!************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - constitutive equations * !* - Schmid matrices calculation * !* - Hardening matrices definition * !* - Parameters definition * !* - orientations? * !************************************ MODULE constitutive !*** Include other modules *** use prec, only: pReal,pInt ! NB: 'only'-commend may not be needed implicit none !***************************** !* Material parameters * !***************************** !* Character * character*80, allocatble :: TCfile(:),ODFfile(:) ! NB: orientation files TCfile(number of material) !* Integer * integer(pInt) Nmats ! NB: Number of materials (read in material file) integer(pInt), allocatable :: crystal_structure(:) ! NB: crystal_structure(number of material)=1-3 integer(pInt) Nslip(3) ! NB: Number of systems for each crystal structure (3) !* Real * real(pReal), allocatable :: Cslip_66(:,:,:) ! NB: Cslip_66(1:6,1:6,number of materials) real(pReal), allocatable :: s0_slip(:),gdot0_slip(:),n_slip(:) real(pReal), allocatable :: h0(:),w0(:),s_sat(:) ! NB: Parameters(number of materials) real(pReal), allocatable :: hardening_matrix(:,:,:) ! NB: hardening_matrix(48,48,3) real(pReal), parameter :: latent_hardening=1.4_pReal real(pReal) sn(3,48,3),sd(3,48,3) ! NB: slip normale and slip direction for 3 crystal structures ! Is 48 always the maximum number of systems? real(pReal) Sslip(3,3,48,3),Sslip_v(6,48,3) ! NB: Schmid matrices and corresponding Schmid vectors !*** Slip systems for FCC structures (1) *** Nslip(1)=12_pInt !* System {111}<110> Sort according Eisenlohr&Hantcherli data sd(:, 1,1)/ 0, 1,-1/ ; data sn(:, 1,1)/ 1, 1, 1/ data sd(:, 2,1)/-1, 0, 1/ ; data sn(:, 2,1)/ 1, 1, 1/ data sd(:, 3,1)/ 1,-1, 0/ ; data sn(:, 3,1)/ 1, 1, 1/ data sd(:, 4,1)/ 0,-1,-1/ ; data sn(:, 4,1)/-1,-1, 1/ data sd(:, 5,1)/ 1, 0, 1/ ; data sn(:, 5,1)/-1,-1, 1/ data sd(:, 6,1)/-1, 1, 0/ ; data sn(:, 6,1)/-1,-1, 1/ data sd(:, 7,1)/ 0,-1, 1/ ; data sn(:, 7,1)/ 1,-1,-1/ data sd(:, 8,1)/-1, 0,-1/ ; data sn(:, 8,1)/ 1,-1,-1/ data sd(:, 9,1)/ 1, 1, 0/ ; data sn(:, 9,1)/ 1,-1,-1/ data sd(:,10,1)/ 0, 1, 1/ ; data sn(:,10,1)/-1, 1,-1/ data sd(:,11,1)/ 1, 0,-1/ ; data sn(:,11,1)/-1, 1,-1/ data sd(:,12,1)/-1,-1, 0/ ; data sn(:,12,1)/-1, 1,-1/ !*** Slip systems for BCC structures (2) *** Nslip(2)=48_pInt !* System {110}<111> !* Sort? data sd(:, 1,2)/ 1,-1, 1/ ; data sn(:, 1,2)/ 0, 1, 1/ data sd(:, 2,2)/-1,-1, 1/ ; data sn(:, 2,2)/ 0, 1, 1/ data sd(:, 3,2)/ 1, 1, 1/ ; data sn(:, 3,2)/ 0,-1, 1/ data sd(:, 4,2)/-1, 1, 1/ ; data sn(:, 4,2)/ 0,-1, 1/ data sd(:, 5,2)/-1, 1, 1/ ; data sn(:, 5,2)/ 1, 0, 1/ data sd(:, 6,2)/-1,-1, 1/ ; data sn(:, 6,2)/ 1, 0, 1/ data sd(:, 7,2)/ 1, 1, 1/ ; data sn(:, 7,2)/-1, 0, 1/ data sd(:, 8,2)/ 1,-1, 1/ ; data sn(:, 8,2)/-1, 0, 1/ data sd(:, 9,2)/-1, 1, 1/ ; data sn(:, 9,2)/ 1, 1, 0/ data sd(:,10,2)/-1, 1,-1/ ; data sn(:,10,2)/ 1, 1, 0/ data sd(:,11,2)/ 1, 1, 1/ ; data sn(:,11,2)/-1, 1, 0/ data sd(:,12,2)/ 1, 1,-1/ ; data sn(:,12,2)/-1, 1, 0/ !* System {112}<111> !