!************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - constitutive equations * !* - Schmid matrices calculation * !* - Hardening matrices definition * !* - Parameters definition * !* - orientations * !************************************ MODULE constitutive !*** Include other modules *** use prec, only: pReal,pInt implicit none ! MISSING consistency check after reading 'mattex.mpie' character(len=300), parameter :: mattexFile = 'mattex.mpie' !************************************* !* Definition of material properties * !************************************* !* Number of materials integer(pInt) material_maxN !* Crystal structure and number of selected slip systems per material integer(pInt), dimension(:) , allocatable :: material_CrystalStructure integer(pInt), dimension(:) , allocatable :: material_Nslip !* Maximum number of selected slip systems over materials integer(pInt) material_maxNslip !* Elastic constants and matrices real(pReal), dimension(:) , allocatable :: material_C11 real(pReal), dimension(:) , allocatable :: material_C12 real(pReal), dimension(:) , allocatable :: material_C13 real(pReal), dimension(:) , allocatable :: material_C33 real(pReal), dimension(:) , allocatable :: material_C44 real(pReal), dimension(:,:,:), allocatable :: material_Cslip_66 !* Visco-plastic material parameters real(pReal), dimension(:) , allocatable :: material_s0_slip real(pReal), dimension(:) , allocatable :: material_gdot0_slip real(pReal), dimension(:) , allocatable :: material_n_slip real(pReal), dimension(:) , allocatable :: material_h0 real(pReal), dimension(:) , allocatable :: material_s_sat real(pReal), dimension(:) , allocatable :: material_w0 !************************************ !* Definition of texture properties * !************************************ !* Number of textures, maximum number of Gauss and Fiber components integer(pInt) texture_maxN integer(pInt) texture_maxNGauss integer(pInt) texture_maxNFiber !* Textures definition character(len=80), dimension(:), allocatable :: texture_ODFfile character(len=80), dimension(:), allocatable :: texture_symmetry integer(pInt), dimension(:) , allocatable :: texture_Ngrains integer(pInt), dimension(:) , allocatable :: texture_NGauss integer(pInt),dimension(:) , allocatable :: texture_NFiber integer(pInt),dimension(:) , allocatable :: texture_NRandom integer(pInt),dimension(:) , allocatable :: texture_totalNgrains real(pReal), dimension(:,:,:) , allocatable :: texture_Gauss real(pReal), dimension(:,:,:) , allocatable :: texture_Fiber real(pReal), dimension(:,:,:,:), allocatable :: constitutive_EulerAngles !************************************ !* Grains * !************************************ integer(pInt) constitutive_maxNgrains integer(pInt), dimension(:,:) , allocatable :: constitutive_Ngrains integer(pInt), dimension(:,:,:) , allocatable :: constitutive_matID real(pReal), dimension(:,:,:) , allocatable :: constitutive_matVolFrac integer(pInt), dimension(:,:,:) , allocatable :: constitutive_texID real(pReal), dimension(:,:,:) , allocatable :: constitutive_texVolFrac !************************************ !* State variables * !************************************ integer(pInt) constitutive_maxNstatevars integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nstatevars real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_old real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_new !************************************ !* Results * !************************************ integer(pInt) constitutive_maxNresults integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults real(pReal), dimension(:,:,:,:), allocatable :: constitutive_results !************************************ !* Crystal structures * !************************************ !* Number of crystal structures (1-FCC,2-BCC,3-HCP) integer(pInt), parameter :: constitutive_MaxCrystalStructure = 3 !* Total number of slip systems per crystal structure !* (as to be changed according the definition of slip systems) integer(pInt), dimension(constitutive_MaxCrystalStructure), parameter :: constitutive_MaxNslipOfStructure = & reshape((/12,48,12/),(/constitutive_MaxCrystalStructure/)) !* Maximum number of slip systems over crystal structures integer(pInt), parameter :: constitutive_MaxMaxNslipOfStructure = 48 !