CPFEM_in,cp_en)=& constitutive_results(1:constitutive_Nresults,iori,CPFEM_in,cp_en)!ÄÄÄÄ return endif ! ! *** Calculation of stress and resistences with a cut timestep *** ! *** when first try did not converge *** jcut=1_pInt dt_i=0.5_pReal*CPFEM_dt delta_Fg=0.5_pReal*(CPFEM_ffn1-CPFEM_ffn) Fg_i=CPFEM_ffn+delta_Fg Tstar_v=Tstar_v_h state_new_i=state_new_h ! *** Start time *** time=dt_i do while (time<=CPFEM_dt) call CPFEM_stress_int(cs, cd, time, cp_en,CPFEM_in, iori, ising, icut, iconv, isjaco, phi1, PHI, phi2,& CPFEM_ffn, Fg_i,Fp_old,Fp_new,g_old,g_new,state_old, state_new_i, Tstar_v) if ((iconv==0).AND.(ising==0)) then time=time+dt_i Fg_i=Fg_i+delta_Fg Tstar_v_h=Tstar_v state_new_h=state_new_i else jcut=jcut+1_pInt if (jcut>ncut) then icut=1_pInt return endif dt_i=0.5_pReal*dt_i time=time-dt_i delta_Fg=0.5_pReal*delta_Fg Fg_i=Fg_i-delta_Fg Tstar_v=Tstar_v_h state_new_i=state_new_h endif enddo ! ! *** Final calculation of stress and resistences with full timestep *** state_new=state_new_i call CPFEM_stress_int(cs, cd, CPFEM_dt, cp_en,CPFEM_in, iori, ising, icut, iconv, isjaco, phi1, PHI, phi2,& CPFEM_ffn, CPFEM_ffn1,Fp_old,Fp_new,g_old,g_new,state_old, state_new, Tstar_v) ! *** Update the differents matrices for t=t1 *** CPFEM_Fp_new(:,:,iori,CPFEM_in,cp_en) = Fp_new constituitive_state_new(:,iori,CPFEM_in,cp_en) = state_new CPFEM_g_new(:,iori,CPFEM_in,cp_en) = g_new CPFEM_sigma_new(:,iori,CPFEM_in,cp_en) = Tstar_v ! *** Update the results plotted in MENTAT *** CPFEM_results(1,iori,CPFEM_in,cp_en) = phi1 CPFEM_results(2,iori,CPFEM_in,cp_en) = PHI CPFEM_results(3,iori,CPFEM_in,cp_en) = phi2 CPFEM_results(4,iori,CPFEM_in,cp_en) = sum(g_new) return end subroutine ! ! subroutine CPFEM_stress_int(& cs,& ! Cauchy stress vector dcs_de,& ! Consistent tangent dt,& ! Time increment cp_en,& ! Element number CPFEM_in,& ! Integration point number iori,& ! number of orintation ising,& ! flag for singular matrix icut,& ! flag for too many cut backs iconv,& ! flag for non convergence isjaco,& ! flag whether to calculate Jacoby matrix phi1,& ! Euler angle PHI,& ! Euler angle phi2,& ! Euler angle Fg_old,& ! Old global deformation gradient Fg_new,& ! New global deformation gradient Fp_old,& ! Old plastic deformation gradient Fp_new,& ! New plastic deformation gradient state_old,& ! Old state variable array state_new,& ! New state variable array Tstar_v) ! Second Piola-Kirschoff stress tensor !******************************************************************** ! This routine 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 !******************************************************************** use prec, only: pReal,pInt use constitutive, only: constitutive_Nstatevars implicit none ! ! *** Definition of variables *** ! *** Subroutine parameters *** real(pReal) cs(6), dcs_de(6,6), dt, phi1, PHI, phi2, Fg_old(3,3), Fg_new(3,3) real(pReal) Fp_old(3,3), Fp_new(3,3), state_old(constitutive_Nstatevars) real(pReal) state_new(constitutive_Nstatevars), Tstar_v(6) integer(pInt) cp_en, CPFEM_in, iori, ising, icut, iconv, isjaco ! *** Local variables *** integer(pInt) ic real(pReal) Fe(3,3), R(3,3), U(3,3), dev(6), dF(3,3), Fg2(3,3), sgm2(6) real(pReal) state2(constitutive_Nstatevars), Fp2(3,3), cs1(6) ! *** Numerical parameters *** real(pReal), parameter :: pert_ct=1.0e-5_pReal ! *** Error treatment *** iconv = 0 ising = 0 ! ********************************************* ! *** Calculation of the new Cauchy stress *** ! ********************************************* ! *** Call Newton-Raphson method *** call NEWTON_RAPHSON(dt,cp_en,CPFEM_in,iori,Fg_old,Fg_new,Fp_old,Fp_new,Fe,state_old,state_new,Tstar_v,cs,iconv,ising) ! ! *** Calculation of the new