* Sort? data sd(:,13,2)/-1, 1, 1/ ; data sn(:,13,2)/ 2, 1, 1/ data sd(:,14,2)/ 1, 1, 1/ ; data sn(:,14,2)/-2, 1, 1/ data sd(:,15,2)/ 1, 1,-1/ ; data sn(:,15,2)/ 2,-1, 1/ data sd(:,16,2)/ 1,-1, 1/ ; data sn(:,16,2)/ 2, 1,-1/ data sd(:,17,2)/ 1,-1, 1/ ; data sn(:,17,2)/ 1, 2, 1/ data sd(:,18,2)/ 1, 1,-1/ ; data sn(:,18,2)/-1, 2, 1/ data sd(:,19,2)/ 1, 1, 1/ ; data sn(:,19,2)/ 1,-2, 1/ data sd(:,20,2)/-1, 1, 1/ ; data sn(:,20,2)/ 1, 2,-1/ data sd(:,21,2)/ 1, 1,-1/ ; data sn(:,21,2)/ 1, 1, 2/ data sd(:,22,2)/ 1,-1, 1/ ; data sn(:,22,2)/-1, 1, 2/ data sd(:,23,2)/-1, 1, 1/ ; data sn(:,23,2)/ 1,-1, 2/ data sd(:,24,2)/ 1, 1, 1/ ; data sn(:,24,2)/ 1, 1,-2/ !* System {123}<111> !* Sort? data sd(:,25,2)/ 1, 1,-1/ ; data sn(:,25,2)/ 1, 2, 3/ data sd(:,26,2)/ 1,-1, 1/ ; data sn(:,26,2)/-1, 2, 3/ data sd(:,27,2)/-1, 1, 1/ ; data sn(:,27,2)/ 1,-2, 3/ data sd(:,28,2)/ 1, 1, 1/ ; data sn(:,28,2)/ 1, 2,-3/ data sd(:,29,2)/ 1,-1, 1/ ; data sn(:,29,2)/ 1, 3, 2/ data sd(:,30,2)/ 1, 1,-1/ ; data sn(:,30,2)/-1, 3, 2/ data sd(:,31,2)/ 1, 1, 1/ ; data sn(:,31,2)/ 1,-3, 2/ data sd(:,32,2)/-1, 1, 1/ ; data sn(:,32,2)/ 1, 3,-2/ data sd(:,33,2)/ 1, 1,-1/ ; data sn(:,33,2)/ 2, 1, 3/ data sd(:,34,2)/ 1,-1, 1/ ; data sn(:,34,2)/-2, 1, 3/ data sd(:,35,2)/-1, 1, 1/ ; data sn(:,35,2)/ 2,-1, 3/ data sd(:,36,2)/ 1, 1, 1/ ; data sn(:,36,2)/ 2, 1,-3/ data sd(:,37,2)/ 1,-1, 1/ ; data sn(:,37,2)/ 2, 3, 1/ data sd(:,38,2)/ 1, 1,-1/ ; data sn(:,38,2)/-2, 3, 1/ data sd(:,39,2)/ 1, 1, 1/ ; data sn(:,39,2)/ 2,-3, 1/ data sd(:,40,2)/-1, 1, 1/ ; data sn(:,40,2)/ 2, 3,-1/ data sd(:,41,2)/-1, 1, 1/ ; data sn(:,41,2)/ 3, 1, 2/ data sd(:,42,2)/ 1, 1, 1/ ; data sn(:,42,2)/-3, 1, 2/ data sd(:,43,2)/ 1, 1,-1/ ; data sn(:,43,2)/ 3,-1, 2/ data sd(:,44,2)/ 1,-1, 1/ ; data sn(:,44,2)/ 3, 1,-2/ data sd(:,45,2)/-1, 1, 1/ ; data sn(:,45,2)/ 3, 2, 1/ data sd(:,46,2)/ 1, 1, 1/ ; data sn(:,46,2)/-3, 2, 1/ data sd(:,47,2)/ 1, 1,-1/ ; data sn(:,47,2)/ 3,-2, 1/ data sd(:,48,2)/ 1,-1, 1/ ; data sn(:,48,2)/ 3, 2,-1/ !*** Slip systems for HCP structures (3) *** Nslip(3)=12_pInt !* Basal systems {0001}<1120> !* 1- (0 0 0 1)[-2 1 1 0] !* 2- (0 0 0 1)[ 1 -2 1 0] !* 3- (0 0 0 1)[ 1 1 -2 0] !* Plane (hkil)->(hkl) !* Direction [uvtw]->[(u-t) (v-t) w] !* Automatical transformation from Bravais to Miller !* not done for the moment !* Sort? data sd(:, 1,3)/-1, 0, 0/ ; data sn(:, 1,3)/ 0, 0, 1/ data sd(:, 2,3)/ 0,-1, 0/ ; data sn(:, 2,3)/ 0, 0, 1/ data sd(:, 3,3)/ 1, 1, 0/ ; data sn(:, 3,3)/ 0, 0, 1/ !* 1st type prismatic systems {1010}<1120> !* 1- ( 0 1 -1 0)[-2 1 1 0] !* 2- ( 1 0 -1 0)[ 1 -2 1 0] !* 3- (-1 1 0 0)[ 1 1 -2 0] !* Sort? data sd(:, 4,3)/-1, 0, 0/ ; data sn(:, 4,3)/ 0, 1, 0/ data sd(:, 5,3)/ 0,-1, 0/ ; data sn(:, 5,3)/ 1, 0, 0/ data sd(:, 6,3)/ 1, 1, 0/ ; data sn(:, 6,3)/-1, 1, 0/ !* 1st type 1st order pyramidal systems {1011}<1120> !* 1- ( 0 -1 1 1)[-2 1 1 0] !* 2- ( 0 1 -1 1)[-2 1 1 0] !* 3- (-1 0 1 1)[ 1 -2 1 0] !* 4- ( 1 0 -1 1)[ 1 -2 1 0] !* 5- (-1 1 0 1)[ 1 1 -2 0] !* 6- ( 1 -1 0 1)[ 1 1 -2 0] !