!************************************ !* Module: CONSTITUTIVE * !************************************ !* contains: * !* - parameters definition * !* - constitutive equations * !* - 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 * !************************************* !* Physical parameter, attack_frequency != Debye frequency real(pReal), parameter :: attack_frequency = 1.0e10_pReal !* Physical parameter, Boltzman constant in mJ/Kelvin real(pReal), parameter :: Kb = 1.38e-20_pReal !************************************* !* 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_Gmod real(pReal), dimension(:,:,:), allocatable :: material_Cslip_66 !* Visco-plastic material parameters real(pReal), dimension(:) , allocatable :: material_rho0 real(pReal), dimension(:) , allocatable :: material_bg real(pReal), dimension(:) , allocatable :: material_Qedge real(pReal), dimension(:) , allocatable :: material_tau0 real(pReal), dimension(:) , allocatable :: material_c1 real(pReal), dimension(:) , allocatable :: material_c2 real(pReal), dimension(:) , allocatable :: material_c3 real(pReal), dimension(:) , allocatable :: material_c4 real(pReal), dimension(:) , allocatable :: material_c5 real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff !************************************ !* 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 real(pReal), dimension(:) , allocatable :: constitutive_passing_stress real(pReal), dimension(:) , allocatable :: constitutive_jump_width real(pReal), dimension(:) , allocatable :: constitutive_activation_volume real(pReal), dimension(:) , allocatable :: constitutive_rho_m real(pReal), dimension(:) , allocatable :: constitutive_rho_f real(pReal), dimension(:) , allocatable :: constitutive_rho_p real(pReal), dimension(:) , allocatable :: constitutive_g0_slip !************************************ !* Interaction matrices * !************************************ real(pReal), dimension(:,:,:), allocatable :: constitutive_Pforest real(pReal), dimension(:,:,:), allocatable :: constitutive_Pparallel !************************************ !* Results * !************************************ integer(pInt) constitutive_maxNresults integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults real(pReal), dimension(:,:,:,:), allocatable :: constitutive_results CONTAINS !**************************************** !* - constitutive_Init !* - constitutive_CountSections !* - constitutive_Parse_UnknownPart !* - constitutive_Parse_MaterialPart !* - constitutive_Parse_TexturePart !* - constitutive_Parse_MatTexDat !* - constitutive_Assignment !* - constitutive_HomogenizedC !* - constitutive_Microstructure !* - constitutive_LpAndItsTangent !* - consistutive_DotState !**************************************** subroutine constitutive_Init() !************************************** !* Module initialization * !************************************** call constitutive_Parse_MatTexDat(mattexFile) call constitutive_Assignment() 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)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (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)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (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)=='#' .OR. positions(1)==0) then ! skip comment and empty lines cycle elseif (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,pReal use IO use crystal, only: crystal_MaxMaxNslipOfStructure implicit none !* Definition of variables character(len=80) line,tag integer(pInt), parameter :: maxNchunks = 2 integer(pInt) i,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)=='#' .OR. positions(1)==0) then ! skip comment and empty lines 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 ('rho0') !* conversion in 1/mm˛ material_rho0(section)=IO_floatValue(line,positions,2)/1.0e6_pReal case ('interaction_coefficient') do i=1,crystal_MaxMaxNslipOfStructure material_SlipIntCoeff(i,section)=IO_floatValue(line,positions,i+1) enddo case ('bg') !* conversion in mm material_bg(section)=IO_floatValue(line,positions,2)*1.0e3_pReal case ('Qedge') !* conversion in mJ/Kelvin material_Qedge(section)=IO_floatValue(line,positions,2)*1.0e3_pReal case ('tau0') material_tau0(section)=IO_floatValue(line,positions,2) case ('c1') material_c1(section)=IO_floatValue(line,positions,2) case ('c2') material_c2(section)=IO_floatValue(line,positions,2) case ('c3') material_c3(section)=IO_floatValue(line,positions,2) case ('c4') material_c4(section)=IO_floatValue(line,positions,2) case ('c5') material_c5(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)=='#' .OR. positions(1)==0) then ! skip comment and empty lines 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, IO_open_file use math, only: math_Mandel3333to66, math_Voigt66to3333 use crystal, only: crystal_MaxMaxNslipOfStructure implicit none !