* Slip direction, slip normales and Schmid matrices real(pReal), dimension(3,3,constitutive_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: constitutive_Sslip real(pReal), dimension(6,constitutive_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: constitutive_Sslip_v real(pReal), dimension(3,constitutive_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: constitutive_sn real(pReal), dimension(3,constitutive_MaxMaxNslipOfStructure,constitutive_MaxCrystalStructure) :: constitutive_sd !*** Slip systems for FCC structures (1) *** !* System {111}<110> Sort according Eisenlohr&Hantcherli data constitutive_sd(:, 1,1)/ 0, 1,-1/ ; data constitutive_sn(:, 1,1)/ 1, 1, 1/ data constitutive_sd(:, 2,1)/-1, 0, 1/ ; data constitutive_sn(:, 2,1)/ 1, 1, 1/ data constitutive_sd(:, 3,1)/ 1,-1, 0/ ; data constitutive_sn(:, 3,1)/ 1, 1, 1/ data constitutive_sd(:, 4,1)/ 0,-1,-1/ ; data constitutive_sn(:, 4,1)/-1,-1, 1/ data constitutive_sd(:, 5,1)/ 1, 0, 1/ ; data constitutive_sn(:, 5,1)/-1,-1, 1/ data constitutive_sd(:, 6,1)/-1, 1, 0/ ; data constitutive_sn(:, 6,1)/-1,-1, 1/ data constitutive_sd(:, 7,1)/ 0,-1, 1/ ; data constitutive_sn(:, 7,1)/ 1,-1,-1/ data constitutive_sd(:, 8,1)/-1, 0,-1/ ; data constitutive_sn(:, 8,1)/ 1,-1,-1/ data constitutive_sd(:, 9,1)/ 1, 1, 0/ ; data constitutive_sn(:, 9,1)/ 1,-1,-1/ data constitutive_sd(:,10,1)/ 0, 1, 1/ ; data constitutive_sn(:,10,1)/-1, 1,-1/ data constitutive_sd(:,11,1)/ 1, 0,-1/ ; data constitutive_sn(:,11,1)/-1, 1,-1/ data constitutive_sd(:,12,1)/-1,-1, 0/ ; data constitutive_sn(:,12,1)/-1, 1,-1/ !*** Slip systems for BCC structures (2) *** !* System {110}<111> !* Sort? data constitutive_sd(:, 1,2)/ 1,-1, 1/ ; data constitutive_sn(:, 1,2)/ 0, 1, 1/ data constitutive_sd(:, 2,2)/-1,-1, 1/ ; data constitutive_sn(:, 2,2)/ 0, 1, 1/ data constitutive_sd(:, 3,2)/ 1, 1, 1/ ; data constitutive_sn(:, 3,2)/ 0,-1, 1/ data constitutive_sd(:, 4,2)/-1, 1, 1/ ; data constitutive_sn(:, 4,2)/ 0,-1, 1/ data constitutive_sd(:, 5,2)/-1, 1, 1/ ; data constitutive_sn(:, 5,2)/ 1, 0, 1/ data constitutive_sd(:, 6,2)/-1,-1, 1/ ; data constitutive_sn(:, 6,2)/ 1, 0, 1/ data constitutive_sd(:, 7,2)/ 1, 1, 1/ ; data constitutive_sn(:, 7,2)/-1, 0, 1/ data constitutive_sd(:, 8,2)/ 1,-1, 1/ ; data constitutive_sn(:, 8,2)/-1, 0, 1/ data constitutive_sd(:, 9,2)/-1, 1, 1/ ; data constitutive_sn(:, 9,2)/ 1, 1, 0/ data constitutive_sd(:,10,2)/-1, 1,-1/ ; data constitutive_sn(:,10,2)/ 1, 1, 0/ data constitutive_sd(:,11,2)/ 1, 1, 1/ ; data constitutive_sn(:,11,2)/-1, 1, 0/ data constitutive_sd(:,12,2)/ 1, 1,-1/ ; data constitutive_sn(:,12,2)/-1, 1, 0/ !* System {112}<111> !* Sort? data constitutive_sd(:,13,2)/-1, 1, 1/ ; data constitutive_sn(:,13,2)/ 2, 1, 1/ data constitutive_sd(:,14,2)/ 1, 1, 1/ ; data constitutive_sn(:,14,2)/-2, 1, 1/ data constitutive_sd(:,15,2)/ 1, 1,-1/ ; data constitutive_sn(:,15,2)/ 2,-1, 1/ data constitutive_sd(:,16,2)/ 1,-1, 1/ ; data constitutive_sn(:,16,2)/ 2, 1,-1/ data constitutive_sd(:,17,2)/ 1,-1, 1/ ; data constitutive_sn(:,17,2)/ 1, 2, 1/ data constitutive_sd(:,18,2)/ 1, 1,-1/ ; data constitutive_sn(:,18,2)/-1, 2, 1/ data constitutive_sd(:,19,2)/ 1, 1, 1/ ; data constitutive_sn(:,19,2)/ 1,-2, 1/ data constitutive_sd(:,20,2)/-1, 1, 1/ ; data constitutive_sn(:,20,2)/ 1, 2,-1/ data constitutive_sd(:,21,2)/ 1, 1,-1/ ; data constitutive_sn(:,21,2)/ 1, 1, 2/ data constitutive_sd(:,22,2)/ 1,-1, 1/ ; data constitutive_sn(:,22,2)/-1, 1, 2/ data constitutive_sd(:,23,2)/-1, 1, 1/ ; data constitutive_sn(:,23,2)/ 1,-1, 2/ data constitutive_sd(:,24,2)/ 1, 1, 1/ ; data constitutive_sn(:,24,2)/ 1, 1,-2/ !* System {123}<111> !* Sort? data constitutive_sd(:,25,2)/ 1, 1,-1/ ; data constitutive_sn(:,25,2)/ 1, 2, 3/ data constitutive_sd(:,26,2)/ 1,-1, 1/ ; data constitutive_sn(:,26,2)/-1, 2, 3/ data constitutive_sd(:,27,2)/-1, 1, 1/ ; data constitutive_sn(:,27,2)/ 1,-2, 3/ data constitutive_sd(:,28,2)/ 1, 1, 1/ ; data constitutive_sn(:,28,2)/ 1, 2,-3/ data constitutive_sd(:,29,2)/ 1,-1, 1/ ; data constitutive_sn(:,29,2)/ 1, 3, 2/ data constitutive_sd(:,30,2)/ 1, 1,-1/ ; data constitutive_sn(:,30,2)/-1, 3, 2/ data constitutive_sd(:,31,2)/ 1, 1, 1/ ; data constitutive_sn(:,31,2)/ 1,-3, 2/ data constitutive_sd(:,32,2)/-1, 1, 1/ ; data constitutive_sn(:,32,2)/ 1, 3,-2/ data constitutive_sd(:,33,2)/ 1, 1,-1/ ; data constitutive_sn(:,33,2)/ 2, 1, 3/ data constitutive_sd(:,34,2)/ 1,-1, 1/ ; data constitutive_sn(:,34,2)/-2, 1, 3/ data constitutive_sd(:,35,2)/-1, 1, 1/ ; data constitutive_sn(:,35,2)/ 2,-1, 3/ data constitutive_sd(:,36,2)/ 1, 1, 1/ ; data constitutive_sn(:,36,2)/ 2, 1,-3/ data constitutive_sd(:,37,2)/ 1,-1, 1/ ; data constitutive_sn(:,37,2)/ 2, 3, 1/ data