* Sort? data sd(:, 7,3)/-1, 0, 0/ ; data sn(:, 7,3)/ 0,-1, 1/ data sd(:, 8,3)/ 0,-1, 0/ ; data sn(:, 8,3)/ 0, 1, 1/ data sd(:, 9,3)/ 1, 1, 0/ ; data sn(:, 9,3)/-1, 0, 1/ data sd(:,10,3)/-1, 0, 0/ ; data sn(:,10,3)/ 1, 0, 1/ data sd(:,11,3)/ 0,-1, 0/ ; data sn(:,11,3)/-1, 1, 1/ data sd(:,12,3)/ 1, 1, 0/ ; data sn(:,12,3)/ 1,-1, 1/ contains !**************************************** !* - constitutive_init * !* - constitutive_calc_SchmidM * !* - constitutive_calc_HardeningM * !* - constitutive_parse_materialDat * !* - orientation reading???? * !* - constitutive_calc_SlipRates * !* - constitutive_calc_Hardening * !* - consistutive_calc_PlasVeloGradient * !* - CPFEM_CauchyStress??????? * !**************************************** subroutine constitutive_init() !************************************** !*** Module initialization *** !************************************** call constitutive_calc_SchmidM() call constitutive_calc_hardeningM() call constitutive_parse_materialDat() end subroutine subroutine constitutive_calc_SchmidM() !************************************** !*** Calculation of Schmid matrices *** !************************************** use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) i,j,k,l real(pReal) invNorm !* Iteration over the crystal structures do l=1,3 !* Iteration over the systems do k=1,Nslip(l) !* Defintion of Schmid matrix forall (i=1:3,j=1:3) Sslip(i,j,k,l)=sd(i,k,l)*sn(j,k,l) endforall !* Normalization of Schmid matrix invNorm = dsqrt(1.0_pReal/ & (sn(1,k,l)**2+sn(2,k,l)**2+sn(3,k,l)**2)* & (sd(1,k,l)**2+sd(2,k,l)**2+sd(3,k,l)**2)) Sslip(:,:,k,l)=Sslip(:,:,k,l)*invNorm !* Vectorization of normalized Schmid matrix !* according MARC component order 11,22,33,12,23,13 Sslip_v(1,k,l)=Sslip(1,1,k,l) Sslip_v(2,k,l)=Sslip(2,2,k,l) Sslip_v(3,k,l)=Sslip(3,3,k,l) Sslip_v(4,k,l)=Sslip(1,2,k,l)+Sslip(2,1,k,l) Sslip_v(5,k,l)=Sslip(2,3,k,l)+Sslip(3,3,k,l) Sslip_v(6,k,l)=Sslip(1,3,k,l)+Sslip(3,1,k,l) enddo enddo end subroutine subroutine constitutive_calc_HardeningM() !**************************************** !*** Hardening matrix (see Kalidindi) *** !**************************************** use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) i,j,k,l !* Initialization of the hardening matrix hardening_matrix=latent_hardening !* Iteration over the crystal structures do l=1,3 select case(l) !* Hardening matrix for FCC structures case (1) do k=1,10,3 forall (i=1:3,j=1:3) hardening_matrix(k-1+i,k-1+j,l)=1.0_pReal endforall enddo !* Hardening matrix for BCC structures case (2) do k=1,11,2 forall (i=1:2,j=1:2) hardening_matrix(k-1+i,k-1+j,l)=1.0_pReal endforall enddo do k=13,48 hardening_matrix(k,k,l)=1.0_pReal enddo !* Hardening matrix for HCP structures case (3) forall (i=1:3,j=1:3) hardening_matrix(i,j,l)=1.0_pReal endforall do k=4,12 hardening_matrix(k,k,l)=1.0_ZdRe enddo end select enddo end subroutine !* NOT YET IMPLEMENTED *! subroutine constitutive_parse_materialDat() !**************************************** !*** Reading parameter files *** !