orientation *** call math_pDecomposition(Fe,U,R,ising) if (ising==1) then return endif call math_RtoEuler(transpose(R),phi1,PHI,phi2) ! ! *** Choice of the calculation of the consistent tangent *** if (isjaco==0) return ! ! ********************************************* ! *** Calculation of the consistent tangent *** ! ********************************************* ! ! *** Calculation of the consistent tangent with perturbation *** ! *** Perturbation on the component of Fg *** do ic=1,6 ! ! *** Method of small perturbation dev=0 if(ic<=3) dev(ic) = pert_ct if(ic>3) dev(ic) = pert_ct/2 dF=matmul(math_conv6to33(dev),Fg_old) Fg2=Fg_new+dF sgm2=Tstar_v state2=state_new ! *** Calculation of the perturbated Cauchy stress *** call NEWTON_RAPHSON(dt,cp_en,CPFEM_in,iori,Fg_old,Fg2,Fp_old,Fp2,Fe,state_old,tauc2,sgm2,cs1,iconv,ising) ! ! *** Consistent tangent *** dcs_de(:,ic)=(cs1-cs)/pert_ct enddo ! return end subroutine ! ! subroutine NEWTON_RAPHSON(& dt,& cp_en,& ! Element number CPFEM_in,& ! Integration point number iori,& ! number of orintation Fg_old,& Fg_new,& Fp_old,& Fp_new,& Fe,& state_old,& state_new,& Tstar_v,& cs,& iconv,& ising) !*********************************************************************** !*** NEWTON-RAPHSON Calculation *** !*********************************************************************** use prec, only: pReal,pInt use constitutive, only: constitutive_Nstatevars use math implicit none ! *** Definition of variables *** ! *** Subroutine parameters *** real(pReal) dt,Fg_old(3,3),Fg_new(3,3),Fp_old(3,3),Fp_new(3,3), Fe(3,3) real(pReal) state_old(constitutive_Nstatevars), state_new(constitutive_Nstatevars) real(pReal) Tstar_v(6), cs(6) integer(pInt) cp_en, CPFEM_in, iori, iconv, ising ! *** Local variables *** real(pReal) crite, tol_in, tol_out, invFp_old(3,3), det, A(3,3), C66(6,6), Lp(3,3), dLp(3,3,6) real(pReal) tLp(3,3), help(3,3), help1(6), Tstar0_v(6), R1(6), norm1, tdLp(3,3) real(pReal) dstate(constitutive_Nstatevars), R2(6), norm2, invFp_new(3,3), Estar(3,3) real(pReal) Estar_v(6) integer(pInt) iouter, iinner , Jacobi(6,6), inv_Jacobi(6,6), dTstar_v(6), dummy, err ! *** Numerical parameters *** integer(pInt), parameter :: nouter = 50_pInt real(pReal), parameter :: tol_outer = 1.0e-4_pReal integer(pInt), parameter :: ninner = 2000_pInt real(pReal), parameter :: tol_inner = 1.0e-3_pReal real(pReal), parameter :: eta = 13.7_pReal crite=eta*constitutive_s0_slip/constitutive_n_slip !ÄÄÄ ! ! *** Tolerances *** tol_in = tol_inner*s0_slip !ÄÄÄ tol_out = tol_outer*s0_slip !ÄÄÄ ! ! *** Error treatment *** iconv = 0 ising = 0 ! ! initialize new state state_new=state_old ! *** Calculation of Fp_old(-1) *** call invert3x3(Fp_old, invFp_old, det, err) !ÄÄÄ if (err==1_pInt) then ising=1 return endif ! ! *** Calculation of A and T*0 (see Kalidindi) *** A = matmul(Fg_new,invFp_old) A = matmul(transpose(A), A) C_66=constitutive_homogenizedC(iori, CPFEM_in, cp_en) !ÄÄÄ ! ! *** Second level of iterative procedure: Resistences *** do iouter=1,nouter ! *** First level of iterative procedure: Stresses *** do iinner=1,ninner ! ! *** Calculation of gdot_slip *** call constitutive_LpAndItsTangent(Lp, dLp, iori, CPFEM_in, cp_en) I3tLp = math_I3-dt*Lp help=matmul(transpose(I3tLp),matmul(A, I3tLp))-math_I3 Tstar0_v = 0.5_pReal * matmul(C66, math_33to6(help)) R1=Tstar_v-Tstar0_v norm1=maxval(abs(R1)) if (norm1crite) then dTstar_v(i)=sign(crite,dTstar_v(i)) endif enddo Tstar_v=Tstar_v-dTstar_v ! enddo iconv=1 return ! *** End of the first level of iterative procedure *** 100 dstate=dt*constitutive_dotState(Tstar_v, iori, CPFEM_in, cp_en) ! *** Arrays of residuals *** R2=state_new-state_old-dstate norm2=maxval(abs(R2)) if (norm2