constitutive_sd(:,38,2)/ 1, 1,-1/ ; data constitutive_sn(:,38,2)/-2, 3, 1/ data constitutive_sd(:,39,2)/ 1, 1, 1/ ; data constitutive_sn(:,39,2)/ 2,-3, 1/ data constitutive_sd(:,40,2)/-1, 1, 1/ ; data constitutive_sn(:,40,2)/ 2, 3,-1/ data constitutive_sd(:,41,2)/-1, 1, 1/ ; data constitutive_sn(:,41,2)/ 3, 1, 2/ data constitutive_sd(:,42,2)/ 1, 1, 1/ ; data constitutive_sn(:,42,2)/-3, 1, 2/ data constitutive_sd(:,43,2)/ 1, 1,-1/ ; data constitutive_sn(:,43,2)/ 3,-1, 2/ data constitutive_sd(:,44,2)/ 1,-1, 1/ ; data constitutive_sn(:,44,2)/ 3, 1,-2/ data constitutive_sd(:,45,2)/-1, 1, 1/ ; data constitutive_sn(:,45,2)/ 3, 2, 1/ data constitutive_sd(:,46,2)/ 1, 1, 1/ ; data constitutive_sn(:,46,2)/-3, 2, 1/ data constitutive_sd(:,47,2)/ 1, 1,-1/ ; data constitutive_sn(:,47,2)/ 3,-2, 1/ data constitutive_sd(:,48,2)/ 1,-1, 1/ ; data constitutive_sn(:,48,2)/ 3, 2,-1/ !*** Slip systems for HCP structures (3) *** !* Basal systems {0001}<1120> (independent of c/a-ratio) !* 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 constitutive_sd(:, 1,3)/-1, 0, 0/ ; data constitutive_sn(:, 1,3)/ 0, 0, 1/ data constitutive_sd(:, 2,3)/ 0,-1, 0/ ; data constitutive_sn(:, 2,3)/ 0, 0, 1/ data constitutive_sd(:, 3,3)/ 1, 1, 0/ ; data constitutive_sn(:, 3,3)/ 0, 0, 1/ !* 1st type prismatic systems {1010}<1120> (independent of c/a-ratio) !* 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 constitutive_sd(:, 4,3)/-1, 0, 0/ ; data constitutive_sn(:, 4,3)/ 0, 1, 0/ data constitutive_sd(:, 5,3)/ 0,-1, 0/ ; data constitutive_sn(:, 5,3)/ 1, 0, 0/ data constitutive_sd(:, 6,3)/ 1, 1, 0/ ; data constitutive_sn(:, 6,3)/-1, 1, 0/ !* 1st type 1st order pyramidal systems {1011}<1120> !* plane normales depend on the c/a-ratio !* 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 constitutive_sd(:, 7,3)/-1, 0, 0/ ; data constitutive_sn(:, 7,3)/ 0,-1, 1/ data constitutive_sd(:, 8,3)/ 0,-1, 0/ ; data constitutive_sn(:, 8,3)/ 0, 1, 1/ data constitutive_sd(:, 9,3)/ 1, 1, 0/ ; data constitutive_sn(:, 9,3)/-1, 0, 1/ data constitutive_sd(:,10,3)/-1, 0, 0/ ; data constitutive_sn(:,10,3)/ 1, 0, 1/ data constitutive_sd(:,11,3)/ 0,-1, 0/ ; data constitutive_sn(:,11,3)/-1, 1, 1/ data constitutive_sd(:,12,3)/ 1, 1, 0/ ; data constitutive_sn(:,12,3)/ 1,-1, 1/ !*********************************************** !* slip-slip interaction * !*********************************************** !* (defined for the moment as crystal structure property and not as material property) !* (may be changed in the future) real(pReal), dimension(constitutive_MaxMaxNslipOfStructure,constitutive_MaxMaxNslipOfStructure,& constitutive_MaxCrystalStructure) :: constitutive_HardeningMatrix real(pReal), parameter :: constitutive_LatentHardening=1.4_pReal CONTAINS !**************************************** !* - constitutive_Init !* - constitutive_SchmidMatrices !* - constitutive_HardeningMatrices !* - constitutive_CountSections !* - constitutive_Parse_UnknownPart !* - constitutive_Parse_MaterialPart !* - constitutive_Parse_TexturePart !* - constitutive_Parse_MatTexDat !* - constitutive_Assignment !* - constitutive_HomogenizedC !* - constitutive_LpAndItsTangent !* - consistutive_DotState !**************************************** subroutine constitutive_Init() !************************************** !* Module initialization * !************************************** call constitutive_SchmidMatrices() call constitutive_HardeningMatrices() call constitutive_Parse_MatTexDat(mattexFile) call constitutive_Assignment() end subroutine subroutine constitutive_SchmidMatrices() !************************************** !* 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,constitutive_MaxNslipOfStructure(l) !* Defintion of Schmid matrix forall (i=1:3,j=1:3) constitutive_Sslip(i,j,k,l)=constitutive_sd(i,k,l)*constitutive_sn(j,k,l) endforall !* Normalization of Schmid matrix invNorm=dsqrt(1.0_pReal/((constitutive_sn(1,k,l)**2+constitutive_sn(2,k,l)**2+constitutive_sn(3,k,l)**2)*& (constitutive_sd(1,k,l)**2+constitutive_sd(2,k,l)**2+constitutive_sd(3,k,l)**2))) constitutive_Sslip(:,:,k,l)=constitutive_Sslip(:,:,k,l)*invNorm !* Vectorization of normalized Schmid matrix constitutive_Sslip_v(1,k,l)=constitutive_Sslip(1,1,k,l) constitutive_Sslip_v(2,k,l)=constitutive_Sslip(2,2,k,l) constitutive_Sslip_v(3,k,l)=constitutive_Sslip(3,3,k,l) !