**************************************** use prec, only: pReal,pInt implicit none !* Definition of variables character*80 line integer(pIn) i,j,k,l,positions(4) ! MISSING: needs to be 2 pass ! first pass to count Nmats and allocate ! 2nd pass to read actual parameters write(6,*) '## constitutive_parse_materialDat ##' write(6,*) constitutive_Nmats = 1 open(200,FILE='material.mpie',ACTION='READ',STATUS='OLD',ERR=100) read(200,610,ERR=200,END=200) line IF( line(1:1).ne.'[' )THEN WRITE(6,*) 'Problem with mat file: no mat. in 1st line' ELSE WRITE(6,*) 'Reading mat. data' DO WHILE( .true. ) READ(200,610,END=220) line IF( line(1:1).eq.'[' )THEN constitutive_Nmats = constitutive_Nmats+1 ELSE positions = IO_stringPos(line,2) ! parse 2 parts SELECT CASE (IO_stringValue(line,positions,1)) CASE ('s0_slip') s0_slip(mat) = IO_floatValue(line,positions,2) CASE ('g0_slip') g0_slip(mat) = IO_floatValue(line,positions,2) CASE ('n_slip') n_slip(mat) = IO_intValue(line,positions,2) CASE ('h0') h0(mat) = IO_floatValue(line,positions,2) CASE ('w0') w0(mat) = IO_floatValue(line,positions,2) CASE ('tauc_sat') tauc_sat(mat) = IO_floatValue(line,positions,2) CASE ('C11') C11(mat) = IO_floatValue(line,positions,2) CASE ('C12') C12(mat) = IO_floatValue(line,positions,2) CASE ('C44') C44(mat) = IO_floatValue(line,positions,2) CASE ('TCfile') TCfile(mat) = IO_stringValue(line,positions,2) CASE ('ODFfile') ODFfile(mat) = IO_stringValue(line,positions,2) CASE ('Ngrains') Ngrains(mat) = IO_intValue(line,positions,2) CASE DEFAULT WRITE(6,*) 'Unknown mat. parameter ',line END IF END DO END IF 220 continue close(200) ! ** Defintion of stiffness matrices ** ! MISSING: this needs to be iterated over the materials Cslip_66 = 0.0_pRe do i=1,3 do j=1,3 Cslip_66(i,j) = C12 enddo Cslip_66(i,i) = C11 Cslip_66(i+3,i+3) = C44 enddo Cslip_3333(:,:,:,:) = math_66to3333(Cslip_66(:,:)) ! *** Transformation to get the MARC order *** ! *** 11,22,33,12,23,13 *** ! MISSING this should be outsourced to FEM-spec temp=Cslip_66(4,:) Cslip_66(4,:)=Cslip_66(6,:) Cslip_66(6,:)=Cslip_66(5,:) Cslip_66(5,:)=temp temp=Cslip_66(:,4) Cslip_66(:,4)=2.0d0*Cslip_66(:,6) Cslip_66(:,6)=2.0d0*Cslip_66(:,5) Cslip_66(:,5)=2.0d0*temp ! *** Output to MARC output file *** write(6,*) 'Material data:' write(6,*) 'Slip parameter:(s0_slip,g0_slip,n_slip)' write(6,*) s0_slip,g0_slip,n_slip write(6,*) 'Slip hardening parameter:(h0,tauc_sat,w0)' write(6,*) h0,tauc_sat,w0 write(6,*) 'Elasticity matrix:' write(6,*) Cslip_66(1,:) write(6,*) Cslip_66(2,:) write(6,*) Cslip_66(3,:) write(6,*) Cslip_66(4,:)/2.0d0 write(6,*) Cslip_66(5,:)/2.0d0 write(6,*) Cslip_66(6,:)/2.0d0 write(6,*) call flush(6) ! END OF MISSING mat iterations return 100 call _error(110) 200 call _error(210) end !* NOT YET IMPLEMENTED *! subroutine READ_ORIENTATIONS !*********************************************************************** !*** This routine reads orientations from 'orientations.mpie' *** !