* Definition of variables character(len=*) filename character(len=80) part,formerPart integer(pInt) sectionCount,i,j,k, fileunit ! set fileunit fileunit=200 !----------------------------- !* First reading: number of materials and textures !----------------------------- !* determine material_maxN and texture_maxN from last respective parts if(IO_open_file(fileunit,filename)==.false.) goto 100 part = '_dummy_' do while (part/='') formerPart = part call constitutive_CountSections(fileunit,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_Gmod(material_maxN)) ; material_Gmod=0.0_pReal allocate(material_Cslip_66(6,6,material_maxN)) ; material_Cslip_66=0.0_pReal allocate(material_rho0(material_maxN)) ; material_rho0=0.0_pReal allocate(material_SlipIntCoeff(crystal_MaxMaxNslipOfStructure,material_maxN)) ; material_SlipIntCoeff=0.0_pReal allocate(material_bg(material_maxN)) ; material_bg=0.0_pReal allocate(material_Qedge(material_maxN)) ; material_Qedge=0.0_pReal allocate(material_tau0(material_maxN)) ; material_tau0=0.0_pReal allocate(material_c1(material_maxN)) ; material_c1=0.0_pReal allocate(material_c2(material_maxN)) ; material_c2=0.0_pReal allocate(material_c3(material_maxN)) ; material_c3=0.0_pReal allocate(material_c4(material_maxN)) ; material_c4=0.0_pReal allocate(material_c5(material_maxN)) ; material_c5=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(fileunit) part = '_dummy_' do while (part/='') select case (part) case ('textures') part = constitutive_assignNGaussAndFiber(fileunit) case default part = constitutive_Parse_UnknownPart(fileunit) 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(fileunit) part='_dummy_' do while (part/='') select case (part) case ('materials') part=constitutive_Parse_MaterialPart(fileunit) case ('textures') part=constitutive_Parse_TexturePart(fileunit) case default part=constitutive_Parse_UnknownPart(fileunit) end select enddo close(fileunit) !* Construction of the elasticity matrices do i=1,material_maxN material_Gmod(i)=material_C44(i) 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(200) ! 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 use crystal, only: crystal_MaxNslipOfStructure,crystal_SlipIntType,crystal_sn,crystal_st implicit none !* Definition of variables integer(pInt) e,i,j,k,l,m,o,g,s integer(pInt) matID,texID real(pReal) K_inter,x,y 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 allocate(constitutive_Pforest(constitutive_maxNstatevars,constitutive_maxNstatevars,material_maxN)) constitutive_Pforest=0.0_pReal allocate(constitutive_Pparallel(constitutive_maxNstatevars,constitutive_maxNstatevars,material_maxN)) constitutive_Pparallel=0.0_pReal allocate(constitutive_rho_p(constitutive_maxNstatevars)) ; constitutive_rho_p=0.0_pReal allocate(constitutive_rho_f(constitutive_maxNstatevars)) ; constitutive_rho_f=0.0_pReal allocate(constitutive_rho_m(constitutive_maxNstatevars)) ; constitutive_rho_m=0.0_pReal allocate(constitutive_passing_stress(constitutive_maxNstatevars)) ; constitutive_passing_stress=0.0_pReal allocate(constitutive_jump_width(constitutive_maxNstatevars)) ; constitutive_jump_width=0.0_pReal allocate(constitutive_activation_volume(constitutive_maxNstatevars)) ; constitutive_activation_volume=0.0_pReal allocate(constitutive_g0_slip(constitutive_maxNstatevars)) ; constitutive_g0_slip=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_rho0(matID) constitutive_state_new(l,g,i,e) = material_rho0(matID) end forall enddo ! components enddo ! multiplicity enddo ! ip enddo ! cp_element !* Construction of the hardening matrices do i=1,material_maxN !* Iteration over the systems do j=1,constitutive_maxNstatevars do k=1,constitutive_maxNstatevars !* Hardening type * select case (crystal_SlipIntType(j,k,i)) case (0) K_inter=0.0_pReal case (1) K_inter=material_SlipIntCoeff(1,i) case (2) K_inter=material_SlipIntCoeff(2,i) case (3) K_inter=material_SlipIntCoeff(3,i) case (4) K_inter=material_SlipIntCoeff(4,i) case (5) K_inter=material_SlipIntCoeff(5,i) case (6) K_inter=material_SlipIntCoeff(6,i) end select !* Projection of the dislocation * x=dot_product(crystal_sn(:,j,i),crystal_st(:,k,i)) y=1.0_pReal-x**(2.0_pReal) !