* be compatible with Mandel notation of Tstar constitutive_Sslip_v(4,k,l)=(constitutive_Sslip(1,2,k,l)+constitutive_Sslip(2,1,k,l))/dsqrt(2.0_pReal) constitutive_Sslip_v(5,k,l)=(constitutive_Sslip(2,3,k,l)+constitutive_Sslip(3,3,k,l))/dsqrt(2.0_pReal) constitutive_Sslip_v(6,k,l)=(constitutive_Sslip(1,3,k,l)+constitutive_Sslip(3,1,k,l))/dsqrt(2.0_pReal) enddo enddo end subroutine subroutine constitutive_HardeningMatrices() !**************************************** !* 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 constitutive_HardeningMatrix=constitutive_LatentHardening !* Iteration over the crystal structures do l=1,3 select case(l) !* Hardening matrix for FCC structures case (1) forall (k=1:10:3,i=0:2,j=0:2) constitutive_HardeningMatrix(k+i,k+j,l)=1.0_pReal endforall !* Hardening matrix for BCC structures case (2) forall (k=1:11:2,i=0:1,j=0:1) constitutive_HardeningMatrix(k+i,k+j,l)=1.0_pReal endforall forall (k=13:48) constitutive_HardeningMatrix(k,k,l)=1.0_pReal endforall !* Hardening matrix for HCP structures case (3) forall (i=1:3,j=1:3) constitutive_HardeningMatrix(i,j,l)=1.0_pReal endforall forall (k=4:12) constitutive_HardeningMatrix(k,k,l)=1.0_pReal endforall end select enddo end subroutine subroutine constitutive_CountSections(file,count,part) !********************************************************************* !* This subroutine reads a "part" from the input file until the next * !* part is reached and counts the number of "sections" in the part * !* INPUT: * !* - file : file ID * !* OUTPUT: * !* - part : name of the next "part" * !* - count : number of sections inside the current "part" * !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) part,line,tag integer(pInt) file,count integer(pInt), dimension(3) :: positions count=0 part='' do read(file,'(a80)',END=100) line positions=IO_stringPos(line,1) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then part=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then count=count+1 endif enddo 100 return end subroutine character(len=80) function constitutive_assignNGaussAndFiber(file) !********************************************************************* !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) line,tag integer(pInt) file,section integer(pInt), dimension(3) :: positions constitutive_assignNGaussAndFiber='' section = 0_pInt do read(file,'(a80)',END=100) line positions=IO_stringPos(line,1) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_assignNGaussAndFiber=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 texture_NGauss(section) = 0_pInt texture_NFiber(section) = 0_pInt elseif (tag=='(gauss)') then texture_NGauss(section)=texture_NGauss(section)+1 elseif (tag=='(fiber)') then texture_NFiber(section)=texture_NFiber(section)+1 endif enddo 100 return end function character(len=80) function constitutive_Parse_UnknownPart(file) !********************************************************************* !* read an unknown "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt use IO, only: IO_stringPos,IO_stringValue,IO_lc implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 1 integer(pInt) file integer(pInt), dimension(1+2*maxNchunks) :: positions constitutive_parse_unknownPart='' do read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_Parse_UnknownPart=tag(2:len_trim(tag)-1) exit endif enddo 100 return end function character(len=80) function constitutive_Parse_MaterialPart(file) !********************************************************************* !* This function reads a material "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt use IO implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 2 integer(pInt) file,section integer(pInt), dimension(1+2*maxNchunks) :: positions section = 0 constitutive_parse_materialPart = '' do while(.true.) read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) ! parse leading chunks tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#') then ! skip comment line cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_parse_materialPart=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 else if (section>0) then select case(tag) case ('crystal_structure') material_CrystalStructure(section)=IO_intValue(line,positions,2) case ('nslip') material_Nslip(section)=IO_intValue(line,positions,2) case ('c11') material_C11(section)=IO_floatValue(line,positions,2) case ('c12') material_C12(section)=IO_floatValue(line,positions,2) case ('c13') material_C13(section)=IO_floatValue(line,positions,2) case ('c33') material_C33(section)=IO_floatValue(line,positions,2) case ('c44') material_C44(section)=IO_floatValue(line,positions,2) case ('s0_slip') material_s0_slip(section)=IO_floatValue(line,positions,2) case ('gdot0_slip') material_gdot0_slip(section)=IO_floatValue(line,positions,2) case ('n_slip') material_n_slip(section)=IO_floatValue(line,positions,2) case ('h0') material_h0(section)=IO_floatValue(line,positions,2) case ('s_sat') material_s_sat(section)=IO_floatValue(line,positions,2) case ('w0') material_w0(section)=IO_floatValue(line,positions,2) end select endif endif enddo 100 return end function character(len=80) function constitutive_Parse_TexturePart(file) !