*********************************************************************** use mpie use Zahlendarstellung, only: ZdRe,ZdIn implicit none ! *** Definition of variables *** integer(ZdIn) i,j ! *** Read 'orientations.mpie' file *** open(100,FILE='orientations.mpie',ACTION='READ',STATUS='OLD', & ERR=100) read(100,*,ERR=200,END=200) ! *** Read number of states, maximum of components over the states *** read(100,*,ERR=200,END=200) mpie_nmat,mpie_norimx ! *** Allocate memory for the arrays *** allocate(mpie_mat(mpie_nmat,2+7*mpie_norimx)) allocate(mpie_cko(mpie_nmat,4:35,3,0:35,2)) allocate(mpie_ckofile(mpie_nmat,80)) allocate(mpie_odfmax(mpie_nmat)) mpie_mat=0.0_ZdRe mpie_cko=0.0_ZdRe mpie_ckofile='' mpie_odfmax=0.0_ZdRe ! *** Read the different states *** do i=1,mpie_nmat read(100,*,ERR=200,END=200) ! *** Number of component and symmetry *** read(100,*,ERR=200,END=200) mpie_mat(i,1),mpie_mat(i,2) ! *** If symmetry = 2, use direct ODF sampling,i.e. read coefficience *** if (mpie_mat(i,2)==2_ZdIn) then read(100,'(80A)',ERR=200,END=201) mpie_ckofile(i,:) 201 call mpie_read_ckofile(mpie_cko(i,:,:,:,:), & mpie_ckofile(i,:)) call mpie_odf_max(mpie_cko(i,:,:,:,:),mpie_odfmax(i)) ! *** Set volume fraction to inverse of orientation number for each orientation *** do j=1,int(mpie_mat(i,1),ZdIn) mpie_mat(i,2+7*j)=1/mpie_mat(i,1) enddo else ! *** Read for every component: *** ! *** gauss: euler angles (phi1, PHI, phi2), dummy, scatter, volume fraction *** ! *** fiber: alpha1, alpha2, beta1, beta2, scatter, volume fraction *** do j=1,int(mpie_mat(i,1),ZdIn) read(100,*,ERR=200,END=200) mpie_mat(i,7*j-4), & mpie_mat(i,7*j-3),mpie_mat(i,7*j-2), & mpie_mat(i,7*j-1),mpie_mat(i,7*j), & mpie_mat(i,7*j+1),mpie_mat(i,7*j+2) enddo endif enddo close(100) ! *** Output to MARC output file *** write(6,*) 'MPIE Material Routine Ver. 0.1 by L. Hantcherli' write(6,*) write(6,*) 'Orientations data:' write(6,*) 'Number of materials: ', mpie_nmat write(6,*) 'Maximum number of components: ', mpie_norimx write(6,*) do i=1,mpie_nmat write(6,*) 'State', i if (mpie_mat(i,2)==2_ZdIn) then write(6,*) mpie_ckofile(i,:),mpie_mat(i,9),mpie_odfmax(i) else write(6,*) mpie_mat(i,:) endif write(6,*) enddo call flush(6) return 100 call _error(100) 200 call _error(200) end subroutine constitutive_calc_SlipRates( & matID, & tau_slip, & tauc_slip, & gdot_slip, & dgdot_dtaucslip & ) !********************************************************************* !* This subroutine contains the constitutive equation for the slip * !* rate on each slip system * !* INPUT: * !* - matID : material identifier * !* - tau_slip : applied shear stress on each slip system * !* - tauc_slip : critical shear stress on each slip system * !* OUTPUT: * !* - gdot_slip : slip rate on each slip system * !* - dgdot_dtaucslip : derivative of slip rate on each slip system * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) matID,i real(pReal), tau_slip(Nslip(crystal_structure(matID))) real(pReal), tauc_slip_new(Nslip(crystal_structure(matID))) real(pReal), gdot_slip(Nslip(crystal_structure(matID))) real(pReal), dgdot_dtaucslip(Nslip(crystal_structure(matID))) !