* Interaction matrix * constitutive_Pforest(j,k,i)=abs(x)*K_inter if (y>0.0_pReal) then constitutive_Pparallel(j,k,i)=sqrt(y)*K_inter else constitutive_Pparallel(j,k,i)=0.0_pReal endif enddo enddo enddo 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_Microstructure(state,Tp,ipc,ip,el) !********************************************************************* !* This function calculates from state needed variables * !* INPUT: * !* - state : state variables * !* - Tp : temperature * !* - 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) Tp real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Quantities derivated from state constitutive_rho_f=matmul(constitutive_Pforest(1:constitutive_Nstatevars(ipc,ip,el),& 1:constitutive_Nstatevars(ipc,ip,el),matID),state) constitutive_rho_p=matmul(constitutive_Pparallel(1:constitutive_Nstatevars(ipc,ip,el),& 1:constitutive_Nstatevars(ipc,ip,el),matID),state) do i=1,material_Nslip(matID) constitutive_passing_stress(i)=material_tau0(matID)+material_c1(matID)*material_Gmod(matID)*material_bg(matID)*& sqrt(constitutive_rho_p(i)) constitutive_jump_width(i)=material_c2(matID)/sqrt(constitutive_rho_f(i)) constitutive_activation_volume(i)=material_c3(matID)*constitutive_jump_width(i)*material_bg(matID)**2.0_pReal constitutive_rho_m(i)=(2.0_pReal*Kb*Tp*sqrt(constitutive_rho_p(i)))/& (material_c1(matID)*material_c3(matID)*material_Gmod(matID)*constitutive_jump_width(i)*material_bg(matID)**3.0_pReal) constitutive_g0_slip(i)=constitutive_rho_m(i)*material_bg(matID)*attack_frequency*constitutive_jump_width(i)*& exp(-(material_Qedge(matID)+constitutive_passing_stress(i)*constitutive_activation_volume(i))/& (Kb*Tp)) enddo end subroutine subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,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 * !* - Tp : temperature * !* - 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 use crystal, only: crystal_Sslip,crystal_Sslip_v implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i,k,l,m,n real(pReal) Tp 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,crystal_Sslip_v(:,i,material_CrystalStructure(matID))) gdot_slip(i)=constitutive_g0_slip(i)*sinh((abs(tau_slip(i))*constitutive_activation_volume(i))/(Kb*Tp))*& sign(1.0_pReal,tau_slip(i)) Lp=Lp+gdot_slip(i)*crystal_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)=((constitutive_g0_slip(i)*constitutive_activation_volume(i))/(Kb*Tp))*& cosh((abs(tau_slip(i))*constitutive_activation_volume(i))/(Kb*Tp)) 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)*crystal_Sslip(k,l,i,material_CrystalStructure(matID))* & (crystal_Sslip(m,n,i,material_CrystalStructure(matID))+ & crystal_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,Tp,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 * !* - Tp : temperature * !* - 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 use crystal, only: crystal_Sslip_v implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i real(pReal) Tp,tau_slip,gdot_slip real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state,lock,recovery !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) !* Hardening of each system do i=1,constitutive_Nstatevars(ipc,ip,el) tau_slip = dot_product(Tstar_v,crystal_Sslip_v(:,i,material_CrystalStructure(matID))) gdot_slip = constitutive_g0_slip(i)*sinh((abs(tau_slip)*constitutive_activation_volume(i))/(Kb*Tp))*& sign(1.0_pReal,tau_slip) if (abs(tau_slip)>1.0e-20_pReal) then lock(i)=(material_c4(matID)*sqrt(constitutive_rho_f(i))*abs(gdot_slip))/material_bg(matID) recovery(i)=material_c5(matID)*state(i)*abs(gdot_slip) constitutive_dotState(i)=lock(i)-recovery(i) else constitutive_dotState(i)=0.0_pReal endif enddo return end function function constitutive_post_results(Tstar_v,state,dt,Tp,ipc,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - state : current microstructure * !* - dt : current time increment * !* - Tp : temperature * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt use crystal, only: crystal_Sslip_v implicit none !* Definition of variables integer(pInt) ipc,ip,el integer(pInt) matID,i real(pReal) dt,Tp,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) if(constitutive_Nresults(ipc,ip,el)==0) return do i=1,material_Nslip(matID) constitutive_post_results(i) = state(i) tau_slip=dot_product(Tstar_v,crystal_Sslip_v(:,i,material_CrystalStructure(matID))) constitutive_post_results(i+material_Nslip(matID)) = & dt*constitutive_g0_slip(i)*sinh((abs(tau_slip)*constitutive_activation_volume(i))/(Kb*Tp))*& sign(1.0_pReal,tau_slip) enddo return end function END MODULE