********************************************************************* !* This function reads a texture "part" from the input file until * !* the next part is reached * !* INPUT: * !* - file : file ID * !********************************************************************* use prec, only: pInt use IO use math, only: inRad implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 13 ! may be more than 10 chunks ..? integer(pInt) file,section,gaussCount,fiberCount,i integer(pInt), dimension(1+2*maxNchunks) :: positions section = 0 gaussCount = 0 fiberCount = 0 constitutive_parse_texturePart = '' do while(.true.) read(file,'(a80)',END=100) line positions=IO_stringPos(line,maxNchunks) ! parse leading chunks tag=IO_lc(IO_stringValue(line,positions,1)) if (tag(1:1)=='#') then ! skip comment line cycle elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then constitutive_parse_texturePart=tag(2:len_trim(tag)-1) exit elseif (tag(1:1)=='[') then section=section+1 gaussCount=0 fiberCount=0 else if (section>0) then select case(tag) case ('hybridIA') texture_ODFfile(section)=IO_stringValue(line,positions,2) case ('(gauss)') gaussCount=gaussCount+1 do i=2,10,2 tag=IO_lc(IO_stringValue(line,positions,i)) select case (tag) case('phi1') texture_Gauss(1,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('phi') texture_Gauss(2,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('phi2') texture_Gauss(3,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('scatter') texture_Gauss(4,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad case('fraction') texture_Gauss(5,gaussCount,section)=IO_floatValue(line,positions,i+1) end select enddo case ('(fiber)') fiberCount=fiberCount+1 do i=2,12,2 tag=IO_lc(IO_stringValue(line,positions,i)) select case (tag) case('alpha1') texture_fiber(1,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('alpha2') texture_fiber(2,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('beta1') texture_fiber(3,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('beta2') texture_fiber(4,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('scatter') texture_fiber(5,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad case('fraction') texture_fiber(6,fiberCount,section)=IO_floatValue(line,positions,i+1) end select enddo case ('ngrains') texture_Ngrains(section)=IO_intValue(line,positions,2) case ('symmetry') texture_symmetry(section)=IO_stringValue(line,positions,2) end select endif endif enddo 100 return end function subroutine constitutive_Parse_MatTexDat(filename) !********************************************************************* !* This function reads the material and texture input file * !* INPUT: * !* - filename : name of input file * !********************************************************************* use prec, only: pReal,pInt use IO, only: IO_error use math, only: math_Mandel3333to66, math_Voigt66to3333 implicit none !* Definition of variables character(len=*) filename character(len=80) part,formerPart integer(pInt) sectionCount,i,j,k !----------------------------- !* First reading: number of materials and textures !----------------------------- !* determine material_maxN and texture_maxN from last respective parts open(1,FILE=filename,ACTION='READ',STATUS='OLD',ERR=100) part = '_dummy_' do while (part/='') formerPart = part call constitutive_CountSections(1,sectionCount,part) select case (formerPart) case ('materials') material_maxN = sectionCount case ('textures') texture_maxN = sectionCount end select enddo !