* Iteration over the systems do i=1,Nslip(crystal_structure(matID)) gdot_slip(i)=gdot0_slip(matID)*(abs(tau_slip(i))/tauc_slip(i)) & **n_slip(matID)*sign(1.0_pReal,tau_slip(i)) dgdot_dtaucslip(i)=gdot0_slip(matID)*(abs(tau_slip(i))/tauc_slip(i)) & **(n_slip(matID)-1.0_pReal) & *n_slip(matID)/tauc_slip(i) enddo return end subroutine subroutine constitutive_calc_Hardening( & matID, & tauc_slip, & gdot_slip, & dtauc_slip & ) !********************************************************************* !* This subroutine calculates the increment in critical shear stress * !* due to plastic deformation on each slip system * !* INPUT: * !* - matID : material identifier * !* - tauc_slip : critical shear stress on each slip system * !* - gdot_slip : slip rate on each slip system * !* OUTPUT: * !* - dtauc_slip : increment of hardening due to slip on each system * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) matID,i,j real(pReal) tauc_slip_new(Nslip(crystal_structure(matID))) real(pReal) gdot_slip(Nslip(crystal_structure(matID))) real(pReal) dtauc_slip(Nslip(crystal_structure(matID))) real(pReal) self_hardening(Nslip(crystal_structure(matID))) !* Self-Hardening of each system do i=1,Nslip(crystal_structure(matID)) self_hardening(i)=h0(matID)*(1.0_pReal-tauc_slip(i)/ & s_sat(matID))**w0(matID)*abs(gdot_slip(i)) enddo !* Hardening for all systems i=Nslip(crystal_structure(matID)) j=crystal_structure(matID) dtauc_slip=matmul(hardening_matrix(i,i,j),selfhr) return end subroutine plastic_vel_grad(dt,tau_slip,tauc_slip_new,Lp) C ************************************************************* C Subroutine calculates the plastic velocity gradient given the C slip rates C Input: dt : time step C tau_slip : shear stress on each slip system on each C slip system C tauc_slip_new : critical shear stress needed for slip on each C slip system C Output: Lp : plastic velocity gradient C gdot_slip : slip rate on each slip system C ************************************************************* use mpie use Zahlendarstellung implicit none real(ZdRe) dt,tau_slip(nslip),tauc_slip_new(nslip), & Lp(3,3),gdot_slip(nslip) integer(ZdIn) i Lp=0 do i=1,nslip gdot_slip(i)=g0_slip*(abs(tau_slip(i))/tauc_slip_new(i)) & **n_slip*sign(1.0_ZdRe,tau_slip(i)) Lp=Lp+gdot_slip(i)*Sslip(i,:,:) enddo return end function CPFEM_Cauchy(Estar_v,Fe,C66) C *************************************************************** C Subroutine calculates the cauchy from the elastic strain tensor C Input: Estar_v : elastic strain tensor (in vector form) C Fe : elastic deformation gradient C C66 : Stiffness Tensor C Output: cs : cauchy stress C Local: Tstar_v,Tstar,mm,det C *************************************************************** use math use prec implicit none real(pRe) Estar_v(6),Fe(3,3),C66(6,6),CPFEM_Cauchy(6) real(pRe) det,mm(3,3),Tstar(3,3) integer(pIn) i det = math_det(Fe) Tstar = math_6to33(matmul(C66,Estar_v)) mm=matmul(matmul(Fe,Tstar),transpose(Fe))/det CPFEM_Cauchy = math_33to6(mm) return end function end module