* Array allocation allocate(material_CrystalStructure(material_maxN)) ; material_CrystalStructure=0_pInt allocate(material_Nslip(material_maxN)) ; material_Nslip=0_pInt allocate(material_C11(material_maxN)) ; material_C11=0.0_pReal allocate(material_C12(material_maxN)) ; material_C12=0.0_pReal allocate(material_C13(material_maxN)) ; material_C13=0.0_pReal allocate(material_C33(material_maxN)) ; material_C33=0.0_pReal allocate(material_C44(material_maxN)) ; material_C44=0.0_pReal allocate(material_Cslip_66(6,6,material_maxN)) ; material_Cslip_66=0.0_pReal allocate(material_s0_slip(material_maxN)) ; material_s0_slip=0.0_pReal allocate(material_gdot0_slip(material_maxN)) ; material_gdot0_slip=0.0_pReal allocate(material_n_slip(material_maxN)) ; material_n_slip=0.0_pReal allocate(material_h0(material_maxN)) ; material_h0=0.0_pReal allocate(material_s_sat(material_maxN)) ; material_s_sat=0.0_pReal allocate(material_w0(material_maxN)) ; material_w0=0.0_pReal allocate(texture_ODFfile(texture_maxN)) ; texture_ODFfile='' allocate(texture_Ngrains(texture_maxN)) ; texture_Ngrains=0_pInt allocate(texture_symmetry(texture_maxN)) ; texture_symmetry='' allocate(texture_NGauss(texture_maxN)) ; texture_NGauss=0_pInt allocate(texture_NFiber(texture_maxN)) ; texture_NFiber=0_pInt allocate(texture_NRandom(texture_maxN)) ; texture_NRandom=0_pInt !----------------------------- !* Second reading: number of Gauss and Fiber !----------------------------- rewind(1) part = '_dummy_' do while (part/='') select case (part) case ('textures') part = constitutive_assignNGaussAndFiber(1) case default part = constitutive_Parse_UnknownPart(1) end select enddo !* Array allocation texture_maxNGauss=maxval(texture_NGauss) texture_maxNFiber=maxval(texture_NFiber) allocate(texture_Gauss(5,texture_maxNGauss,texture_maxN)) ; texture_Gauss=0.0_pReal allocate(texture_Fiber(6,texture_maxNFiber,texture_maxN)) ; texture_Fiber=0.0_pReal !----------------------------- !* Third reading: materials and textures are stored !----------------------------- rewind(1) part='_dummy_' do while (part/='') select case (part) case ('materials') part=constitutive_Parse_MaterialPart(1) case ('textures') part=constitutive_Parse_TexturePart(1) case default part=constitutive_Parse_UnknownPart(1) end select enddo close(1) !* Construction of the elasticity matrices do i=1,material_maxN select case (material_CrystalStructure(i)) case(1:2) ! cubic(s) do k=1,3 do j=1,3 material_Cslip_66(k,j,i)=material_C12(i) enddo material_Cslip_66(k,k,i)=material_C11(i) material_Cslip_66(k+3,k+3,i)=material_C44(i) enddo case(3) ! hcp material_Cslip_66(1,1,i)=material_C11(i) material_Cslip_66(2,2,i)=material_C11(i) material_Cslip_66(3,3,i)=material_C33(i) material_Cslip_66(1,2,i)=material_C12(i) material_Cslip_66(2,1,i)=material_C12(i) material_Cslip_66(1,3,i)=material_C13(i) material_Cslip_66(3,1,i)=material_C13(i) material_Cslip_66(2,3,i)=material_C13(i) material_Cslip_66(3,2,i)=material_C13(i) material_Cslip_66(4,4,i)=material_C44(i) material_Cslip_66(5,5,i)=material_C44(i) material_Cslip_66(6,6,i)=0.5_pReal*(material_C11(i)-material_C12(i)) end select material_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(material_Cslip_66(:,:,i))) enddo ! MISSING some consistency checks may be..? ! if ODFfile present then set NGauss NFiber =0 return 100 call IO_error(110) ! corrupt materials_textures file end subroutine subroutine constitutive_Assignment() !********************************************************************* !* This subroutine assign material parameters according to ipc,ip,el * !********************************************************************* use prec, only: pReal,pInt use math, only: math_sampleGaussOri,math_sampleFiberOri,math_sampleRandomOri,math_symmetricEulers,math_EulerToR use mesh, only: mesh_NcpElems,FE_Nips,FE_mapElemtype,mesh_maxNips,mesh_element use IO, only: IO_hybridIA implicit none !* Definition of variables integer(pInt) e,i,k,l,m,o,g,s integer(pInt) matID,texID integer(pInt), dimension(:,:,:), allocatable :: hybridIA_population integer(pInt), dimension(texture_maxN) :: Ncomponents,Nsym,multiplicity,sumVolfrac,ODFmap,sampleCount real(pReal), dimension(3,4*(1+texture_maxNGauss+texture_maxNfiber)) :: Euler real(pReal), dimension(4*(1+texture_maxNGauss+texture_maxNfiber)) :: texVolfrac ! process textures o = 0_pInt ! ODF counter ODFmap = 0_pInt ! blank mapping sampleCount = 0_pInt ! count orientations assigned per texture do texID=1,texture_maxN if (texture_ODFfile(texID)=='') then sumVolfrac(texID) = sum(texture_gauss(5,:,texID))+sum(texture_fiber(6,:,texID)) if (sumVolfrac(texID)<1.0_pReal) texture_NRandom(texID) = 1_pInt ! check whether random component missing select case (texture_symmetry(texID)) ! set symmetry factor case ('orthotropic') Nsym(texID) = 4_pInt case ('monoclinic') Nsym(texID) = 2_pInt case default Nsym(texID) = 1_pInt end select Ncomponents(texID) = texture_NGauss(texID)+texture_NFiber(texID)+texture_NRandom(texID) else ! hybrid IA o = o+1 ODFmap(texID) = o ! remember mapping Ncomponents(texID) = 1_pInt ! single "component" Nsym(texID) = 1_pInt ! no symmetry (use full ODF instead) endif ! adjust multiplicity and number of grains per IP of components multiplicity(texID) = max(1_pInt,texture_Ngrains(texID)/Ncomponents(texID)/Nsym(texID)) if (mod(texture_Ngrains(texID),Ncomponents(texID)*Nsym(texID)) /= 0_pInt) then texture_Ngrains(texID) = multiplicity(texID)*Ncomponents(texID)*Nsym(texID) write (6,*) 'changed Ngrains to',texture_Ngrains(texID),' for texture',texID endif enddo !* publish globals constitutive_maxNgrains = maxval(texture_Ngrains) constitutive_maxNstatevars = maxval(material_Nslip) + 0_pInt constitutive_maxNresults = 1_pInt !* calc texture_totalNgrains allocate(texture_totalNgrains(texture_maxN)) ; texture_totalNgrains=0_pInt do i=1,mesh_NcpElems texID = mesh_element(4,i) texture_totalNgrains(texID) = texture_totalNgrains(texID) + FE_Nips(FE_mapElemtype(mesh_element(2,i)))*texture_Ngrains(texID) enddo ! generate hybridIA samplings for ODFfile textures to later draw from these populations allocate(hybridIA_population(3,maxval(texture_totalNgrains,ODFmap /= 0),o)) do texID = 1,texture_maxN if (ODFmap(texID) > 0) & hybridIA_population(:,:,ODFmap(texID)) = IO_hybridIA(texture_totalNgrains(texID),texture_ODFfile(texID)) enddo !* Array allocation allocate(constitutive_Ngrains(mesh_maxNips,mesh_NcpElems)) ; constitutive_Ngrains=0_pInt allocate(constitutive_matID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_matID=0_pInt allocate(constitutive_texID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_texID=0_pInt allocate(constitutive_MatVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_MatVolFrac=0.0_pReal allocate(constitutive_TexVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_TexVolFrac=0.0_pReal allocate(constitutive_EulerAngles(3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_EulerAngles=0.0_pReal allocate(constitutive_Nresults(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nresults=0_pInt allocate(constitutive_results(constitutive_maxNresults,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) constitutive_results=0.0_pReal allocate(constitutive_Nstatevars(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nstatevars=0_pInt allocate(constitutive_state_old(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) constitutive_state_old=0.0_pReal allocate(constitutive_state_new(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) constitutive_state_new=0.0_pReal !* Assignment of all grains in all IPs of all cp-elements do e=1,mesh_NcpElems matID=mesh_element(3,e) texID=mesh_element(4,e) do i=1,FE_Nips(FE_mapElemtype(mesh_element(2,e))) g = 0_pInt ! grain counter do m = 1,multiplicity(texID) o = 0_pInt ! component counter if (texture_ODFfile(texID)=='') then do k = 1,texture_nGauss(texID) ! *** gauss *** o = o+1 Euler(:,o) = math_sampleGaussOri(texture_Gauss(1:3,k,texID),texture_Gauss(4,k,texID)) texVolFrac(o) = texture_Gauss(5,k,texID) enddo do k = 1,texture_nFiber(texID) ! *** fiber *** o = o+1 Euler(:,o) = math_sampleFiberOri(texture_Fiber(1:2,k,texID),texture_Fiber(3:4,k,texID),texture_Fiber(5,k,texID)) texVolFrac(o) = texture_Fiber(6,k,texID) enddo do k = 1,texture_nRandom(texID) ! *** random *** o = o+1 Euler(:,o) = math_sampleRandomOri() texVolfrac(o) = 1.0_pReal-sumVolfrac(texID) enddo else ! *** hybrid IA *** o = 1 ! only singular orientation, i.e. single "component" Euler(:,o) = hybridIA_population(:,1+sampleCount(texID),ODFmap(texID)) texVolfrac(o) = 1.0_pReal endif if (Nsym(texID) > 1) then ! symmetry generates additional orientations forall (k=1:o) Euler(:,1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = & math_symmetricEulers(texture_symmetry(texID),Euler(:,k)) texVolfrac(1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = texVolfrac(k) end forall endif do s = 1,Nsym(texID)*o ! loop over orientations to be assigned to ip (ex multiplicity) g = g+1 ! next "grain" sampleCount(texID) = sampleCount(texID)+1 ! next member of population constitutive_matID(g,i,e) = matID ! copy matID of element constitutive_texID(g,i,e) = texID ! copy texID of element constitutive_MatVolFrac(g,i,e) = 1.0_pReal ! singular material (so far) constitutive_TexVolFrac(g,i,e) = texVolfrac(s)/multiplicity(texID)/Nsym(texID) constitutive_Nstatevars(g,i,e) = material_Nslip(matID) ! number of state variables (i.e. tau_c of each slip system) constitutive_Nresults(g,i,e) = 0 ! number of constitutive results constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation forall (l=1:constitutive_Nstatevars(g,i,e)) ! initialize state variables constitutive_state_old(l,g,i,e) = material_s0_slip(matID) constitutive_state_new(l,g,i,e) = material_s0_slip(matID) end forall enddo ! components enddo ! multiplicity enddo ! ip enddo ! cp_element end subroutine function constitutive_homogenizedC(ipc,ip,el) !********************************************************************* !* This function returns the homogenized elacticity matrix * !* INPUT: * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) ipc,ip,el real(pReal), dimension(6,6) :: constitutive_homogenizedC !* Homogenization scheme constitutive_homogenizedC=constitutive_MatVolFrac(ipc,ip,el)*material_Cslip_66(:,:,constitutive_matID(ipc,ip,el)) return end function subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar, Tstar_v,state,ipc,ip,el) !********************************************************************* !* This subroutine contains the constitutive equation for * !* calculating the velocity gradient * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - Lp : plastic velocity gradient * !* - dLp_dTstar : derivative of Lp (4th-order tensor) * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i,k,l,m,n real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(3,3) :: Lp real(pReal), dimension(3,3,3,3) :: dLp_dTstar real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state,gdot_slip,dgdot_dtauslip,tau_slip !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Calculation of Lp Lp = 0.0_pReal do i=1,material_Nslip(matID) tau_slip(i)=dot_product(Tstar_v,constitutive_Sslip_v(:,i,material_CrystalStructure(matID))) gdot_slip(i)=material_gdot0_slip(matID)*(abs(tau_slip(i))/state(i))**& material_n_slip(matID)*sign(1.0_pReal,tau_slip(i)) Lp=Lp+gdot_slip(i)*constitutive_Sslip(:,:,i,material_CrystalStructure(matID)) enddo !* Calculation of the tangent of Lp dLp_dTstar=0.0_pReal do i=1,material_Nslip(matID) dgdot_dtauslip(i) = material_gdot0_slip(matID)*(abs(tau_slip(i))/state(i))**& (material_n_slip(matID)-1.0_pReal)*material_n_slip(matID)/state(i) forall (k=1:3,l=1:3,m=1:3,n=1:3) dLp_dTstar(k,l,m,n) = dLp_dTstar(k,l,m,n)+ & dgdot_dtauslip(i)*constitutive_Sslip(k,l,i,material_CrystalStructure(matID))* & (constitutive_Sslip(m,n,i,material_CrystalStructure(matID))+ & constitutive_Sslip(n,m,i,material_CrystalStructure(matID)))/2.0_pReal ! force m,n symmetry endforall enddo return end subroutine function constitutive_dotState(Tstar_v,state,ipc,ip,el) !********************************************************************* !* This subroutine contains the constitutive equation for * !* calculating the velocity gradient * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_DotState : evolution of state variable * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i real(pReal) tau_slip,gdot_slip real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state,self_hardening !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Self-Hardening of each system do i=1,constitutive_Nstatevars(ipc,ip,el) tau_slip = dot_product(Tstar_v,constitutive_Sslip_v(:,i,material_CrystalStructure(matID))) gdot_slip = material_gdot0_slip(matID)*(abs(tau_slip)/state(i))**& material_n_slip(matID)*sign(1.0_pReal,tau_slip) self_hardening(i)=material_h0(matID)*(1.0_pReal-state(i)/& material_s_sat(matID))**material_w0(matID)*abs(gdot_slip) enddo !* Hardening for all systems constitutive_dotState=matmul(constitutive_HardeningMatrix(1:material_Nslip(matID),1:material_Nslip(matID),& material_CrystalStructure(matID)),self_hardening) return end function function constitutive_post_results(Tstar_v,state,dt,ipc,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - dt : current time increment * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i real(pReal) dt,tau_slip real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state real(pReal), dimension(constitutive_Nresults(ipc,ip,el)) :: constitutive_post_results !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) do i=1,material_Nslip(matID) constitutive_post_results(i) = state(i) tau_slip=dot_product(Tstar_v,constitutive_Sslip_v(:,i,material_CrystalStructure(matID))) constitutive_post_results(i+material_Nslip(matID)) = & dt*material_gdot0_slip(matID)*(abs(tau_slip)/state(i))**material_n_slip(matID)*sign(1.0_pReal,tau_slip) enddo return end function END MODULE